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Monks, Manuscripts and Sundials

History of Science and Medicine Library VOLUME 13

Medieval and Early Modern Science Editors

J.M.M.H. Thijssen, Radboud University, Nijmegen C.H. Lüthy, Radboud University, Nijmegen Editorial Consultants

Joël Biard, University of Tours Simo Knuuttila, University of Helsinki John E. Murdoch, Harvard University Jürgen Renn, Max-Planck-Institute for the History of Science Theo Verbeek, University of Utrecht

VOLUME 11

Monks, Manuscripts and Sundials The Navicula in Medieval England

By

Catherine Eagleton

LEIDEN • BOSTON 2010

On the cover: (front) The Oxford navicula, front (Museum of the History of Science, inv. no. 54358). (back) The Oxford navicula, back (Museum of the History of Science, inv. no. 54358). Reproduced by permission of the Museum of the History of Science, Oxford. This book is printed on acid-free paper. Library of Congress Cataloging-in-Publication Data Eagleton, Catherine. Monks, manuscripts, and sundials : the navicula in medieval England / by Catherine Eagleton. p. cm. — (History of science and medicine library ; v. 13) Includes bibliographical references and index. ISBN 978-90-04-17665-2 (hardback : alk. paper) 1. Sundials—History— To 1500—Sources. 2. Sundials—Great Britain—History—Sources. I. Title. QB215.E116 2010 681.1’11209420902–dc22 2009043296

ISSN 1872-0684 ISBN 978 9004 17665 2 Copyright 2010 by Koninklijke Brill NV, Leiden, The Netherlands. Koninklijke Brill NV incorporates the imprints Brill, Hotei Publishing, IDC Publishers, Martinus Nijhoff Publishers and VSP. All rights reserved. No part of this publication may be reproduced, translated, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without prior written permission from the publisher. Brill has made all reasonable efforts to trace all right holders to any copyrighted material used in this work. In cases where these efforts have not been successful the publisher welcomes communications from copyright holders, so that the appropriate acknowledgements can be made in future editions, and to settle other permission matters. Authorization to photocopy items for internal or personal use is granted by Brill provided that the appropriate fees are paid directly to The Copyright Clearance Center, 222 Rosewood Drive, Suite 910, Danvers, MA 01923, USA. Fees are subject to change. printed in the netherlands

CONTENTS List of figures ..................................................................................... Acknowledgements .............................................................................

vii xi

Chapter One Monks, manuscripts and sundials: the navicula in medieval England ......................................................................

1

Chapter Two

Five fifteenth-century sundials .............................

7

Chapter Three

Manuscript sources about the navicula ............

23

Chapter Four

Calendar tables and latitude lists .........................

39

Chapter Five Texts, instruments, diagrams and relations between them ..................................................................................

51

Chapter Six

77

Using a sundial, understanding the heavens? ......

Chapter Seven

The navicula and the organum ptolomei ..........

93

Chapter Eight How sixteenth-century books redefined a medieval sundial ............................................................................. 121 Appendix One

Group A navicula manuscripts .......................... 165

Appendix Two

Group A navicula manuscripts ......................... 191

Appendix Three

Group A navicula manuscripts ....................... 201

Appendix Four

Group A stemmatics ........................................... 215

Appendix Five

Group B navicula manuscripts .......................... 227

Appendix Six

The group C navicula manuscript ....................... 241

vi

contents

Appendix Seven

The group D navicula manuscript .................. 245

Appendix Eight

The group E navicula text ................................. 257

Appendix Nine Organum Ptolomei ita sit . . . .............................. 265 Bibliography ......................................................................................... 279 Index ..................................................................................................... 287

LIST OF FIGURES Fig. 1 Fig. 2 Fig. 3 Fig. 4 Fig. 5 Fig. 6

Fig. 7

Fig. 8 Fig. 9 Fig. 10 Fig. 11

Fig. 12

Fig. 13 Fig. 14

The Oxford navicula, front and back (Museum of the History of Science, inv. no. 54358). ..................... The Greenwich navicula, front and back (National Maritime Museum, inv. no. AST 1146). .................... The Geneva navicula, front and back (Musée d’Histoire des Sciences, inv. no. 2139). ...................... The Gentleman’s Magazine navicula, back and front (W. B. (1787)). ................................................................ The Florence navicula, front and back (Istituto e Museo di Storia della Scienza, inv. no. 3163). .......... Divisions for the mast (left) and bead (right) scales, according to the exemplar construction of the navicula. ........................................................................... The body of the navicula and the division of the latitude scale on the mast, according to the exemplar construction of the navicula. ...................... Diagram reconstructed from the instructions in manuscript AB. ............................................................... The navicula, front and back, from Aberdeen University Library, MS 123, ff. 65v and 65r. ............. Diagrams from Aberdeen, University Library, MS 123, ff. 44v (left) and 40r (right). ......................... The body of the navicula from the group B text in London, Royal College of Physicians, MS 358, showing the body of the navicula (f. 24v) and the construction of the bead and mast scales (f. 25r). ... Diagrams showing the construction of the bead and mast scales according to the group A construction text, from Trinity College, Cambridge, MS O.5.26, f. 117r and f. 117v. ......................................................... Template diagrams in Cambridge University Library MS Ee.III.61, ff. 191v–192r ............................ The construction of the bead and mast scales, from Oxford, Bodleian Library, MS Bodley 68, ff. 43v and 44r. ............................................................................

8 10, 11 14, 15 16 18, 19

30, 31

32 35 52, 53 54, 55

58, 59

62, 63 65

66, 67

viii Fig. 15

Fig. 16 Fig. 17 Fig. 18

Fig. 19 Fig. 20 Fig. 21

Fig. 22

Fig. 23

Fig. 24

Fig. 25 Fig. 26

Fig. 27

Fig. 28 Fig. 29

list of figures Alternate figures for the bead and mast scales, from Oxford, Bodleian Library, MS Bodley 68, ff. 44v–45r. .................................................................. 68, 69 Diagram for the hour lines and latitude scale, from Oxford, Bodleian Library, MS 68, f. 43r. ..... 72 A 14th-century gold noble. ...................................... 87 Diagram of the organum ptolomei in Vienna, Österreichische Nationalbibliothek MS 5418, f. 182r. .......................................................................... 96 Diagram from Vienna, Österreichische Nationalbibliothek MS 5258, f. 81r. ........................ 97 Lund University Library, MS 47, f. 44v. ................ 99 Regiomontanus’ printed version of the instrument sometimes known as the organum ptolomei, but titled by him ‘general horary quadrant’. ................ 101 Diagram from Yale MS 24, f. 448r, showing the geometry of the organum ptolomei, but not its physical form. ............................................................. 102 The division of the bead and mast scales according to the navicula geometry and the division of the bead and mast scales according to the organum ptolomei and Regiomontanus dial geometry. ..................................................................... 104, 105 Diagram showing the geometry of the construction of mast scales according to the navicula and organum ptolomei geometries. ......... 108 The British Museum dial, as recorded in the register on its acquisition in 1893. .......................... 111 A dial dated 1527, and inscribed with the name Roger Brechte, in the collections of the Museum of the History of Science, Oxford (inv. no. 26323). ... 113 Diagram showing the relative positions of the 60-degree line on the Regiomontanus dial, the navicula and the Geneva navicula. .......................... 115 Diagrams from Weimar, Anna Amalia Library, MS Fol Max 29, ff. 62v, 63r, 63v. ............................ 124–127 Ship-shaped dial in the Museo Poldi Pezzoli, Milan (inv. no. 4277, reproduced in Brusa (1980)). This instrument is made of ivory, and signed “Opus Orontii F.” ...................................................... 130, 131

list of figures Fig. 30 Fig. 31

Fig. 32

Fig. 33

Fig. 34

Fig. 35 Fig. 36 Fig. 37

Fig. 38

Fig. 39 Fig. 40 Fig. 41 Fig. 42 Fig. 43 Fig. 44 Fig. 45 Fig. 46

Finé’s printed version of the dial shaped like a ship, from Finé (1560), 184 and 187. ..................... The Whipple ship-shaped dial, inv. no. 731. It is called the “Whipple” dial to distinguish it from another instrument in the collections of the same museum. ............................................................ Numbers of the scale on the back of the mast and from the latitude scale on the front of the mast on the Whipple dial. .................................................. Kircher’s columba dial, from his Ars magna lucis et umbrae (1646), facing page 506 in most copies of the book, but wrongly placed at page 560 in this copy. ..................................................................... The Cambridge dial, in the collections of the Whipple Museum of the History of Science (inv. no. 5902). ........................................................... Diagrams of the Regiomontanus dial from Munster (1532), 29 and 30. ...................................... Diagrams of quadrants, from Clavius (1581), 647 and 648. ................................................................ Oronce Finé’s diagram showing the construction of the Regiomontanus dial (from Finé (1560), 179). .............................................................................. Clavius’ diagram of the same instrument, showing many of the same features, including the jointed arm drawn off to one side of the instrument (from Clavius (1581), 628). ...................................... Diagram showing the geometry of the dial, from Bullant (1564), 106. ................................................... Bullant’s diagrams of the parts of the instrument, from Bullant (1564), 107. ......................................... Oxford, Bodleian Library, MS Bodley 68, f. 38v. .... Emmanuel College, Cambridge, MS 36, f. 41r. .... Oxford, Bodleian Library, MS Bodley 607, f. 16r. Stemma of group A manuscripts on the construction of the navicula. ................................... Stemma of group A manuscripts on the use of the navicula. ....................................................................... Stemma of group A manuscripts on the use of the navicula. .......................................................................

ix

132, 133

134, 135

137

142

146, 147 152, 153 154, 155

157

158 162 163 176 193 203 218 218 219

x Fig. 47 Fig. 48 Fig. 49 Fig. 50

list of figures London, Royal College of Physicians, MS 358, f. 19r. Aberdeen University Library, MS 123, f. 44v. ............. Oxford, Bodleian Library, MS Ashmole 188, f. 97r. ... Vienna, Österreichische Nationalbibliothek, MS 5418, f. 180r. .................................................................................

230 248 259 270

ACKNOWLEDGEMENTS I began to research the navicula when, as an undergraduate student, Dr Liba Taub of the Whipple Museum of the History of Science showed me the ship-shaped dial in their collection and encouraged me to find out more about it. For this, and for their support in the years since then, I would particularly like to thank the staff of the Whipple Museum. Later, the navicula became a major focus of my doctoral research. In completing this, I benefited from the support of the Department of History and Philosophy of Science at the University of Cambridge, and am grateful to my supervisors, Dr Liba Taub and Dr Adam Mosley, for their comments and questions, and, above all, their enthusiasm. I would also like to gratefully acknowledge the help of others: Dr Tessa Webber convinced me that I could read 15thcentury handwriting, the Latin Therapy Group helped me to translate the texts once I had transcribed them, Dr Matthew Spencer showed me how to construct manuscript stemmas, Dr Suzanne Karr-Schmidt shared her images of a hard-to-access manuscript and some unusual prints, and Jennifer Rampling worked with me to check transcriptions and translations before publication. Outside Cambridge, museums and libraries around the world provided invaluable assistance, and I would like to thank the large number of curators, librarians, and others, who enabled me to have access to objects and books in their collections, and answered my queries. Finally, none of this would have been possible without the generous support of those who funded my research, including the Arts and Humanities Research Council, the Medieval Academy of America, a Neil Ker Memorial Award from the British Academy, and the British Museum Research Board.

CHAPTER ONE

MONKS, MANUSCRIPTS AND SUNDIALS: THE NAVICULA IN MEDIEVAL ENGLAND The navicula is a portable sundial that can be used at any latitude to tell the time. It is regarded with fascination by historians of scientific instruments; Derek J. de Solla Price described it as “one of the most ingenious and sophisticated mathematical artefacts of the Middle Ages”1 on account of its mathematical complexity and its attractive form. The perceived rarity of the surviving instruments lends them a glamour and intrigue that some other types of sundial do not enjoy. This interesting instrument tells the time in equal and unequal hours, enables the calculation of the length of daylight (from the time of sunrise and sunset) and the calculation of latitude, and thanks to the shadow square on the back the instrument can be used for a wide variety of measuring of heights and depths of walls and wells. Influenced by the perceived rarity of the navicula, scholars have tended to complain about the lack of evidence available to find out more about this dial, and consequently scholarship about the navicula has often been based on conjecture rather than on hard facts. However, there are a significant number of manuscripts—sixteen in all, containing copies of texts and diagrams describing the construction and use of the instrument—which provide a picture of the uses and users of the late medieval navicula. I argue that in light of all the available evidence, it appears that the navicula was much more common than is usually thought and that interest in it continued through the sixteenth, seventeenth and eighteenth centuries. By tracking the navicula through these years, it is possible to see how it came to be perceived as a rarity, a curiosity, a charming but unusual astronomical instrument.

1

Price, “The little ship of Venice.”

2

chapter one Origins

Despite the best attempts of scholars to ascertain an approximate date and place for the “invention” of the navicula, and despite the wealth of manuscript evidence now available, there is little to tell us when, where or by whom the navicula was first devised. For every argument that can be advanced, it is often possible to suggest the opposite argument from the same evidence. Derek J. de Solla Price argued that the fact that there was apparently a sudden increase in interest in the late fourteenth century, and that some texts and instruments have a link to Oxford is significant.2 He suggests that this means that the navicula, in text or instrument form, arrived from the near East via Spain with many of the other texts of the Merton School.3 Giuseppe Brusa suggests that the 200-year gap between the flourishing of European interest in scientific instruments and the making of the surviving naviculae and the copying of the texts about them is significant, indicating that the navicula was invented or discovered in the fourteenth century.4 However, for both these arguments, there is neither evidence to back up the suggestions, nor evidence to the contrary. Most recently, David King has written on the origins of the navicula, arguing that most of its components were known in ninthcentury Baghdad, perhaps developed by the mathematician and scholar Habash, since he was capable of working through all the necessary trigonometric calculations. Therefore, he argues, this is the time and place to which we might trace the origins of the navicula. King allows that this hypothetical ninth-century instrument might not have had the distinctive ship shape that most easily characterises the navicula, but is convinced that medieval Europeans could not have invented such an instrument.5 However, it is clear that medieval European scholars developed new or improved versions of the instruments they

2

Price, The little ship of Venice,” 400. A group of people at and associated with Merton College, Oxford in the fourteenth century interested in natural philosophy and its related instruments, and who did much work on old Arabic texts that had been brought over by scholars, translators and others. See Gunther, Early Science in Oxford, vol. 2, 43–69; and Sylla, “The Oxford Calculators.” 4 Brusa, “Le navicelle orarie di Venezia.” 5 King, World-maps, 351–2: “the navicula de Venetiis, a veritable medieval computer from 14th-century England, [is] surely too sophisticated to have been conceived in medieval Europe.” 3

monks, manuscripts and sundials

3

discussed and used, and also that they invented some new types of instrument.6 King rightly states that “the history of universal horary dials from its beginnings to the late Renaissance calls out for a detailed investigation”7 In the manuscripts describing the navicula there is some indirect evidence for the date of compilation of the texts, since several of them name the ‘new calendar’, which is most likely to be the one compiled by John Somer in 1380.8 Some of the same texts describe the navicula as a ‘new instrument’, suggesting a late fourteenth century date for the invention of the instrument and the compilation of texts about it.9 In the mid fifteenth century John Whethamstede, Abbot of St Albans, names a certain Peter of Muchelney as the inventor of the ship-dial.10 However, as John North points out, nothing is known about who this Peter is, and this information is therefore somewhat isolated and cannot presently be linked with any other evidence to give a date or context for the navicula’s origins.11 In a footnote to an article on a different topic, John North outlines what must be regarded as the most practical view on the origins of the navicula: These instruments derive ultimately from Ptolemy’s Analemma (translated as Liber de annalemmate by William of Moerbeke). They included the navicula-type sundial (“little ship of Venice”). The same projection appears to have been revived by Regiomontanus for the sundial known by his name (universal rectilinear altitude dial).12

As North suggests, similar geometry underlies the navicula, the organum ptolomei and the Regiomontanus dial.13 This geometry is that considered in the Analemma of Ptolemy. Since this became available in Latin following a translation from Greek, completed in around 1269

6 A particularly noteworthy example is Richard of Wallingford, whose skill and achievements are discussed in detail in North, Richard of Wallingford. 7 King, “14th-century England or 9th-century Baghdad,” 220. 8 See p. 75 note 24; appendix 2, p. 195, line 6; appendix 3, p. 207, line 1; and appendix 7, p. 251, lines 23–26. 9 Appendix 3, p. 204, line 1. 10 Eagleton, “John Whethamstede.” 11 North, Richard of Wallingford, appendix 1, 113. 12 North, “Werner, Apian, Blagrave and the Meteoroscope,” 58, note 7. 13 See chapter 7 on the distinctive features of and relationships between these three types of dial.

4

chapter one

by William Moerbeke,14 we might tentatively put the date of development of the navicula between this date, and the earliest surviving instruments and texts, in the late fourteenth century, perhaps. However, the evidence so far available is not conclusive, and any suggestions about the origins of the navicula must be considered carefully. Just as a manuscript text can be compiled from a number of sources, as well as including original material, the navicula could have been “compiled” from a number of components, some of which were drawn from instruments and texts with Islamic ancestry, some of which were medieval developments, and some of which were taken from other medieval European astronomical texts and instruments. Until stronger evidence comes to light, it will not be possible to make firm statements about the development of the navicula, and neither should we look for a single date for the arrival of the instrument, fully formed, in the world. Name The name of the instrument, navicula, literally means ‘little ship’ in Latin,15 and it has often been known as navicula de venetiis. This name comes from the two manuscripts on the instrument that have been studied—Oxford, Bodleian Library, MS Bodley 68, and Cambridge, Trinity College, MS O.5.26—both of which name the instrument navicula de venetiis or ‘little ship of Venice’ in the opening line. A number of theories have been advanced to explain the name, but the simplest explanation is that Venice, a major port in this period, was a name associated with ships and shipping. Calling a sundial de venetiis could have been a double reference both to the sea power of Venice, and to its trade in luxury goods, for example.16 However, considering the larger group of manuscript material now available, only three of the sixteen copies give the instrument the name navicula de venetiis,

14 Heiberg, Claudii Ptolemaei Opera, 189–223. See also Neugebauer, History of Ancient Mathematical Astronomy, vol. 2, 839–56. 15 Some writers and museums have incorrectly given the name of the instrument as naviculum, which assumes navicula to be a genitive singular noun. It is clear from the manuscript evidence that it is instead the diminutive form of the nominative noun navis. 16 For European trade, and the voyages of Venetian galleys, see Spufford, Power and Profit, 397–405.

monks, manuscripts and sundials

5

all others referring to it simply as navicula or navis.17 This, along with inventory and other references discussed in chapter 6, suggest that to its medieval makers and users the instrument was known simply as navicula, and that is therefore the name used throughout this book. The ship-themed design and name is carried through into the vocabulary used for the parts of the instrument, with all manuscripts using the same names. The central mast (malus) pivots around the central pivot (cavilla), allowing the instrument to be set according to the date in the year, with the foot of the mast (pes mali) indicating the date on the scale for the mast (figura pro gubernacione mali). A cursor (cursor) slides on the mast, to set the latitude. The plumb-bob is pulled over the midday line (linea meridionalis), and the bead (margarita or noduli) slides along until it lies over the midday line. Holding the instrument up, and ensuring that the sun falls through both pinholes (foramina) on the castellated plates (tabula), the position of the sliding bead on the hour lines indicates the time. This book focuses on this interesting medieval English instrument, and begins by describing the five fifteenth-century naviculae and sixteen manuscript texts which will form the basis for its study. Looking at the design of the navicula, and the relationships and differences between the evidence contained in the texts, images and objects, I will show that complete information about the instrument is available only in a combination of all these information sources. The overlap between the craft and text traditions, and some specific features of the manuscript illustrations and the surviving instruments, indicate that there was a standard design of navicula in the fifteenth century. The manuscripts and instruments can also tell us about the uses and users of the navicula, and the links between using a small portable sundial and theoretical considerations of the heavens and of astronomy. Although the picture that emerges accords in some ways with scholarship previously published, which is based on a very limited set of evidence, the new manuscript evidence allows a more convincing assessment of the position of the late medieval navicula. The final sections broaden 17 Study of the Bristol customs accounts of the early 16th century has found that most ships in these documents were described as navicula, with the term navis being reserved for the largest ships. See Evans an Flavin, “Datasets.” It is unlikely that a similar distinction is observed in texts describing the navicula sundial, since in one manuscript (Oxford, Bodleian Library MS Ashmole 188) the terms navicula and navis are used interchangeably.

6

chapter one

out, clarifying the relationship of the English navicula to an instrument described in a number of manuscripts from German-speaking areas—the organum ptolomei—and showing how the navicula was (and was not) included in sundial books in the sixteenth and seventeenth centuries. This last section examines the post-medieval history of the navicula in order to understand the reasons why scholars have been so willing to assume that the navicula was a rare object, a geometrical curiosity, rather than looking for (and finding) the wealth of manuscript evidence to the contrary.

CHAPTER TWO

FIVE FIFTEENTH-CENTURY SUNDIALS Of the naviculae currently known to survive, five are dated to the fifteenth century. Perhaps the best-known instrument is the one described in Robert T. Gunther’s Early Science in Oxford and described there as German,1 although more recent discussions of the instrument have described it as English (figure 1). It is part of the Lewis Evans Collection, preserved in the Museum of the History of Science, Oxford, and was given to Lewis Evans by the Curator of the Norwich Museum in the early twentieth century. It is dated to the mid-fifteenth century,2 and measures 52mm from the noon line to the midnight line of the hour lines on the front of the instrument, and 50mm from the mast pivot to the line of 60 degrees latitude on the mast.3 The scales on the front and back are very worn, and there are signs that those on the back might have at some point been re-engraved, perhaps to make them clearer. The scale on the front at the bottom (for setting the tilt of the mast) is labelled with the zodiac signs, while that on the right (for setting the position of the sliding bead on the plumb-bob) is divided but not labelled. On the mast is a scale of latitudes, divided by five degrees, labelled every 10 degrees, and the scale has been subdivided into marks of single degrees. These subdivisions may have been done by hand rather than having been precisely, geometrically, divided, since they are somewhat uneven. The hour lines on the front are divided into half-hours, and each full hour line has a cross at the top. On the back are an unequal hours diagram and a shadow square: respectively, another method of telling the time, and a device for measuring the heights and depths of things.

1

Gunther, Early science in Oxford, vol. 2, 41. See http://www.mhs.ox.ac.uk/database (accessed 22 February 2008). 3 The measure between the noon to midnight lines, and between the points of 0 and 60 degrees latitude are used here because this allows consideration of the size of the instruments not including any decorative details. This is particularly important in chapter 5, where I discuss the manuscript diagrams showing how to make a navicula. 2

8

chapter two

Fig. 1A Fig. 1 The Oxford navicula, front and back (Museum of the History of Science, inv. no. 54358). Reproduced by permission of the Museum of the History of Science, Oxford.

five fifteenth-century sundials

Fig. 1B

9

10

chapter two

Fig. 2A Fig. 2 The Greenwich navicula, front and back (National Maritime Museum, inv. no. AST 1146). Reproduced by permission of the National Maritime Museum, London.


Fig. 2B

11

12

chapter two

Similar in size to the Oxford dial is another, in the collections of the National Maritime Museum, Greenwich (AST 1146 figure 2).4 It measures 51mm from 12 to 12 on the hourlines, and the mast measures 49mm from the pivot to the 60 degree line. As on the Oxford dial, the hour lines are divided into half-hours, the scale for setting the tile of the mast by the zodiac signs, and the latitude scale is marked by 10 degrees, subdivided to five, and then to single degrees, again probably by hand. Compared to the Oxford instrument, the scales on this navicula are very much less worn, perhaps because this instrument was lost soon after it was made. In 1989 it was found near the site of the Cistercian Abbey at Sibton, Suffolk, by metal detectorists. However, this navicula is not exactly the same as the Oxford one, since despite the similar size of the two instruments, the Greenwich example has on the back of the mast a table of the latitudes of York (53 40), Northampton (52 20), Oxford (51 50), London (51 34) and Exeter (51 0). On the back of the instrument body is a table giving the dates on which the sun enters each zodiac sign: Capricorn—13th December Aquarius—11th January Pisces—1[2th] February5 Aries—12th March Taurus—12th April Gemini—13th May Cancer—13th June Leo—15th July Virgo—15th August Libra—15th September Scorpio—15th October Sagittarius—15th November

This information helps the user of the instrument set the tilt of the mast according to the zodiac scale on the front of the instrument, and is also found on another surviving example of the navicula, in the Musée d’Histoire des Sciences, Geneva (inv. no. 2139 figure 3). This instrument is significantly larger than the Greenwich instrument (83mm from 12 to 12 and 73mm from pivot to 60 degrees on the

4

Higton, Sundials at Greenwich, 249–50. Corrosion means the value for Pisces is difficult to read. It is supplied here from manuscript tables giving the same values for the beginnings of each zodiac sign, on which see chapter 4. 5


13

mast). It is in extremely good condition, having been in the same private collection since at least the late eighteenth century, until it was sold at Sotheby’s on 25th February 1993.6 Although larger than the other instruments, the design is substantially the same. The zodiac scale is marked with signs, and the side scale is divided but not marked. As on the smaller instruments, the top of each whole hour on the front is marked with a cross, although the hours are subdivided into three (rather than two) parts. The mast is marked every 5 degrees, and subdivided to single degrees, although it is slightly too short according to the geometry by which the instrument was constructed.7 The towns and latitudes listed on the back of the mast are the same places, with the same latitude values, as on the Greenwich navicula, except for the last: in place of Exeter (51 0), the Geneva instrument has Winchester (51 0). The tables showing the date on which the sun enters each zodiac sign have the same dates as seen on the Greenwich navicula. Evidence for the existence of another instrument is given by an engraved drawing published in the Gentleman’s Magazine in 1787 (figure 4).8 On December 7th 1786 WB wrote to the editor of Gentleman’s Magazine describing his “ancient” sundial: MR. URBAN Colchester, Dec. 7. Herewith I send you drawings of both sides of an ancient sundial, answering the purpose of a quadrant, &c. made of brass, the middle, or upright piece of which is moveable to any of the twelve signs (see Plate II). I have been so particular in the delineation as to measure the lines accurately, that any of your readers (if they were so minded) might have one made from this copy as correct as the original. Yours, &c. W. B.

6 In 1992, before it was sold, the Geneva dial was compared to the Oxford and Greenwich dials, and it was concluded that the Geneva dial could date from the fifteenth or eighteenth centuries, with roughly equal certainty. Minutes of a meeting at Greenwich are preserved in the object file for the navicula at the Museum of the History of Science, Oxford. After being sold at auction, it was then sold to the Musée d’Histoire des Sciences. See Trevor Phillip & Sons, The Late-Mediaeval Navicula, where the instrument, based on study by Prof Gerard l’E. Turner, is confidently dated to the fifteenth century. 7 See chapter 7 below, and also King, “14th-century England or 9th-century Baghdad,” 205–8. The Geneva navicula should have a mast measuring 79mm to the 60 degree line. 8 On this and other references to scientific instruments in the Gentleman’s Magazine, see Delehar, “Illustrations of scientific instruments.”

14

chapter two

Fig. 3A Fig. 3 The Geneva navicula, front and back (Musée d’Histoire des Sciences, inv. no. 2139). Reproduced by permission of Musée d’Histoire des Sciences de Genève.


Fig. 3B

15

16

chapter two

Fig. 4

The Gentleman’s Magazine navicula, back and front (W. B. (1787)).

The note and engraved drawings of the navicula were published the following year.9 This instrument shares with the Geneva navicula the division of hours into three parts and the presence of latitude list and solar table (with the same values as the Greenwich and Geneva instruments). There is, however, no indication of scale, and so no way of knowing what size the original instrument was. The only clue is given by the relative size of the numerals marking the hour lines— these look more like those on the larger Geneva navicula than those on the smaller Greenwich and Oxford instruments. The diagram is constructed with hourlines measuring 55mm from the midnight to midday line. The mast measures 51mm from the pivot to the 60 degree line. Given that the Geneva navicula, stylistically most similar to this instrument, has a mast that is slightly too short while this instrument has a mast of the correct length, and also because of the presence on this navicula of Exeter (51 0) where the Geneva instrument has Winchester, it is unlikely that this illustration was taken from the Geneva instrument. Instead, it represents another, now lost, navicula.10 9

W. B., “Herewith I send you drawings.” The diagrams are geometrically accurate, although it is of course not possible to know what size the instrument they depict would have been. 10


17

The final instrument included in this section is kept at the Istituto e Museo di Storia della Scienza, Florence, and it is of very different design to the other four (inv. no. 3163 figure 5). It has recently been studied by Anthony Turner, who suggests that it should be redated and relocated to fifteenth-century England, rather than sixteenth-century Germany.11 This instrument is interesting in that it appears to be unfinished: the scales are not marked with all the numbers and letters necessary to use the instrument, although it otherwise has fine and accurate engraving. Even if finished, this instrument would have been stylistically very different from the other English naviculae: the sights at the upper left and right of the body are much smaller, and the calendar is engraved both with zodiac signs (on the front) and calendar months (on the back), removing the need for the tables showing when the sun enters each sign that are found on other instruments. The hours are divided into thirds, with crosses at the top—a feature shared by all five fifteenth-century instruments—and the mast is almost exactly the right length (pivot to 60 degree line 78mm) for the size of hour lines chosen for the instrument (80mm from midnight to midday line). The mast is divided by 5 degrees and subdivided in the same way as the other surviving naviculae, with points marked at every degree. The 5 degree marks have been drawn as arcs rather than as straight lines or points, indicating that this was done with a pair of compasses. This navicula came into the IMSS, Florence, from the Medici collections, but it is not currently known how it came to be in that collection. In the future, work in the extensive Medici archives may one day uncover more information. Certainly, during the sixteenth and seventeenth centuries many people visited the Medici court, then among the most powerful in Europe, and any one of them could have brought a curious English instrument with them. These five instruments are all dated to the fifteenth century, but none is inscribed with a date of manufacture, mark of ownership, or other clue that allows more accurate consideration of when, where and for whom they were made. This assumption about the dating is backed up by close scrutiny of the letter and number forms used to mark out the scales, but it is nonetheless essential to consider all available manuscript evidence in order to more closely date or locate the

11

Turner, Catalogue of sundials.

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Fig. 5A Fig. 5 The Florence navicula, front and back (Istituto e Museo di Storia della Scienza, inv. no. 3163). Reproduced by permission of Istituto e Museo di Storia della Scienza, Florence.


Fig. 5B

19

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surviving objects, and to fully understand the contexts in which they were made and used. It is clear that four of the five surviving instruments are remarkable in their stylistic similarities; only one (the Florence navicula)12 is different. The Oxford, Greenwich, Geneva and Gentleman’s Magazine naviculae all have the same design for the sights on the upper left and right parts of the body of the instrument, with three raised rows, the uppermost of which is castellated. The pinhole sights are in the flat plate on the end of these castellated parts. The top of the masts on these four instruments is also similar, although there are more differences here. The mast sliders on the Geneva and Gentleman’s Magazine naviculae have the same three rows and castellation as the sights, and although the top of the mast of the Greenwich navicula is simpler than these, the slider has the characteristic three row design. The Oxford navicula has three rows but no castellation at the top of the mast, in line with the simpler design and construction of this instrument compared to the others. These stylistic similarities and differences suggest that the Oxford and Greenwich instruments may possibly be grouped together, and that the Geneva and Gentleman’s Magazine navicula are very similar to each other. In comparison, the Florence navicula is very different: there is little decoration anywhere on the instrument, and the sights are much smaller relative to the overall size of the navicula. The top of the mast simply ends in a ring from which to suspend the instrument, perhaps from the owner’s belt if they were carrying it around. Among the five fifteenth-century dials there are differences in the marking of the hour lines, which strengthen the grouping of these instruments suggested above. The Oxford and Greenwich dials have the hours subdivided into two parts, while the Geneva, Gentleman’s Magazine and Florence instruments have the hours subdivided into three parts. Both divisions were used: some texts on the use of the navicula explain that the hours can be divided into two or three parts, while others do not specify any subdivision of the hours.13 On all five

12 This navicula ended up in the great Medici collection in Florence by 1776, when it appears in an inventory. See Turner, Catalogue of sundials; and Brusa, “Le navicelle orarie di Venezia,” 56, for details. 13 See appendix 1, p. 181, line 5; appendix 2, p. 192, line 21; and appendix 3, p. 204, line 10.


21

instruments the top of each hour line is marked with a cross, as specified in the group A construction texts. In addition, setting aside the Gentleman’s Magazine illustrations, which may or may not be the same size as the navicula they were based on, the surviving instruments are of two basic sizes: around 50mm between the midnight and midday lines (Oxford and Greenwich), and around 80mm between the midnight and midday lines (Geneva and Florence). It isn’t clear whether this indicates that the surviving instruments were made from a set of templates of a standard size, as there are at the same time differences between instruments of similar size or decoration. For example, the Geneva navicula’s mast is shorter than it should be, perhaps because the craftsman used the wrong line on the mast scale template when putting it together.14 Also, as outlined above, the presence of tables of latitudes and of the dates when the sun enters each zodiac sign on one of the smaller instruments (Greenwich) but not the other (Oxford) indicates that the decision to include them was based not on the size of the instrument, but on the requirements of the customer or the preference of the maker. A final detail that can shed light on the relationship between instruments is the engraved numerals. This evidence must be used with caution, however, because the Oxford navicula is much more worn than the others and it may be the case that some of the scales have been re-engraved on this dial, and the illustration from the Gentleman’s Magazine, although apparently very accurate, may not be an absolutely faithful representation of the original instrument. Nonetheless, looking closely at the four stylistically similar naviculae, it is clear that differences in the numerals show them to have been made by different craftsmen, and therefore not to be the product of one workshop or maker. The Greenwich navicula, although a similar size to the Oxford instrument, has noticeably different forms of numerals, especially 1, 5, 6, 7 and 9. The numerals on the Geneva navicula are different to either instrument, being more even in size and positioning as well as having noticeably differently shaped numerals 3 and 9. The Gentleman’s Magazine navicula illustration shows numerals similar to those on the Geneva instrument, in terms of their size, shape, and positioning. Therefore, although the Oxford and Greenwich naviculae are similar to each other, it is not possible to claim that they were

14

See chapter 7.

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made by the same maker. Instead, their similar size and decorative style, combined with the more basic construction and engraving, suggest that they represent the more ‘everyday’ type of navicula, made to be inexpensive by comparison with the larger and more carefully engraved Geneva navicula. More generally, the existence of several different texts about how to make and use the navicula, combined with the stylistic differences between the surviving instruments, suggests that there were several craftsmen involved in making naviculae. At the same time, the striking similarities between surviving instruments provide evidence for the circulation of a standard design. The navicula may have been well known in a certain design, reflected in the surviving instruments, and so new instruments were made according to this.

CHAPTER THREE

MANUSCRIPT SOURCES ABOUT THE NAVICULA Scholars working on the navicula have concentrated on just two manuscripts: Oxford, Bodleian Library, MS Bodley 68 and, to a lesser extent, Cambridge, Trinity College, MS O.5.26. In a footnote to his 1966–7 article on a different subject, John North mentioned the existence of other manuscript texts on the navicula: “There are four MSS in Oxford . . . dealing with the navicula, and another in the British Museum.”1 Although North gave no details, presumably he found them by looking up “navicula” in the index of the then-recently published Catalogue of Incipits of Medieval Scientific Writings in Latin.2 Such a consultation does indeed give details of four Oxford manuscripts (those with sigils DG, BL1, BL2 and RA in the discussion below) and one London manuscript (sigil EG in the discussion below). Unfortunately, in the decades since the publication of Thorndike and Kibre’s essential research tool, and John North’s note pointing to unnoticed navicula manuscripts, no author appears to have consulted the available manuscript texts, relying instead only on the published editions of two of them.3 I have transcribed, translated and studied the five texts listed in Thorndike and Kibre—those edited by Gunther and mentioned by North, along with the Middle English work edited by Price—and add to them a further nine previously unnoticed manuscript copies of texts on the navicula, plus one set of diagrams, giving a total of sixteen manuscript copies of five different works on the instrument. Whereas previous scholars have used two manuscript texts, copies of the same work, I have studied sixteen manuscripts, copies of five different texts. This enables more detailed study of the navicula, firstly suggesting that it was not a particularly unusual instrument, in contrast to modern scholars’ descriptions of it as a rare or curious object. Most of

1

North, “Werner, Apian, Blagrave and the meteoroscope,” 58, note 7. Thorndike and Kibre, Catalogue of medieval scientific writings in Latin. 3 Gunther, Early science in Oxford, vol. 2, 38–41; and Price, “The little ship of Venice.” 2

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the surviving navicula manuscripts date from the fifteenth century, backing up the provisional dating of the surviving instruments to that century. In addition, it is likely that other manuscript copies survive that are not described here; some of those now available were previously ignored because catalogue entries are either extremely brief (the navicula text in MS Wood D8, described below, is not mentioned in the Bodleian Library’s Summary Catalogue)4 or incorrect (the navicula text in MS Ashmole 188 was wrongly catalogued as a meteorological instrument).5 The sixteen manuscripts under consideration are grouped according to the type of construction used for the instrument, the contents of the section on use of the navicula and the type of diagrams included in the text. Fuller discussions are found in the appendices, along with transcription and translation of the texts. Nine of the sixteen manuscripts contain texts on constructing and using the navicula that are related to those edited by Gunther and Price: called ‘group A’ below. Three further manuscripts describe a different way of constructing the navicula—these are copies of a previously unknown work, and are here referred to as ‘group B’. The final three manuscripts are all unique copies of previously unknown texts on making and using the navicula, and are given as groups C, D and E below. In the appendices I transcribe and translate four of the five medieval texts on the navicula, including that previously edited by Robert T. Gunther since his version of the text is problematic.6 The fifth text (group C) cannot at present be studied in detail, since there are no records of its location or ownership since it was stolen from the library of Trinity College, Cambridge, in 1838.7 The sigils assigned are as follows: Group A

4

BL1 BL2 DI EM PH1 PH2

Oxford, Bodleian Library, MS Bodley 68 Oxford, Bodleian Library, MS Bodley 607 Oxford, Bodleian Library, MS Digby 98 Cambridge, Emmanuel College, MS36 London, Royal College of Physicians, MS358 London, Royal College of Physicians, MS384

Hunt, Watson and Macray, Digby manuscripts, vol. 2, part II, 1185, no. 8528. “Libellus de usu naviculae, sive instrumenti cujusdam meteorologici,” see “MS Ashmole 188” in Black, manuscripts bequeathed unto the university by Sir Elias Ashmole. 6 See Gunther, Early science in Oxford, vol. 2, 375–9. A page of the text and one of the diagrams are missed out of Gunther’s edition. 7 See appendix 6. 5

manuscript sources about the navicula RA TO1 WO CUL Group B AD EG PH1 Group C TO2 Group D AB Group E AS

25

Oxford, Bodleian Library, MS Rawlinson D248 Cambridge, Trinity College, MS O.5.26 Oxford, Bodleian Library, MS Wood D8 Cambridge, University Library, MS Ee.III.618 London, British Library, MS Additional 23002 London, British Library, MS Egerton 2622 London, Royal College of Physicians, MS358 Cambridge, Trinity College, MS O.8.16 Aberdeen, University Library, MS123 Oxford, Bodleian Library, MS Ashmole 188

Group A Group A is the largest, with nine copies of this text and one set of diagrams surviving, and within it there is also the most variation: some manuscripts include instructions for making and using the navicula, others discuss just the construction or the use of the instrument. The construction of the navicula according to the group A texts involves first making three templates, for the mast scale (at the bottom of the instrument), the bead scale (on the right hand side), and hour lines and the latitude scale on the mast. The text then explains how to use these templates to make a navicula. In those texts that contain a section on the construction of the navicula, the wording of this part on making the instrument is remarkably consistent across all copies. However, of the available manuscripts, none has a complete version of all the sections on the construction and use of the instrument that are present in any of them and, as I show in appendix 4, the group’s copying history and the variation between copies suggests that there were once a significantly larger number of copies of this text. The group A text in English (TO1) is a very literal translation from a Latin text close (but not identical) to the Latin copies in DI, PH1 and BL1. Price, in his edition of TO1, writes: It seems to be a direct and rather literal translation (though perhaps with a few original insertions) from the Latin text, using a version similar to but not identical with that edited by Gunther.9

8

CUL is not discussed here, since it does not include any of the group A text, consisting only of a set of diagrams. See chapter 5, p. 83, for a discussion of these diagrams. 9 Price, “The little ship of Venice,” 401. The “Latin text edited by Gunther” is BL1.

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The closeness of the translation is indicated by the glossing of some words to explain technical terms, by the scribe. These insertions are underlined, for example “Cum uolueris nauicule componere, . . .” is rendered in English as “Whan thou wolt compowne or make the schippe . . .” The underlining of ‘or make’ enables the sense to be clear in English even though that language was lacking a rich technical vocabulary for this kind of text. It indicates which words the scribe has added in English that were not present in the Latin. Beyond the fact that surviving texts on the construction of the navicula usually also contain a short version of the text on its use, and others contain just the text on how to use the instrument, there is little homogeneity in the content of these treatises. Some (PH2 and WO) discuss only how to tell the time and find the length of day, the midday solar altitude and, from this, the latitude. PH2 (but not WO) contains a table of latitudes to enable the slider on the mast to be accurately set for a particular town. EM is a version of the text similar to WO but expanded to discuss a variant form of the instrument, which has mast and bead scales labelled with calendar months as well as the more usual zodiac signs. EM also contains a table of latitudes and, uniquely, a table explaining that the first hour line represents both 11am and 1pm; the second 10am and 2pm; and so on. This information is described in the text of other copies, but in EM has been extracted and put into a table.10 Most short versions of the text on the use of the navicula include only sections explaining how to tell the time using the front of the instrument. The longer versions found in RA and BL2 have been expanded to include material on telling the time in unequal hours, and on measuring heights and depths using the shadow square and unequal hours diagram on the back of the navicula. RA is less detailed than BL2, including only one section on measuring the height of a tower using the navicula. BL2 contains the most detailed treatment of the use of the navicula for measuring heights and depths. It includes sections on measuring the height of something, on measuring the height of something whose base is inaccessible, on measuring the depth of a well, and on measuring the size of an area. In common with some surviving instruments, PH1 and BL1 also contain useful tables of the date on which the sun enters each sign

10

See appendix 2, p. 192, lines 8–18.

manuscript sources about the navicula

27

(useful for setting the date on the navicula) and a table of latitudes of towns (useful for setting the slider to the correct position on the mast). They also have complementary information such as the section on telling the time from the stars, which allows the user to tell the time during the night. According to this section (found in texts in the main subgroup of A: PH1, BL1), you find the star time by lining the navicula up with a chosen star, just as with the sun during the day, and then add or subtract an hour for each 15 days that the nadir of the sun precedes or follows the longitude of the star, given in the calendar.11 However, in spite of their differences the A group texts contain much material in common, whether or not a particular copy describes the construction. It looks likely that the group A texts originated from a text which contained the template construction method as well as a shorter version of the section on the use of the instrument. That there are a significant number of extant copies of texts on using the navicula suggests that there were different readerships, needing different information about it, along with significant alteration of the texts to suit the needs or interests of particular users or copyists. A craftsman making naviculae in quantity would need the section on construction from templates, while someone buying or receiving a gift of a navicula would only need the section on how to use it. Some of the longer versions of the group A text on the use of the navicula have been rewritten to include material that was previously in the construction sections. For example, at the start of the section on telling the time, manuscripts RA and BL2 have an extra section explaining the subdivision of the zodiac signs, and how the days lengthen and shorten as the sun moves through the year—material that is in the construction section where this is present in other copies. The section then restarts, with the same wording as texts like BL1. Therefore, when the usage texts separated from the construction text, it was done deliberately, with material useful for understanding the instrument’s functionality added, rather than being an accidental separation of one section of the text from another. Because of these changes in content, there are three transcriptions of group A manuscripts in appendices 1, 2 and 3. The first, based on

11 Such a calendar is found in the same quire as the navicula text and diagrams in BL1, giving that booklet the feel of a compilation of all the information you would need in order to use the instrument.

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BL1, notes the differences between this text and TO1, DI, PH1, PH2 and WO, and provides a transcription of the sections omitted by Gunther. The second is a transcription of EM, a manuscript that is close to WO. However, the unique additions and re-orderings found in EM mean that it would be difficult to include its variant readings in a single transcription of the group A text. Similarly, RA and BL2 are related to the main subgroup, but are much expanded, and so are transcribed separately from the other manuscript copies. Group B Group B is represented by three surviving copies: one that is complete (PH1), and two incomplete versions (EG and AD) that are probably copied either one from the other, or from a common source. These texts describe how to make a single navicula, without first making a set of templates, and are titled “How to quickly and accurately make a navicula . . .” This perhaps suggests that this text was written later than the group A construction from templates, by someone who needed only to make one instrument, rather than a set of templates, and who emphasised the speed and accuracy of this exemplar-based method.12 That either AD was copied from EG, or both from a common source, is shown by the fact that AD contains only texts that appear in EG, and that the wording of the navicula text is virtually identical, ending in the same place. It is striking that AD, EG and PH1 all contain copies of Chaucer’s Treatise on the Astrolabe; however there is no direct evidence that all three were copied from the same source.13 Of the three manuscripts, only PH1 includes a set of diagrams with the text, and it is not clear whether the scribe drew these at the same time as the text was copied, or they were constructed by him (or someone else) later in the fifteenth century. They include diagrams for the hour lines and scales for setting the mast and the bead, but not the latitude scale for the mast. However, following the manuscript instructions, it is possible to reconstruct a complete version of the exemplar construction diagram (figures 6 and 7). For clarity, the scale for setting

12

The differences between the template-based and exemplar-based methods are discussed below, pp. 38, 56, 61 and 64–5. 13 See Eisner, A Treatise on the Astrolabe, 53 and 62–3; and Eagleton, “A previously unnoticed fragment.”


29

the bead and the scale for setting the mast are shown separately from the body of the navicula, although according to the instructions they could be drawn on the main diagram. Also, the construction specifies that the zodiac signs should be divided into six parts each, whereas in the following diagrams they are shown divided into only two parts each. Group C Group C is represented by just one text, and unfortunately this manuscript’s location is not known, since it was stolen from Trinity College Library, Cambridge, in 1838. Nonetheless, detailed library and sale records allow a certain amount about it to be reconstructed. The text, titled Practica Iohannis Slape de Compositione Navis, Quadrantis & Chilindri, was item number 18 in the manuscript, and among the diagrams at the end of the manuscript were “tres figurae pro navicula”. In addition, it is striking that all the catalogue entries give the same author’s name, Master John Slape, in describing the book. Gunther went as far as to suggest that Slape might have been the author of the text on the navicula he edited (the group A text):14 T Allen is stated to have been the owner in 1622 of a MS 8vo codex, now lost, which contained a treatise De compositione navis, quadrantis et cylindre by an otherwise unknown author, John Slape. Was he perhaps the author of the Navicula?

Also interesting is a reference to three diagrams for the construction of the navicula. There is no indication as to what these showed, but since both the template-based and the single-exemplar constructions use three diagrams, this gives no indication as to which kind of construction this manuscript contained. It is therefore difficult to tell whether this text might be related to any of the others. Gunther’s claim that John Slape might have been the author of the group A navicula construction text is surely pushing the available evidence too far in the light of the existence of several variant forms of this text, as well as other treatises on construction of the instrument.

14

Gunther, Early science in Oxford, vol. 2, 379.

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Fig. 6A Fig. 6 Divisions for the mast (left) and bead (right) scales, according to the exemplar construction of the navicula.


Fig. 6B

31

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Fig. 7 The body of the navicula and the division of the latitude scale on the mast, according to the exemplar construction of the navicula.


33

Group D The group D text probably descends from sources including a group B text: some sections contain very similar wording, indicating that there is a strong link:15 PH1 (group B)

AB (group D)

in circulum directum perintus descriptum. et vlterius a circulo directo in archum .s.t. hoc modo.

in a direct cercylle wit owtyn grete difficulte þay may not be discryuyd or diuidid þer for diuid þam wit þis craft followand

There are also similarities in the way that some sections are described. For example, the construction of the scale for setting the bead is a little unclear at first sight. In contrast to the template-based construction (in which the auxiliary arcs are drawn outside the guide circle in both cases), the exemplar construction has the auxiliary arcs inside the guide circle when constructing the scale for the bead. This ensures that the scale fits between the two points of maximum solar declination. However, in both group B and group D the instructions tell you simply to describe part of a circle as far as line HI, without explaining that you first need to alter the distance between the feet of the compasses to equal the distance CH or CI (see figures 8 and 6B). However, there are also many differences between the two, including that the diagram lettering is different from that in the group B texts, and the construction of the scale for setting the mast is different, although using the same geometry.16 The group D text also has a different method of transferring the divisions of the latitude scale onto the mast—group B texts describe using a ruler to draw parallel lines, where AB describes marking the divisions with the compasses. At this stage of the instructions, AB contains a redundant section describing how the mast divisions should be transferred onto other lines around the circle in addition to transferring them onto the mast (OV, OM and OP in figure 8). These differences mean that it should be included here as the sole survivor of a separate group, albeit one descended from group B, rather than a variant form of the group B text.

15

Appendix 5, p. 233, lines 2–3; and appendix 7, p. 249, lines 35–6. See chapter 7 on a simplified version of the geometry, which developed later in German-speaking lands. 16

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The copy in AB is in English, but there are indications that the text was translating directly from Latin rather than copying an English text. For example, when he wrote “deinde þen þo diuisiones . . .” or “Item also fro B . . .” it is likely that the Latin words at the start of the sentences were copied by accident before the scribe then translated them and continued in English. There is further evidence of the scribe’s interest in translation in the manuscript—a text about the construction of a horizontal dial is given first in Latin and then translated into English. AB also shares some geometrical features with some versions of an instrument called the organum ptolomei, discussed in detail later, which could point to a link between them or between texts about them.17 Construction of the scales for the mast and the bead in the exemplar construction method is fiddly, since the subdivisions of the auxiliary arcs result in very small divisions, difficult to draw and transfer accurately onto the edge of the instrument. To overcome this difficulty, AB describes a slightly different way of marking the divisions of the mast scale. It instructs the maker to divide the scale for the mast above the instrument, on a large circle, and then transfer the lines through centre O to the bottom of the body of the instrument. After the section describing the construction of divisions on arc KV, there follow these instructions: . . . and in the spaces between the initial lines of the signs write the names of the signs so that in the first inner part towards V, [let] Capricorn be written, in the second Aquarius, in the third Pisces, in the fourth Aries, in the fifth Taurus, in the Sixth Gemini. Then in the first lower or outer space towards X [let] Capricorn be written, then Aquarius, Pisces, Aries, Taurus, Gemini, in the other spaces [let] the others be written. And this is the inscription of the signs on the lower part of the ship for setting of the mast.18

These seem to contain a redundancy—describing the inscription of the first row of zodiac signs twice, once with Capricorn towards V (on the right of the upper part of the diagram) and once with it towards X (on the left of the lower part of the diagram). To make sense of this, we must assume that a stage of the instructions have been missed out. Those lines would explain that to mark the divisions on the lower part

17 18

On the organum ptolomei, see chapter 7. Appendix 7, p. 250, lines 23–6.


Fig. 8

35

Diagram reconstructed from the instructions in manuscript AB.

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of the navicula you need to extend the lines from the divisions on KV through centre O, out towards the bottom of the body of the navicula (perhaps marking the divisions along arc ST) with Capricorn to the left (as you look at the diagram). That the divisions are to be transferred to the bottom of the navicula is indicated by the final line, concluding the section on inscribing the signs on the lower part of the dial. Group E The final type of manuscript, group E, is represented by just one text (AS) which is found in a collection of texts assembled ca. 1535 by an anonymous English writer. Scribal errors in the Libellus de Usu Navicula show that it was copied from a book or manuscript, rather than being an original composition by the (unknown) author. For example, in the lines below, the scribe has probably skipped up a line and copied “constituto” again, before realising his mistake, crossing it out, and continuing with “notatum”: Constituto cursore super gradum altitudinis poli in ipso malo constitutum notatum, convenit vt liniolae quae in pede . . .19

There remains the possibility that AS is a much altered copy of a group A text, but no intermediaries survive to indicate this link, and the wording of the text is very different, so it is included here as group E. The contents of the text are similar to those in the A group texts on the use of the navicula: 1. 2. 3. 4. 5. 6. 7.

finding the time finding the time of sunrise and sunset finding the length of the day and night finding the latitude of a region finding planetary/unequal hours finding the height and depth of things (not copied)20 finding the interposition of the sun in the signs (not copied)

Common to all texts on the use of the navicula in all groups are sections on telling the time, finding the length of day, and the latitude of a region. To use the navicula to tell the time, the slider on the mast

19

Appendix 8, p. 258, line 22. Only the first five sections were copied, but the second page is not full. It is difficult to tell whether the scribe ran out of time, was working from an imperfect copy, or deliberately omitted the last two sections. 20


37

is set to the latitude of the observer. Then, the mast is tilted to point to the sun’s position in the zodiac. The weighted thread is pulled over the degree of the sun in the zodiac and the moveable bead slid to lie over the 12 o’clock line. Then, when the navicula is tilted so that the sun’s rays fall through both pinhole sights, the position of the moveable bead shows the time. The use of the navicula for calculation as well as for observation is shown by the measurement of the length of the day, which involves setting the navicula for the date and then holding the thread parallel to the hour lines and reading off the times of sunrise and sunset. Using the shadow square on the back the height and depth of buildings and wells can be found, and the unequal hours diagram provides an alternative way of telling the time. From the number of manuscripts and instruments surviving, and the variation between the various texts discussed here, representing five different works on the instrument, it is clear that the navicula was widely discussed, constructed and used. Texts about using the navicula were rewritten to bring in useful material from other sources,21 and all five fifteenth-century naviculae were made according to the same geometry—the geometry generated by both methods for constructing the instrument. The template-based (group A) and exemplar-based (groups B and D) constructions generate the same geometry, with the same length mast and the same subdivisions of the zodiac signs. There is therefore no easy way to tell whether a surviving instrument has been made according to one method or to the other. There are some small differences between the two methods, including that group A manuscripts give a value of 24 degrees for the maximum solar declination, while groups B and D give 23 and a half degrees. There are, however, two reasons why this would not be a reliable guide to which construction method has been used to make a surviving instrument. First, several standard values for the maximum solar declination were circulating in the fifteenth century: 23 degrees 33 minutes was the value used in the influential Toledan astronomical tables, and this value was used alongside a value of 24 degrees in the annotations of the scribe of PH1.22 Second, the accuracy of engraving might not enable a difference of half a degree to be determined on a small, portable instrument (surviving naviculae are around 50–80mm across). Another feature 21 For example, the inclusion of material from a text about the quadrans vetus in navicula manuscript BL2. 22 See manuscript description in appendix 1.

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which is different between the group A and groups B and D texts is the subdivision of the hour lines. Only group A texts specify that they can be divided into two or three parts, and it is only these texts that specify the marking of crosses at the top of the hour lines. However, these are not differences that are significant enough to assign a surviving instrument to the template or the exemplar construction method: there is no text in the group B and D manuscripts specifying an alternative, and it could be that makers using a group B or D text knew enough about how other naviculae looked to include these features on their instruments, and conversely that someone working from a group A text to make a smaller instrument might decide, say, not to subdivide the hour lines. Group A texts describe the construction of templates for making naviculae in quantity, while group B describe how to make a single instrument without templates. The opening of the group B texts “to quickly and accurately make a navicula . . .” suggests that there was also demand for a method that did not involve going to the trouble of making templates, as well as makers who were perhaps making more than one navicula, for whom the trouble and expense of making templates (on sheets of brass) would have been worthwhile. Jan Kragten has argued that the Oxford and Greenwich naviculae have both been made with the mast and bead scales transposed, that is that the wrong template has been used for each of the calendar scales.23 This may indicate that they were made by the same person or workshop, but may also indicate that this was an easy mistake to make when working with templates that look very similar to the naked eye.24 In addition, Kragten’s calculations were made from photographs rather than from the instruments themselves, and so may be distorted by this. In any case, the existence of both template-based and exemplar-based constructions suggests both that for some makers there was enough demand to go to the expense and effort of making templates and therefore making naviculae in quantity, and that others only wanted to make a single instrument, or were perhaps interested in understanding the geometry behind its construction. More importantly, the evidence suggests that navicula texts were altered to suit particular users, copyists, readers or craftsmen, and that the sources discussed here include a changing and changeable set of methods for making and using a complex and attractive geometrical object.

23 24

Kragten, The Venetian Ship of Sibton Abbey. See chapter 7.

CHAPTER FOUR

CALENDAR TABLES AND LATITUDE LISTS Three of the surviving naviculae have on the back a table of dates on which the sun enters each sign of the zodiac, and on the back of the mast a list of towns and their latitudes (Greenwich, Geneva, Gentleman’s Magazine). The table showing when the sun enters each zodiac sign is useful in converting between calendar and astronomical dates, for setting the tilt of the mast and the position of the bead. The latitude list is needed for setting the position of the slider on the mast, and the English towns listed on the instruments were probably an aidememoire for users of the instrument. Comparing these with the information in manuscript texts on the instruments shows a remarkable similarity between the two types of evidence. The tables of the entry of the sun into each zodiac sign are the same on the instruments as in four of the manuscript texts (BL1, PH2, PH1, AB). The values given are: Aquarius Pisces Aries Taurus Gemini Cancer

January 11th February 12th March 12th April 12th May 13th June 13th

Leo Virgo Libra Scorpio Sagittarius Capricorn

July 15th August 15th September 15th October 15th November 14th December 13th

This similarity of values shows that there was probably a standard set of values used, not just in navicula texts and on instruments. Under the Julian calendar, however, the dates on which the sun entered each sign changed gradually and tables like those above would become less accurate as time went on. Added to manuscript PH1, by a different scribe than the one who copied the navicula text, there is a table that was copied or written in 1513, and which shows different values:1 Aquarius January 10th Pisces February 9th Aries March 10th

1

Table on f. 96v.

Leo Virgo Libra

July 14th August 14th September 14th

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chapter four Taurus Gemini Cancer

April 11th May 12th June 12th

Scorpio October 14th Sagittarius November 13th Capricorn December 12th

There is, however, no evidence that naviculae were made with revised tables engraved on them. This could be taken to indicate that this is because the surviving naviculae were made within a relatively short period of time, before a new set of values for the sun’s entry into each sign circulated, or that the values circulating in navicula texts were used after new values would have been more accurate, without the craftsmen checking them against the most recent tables. However, to infer too much from this kind of data is risky. Instrument historians sometimes use the date on which the start of Aries is marked as a way of dating undated instruments, especially astrolabes. This relies on calculation of the precession of the equinoxes, and the comparison of instruments with the resulting values for the date on which the sun actually entered Aries in a particular year, assuming that the instrument would have been made with an accurate value for that year. In his critique on this method, Gerard Turner compared the marked first point of Aries on dated astrolabes, with the date of their manufacture.2 He shows that there were errors of up to 287 years either way, and thus these methods “do not warrant the status they have been accorded because there are too many uncertainties.”3 Similarly, it would be unwise to use the similarities between the manuscript and instrument tables to estimate any firm dating for either. The 1513 table gives the Vernal Equinox as 10th March, which would lead to a date of c. 1591 according to Michel4 or c. 1663 according to Gunther,5 urging caution in the over-application of this technique to dating undated instruments. Finally, also in PH1, there is a further table of the dates and times of entry of the sun into the signs of the zodiac following the text on the exemplar construction of the navicula.6

2

Turner, “A critique of the use of the first point of Aries.” Turner, “A critique of the use of the first point of Aries,” 554. 4 Turner, “A critique of the use of the first point of Aries,” 550, which is based on Michel, Traité de l’Astrolabe, 139. 5 Turner, “A critique of the use of the first point of Aries,” 550, which is based on Gunther, Early science in Oxford, vol. 2, 187. 6 PH1, f. 20v. 3

calendar tables and latitude lists

41

To know when the sun is in a sign in whichever month The sun enters

Aries in March Taurus in April Gemini in May Cancer in June Leo in July Virgo in August Libra in September Scorpio in October Sagittarius in November Capricorn in December Aquarius in January Pisces in February

12 11 13 13 14 15 14 14 13

2 20 1 12 22 2 18 21 13

12 12 13 13 15 15 15 15 13

8 2 7 18 4 8 0 3 19

12 12 13 14 15 15 15 15 14

14 8 13 10 10 14 6 9 1

12 12 13 14 15 15 15 15 14

20 Equinox 14 19 6 Solstice 16 20 12 Equinox 15 7

12

13

13

5

13

11

13

17 Solstice

11 10

10 3

11 10

16 9

11 10

22 15

12 10

4 21

Day hour day hour day hour day hour the year the the third in a second year bissextile7 after a year bissextile year after a after a bissextile bissextile

This table7 is somewhat different to those considered so far in that it takes account of the fact that the four-year cycle of leap years and non leap years alters the date of the sun’s entry into each sign. It is extremely unlikely that a navicula maker would have chosen the correct value for the year in question, since there is no evidence for makers of any type of instrument doing this.8 It simply would not be possible to set the bead and mast of the navicula accurately enough to take account of the time of day that the sun enters a sign, so this table is not particularly useful in using the instrument either. In light of the links between navicula texts and practical geometry texts it is likely that tables like these form part of the material in the treatises which is intended as much for reference as for practical use with the navicula.

7

A bissextile year is a leap year. Turner, “A critique of the use of the first point of Aries,” 550–1, considers this issue. 8

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They are evidence that texts on the navicula are more than just about making and using an instrument: they allow useful astronomical and geometrical information to be collected, within the framework of a text about an instrument. The more complex table is based on the same values as the simplified ones considered above (the first point of Aries is at some time on the 12th March), and shows a further complication in the use of such data for dating instruments and texts. The values for the first date of Aries vary from 12.183 to 12.8 according to which of the four years in the leap year cycle in being considered. If, say, an astrolabe were engraved with a value of 12.8 March as the first point of Aries there is no accurate way of assigning a date to the instrument. It could be appropriate to date it to the mid-fifteenth century, contemporary with the table above, and assuming it represents the third year after the bissextile year, or it could be a date closer to 1300 if the value is assumed to be that of a leap year. The possible difference of 150 years that results reduces the value of any dating obtained. The matter is complicated further by the fact that it is likely that tables such as these (and by extension, the values used on instruments) were copied from earlier sources rather than being recalculated by scribes or instrument makers. These problems, and the evidence from examples like the 1513 table described above, combine to render this method at best confusing and unreliable, and at worst completely useless for dating medieval instruments. Instrument historians would do well to study the many tables of this type in medieval manuscripts in order to compare this evidence with that of the instruments and thereby reassess the role of standardisation and the circulation of old tables of values. The over-reliance on methods using calculated (or actual) values for astronomical phenomena belies a lack of understanding of medieval manuscript culture and the way that intellectual and cultural life functioned in the Middle Ages. Standardisation and copying were central to that intellectual culture, and even the most technically competent scribes do not appear to have corrected the tables they were copying to ‘bring them up to date’. Moving to the lists of towns and their latitudes, these too show a very similar list of places and latitude values on the instruments and in the manuscripts. All the places listed on the back of the masts of three of the instruments (Greenwich, Geneva and Gentleman’s Magazine) are English towns, providing evidence for the English origins of these instruments. Similarly, all the manuscript texts currently known


43

are strongly linked to England, whether by the lists of predominantly English towns in latitude tables, or by the fact that they were copied or owned by English scribes, collectors or scholars.9 The manuscript lists tend to include a larger number of places, and some have a wider geographical spread. Listed on the instruments are five towns: York (53 40) Northampton (52 20) Oxford (51 50) London (51 34) Exeter (51 0) replaced by Winchester (51 0) on Geneva navicula

The appearance of a standard list of towns and their latitudes on the instruments is striking. Apart from the presence of Winchester in place of Exeter (at the same latitude) on the Geneva navicula, the instruments have identical information on the back of their masts, suggesting that there was a standard set of towns and latitude values circulating, which appeared on naviculae. These towns were among the most important in England at the time, but do not represent a simple list of the most populous or richest towns. London and York were easily the most important towns in England in the later Middle Ages. Both combined lucrative trade with thriving religious communities attracting pilgrims and scholars, and in a ranked list of English towns by taxpaying population in 1377 they are in first and second places respectively.10 Exeter (6th in a ranked list of taxable wealth in 1524–5) and Northampton (39th in the same list)11 were also important centres for the wool and cloth industries,12 and so would have been destinations for merchants and traders. Northampton was also a key staging point on the main road to the North of England, perhaps increasing its importance despite being a smaller town than the others listed. Most of the listed towns had significant religious communities, and several (Exeter, Winchester and York) were engaged in projects of rebuilding or improving the town cathedral during the fourteenth and fifteenth centuries, which would have resulted in the movement

9 See chapter 6 for the owners of navicula books and instruments in the fifteenth century, and chapter 8 for the post-medieval collecting of the instrument. 10 Palliser, The Cambridge Urban History of Britain, vol. 1, 758. 11 Palliser, The Cambridge Urban History of Britain, vol. 1, 765. 12 The letters of the Cely family, wool merchants in the second half of the fifteenth century, make frequent reference to visits to these towns on business. See Hanham, The Cely Letters.

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of goods and people into and out of the town.13 Oxford, a centre of scholarship often linked to astronomical and mathematical subjects, is a town and latitude often seen on other astronomical instruments, and some instruments were designed specifically for the latitude of Oxford.14 Manuscripts on the navicula, and other astronomical instruments, also often contain tables of latitudes of towns, the example below is from RA, and is attached to a text on the use of the navicula. It lists a number of English towns, in roughly north-south order of their latitudes, and includes all of the places marked on the masts of naviculae: Perth (58 0) Newcastle (55 0) Berwick (56 50) York (53 45) Lincoln (53 15) Northampton (52 40) Leicester (51 10) Oxford (51 50) Colchester (51 40) Canterbury (51 36) London (51 34) Exeter (51 0) Winchester (50 15) Hereford (53 25)15

These towns were also important for medieval mapmakers, all of them being marked on various world maps and local maps during the Middle Ages. Rather than simply being navigational or geographical, world maps were used for contemplation and for understanding the world and its history, as charters and representations of power and knowledge.16 A fourteenth-century example of an English mappamundi is that in the Polychronicon of Ranulf Higden, which lists 14 towns: Canterbury, London, Winchester, Lincoln, Stanford, Northampton,

13

Palliser, The Cambridge Urban History of Britain, vol. 1. For example, texts on the cylinder dial describe a form of the instrument for the latitude of Oxford. See Kren, “The Traveller’s Dial.” 15 This final entry added after the main table had been copied. 16 See Edson, Mapping Time and Space; and Hiatt, “The cartographic imagination of Thomas Elmham,” which discusses the relationship between maps and charters in the work of a fifteenth-century scholar. 14


45

Oxford, Exeter, York, Norwich, Worcester, Gloucester, Canterbury and Chichester.17 These are very similar to the towns listed in navicula texts and on the surviving instruments. However, the lack of detailed work on the sources for the representation of England and English towns on medieval world maps makes it difficult to draw any firm conclusions about the sources for the selection of towns shown. Nonetheless, the inclusion of Northampton indicates that this town may have had an importance greater than its taxable wealth or population indicates, probably linked to its position part way up the main northsouth route in England. Some manuscript tables included non-English towns, with the tables in BL1, PH2 and PH1, also including towns in Europe and the wider world along with the English towns:

BL1

PH2

Alexandria Jerusalem Toledo Rome Marseilles Cremona Lyons Paris Constantinople London Canterbury Leicester Colchester York Oxford Berwick

17

31 32 40 41 50 44 45 45 55 48 40 [note] dī: 49 gradus 56 51 40 [note] minuta 34 51 36 52 50 56 54 [note] anthonius askam doctor astrologe dicit 55 52 [note] 51 gradus 30 minuta 56 50

Reproduced in Harvey, Medieval Maps, 34.

Alexandria Jerusalem Toledo Rome Marseilles Cremona Lyons Paris

31 32 40 41 50 44 45 45 55 48 40

Constantinople London Canterbury Leicester Colchester York

56 51 40 51 36 52 50 56 54

Oxford

52

Berwick

56 50

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That these two texts have exactly the same latitude table, along with the similarities in wording of the text on the use of the navicula that each contains, suggests that they were copied from the same source. Some of the places in the lists have different values in the various sources, but these are not often significant in setting the navicula for use. For example, the value given for London in these tables is 51 40 which is different to that on the instruments, 51 34. The latter value is the value that is often given in astronomical texts for the latitude of London, but in order to set the navicula for use, the difference of 6 minutes would be negligible. Similarly for the value for York, which is 54 in the tables and 53 40 on the instruments, and for Oxford, which is 52 in the table and 51 50 on the instruments. Winchester, Exeter and Northampton are not in the tables in BL1 and PH2. The presence of values for the longitude of towns in several of the tables described, and the addition of notes of different latitude values for the towns listed, indicates that their function was broader than to allow the accurate use of the navicula, since longitudes are not needed in the use of the instrument. Instead, they show further evidence that the manuscripts contained useful information for reference and education alongside the practical information about the navicula. The latitude table in manuscript PH1, immediately following the group A text on the navicula, contains a much larger number of towns and their latitudes.18 The table also includes longitudes for the cities and this, combined with its size, suggests that it was not just intended as an aid to using the navicula. The list begins with Scottish and English towns, running north-south, beginning with Perth (58 0), Newcastle (55 0 or 58 0), Berwick (56 20 or 56 50) and Durham (55 20). That the list has been compiled by several scribes, from several sources, can be seen from the two values (in two different hands) for Berwick and Newcastle in the list, and the four values for York given by three different scribes (53 30, 53 40, 54 0, and 54 0). The list includes many European towns, similarly compiled by several scribes from different sources, and including some of the most important centres of learning, among them Paris (48 32 or 48 40 or 48 48, three scribes), Montpellier (44 40 or 44 50, two scribes) and Toledo (39 54, 39 54 or 40 0, two scribes). Beyond Europe, the list includes latitude values for important cities, including Alexandria (31 0), Babylon (30 30 or 34 0),

18

PH1, f. 24r.


47

Carthage (37 0), Constantinople (43 40) and Damascus (33 0, two scribes). The latitude of Jerusalem is specified (32 0), as is that of Arin (0 0), a theoretical location from which measurements were taken by Arab geographers. Comparative material is found in John North’s study of two fifteenth-century lists of towns and their latitudes and longitudes, and his tracing of some of their sources.19 In common with the table shown above, the tables transcribed by North contain more than one value for some of the places, suggesting that as well as being a practical compilation, the table is a record of all the values the scribe could gather. In North’s transcription of the two fifteenth-century lists, many of these towns appear, often with the same latitude values. That some of the values for latitude and longitude are slightly different can perhaps be attributed to scribal error, to the circulation of different—more or less corrupt—versions of this kind of table, or to the use of different sources. The table in PH1 was compiled by several scribes, over a period of time, with the later values probably being added by the same scribe who copied the 1513 table of zodiac signs discussed above. The table therefore seems to have been compiled as a reference work, as a collection of the latitudes and longitudes of all the places the scribes thought were important. This explains the presence of places like York, Durham and London, as well as Jerusalem, Babylon and Arin, especially since the table was in a manuscript owned and annotated by a community of Augustinian canons. This table probably represents the collected standard values for latitudes: the values for London are 51 34 and 51 40, which are the values that are used in navicula texts and on the instruments. The first part of the table shows its link to other navicula texts, since its towns are very similar to those in other latitude tables. The first few towns are in the same order as those in the latitude table that accompanies the navicula usage texts in RA, discussed earlier. This suggests that the navicula latitude table has been expanded to include information from other sources as well as the English towns that were of more practical utility. The scribes appear to have included different values for some of the towns, as if they were less interested in having one value per place than in collecting together all the possible values.

19 North, Horoscopes and History, appendix 1, 186–95. See also Wright, “Notes on the knowledge of latitudes and longitudes.”

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Even the apparently practical lists containing fewer values, like those in BL1 and PH2, and giving only their latitudes, are not solely copied in order to help with the use of the navicula. Because the navicula can only be used at latitudes of greater than about 30 degrees due to the practicality of moving the slider far enough down the mast, places such as Alexandria (31 degrees latitude) are probably not included in these tables just in case someone were to go there with their navicula. Instead, these places are probably included because of their interest to scholars and theologians, their importance in histories and on pilgrimages, or because they were places mentioned in the Bible. Latitude tables often appear in medieval manuscripts, with astronomical texts and tables, in commonplace books, and in calendars. In the navicula texts there appear short versions, with around ten places listed, medium-length tables which include some places in Europe and the Middle East, and long tables including values for many places all over the world. So it is likely that, rather than being an original composition by the authors of the navicula texts, the latitude tables were copied from other sources, which were originally based on the Toledan Tables and other sources, but which formed a tradition of their own in their contents and the values given for latitude. The fact that latitude tables with similar places in them usually appear in astronomical and geometrical texts links the navicula manuscripts to a wider genre of texts on practical geometry or astronomy. In common with Chaucer’s statement in the Treatise on the Astrolabe that he is only a compilator,20 the authors of the navicula texts built them up both from their own descriptions of how to use the instrument, and from standard sources for latitudes, dates, and some of the methods for using the navicula, which were probably based on quadrant treatises. Their medieval copyists recognised this state of affairs, and the scribe of EM explains “I put a table of latitude of English cities, whose latitudes following diverse [sources] you find written.”21 Returning once again to the five surviving fifteenth-century naviculae, of which three have lists of towns and their latitudes on the masts, we now have a richer context within which to place these lists, and to understand where they came from and what their purpose was. In the

20 21

Eisner, A Treatise on the Astrolabe, 108. Appendix 2, p. 194, line before table.


49

case of the Greenwich navicula Hester Higton considers the selection of towns, and in particular the inclusion of Northampton, writing:22 It is probable that the original owner had links to these places and had requested that they were included on the navicula when it was made (unless he made it himself, in which case he could have selected the towns on the mast at will). They are once again an indication that this dial was no doubt the property of a rich man who could commission an instrument exactly to his requirements.

Both because the three surviving naviculae have almost exactly the same towns and latitudes marked on their masts, and because of the standardisation in the textual sources, the choice of towns on the Greenwich navicula was unlikely to have been due to its commissioner. The fact that Northampton was an extremely important trading town and staging post on the main route north means that it is not at all unusual for such a town to appear in this kind of list. Indeed, Northampton appears on medieval mappamundi and itinerary maps, indicating its importance. It is not the case that the surviving naviculae were made with customised places, since all three with towns and their latitudes listed have almost exactly the same places marked. The lists of latitudes circulating in navicula manuscripts list the same towns, often with the same latitude values. The tables showing when the sun enters each zodiac sign likewise include the same values. The links of these manuscripts to a standard set of values circulating in astronomical manuscripts and commonplace books shows that these values were not used only for the navicula, but that the manuscripts on the navicula were compiled from a variety of sources. These manuscript tables accompanying the texts about the navicula could be repositories for geometrical and astronomical information, as well as providing practical information that would help in setting the navicula for use.

22

Higton, Sundials: An Illustrated History, 30.

CHAPTER FIVE

TEXTS, INSTRUMENTS, DIAGRAMS AND RELATIONS BETWEEN THEM The preceding sections discussed the wealth of evidence available to scholars studying the navicula—the instruments and manuscripts that can tell us about this instrument—and the information they contain. The instruments and manuscripts give evidence for a standard design of navicula, with castellated sights and mast-top, and many of the manuscripts are illustrated with diagrams showing the geometry of the instrument. One of these, in AB, shows a navicula very similar to the surviving instruments (figure 9). Although this manuscript does contain a text about the construction of the navicula, whose text refers the reader to a figure, it is very unlikely that this is the missing diagram from that text. It is in a different quire to the navicula text, on a folio that has been re-used, with a list of zodiac signs written on it after the navicula was drawn, and then a lunar and solar volvelle constructed after that, and labelled by a different scribe to the one that copied the text on the navicula. The diagram shows a completed instrument, accurately drawn, although the sights at the upper left and right of the instrument are rather roughly copied. There is no trace of construction lines, suggesting that this diagram was copied or traced, whether from an instrument or another image. Whichever was the case, the illustration shows a navicula very similar to the four surviving fifteenth-century instruments, and of a similar size—72mm between the noon and midnight lines, with a mast measuring 68mm from the 0 to 60 degree points. The drawings also show a navicula with a zodiac date table exactly the same as those on surviving instruments, but because the back of the mast is not shown there is no information about whether it would have had a list of towns and their latitudes on it. The decorative features of the diagram show many similarities with the design of the surviving instruments, details that are not fully specified in any of the known texts on constructing the navicula. No other manuscripts have diagrams like this, showing the whole instrument; other sets of diagrams are more geometrical. This section considers the relationship of these diagrams to the surviving instruments and to the standard design, and therefore their function. Were

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Fig. 9A Fig. 9 The navicula, front and back, from Aberdeen University Library, MS 123, f. 65v and ff. 65r. Reproduced by permission of the University of Aberdeen.

texts, instruments, diagrams and relations

Fig. 9Β

53

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Fig. 10Α Fig. 10

Diagrams from Aberdeen, University Library, MS 123, ff. 44v (left) and 40r (right). Reproduced by permission of the University of Aberdeen.


Fig. 10B

55

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they simple practical aids for making a particular type of sundial, or is there more to them than that? Looking at practical geometrical and instrument manuscripts from the later Middle Ages, there are three main types of diagram illustrating these types of text. Firstly, some images combine pictorial representation and geometric diagram, perhaps showing a building being measured by an instrument (usually a quadrant or an astrolabe), and overlaid with the geometry on which the calculation of height is based. In these illustrations, the representation of the quadrant is schematic, simplified but accurate enough that in conjunction with an instrument you could work out how to measure the tower or well. No equivalent diagrams of the navicula in use are known to survive, and none of the texts on the use of the navicula have diagrams of any kind. The second type of diagram shows details of the geometry of the construction of the instrument, while the third type is an illustration of its finished parts. To clarify the difference between these two types, figure 10 shows two diagrams from another of the texts in manuscript AB. The text describes how to make a quadrant, and is illustrated with two diagrams: one (below, left) showing the geometry of its construction; the other (below, right) showing the parts of the finished instrument. This is clear in the representation of the slider, which in the geometrical diagram is plain (since it is the scales and lines that are of greater importance) but in the finished-parts diagram is shown with curved ends to make it easier to get hold of and slide to the correct position for using the instrument. Together, these diagrams allow a quadrant owner to understand what the various lines on the quadrant relate to, and how the instrument is constructed, while also allowing a maker to understand the geometry of the instrument. They clarify the text, and its instructions, as well as showing the finished form of the instrument.1 Diagrams illustrating texts about the construction of the navicula at first seem to be of the second type—diagrams detailing the geometrical construction but not showing a finished instrument. This is particularly true of the exemplar construction, which describes how to make a single navicula, without first making the templates described in group A texts. The exemplar construction is described in texts in

1 See chapter 8 for discussion of these pairs of diagrams in early printed instrument texts.


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groups B and D, and although the two texts may be related, the link between them is indirect. The group D text in manuscript AB was probably copied from a Latin exemplar, and that exemplar (or one of its ancestors) probably had diagrams, as seen from the statement “as in þo figure truly made playnly it apperys”, which refers directly to a diagram that is not found with the text in AB.2 The group B text has no direct references to diagrams, but one manuscript copy (that in PH1) is illustrated with a set of three diagrams (figure 11). The three diagrams do not appear to have been drawn by the scribe who copied the text, and were perhaps added later along with some calculations of solar altitude, by the Augustinian canons at Thurgarton, Nottinghamshire, to whom this manuscript is closely linked.3 They are not a complete set of diagrams: there is no illustration showing the construction of the latitude scale on the mast. The diagram in figure 11A shows the construction of the front of the navicula, with hour lines, and bead and mast scales. The detail of the bead and mast scales is not shown on this diagram; there are instead simplified circles and arcs indicating where the diagrams on the following page should go, and two more diagrams are provided (figure 11B), showing the details of the construction of these scales. Two more diagrams (above, right) give the detail of the construction of the scales for the bead (the upper diagram, labelled “pro margarita”) and the mast (the lower diagram, labelled “pro fine male”). The letters marked relate to the previous diagram, showing the whole of the front of the instrument, and these diagrams are based on circles of radius 29mm: the same size as the place marker circles on the diagram of the navicula body. These three diagrams clarify the text, and allow someone working through the geometry of the instrument to see the finished diagram that the textual instructions describe. That they were probably added by someone other than the scribe of the text is interesting—perhaps someone worked through the geometry described in the text, and drew these diagrams on the blank leaf following it. Indeed, there is other evidence in PH1 that the canons at Thurgarton made active use of the material in the manuscript in this way; calculations on blank leaves in MS RCP 358 show the Thurgarton canons’ technical competence at calculations

2 3

Appendix 7, p. 249, lines 29–30. See p. 170.

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Fig. 11A Fig. 11 The body of the navicula from the group B text in London, Royal College of Physicians, MS 358, showing the body of the navicula (f. 24v) and the construction of the bead and mast scales (f. 25r). Reproduced by permission of the Royal College of Physicians, London.


Fig. 11B

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based on latitudes and solar altitudes, and other notes show that they probably owned at least one astrolabe.4 The diagrams are, despite illustrating a text about making an instrument, clearly not representations of a finished version of the instrument and, in addition, the diagram showing the body of the navicula is much larger than any surviving instruments. Instead, these illustrations show a finished version of the geometry according to which the instrument might be constructed. Manuscript PH1 also contains a group A text, describing the construction of templates from which a navicula can be made, but it does not include diagrams with that text. Other group A manuscripts are illustrated, with a different set of three diagrams to those seen with the group B text. Three group A texts are illustrated: TO1, DI, BL1. The illustrations in figure 12 are from TO1. These diagrams, showing the geometry of the construction of two of the scales on the navicula, are surprisingly large, given that they are for making an instrument that is usually small in size. They are based on an arc of 182mm, 7.155 inches, which is close to the “half a fote” that is specified by the text for their construction.5 This pair of diagrams are larger than either of the other two surviving sets (in DI and BL1), and the fact that this may be among the earliest surviving navicula manuscripts suggests that the diagrams perhaps started at full size, and that copyists gradually reduced their size to fit on the pages of smaller quires (the pages of TO1 are larger than most of the other manuscripts containing navicula texts). The diagrams in DI are very similar to those in TO1, but smaller, based on a main arc of radius 114mm. Gunther described them as a “rough sketch”6 apparently dismissing them without close study. The fragility of the manuscript means that it must usually be consulted on microfilm, on which the diagrams do indeed look rough and inaccurate. However, consultation of the manuscript reveals that the underlying diagrams are accurately drawn in pale brown ink but have later been roughly overdrawn in thick red ink.7

4

See p. 170. Appendix 1, p. 175, line 3. Price, “The little ship of Venice,” 402, notes: “This device, as so described, is considerably larger than either of the extant examples— approximately three times as big,” apparently having misunderstood the instructions in the text to make templates before making a navicula. 6 Gunther, Early Science in Oxford, vol. 2, 41. 7 The diagrams are labelled “figura pro gubernacione fili et noduli in fabricatione instrumentum quod dicitur navicula” and “figura pro gubernacione mali.” DI, ff. 76v– 77r. 5


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These geometrical diagrams, illustrating the template construction, look at first sight like the second type of diagram described above, because they don’t represent a finished instrument. They clarify the instructions in the text and enable someone to follow the construction by relating the geometrical instructions to a finished template. However, it is also possible to consider the illustrations as finished representations of the templates that the text describes. The diagrams in both manuscripts are accurate enough and large enough that someone could use them to make a navicula without making a set of templates on sheet brass as the text instructs. In this way, the templates can be thought of both as geometrical diagrams, and as illustrations of a finished instrument like those of the horary quadrants shown above, albeit the templates rather than the navicula: they are diagrams of both the second and third type. Even though the diagrams in DI are smaller than the ‘half a foot’ specified in the text, they are still large enough to be used as templates. TO1 is written in Middle English, and although the diagrams are not labelled, they are referred to in the text as instruments, in contrast to other geometrical constructions which are referred to as figures. For example, the text begins by describing the construction of a template for the scale of latitude on the mast, and for the hour lines. This template is not present in TO1, although it was perhaps on a page that has been cut out immediately following the navicula text and diagrams.8 The text then explains how to construct two similar diagrams, one for the scale for setting the tilt of the mast, and the other for setting the position of the bead. For both, the position is set according to the date, which is given according to the sun’s position in the zodiac. Introducing this, the author writes that they are ‘othere instrumentes for figures of signes’—the templates (instrumentes) show how to make the divisions of the scale for the zodiac signs (figures).9 Latin copies of the same text also have this distinction between the templates as instrumenta and scales with geometrical divisions as figurae.10 In contrast, texts describing how to make a single navicula rather than a set of templates, if they refer directly to a set of diagrams at all, use only

8 TO1, page missing between ff. 115 and 116 (the text) and f. 117 (the two surviving diagrams). 9 TO1, f. 115r, transcribed in Rand Schmidt, The Authorship of the Equatorie of the Planetis, 207. 10 Appendix 1, p. 175, lines 2ff.

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Fig. 12A Diagrams showing the construction of the bead and mast scales according to the group A construction text, from Trinity College, Cambridge, MS O.5.26, f. 117r and f. 117v. Reproduced by permission of the Master and Fellows of Trinity College, Cambridge.


Fig. 12B

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the word figura in Latin or figure in Middle English.11 This difference in terminology points to a difference in function for the template diagrams: they are instrumenta to be used in constructing a navicula rather than figurae illustrating the text.12 However, the neat distinction between instrumentum and figura in the texts describing how to construct templates for making a navicula is not always preserved in the labelling of the diagrams accompanying the text. In DI the diagrams are labelled as figurae even though the text of this copy preserves the distinction between instrumentum and figura.13 The practical implication of the word instrumenta is further supported by the survival in one manuscript of a set of templates without their accompanying text (figure 13).14 These are probably related to the group A texts on the navicula, but have not been discussed as part of that group in chapter 3, above, and appendix 4, because they have been separated from the text.15 Each diagram is labelled with its purpose, using the word instrumentum rather than figura. That this is a set of diagrams which are intentionally rather than accidentally separate from the text about constructing a navicula can be seen from the notes added to the diagrams which explain what some of the lines represent: notes which do not appear on any other known sets of navicula templates. For example, on one diagram there is the note ‘a.n. declinatio solis maxima’ which indicates what the angle AN should be. It seems that these templates circulated separately from the full description of the construction of a navicula, providing a quick way to make the instrument without working through all the geometry to make your own set of templates. In DI there is a tantalising piece of evidence that the diagrams may have actually been used as templates in just this way. There are scratch

11

Appendix 6, p. 233, line 12; and appendix 8, p. 249, line 30. When discussing the relationship between instruments and diagrams, James Franklin writes: “Diagrams are not necessarily drawn on paper. For purposes of use, it may be better to inscribe them on something more durable, like metal. For making the inferences, it may be useful to include moving parts.” See Franklin, “Diagrammatic reasoning,” 70. However, the distinction between the terms instrumenta and figura in a text about constructing a navicula suggests that this is very simplified account of the relationship between text, image and object in medieval manuscripts, and that the situation is very much more complex than Franklin would have us believe. 13 The diagrams are labelled “figura pro gubernacione fili et noduli in fabricatione instrumentum quod dicitur navicula” and “figura pro gubernacione mali.” 14 CUL: Cambridge University Library MS Ee.III.61, ff. 191v-193r. On this manuscript, see p. 83. 15 See p. 83. 12


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Fig. 13 Template diagrams in Cambridge University Library MS Ee.III.61, ff. 191v–192r. Reproduced by permission of Cambridge University Library.

marks on the surface of the page that mark in lines that have not been inked in, and these scored lines extend the scale divisions towards the centre of the diagram. There is also a scratched arc 43mm out from the focal point of the construction lines—an arc not on the template diagram, and an arc not needed in order to trace or copy the diagram. However, A circle of radius 43mm is very close to the size of the body of larger naviculae, and it is possible that these scratched lines were made so that the scale divisions could be transferred onto a disc of brass or wood16 of 43mm radius, and a navicula made from this parchment template. Of course, dating scratch lines in the surface of

16 Although few, if any, wooden astronomical instruments survive from the medieval period, they may once have been common. A practical geometry text including instructions for making a quadrant specifies “fiat igitur quadrans hoc modo: accipiatur materia enea. ligne vel auricalcea.” See Hahn, Medieval mensuration, 12–13. In addition, some of the organum ptolomei texts specify that the instrument is to be made from wood, see p. 103 and note 18 on that page.

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Fig. 14A The construction of the bead and mast scales, from Oxford, Bodleian Library, MS Bodley 68, ff. 43v and 44r. Photographs reproduced by permission of the Bodleian Library, University of Oxford.


Fig. 14B

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Fig. 15A Alternate figures for the bead and mast scales, from Oxford, Bodleian Library, MS Bodley 68, ff. 44v 45r. Photographs reproduced by permission of the Bodleian Library, University of Oxford.


Fig. 15B

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the page of a book is impossible, so we do not know when this might have happened. Both TO1 and DI have diagrams for the bead and mast scale, but not the diagram for hour lines and latitude scales on the mast that is found in CUL. It is possible that this third diagram was on the now-missing folio of TO1, but we cannot be sure. A surviving copy of this diagram is in BL1 (figure 16). Robert T. Gunther’s edition of the navicula text in manuscript BL1 is illustrated with his own drawings rather than with photographs, meaning that there are a number of inaccuracies.17 And, unfortunately, just as he has missed a page out of his transcription of the text, Gunther left out one of the diagrams altogether—the diagram for the hour lines and the latitude scale. Further, the published versions of the diagrams are wrongly labelled, with folios 44v/45r and 43v/44r transposed in his reproductions. In short, Gunther’s versions of the BL1 diagrams must be used with caution. In BL1 there are two sets of diagrams (figures 14 and 15) for the bead and mast scales, copied by the same scribe, and labelled as “diagram for the bead[scale]” and “another diagram for the bead[scale]”; “diagram for the mast[scale]” and “another diagram for the mast[scale].”18 The two sets of diagrams showing the construction of the bead and mast scales are different to each other—the second set show the scale divisions constructed on a full circle (as in the diagrams in TO1 and DI) rather than on a semicircle, as seen in the first set of diagrams. In order to fit the second set of diagrams on the page, the illustrator has had to show only half of the navicula body. All four of the diagrams are accurately drawn, with the maximum solar declination shown as 24 degrees, and in each case with a construction circle radius of 47mm. Also, the main arc (the distance between the centre of the navicula body and the constructed scale) is the same in each case, at 103mm. This consistency would enable the diagrams to be used as templates for making naviculae, even though these diagrams are significantly smaller than those in TO1 or DI. The third diagram in manuscript BL1 (figure 16) provides evidence that allows an estimation of the sizes of instrument that are to be made with these templates.

17

Gunther, Early science in Oxford, vol. 2, 38–9. “figura pro nodulo”, BL1 f. 43v; “alia figura pro nodulo”, BL1 f. 44v; “figura pro malo”, BL1 f. 44r; “alia figura pro malo”, BL1 f. 45r. 18


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This is a combination of two geometrical diagrams: that for the construction of the latitude scale on the mast (the upper part) and the hour lines (the lower part). They are drawn together because the relative sizes of the latitude scale and hour lines are extremely important for the accuracy of the instrument’s geometry. This is also the reason why I have measured the surviving instruments not according to their physical size, but according to the distance between the noon and midnight line, and between 0 and 60 degrees latitude. The diagonal lines on the (lower) hour lines diagram give the divisions appropriate to the mast scales marked on the upper diagram, and the bases of the four latitude scale lines shown are at 43mm, 47mm, 52mm and 57mm from point A on the diagram, equivalent to half of the distance between the noon and midnight lines.19 The range of equivalent values for surviving naviculae is 21.5mm to 41.5mm. Thus, this diagram, if used, would produce instruments at least as large as the largest of the surviving naviculae. However, the presence of two sets of diagrams suggests that they were not only intended for using as templates to make a navicula—after all, why would two different sets of diagrams for the bead and mast scales be needed? Clearly the diagrams have a wider purpose than the straightforwardly practical. A feature of the diagrams in BL1 that is not seen in the other sets of geometrical diagrams is that they show part of the navicula body in the illustration. This makes it easier to see how to transfer the scales onto the blank body, and would make the diagrams much easier to use in conjunction with the text—to understand how a navicula has been constructed, rather than how to go about making one—although they would have been more complex to copy than the purely geometrical diagrams in TO1 and DI. It is also interesting that the details shown in the BL1 diagrams correspond with the standard design shared by four of the surviving fifteenth-century instruments and by the diagrams in AB. The same distinctive way of labelling the bead and mast scales is shown, with the hour lines stopping inside the circumference of the instrument in order to fit the scale labels in, and the labels on the mast scale following the text in that the lower row is written upside down, so that each sequence reads easily from left to right. The bead scale on the right-hand side of the navicula is also shown as it appears on most

19

See chapter 7 on the choice of the correct latitude scale for a set of hour lines.

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Fig. 16 Diagram for the hour lines and latitude scale, from Oxford, Bodleian Library, MS 68, f. 43r. Reproduced by permission of the Bodleian Library, University of Oxford.


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surviving instruments, without labels since it would be difficult to fit them in between the circumference and the noon line. These are features not detailed in the text, but seen on the instruments and these diagrams, linking the manuscript and craft traditions together. In addition, there are also features seen on the instruments and described in the texts which are not seen in these diagrams, so it cannot simply be the case that the craftsmen worked from a set of templates like those in CUL, TO1, DI or BL1 to make the instruments. For example, there is no decorative detail given for the castellation on the sights, mast-top or slider, and the group A text instructs the maker to put crosses at the top of whole hour lines, a feature seen on the surviving instruments but not in any of the sets of diagrams. Therefore, the texts and instruments are linked—they are not separate traditions, and the characteristic features of the instruments were known to people copying the texts, and vice versa. These overlapping sources—texts, images and instruments (none of which contains all of the information one would need in order to make a navicula that shared all the features of the four similar surviving examples)—point to the circulation of information about the instrument in some other form. This could be oral information shared by the textual and craft traditions, or images and instruments that were copied to make other instruments. In his survey of medieval model books, R. W. Scheller outlines the ways in which designs circulated in a wide variety of areas of the decorative arts. Among his examples are the production of miniatures in thirteenth-century Paris, which was based around a group of artists working in interrelated workshops on a “large, not mass-produced but already fairly stereotyped output”, and the use that miniaturists made of imported Byzantine ivories as models for their works.20 Scheller argues that the portable work of art can be considered as a form of transmission for a type of object. Extending his argument, I suggest that this is perhaps the form that the circulating navicula design took, whether based in one place, with a group of workshops, or more dispersed, but still based on the same design. This circulation of standard designs was common in notebooks belonging to architects and illuminators, usually including detailed pictures of animals, birds, tracery, figures, geometrical shapes and

20

Scheller, Exemplum, 28. See also Scheller, A Survey of Medieval Model Books.

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other things useful to people like masons and textile artists. No such notebooks are known to contain images of astronomical instruments, but, as Scheller discusses, small portable items can serve as patterns in their own right.21 Since instruments like astrolabes, quadrants and dials are portable, it is also possible that the instruments served as their own patterns. A maker could copy a navicula, or make one by borrowing a set of templates or a construction text, or both. There are a few surviving examples of drawings that might have served as patterns for astronomical instruments in the fifteenth century. A rare example might be Oxford, Bodleian Library, MS Ashmole 191, which contains an object that could be a diagram or an instrument, or both, bound with an early fifteenth-century practical geometry text. Illustrating the sections on using a quadrant to measure the height or width of things are diagrams of the kind discussed at the start of this chapter, with stylised images of the quadrant in use, overlaid with the geometry of the calculation. Immediately preceding the text, on a much smaller leaf is an accurate diagram of a finished quadrant, without any information about the construction of the instrument.22 The quadrant is accurately drawn, so could be used by adding a plumb bob to the piece of parchment, and the diagram is similar in size to surviving metal quadrants—with each straight edge measuring 107mm. It has no construction marks or letters on it that might relate to a construction text that it is supposed to clarify, but the scales and numbers are very clearly marked, with some numbers in red to make it easier to use. It is therefore possible that this is a rare surviving parchment instrument,23 and perhaps also could have served as a pattern so that someone could get a horary quadrant made by an instrument maker. At the very least, it provides further evidence that such diagrams, which could have been copied to make an instrument, were circulating separately from the texts describing their construction.

21

Scheller, Exemplum, 28. Gunther, Early science in Oxford, 171, incorrectly gives the manuscript reference as MS Ashmole 19, which is a later manuscript including heraldic material. This diagram appears on f. 54r of MS Ashmole 191. 23 More examples of paper instruments survive from later periods. See Bryden, “The instrument maker and the printer,” for an overview of seventeenth-century English paper instruments. These include several paper quadrants for pasting onto board or wood. On medieval manuscript volvelles, see Means, “The Vulnerability of Volvelles.” 22


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Returning to the diagrams in AB, showing a completed instrument, these types of illustrations, too, could have circulated with or without a text about the navicula. Indeed, as outlined above, the diagrams in AB are probably unrelated to the construction text contained in that manuscript. These diagrams have another interesting feature that provides further evidence that they were not intended to accompany the construction text: they show a navicula with calendar scale divided into zodiac signs, where the text explains in some detail how to divide the scales by calendar months. Another manuscript, in group A, states that if you are using a navicula which does not have the calendar months marked, you should look at the “new calendar” to find the degree of the sun, in order to set the mast and bead.24 The group D text in AB also specifies this text when describing how to inscribe the calendar month scales, giving evidence that these two texts were originally composed after 1380. In addition to these two texts describing the construction of naviculae with calendar scales, the Florence navicula has both calendar and zodiac scales marked on it. However, this instrument looks very different to the four made according to the standard design, which do not have calendar months on them, instead having the tables of when the sun enters each zodiac sign to allow conversion between the two systems. What, then, is the status of the Florence navicula, which looks very different to the four other fifteenth-century English instruments? There is clear evidence for the English origins of this instrument in that it uses the more complex navicula geometry for its mast and bead scales, and has crosses marking the top of the whole hour lines, and the hours subdivided into three parts—features seen only in group A navicula texts from England.25 This supports the view of Anthony Turner, who has recently redated the instrument to the fifteenth century, and relocated it to England.26 However, unlike the other four surviving navicula, this instrument doesn’t have the calendar scale inscribed within the main circle of the

24 This “new calendar” was probably the work by John Somer written in 1380. See Mooney, The Kalendarium of John Somer, 2. 25 See chapters 2 and 5 on the design of the navicula, and chapter 7 on its geometrical features. 26 Turner, Catalogue of Sundials, Previously described as German and sixteenthcentury.

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body—as on the other four instruments and in the BL1 diagrams, but not described in the text on constructing the navicula—but instead it is outside the instrument’s circumference. Therefore, the design of the Florence navicula derives from the text, but the maker probably did not have any knowledge of the standard design according to which the other surviving instruments were made. In short, this is the kind of navicula that is made when someone closely follows the instructions in the text. The distinctive shape of the instrument—from which its name comes—is a consequence of the geometry. For a set of rectilinear hour lines and tilting mast to work together, the lower edge of the body of the instrument must be curved to enable the position of the mast to be set, and the pinhole sights must be positioned so that they are out of the way of the tilting mast, either side of it. These components will give an instrument that looks very much like a ship, even without any decorative engraving. English naviculae seem to have been decorated in a particular way, emphasising the ship-shape, but that standard design was not followed for the Florence navicula. The variation in the construction of naviculae fits well with the evidence from surviving instruments that they were not all made in the same workshop or by the same maker. The Florence navicula is likely to have been made by someone who did not know about the standard design for which the four other surviving fifteenth-century instruments provide evidence. But even these four very similar instruments were not all made by the same craftsman, and the texts and diagrams do not describe and illustrate all the features of the design. Therefore, it is likely that a standard design circulated, whether in the form of instruments or images of them, or because the craftsmen making naviculae worked in an interconnected group of workshops. This crossover between the craft and written traditions suggests that only a combination of types of evidence—text, image and object—can give us a full picture of the place of the navicula in late medieval England.

CHAPTER SIX

USING A SUNDIAL, UNDERSTANDING THE HEAVENS? Who, then, were the people who wrote and read about the navicula, who used the instruments, and what did they use them for? It is likely, from the survival of smaller and larger versions, that the navicula might have been made for or owned by people with varying amounts of money to spend on a useful little sundial. And just as there is variation between the surviving naviculae, the surviving manuscripts were produced with varying degrees of luxury. None are among the world’s most beautiful gold-embossed codices, but the nicest navicula manuscripts are written in an even, neat, script, rubricated and usually with two- or three-line initials (for example, BL1). At the other end of the spectrum are books, copied by someone for their own use, often written by an interested individual, on paper, with little decoration and sometimes no page ruling (for example, WO). These can tell us much about the social and intellectual contexts of the navicula, and who was interested in the instrument. Just one copy of a text on the navicula is in a booklet that has no context at all: EM. Although Neil Ker catalogued it as belonging to the first part of the manuscript, it is in a different hand, in a separate quire of differently sized paper. So its modern context cannot be used to study the medieval place of the navicula. In addition, apart from a note at the end reading “Haull” there are no marginal notes that can help identify scribe, owners or readers.1 For most of the surviving medieval navicula instruments the situation is similar. Their provenance has long been lost, or was never recorded. An exception to this is the navicula now at the National Maritime Museum, Greenwich, which was found in 1989, by two metal detectorists, near Sibton Abbey, Suffolk. Sibton was the site of a large

1 See appendix 3. It is difficult to work out who ‘Haull’ was: there are a number of sixteenth-century members of Emmanuel College, Cambridge, with names similar to that, and because it is not known when the College acquired manuscript EM; it could equally well have been in another library or private collection when marked by Mr. Hall. See Venn and Venn, Alumni Cantabrigenses, for Anthony Hall (vol. 1 pt. 2, 284), Joseph Hall (vol. 1 pt. 2, 287), and Samuel Hall (vol. 1 pt. 2, 288).

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Cistercian abbey, founded in 1150, which was, by the later Middle Ages, a powerful and wealthy house. At its dissolution in 1536, Sibton reportedly had an income of £250 a year, in part from the wool trade.2 Some members of Cistercian communities studied at Oxford University, and there is evidence that some of these Cisterican monk-scholars had astronomical interests.3 However, the lack of detailed information about the archaeological context of the navicula means that it is difficult to tell when, and by whom, the instrument was lost or buried. There is also evidence linking members of other religious orders to the navicula. A community of Austin Friars is linked both to astronomical instruments in general, and the navicula specifically, by references in manuscript AB. This contains the Middle English group D text on the construction of the navicula, and is loosely linked to the Austin Friary at Warrington by a marginal note giving the date of its foundation. Certainly, the manuscript was copied in that part of England, judging by the Chester dialect of the English, and the marginal notes relating to towns (including Chester) in that area.4 The manuscript contains, among other texts, a copy of Chaucer’s Treatise on the Astrolabe, texts on making the quadrant and a horizontal dial, a calendar with Easter dates, astrological texts and horoscopes, a zodiac man, a family tree showing Henry VI’s direct descent from the Kings of France, the arms of the kings of European countries, a text on the assize of bread, and a remedy for getting rid of fleas. Stronger evidence, directly indicating the presence of a navicula, is given by a booklist from the Augustinian Abbey at Leicester, compiled between 1477 and 1494. It lists a navicula among a group of astronomical instruments, the phrase “per fratrem Charite” indicating that the instrument was acquired for the Abbey by brother William Charite, although it is not clear whether this indicates that he made, gave or bought the instrument: 5 2 For information about Sibton Abbey, see Foot, Williamson and Kerr, Cistercian Abbeys: Sibton. 3 For example, Richard Dove of Buckfast Abbey, on whom see Bell, “A Cisterican at Oxford.” 4 Note on f. 72v of manuscript AB. For comparison, see the archaeological report on objects found at the site of the Austin Friary at Leicester: Mellor and Pearce The Austin Friars, Leicester. 5 Webber and Watson, The Libraries of the Augustinian Canons, 324–5. The note “de auricalco” added in the hand of William Charyte, who was probably responsible for the compilation of the catalogue. The description “per fratrem Charite” should not be taken to indicate that he made the instrument, as this phrase is also used for items

using a sundial, understanding the heavens?

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Nauis per fratrem Charite de auricalco

A smaller community of Augustinian Canons,6 at Thurgarton in Nottinghamshire, or a member of that community, also seems to have owned a navicula and at least one astrolabe, as well as copying PH1. The Canons’ interest in astronomical and medical subjects is attested to by a fifteenth-century booklist, copied by the scribe of PH1.7 Marginal notes made in PH 1, probably in the second quarter of the fifteenth century, read: At Thurgarton the sun declines 24 degrees + according to the ship[dial].8 Cauda Leonis, Alacab, Alhabro, Deneblagedi [and] Menkar are not on the large astrolabe.9 My astrolabe is divided into 180 divisions and then each circle by one degree.10

These references in medieval booklists provide further evidence of a strong link between the craft and written traditions: the owners of naviculae and astrolabes and the manuscripts containing texts about them were not separate groups of people—the instruments seem to have accompanied the texts about them. that he acquired for the library. A similar group of instruments belonging to the York Austin friars is listed in a late fourteenth-century inventory of their library, edited in Humphreys, The Friars’ Libraries, 101: “Instrumenta Astrologica magistri Johannis Erghome| Horologium auricalcium| Astrolabium cum 7 laminis| Quadrans Prefacii iudei| Spera auricalcea| Clok eneum| Astrolabium.” 6 Austin Friars and Augustinian Canons (sometimes called Canons Regular) are two separate orders, despite their similar names. See “Hermits of St Augustine” and “Canons and Canonesses Regular” in the Catholic Encyclopaedia at http://www .newadvent.org/cathen (accessed 22 February 2008). 7 See Webber, “Latin devotional texts,” for analysis of the devotional interests of the Thurgarton Canons shown by this booklist, Webber and Watson, Libraries of the Augustinian Canons, for a transcription of the list, and Eagleton, “A previously unnoticed fragment,” for the link between this list, manuscript PH1, and Chaucer’s Treatise on the Astrolabe. In light of recent scholarship, suggesting that the Augustinian Canons of Leicester made changes to Chaucer’s Canon Yeoman’s Tale to reflect their disapproval of alchemy (see Kline, “Scribal agendas”), it is noteworthy that MS Sloane 3458 contains some interesting diagrams of alchemical or distillation apparatus on f. 25r. 8 PH1, f. 74r: “solem declinati’ .24. grad | apud thurgaton’ | + secundum navem”; “+ secundum navem” was probably added later. 9 PH1, f. 75r: “cauda leonis . alacab . alhabore . deneblagedi . menkar non sunt in magio astrolabio.” 10 PH1, f. 38r: “diuidia per astrolabio meo in 180 diuisiones et tunc quilibet circulis sunt per 1 gradu tunc.”

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Links between texts on the navicula and other astronomical instruments are strong. PH1, from the Augustinian Priory at Thurgarton, contains, along with texts on astrology and astronomy, a copy of Chaucer’s Treatise on the Astrolabe. Other manuscripts contain both Chaucer’s Astrolabe and one of the treatises on the navicula,11 and others contain a navicula text along with some other astrolabe text.12 Several manuscripts contain texts on both the quadrant and the navicula, which is interesting both in light of the fact that many of the same things can be measured using the two instruments, and because of the presence of material from a text on the quadrans vetus in at least one copy of a navicula text, indicating direct links between texts on the two instruments.13 Finally, in the now-missing TO2 the navicula is explicitly linked to the astrolabe, quadrant and cylinder: the otherwise unknown John Slape wrote about all four instruments. Although this manuscript is now lost, book sale records and library catalogues consistently describe one of the texts in it as: the practica of John Slape about the composition of the ship [dial], the quadrant and the cylinder [dial]14

This description is given by several of the catalogue descriptions of the text, perhaps indicating that this was the rubric or title of the text in TO2. However, none of the other navicula texts indicate any link to a John Slape, and since the location of TO2 is currently unknown it is not possible to determine what the contents of the text were, nor the context of the reference to John Slape. In the wording of the text of several manuscripts, a link can be seen to knowledge of other instruments. For example, the group A text explains that the construction of the zodiac scale is like the astrolabe rather than like the quadrant:15 These zodiac figures are made following the form of the astrolabe, and not the quadrant. On the quadrant any degree has its own place, according to its distance from the equinoctial. On the astrolabe the four cardinal degrees have their proper places and no more, just as here in these figures. 11

BL1, PH1, EG, AD, AB. DI, WO, TO2. 13 BL2. See appendix 4. 14 Practica Johannis Slape de composicione navis, quadrantis et cylindri. See p. 29, and appendix 4. 15 Appendix 1, p. 178, lines 20–1. 12


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A specific interest in astronomical instruments is shown by the person who bound together the texts of BL1 on June 20th 1550.16 Although it is not clear whether the navicula treatise in BL1 was originally bound with the other texts (on the annulus and the astrolabe), the quires containing the navicula text contain other material written in the same hand. The navicula text was copied with a calendar (useful for telling the time by the stars, as described at the end of this copy of the navicula text) and a diagram showing the relationship between zodiac and calendar months (for setting the mast to the correct date). These folia seem to be a collection of all the information and instructions you would need to make and use a navicula. The first part of the book, about the annulus and astrolabe, was owned by John Enderby, chaplain of Louth in Lincolnshire, in the fifteenth century.17 He was probably not a member of the Cistercian community at Louth Park, but could have been a priest attached to the church there, which was rebuilt during the fifteenth century, when Louth was prospering due to the income brought by the wool trade.18 Later in the fifteenth century this first part of this manuscript was owned by the abbot of the Benedictine Abbey at Coldingham, Berwickshire, before becoming the property of John Chaunteler of Oxford in the early sixteenth century.19 However, evidence that the book was bound in its current form only in 1550 means that we have no firm evidence that the navicula text in the second half of BL1 was owned by these people. Once again, though, it is clear that instruments and the texts about them are linked to religious men, members of different religious orders, but all with links to Oxford learning and with other astronomical interests. Interest in the navicula was not confined to the orders, however, and there is evidence that churchmen, from a provincial vicar to the dean of Lincoln, copied texts on the navicula. T.P. writes in WO that he copied one of the texts in his manuscript (on horse medicine) at Whittle, Essex, on May 10th 1485, and that he was rector of Blisland, Cornwall. Thomas Ponteshyde’s20 references both to his parish in Cornwall and 16

BL1 f. 48v; see appendix 1. Appendix 1. 18 For surviving books linked to the Cistercian abbey at Louth Park, see Ker, Medieval Libraries of Great Britain, 127. 19 Appendix 1. See Ker, Medieval Libraries of Great Britain, 52, for other manuscripts linked to the Benedictine priory at Coldingham, which was a cell of Durham. 20 Identified by Keiser, “Practical books for the gentleman.” 17

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his location in Essex when copying part of the manuscript give good evidence that he travelled and would have had need of a universal sundial. His collection also includes calendrical tracts, planetary theory and tables, practical geometry, the astrolabe and algorism.21 In short, the texts chosen by Thomas are a practical collection, reflecting the “spiritual and practical needs of the gentry”22 and within this context the text on the use of the navicula in WO is a useful thing—allowing him to tell the time wherever he might be in England. A higher-ranking churchman who copied a text on the navicula was Peter Partriche, dean of Lincoln Cathedral Chapter. He compiled manuscript DI, probably putting together the collection while he was a student in Oxford in the early fifteenth century (AM 1414, DTh 1421).23 The manuscript collection reflects Peter’s learning, and the interests of the Oxford academics, including practical texts on the calendar alongside works by Aristotle, Robert Grosseteste, St Augustine, Simon Bredon, John Peckham and Johannes Sacrobosco. With the text on the navicula are works on the quadrant, cylinder and astrolabe by Robert Grosseteste, showing Partriche’s interest in instruments. After Partriche’s death in 1451, some of his manuscripts were bequeathed to All Soul’s College, Oxford, and to Lincoln Cathedral. In the manuscript there is evidence that DI stayed in Lincoln and was read by other members of the Chapter for at least a century, before being acquired by John Dee for his library.24 The astronomical texts chosen for DI by Peter Partriche are mostly linked to Oxford, whether by the presence of tables calculated for that latitude, by the Oxford connections of their authors, or simply by the fact that he copied the text there. Certainly, Oxford was among the most prominent centres in Europe for study of astronomy and the liberal arts in the fourteenth century. However, manuscript texts on the navicula do not exhibit some of the more severe, scholastic, abbreviations found in university texts, and neither are they confined to manuscript collections of liberal arts texts. Several manuscripts contain texts of the Prophecies of Merlin along with a navicula

21 22 23 24

See Appendix 1 for a list of the texts in his collection. Keiser, “Practical books for the gentleman.” Emden, Biographical Register, 1430–1. On John Dee, see p. 138–9 and the description of manuscript DI in Appendix 1.


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treatise,25 and interest in chiromancy and divination is attested to in other manuscript collections.26 The navicula templates in CUL are part of a compilation put together by Lewis Caerleon, a Cambridge- and Oxford-educated doctor who became prominent in the late fifteenth century.27 Caerleon copied many astronomical texts, and was particularly interested in eclipses, and in works by earlier English astronomers, including Richard of Wallingford, Simon Bredon, John Somer, and others.28 CUL reflects these interests, including texts on the construction of astronomical tables (ff. 1–5) along with sets of astronomical tables (ff. 53–59), and calculations of eclipses and for eclipse tables (ff. 78–92r, 102–3, 138–154). Richard of Wallingford’s Rectangulus is copied and illustrated with diagrams (ff. 6–10r) and the navicula template diagrams are found at the end of the manuscript.29 Another, anonymous, medical man seems to have been linked to TO1. The texts in this manuscript are mostly in English, and contain astronomical and astrological works, including some that link to meteorology and medicine. One of the medical texts includes a bifolium at the centre of a quire that has apparently been carried around separately from the rest of the manuscript, folded into quarters.30 The parts of the page that would have been on the outside when the sheet was folded are dirty, and the text partly rubbed away. The sections on this bifolium, apparently so useful to its owner, relate to subjects including whether a patient will die, whether an expected baby is a boy or a girl, and other useful medical questions. This provides an indication that one of the owners of the manuscript was a medical man, with interests in astrology (indicated by the worn bifolium) and in astronomical instruments and in the navicula.31 However, despite the survival of two Middle English copies of texts on the navicula there is little evidence for an independent vernacular tradition of writing on 25

DI, RA. BL2, TO2. 27 Kibre, “Lewis of Caerleon.” 28 Snedegar, “Caerleon, Lewis.” 29 Cambridge University Library, Catalogue of the Manuscripts, 114–120, describes these diagrams as being “of nautical machines” and suggests that they are in a later hand. 30 TO1, ff. 92–3. 31 On folded manuscript almanacs, see Carey, “What is the folded almanac?” On medieval medical men who were interested in technology, see White, “Medical astrologers and late-medieval technology.” 26

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the instrument. The two copies of texts about the instrument that are in Middle English are both linked to learned men, and closely linked to Latin versions of the text. The copy in AB, possibly linked to a community of Austin Friars, contains both Latin and English texts, as well as one text (on constructing a horizontal dial) which is given in Latin and then translated into English.32 The English text in TO1 is very close to a Latin ancestor, as indicated by the underlined glosses for technical words. Other manuscripts containing texts on the navicula cannot, at present, be linked to a specific individual or institution in medieval England: there are few clues as to who copied or read them in the fifteenth century. But it is sometimes possible to find out about unknown people from the context and contents of their manuscripts, even if their names aren’t known. For example, PH2, a collection of texts on astronomy and medicine in a single, late fifteenth-century hand, was probably someone’s personal collection of interesting or useful texts. It includes works on determining the best time for a journey and casting the nativities of children, on the revolutions of the worlds, the planets and the seasons.33 EG and AD, which share a common source or copyexemplar relationship, contain Chaucer’s Treatise on the Astrolabe as well as texts on planting trees, and questions of natural philosophy: suitable subjects for a gentleman or learned churchman. BL2 includes a number of occult works, including an alchemical work by Bacon, astrological and chiromantic works, but also an ecclesiastical compotus. The manuscript, still in its fifteenth-century binding, has a recess 45mm in diameter in the inside cover, covered with a leather flap, although it is not clear what this would have contained.34 A similar selection is found in the closely-related manuscript containing the other copy of the long version of the group A text on the use of the navicula: RA. In this collection are texts on the wounds of Christ, prophecies of Merlin and Gilda, and a work by Aristotle, along with other theological and practical works, and a text on the

32 See appendix 7, p. 251, line 2. The scribe occasionally repeats words, first in Latin and then in English: “deinde þen þo diuisiones of cercles . . .”, indicating that he was translating from Latin. The text on the horizontal dial, given in English and Latin, is on ff. 66rv. 33 See appendix 1 for a list of its contents. 34 A similar recess in Oxford, Bodleian Library, MS Saville 100 is quadrant-shaped and may have contained an instrument.


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use of the navicula. Finally, the now-lost TO2 is described as containing works on lunar astrology, practical geometry, the interpretation of dreams, and texts about astronomical instruments including the astrolabe, quadrant and navicula.35 These anonymous manuscripts include a variety of subjects, placing interest in the navicula alongside a range of medical, astrological, occult, learned and practical interests. The people who copied and read such manuscripts are unknown, but we know a little of their interests from the other things they copied along with the navicula. It is striking that so many of the owners of navicula instruments and manuscripts who can be identified are religious men: monks, friars, canons and clergy. Indeed, there survives a medieval source naming a Benedictine monk, Peter of Muchelney, as the inventor of the navicula.36 The monks and churchmen of medieval England were the most likely to have received a liberal arts education including the basics of astronomy, perhaps at Oxford University, and so might have developed an interest in astronomical instruments. In addition, the design of the navicula may link it to other medieval religious dials. At the top of each hour line on surviving medieval naviculae is a cross, and this feature of the instrument is specifically mentioned in group A texts on constructing the navicula. The crosses make it easier to tell which are the whole and which the half hour lines. The same feature is seen on monastic and church sundials from medieval England, for example, the famous mass dial on the south wall of St Gregory’s Minster, Kirkdale, Yorkshire, which was engraved c. 1063–65. On this dial, lines divide the face into the unequal hours of the day, and show the times of prayers, which are marked with crosses. This way of marking the times for prayer can be seen on dials across Europe: an example from the thirteenth-century minster at Hameln, Germany, is given by Gerhard Dohrn-van Rossum in his History of the Hour, and another from a parish church in Grabern, Austria, is illustrated in Mario Arnaldi’s article about medieval monastic sundials.37 So the use of crosses to mark the whole hours on the navicula mirrors the crosses on monastic and church dials, marking the times of

35

See appendix 6. Eagleton, “John Whethamstede.” 37 Dohrn-van Rossum, History of the Hour, 32, figure 5; and Arnaldi, “Medieval monastic sundials,” 113, figure 3. 36

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prayer. These dials were familiar to monks and churchmen, as well as to people who lived near a church or monastery with a mass dial on its wall. Sara Schechner suggests that these dials, visible to passers-by on the outside wall of a church, acted as reminders to stop and pray.38 Further religious resonance in the design of the navicula can be seen in its shape: it is a sundial that looks like a ship. Common in the Middle Ages was the idea of life as a pilgrimage, by land or by sea. This analogy was drawn in religious writings as well as in literature, and by the later Middle Ages it was being used for secular and religious reasons. In this context, the ship represents the vessel in which the soul makes its journey through the storms of the sea of life, guided by Fortune.39 The navicula, therefore, could remind its owners of the good, Christian, life, and their passage through life on the way to the New Jerusalem.40 Running alongside the religious interests of late medieval England were its military and trading interests, and here, too, we can see that the navicula could have had a strong iconographic significance for its owners. England had become rich thanks to the wool trade, and this new wealth enriched many towns and ports in England. An English gold coin introduced in the fourteenth century, the noble, had a ship on one side (figure 17).41 A fifteenth-century poem about the political and commercial reasons for sea trade, the Libelle of Englysche Polycye, explains the importance of the ship on the gold noble: For iiii thynges oure noble sheueth to me, Kyng, shype and swerde and pouer of the see.42

This work, probably written in the 1430s, describes English trade with each European country in turn, explaining what the goods traded in each case are, and arguing for an increase in England’s sea power in

38

Schechner, “The material culture of astronomy in daily life,” 196. Burjorjee, “The pilgrimage of Troilus’ sailing heart,” summarises this tradition, and analyses the nautical references in Geoffrey Chaucer’s Troilus and Criseyde, concluding that Troilus’ sea journey is “an analogue and a specific instance of the soul’s progress to its ultimate destination.” Sections II and III outline the medieval tradition of life as a sea-pilgrimage. 40 See chapter 4 for discussion of the lists of towns and their latitudes that are found on surviving naviculae and in the manuscript texts about them. 41 On the gold noble, see Spufford, Money and Its Use in Medieval Europe, 320. 42 Warner, The Libelle of Englysche Polycye, 3, lines 34–5. 39

Fig. 17

A 14th-century gold noble. Reproduced by permission of the Trustees of the British Museum.

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order to protect these interests.43 In light of this iconographic use of the ship on coins to represent the wealth brought by the sea trade, and the need to secure this trade, the navicula sundial would have held significance. It might appeal because of its design as well as because of its functionality—an instrument that combined the twin concerns of display and practical utility. Naviculae were owned, and texts owned or copied, by people from various social groups and professions. It is perhaps inevitable that those whose names are known are linked to monasteries or churches and to Oxford University; these are the kinds of places that kept records of the people associated with them. These were, after all, the people who were Latin-literate, and who understood enough geometry to make or use the navicula. The iconographic resonance of the dial shaped like a ship, representing the journey through life, or the power of England’s sea trade, might have appealed to the very people in late medieval England who would have had enough money to buy a brass sundial. The variation between copies of navicula texts, and the alterations and additions to them indicate that interest in the navicula was not restricted to one group in particular. Navicula texts, being short, were added to collections acquired or copied by people with wide-ranging interests and backgrounds, and these diverse interests, combined with the number of surviving instruments and manuscripts witnessing at least four different texts on the instrument, indicate a more widespread interest in the instrument in late medieval England than has, until now, been supposed. The manuscripts and instruments whose fifteenthcentury owners are known can be linked to canons, churchmen and university scholars, and in all probability some of the unknown owners were gentlemen from other social groups and professions. In line with this variety of owners and interest across different social groups, two of the surviving naviculae look like they are of much higher quality construction, while two are more basic. The navicula manuscripts are perhaps best understood as a changing and changeable selection of information, including material about a sundial but also a vehicle for reference information, education, and

43 In the fifteenth century there is a reference in Sir John Paston’s booklist to a copy of the Libelle of Englysche Polycye, indicating that this powerful wool merchant thought it to be interesting or worthwhile to read this work. See Breeze, “Sir John Paston, Lydgate, and the Libelle of English Polycye.”


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useful methods, drawing on a wide range of sources including geometries and itineraries. The surviving instruments, although related to the manuscripts, and linked by a circulating standard design, are manifestations of just one part of the content of the texts. Combining evidence from both texts and instruments suggests that different kinds of people might have owned or used them: merchants, administrators, scholars, as well as the old nobility, senior churchmen and members of the religious orders. The manuscript texts provide evidence that knowing about the navicula was about more than being able to tell the time, or find your latitude. Most of the manuscript texts on the navicula contain instructions for measuring the height of towers and the depths of wells, linking them to the practical geometrical tradition—in the case of BL2 the link is direct, since this manuscript was expanded by bringing in material from a text on the quadrans vetus.44 In his influential twelfth-century work, Hugh of St Victor divides geometry into theorica and practica and explains that practica: “uses certain instruments and judges by inferring one thing from another on the basis of proportion”.45 Practical geometrical texts would be classified as practica by Hugh, and Steven Victor argues that they are to be understood as pedagogical manuals, linked to the popularisation of mathematical knowledge. He suggests that they were a way of teaching the basic principles of geometry to those who were not educated in the schools and universities, but who might want or need to know some mathematics.46 Similarly, using an instrument and understanding how it was made would help a scholar to know the structure of the universe, and the motion of the sun through the heavens.47

44

See appendix 4. John Murdoch, Album of Science, 161. 46 Victor, Practical Geometry in the high Middle Ages, 53–73; Shelby, “The geometrical knowledge of medieval master masons,” discusses the geometrical knowledge of master masons, gained outside the quadrivium and the formal university education system. 47 Victor, Practical geometry in the high Middle Ages, 21–24, argues that the quadrans vetus texts should be considered as a practical geometry text, as well as a text about an instrument. In another study of the same texts, Nan Hahn considers this link and concludes once again that the quadrans vetus is based on the Geometrie due sunt partes principales. Hahn shows that many of the operations described in the practical geometry text are easier to perform with a quadrant than with the rods, mirrors and shadows that the geometry text relies on, so it is unsurprising that some of the 45

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The contents of the texts on using the navicula give further evidence in support of this view. As well as explaining how to tell the time, find the length of daylight, or the latitude of a region, BL1 includes a discussion of how to find the time at night from the stars, a list of towns and their latitudes, and an explanation of why time varies with latitude. This section, along with that on telling the time from the stars, is added at the end of the text but is also present in the group A text in PH1. It explains the changing length of daylight with latitude, an astronomical topic, but not one that is of use in actually making or using a navicula; rather, it helps someone understand how and why the navicula works. This link between geometry and astronomy, and the use of the navicula, is also seen in the texts on constructing the instrument. Often, when a line is being drawn, there is a brief explanation of what the line is—which of the heavenly lines and circles it relates to. For example:48 make a line, which is called the equinoctial line (group A—main) For the positioning of the cursor, it is noted that the divisions on the mast are degrees of latitudes of cities. The latitude of a city is the distance from the zenith to the equinoctial. The zenith is the point positioned directly above our heads. (group A—EM) Which zodiac is indeed divided by six spaces, and in any such space two signs are placed, each of which is equally far from the first point of Cancer and Capricorn as the other one. And the days will be equally long when the sun is in one of those signs, and so it will be while the sun is under the other one and indeed of equal shortness. And the sun will also have equal altitudes and equal ascensions in those signs (group A—BL2) This circle ZLPM will be circulus articus, the arctic circle (group D)

Thus, texts about the navicula include material that is not only specific to that instrument, like the section on telling the time from the stars or values for longitude of towns, but they also contain information about how and why the instrument works. The texts explain how the lines of the instrument relate to those in the heavens.

sections are shorter and less awkward in the later text. (Hahn, Medieval Mensuration, especially pp. xxxvi to xxxvii). 48 Appendix 1, p. 177, lines 19–20; appendix 2, p. 194, lines 23–5; appendix 3, p. 204, lines 14–16; and appendix 7, p. 249, line 7.


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The Oxford-educated monks, churchmen and scholars who make up the majority of those who can be identified as owning navicula texts or instruments would have been exposed to the kind of theoretical astronomy that these references link to—the Sphaera texts that were standard reading for students in the liberal arts curriculum. So, not only was the navicula a practical object for them, and an instrument with iconographic significance, it also linked to knowledge about the heavens and about geometry. It represents a particularly learned kind of interest in sundials as objects for more than just telling the time. Some of the information in navicula texts relates not to a real material object, but instead to knowing useful things and to knowing how the instrument works, by understanding how it relates to astronomical theory and to geometry. Yes, the navicula tells the time, but so does a stick in the ground, the length of your shadow or the sound of church bells. This fascinating instrument was clearly more than just a timekeeper to the medieval scholars who made, read and wrote about or used it.

CHAPTER SEVEN

THE NAVICULA AND THE ORGANUM PTOLOMEI The discussion in chapter 1 on the origins of the navicula highlighted a problem particular to this instrument: it is one of a number of instruments which all use the same geometry, and which are linked together in different ways by scholars discussing the navicula. The geometry in question is as follows:1 1. Part of the celestial sphere containing the ecliptic is projected onto a flat surface to give parallel hour lines (it is a rectilinear dial). 2. In order that the instrument can be set for any date and latitude, the suspension point of a weighted thread must move relative to these hour lines. These suspension points fall within a triangular area above the hour lines (it is universal for latitude and date). 3. There are several ways that this geometry was turned into a working instrument: the best known are the so-called Regiomontanus dial (the hour lines and latitude/date grid are on a plate, fixed relative to each other, and the suspension point moves over the grid by means of a jointed arm) and the navicula (the hour lines are on the body of the instrument, and the latitude/date are set by means of a slider moving vertically on a rotating rule, graduated for latitude), but there are several others. These practical solutions to the geometry necessary for a universal rectilinear dial may or may not be linked. For example, the fact that the navicula and the Regiomontanus dial share similar geometry may indicate that one developed from the other, but it may equally indicate that they represent different practical solutions to the same geometrical problem and are otherwise unrelated. It is therefore essential to turn to the manuscript sources describing the instruments in order to understand the relationship between them.

1

Mills, “Altitude sundials for seasonal and equal hours.”

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Problems surrounding the relationship between the navicula and its mathematically very close relatives are compounded when this relationship is used to make a point about another instrument. For example, Frederick Stebbins suggests that the navicula was based on the Regiomontanus dial, which developed from the single-latitude capuchin dial, which in turn had developed from the solution of spherical geometry for an altitude dial by some unknown mathematician or astronomer.2 David King has another suggestion: that the Regiomontanus dial developed from either the navicula or the organum ptolomei: . . . the four surviving examples of the navicula from before ca. 1500 are all English. But there was another tradition which surfaced in Vienna in the mid 15th century, of which only manuscripts and one instrument survive. In this tradition, an instrument resembling the navicula, but now without prow and poop, was called by another name usually associated with another instrument, namely, the organum Ptolomaei. It was apparently from the navicula, or at least from this device, that Regiomontanus in the mid 15th century developed his better-known Uhrtäfelchen—the underlying theory is identical, but the new device was easier to use.3

King takes his information on the organum ptolomei from Ernst Zinner, who briefly discussed the development of texts on it in fifteenth—and sixteenth-century Vienna in his astronomische Instrumente.4 There, as well as in his Handschriften, Zinner describes manuscript texts with two incipits, one starting ‘organum ptolomei ita sit . . .’ and the other beginning ‘organum ptolomei ad multas prouincias . . .’5 However, consultation of the surviving manuscripts shows that the second group are not as homogeneous as Zinner’s listings would suggest, and also that there are a number of texts not discussed by him which can help make sense of what the organum ptolomei is (as well as what it is not). The organum ptolomei ita sit text survives in four copies currently accessible to scholars, along with another listed by Zinner whose current location is unknown.6 The earliest manuscript copy may have been copied in or around 1434 and closely related to it is another of the four manuscripts. Of the five copies of the text currently known,

2

Stebbins, “A medieval portable sundial.” King, World-Maps, 352. See also an extended version of the same argument, in King, In Synchrony with the Heavens, 22 and 267–335. 4 Zinner, Deutsche und niederländische astronomische Instrumente, 111. 5 Zinner, Verzeichnis der astronomischen Handschriften, nos. 9778–9781. 6 See appendix 9. 3

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all but one were illustrated with a diagram showing the instrument described. However, the instrument is no longer referred to as a shipshaped on, with the text explaining instead that: And regarding the residual shape of a certain musical instrument, it is abandoned, and truly I believe it took the name only.7

Nonetheless, the rotating central bar is called the ‘mast’ throughout the text, suggesting that not only is the organum ptolomei ita sit text related to those describing the navicula, but that it derives from them, perhaps from one of the exemplar-type constructions that describe how to make a single navicula.8 There are other differences, most significantly that the organum ptolomei texts use a simplified version of the geometry of the navicula manuscripts, and where the navicula texts tend to have geometric diagrams, these manuscripts show the completed instrument, albeit in a geometric-style diagram (figure 18). A few decades later, in the mid fifteenth century, things start to get more complicated. We see new variants of the organum ptolomei text appearing, including one ‘Quadratum horarium pro multas regionibus diuersarum latitudinum factus hoc modo . . .’ This instrument has the hour lines and a grid for latitude and date inscribed on a flat plate, with a ruler rotating about the centre, and a sliding cursor with plumb-bob sliding on the ruler, and is illustrated in a diagram accompanying the text: In this text, the organum ptolomei has lost the ship shape and terminology (the rotating bar is no longer called ‘mast’, but is instead referred to as the ‘rule’). This copy was, according to Zinner, made by Regiomontanus in or around 1457, and Regiomontanus is also named as the author of a text titled ‘Quadrantis Organi Ptolomei similis . . .’9 This latter text witnesses an important change in the description of the instrument—instead of a tilting ruler tracing out arcs above the centre of the hour lines, it has straight lines for the lines of latitude, over which is placed a rotating rule, along which a plumb-bob slides, in order to put the suspension point of the thread in the correct place over the latitude/date grid (figure 19). However, it is likely that Regiomontanus was not personally responsible for the change from the curved latitude

7 8 9

Appendix 9, p. 273, lines 18–20. See appendices 5, 7 and 9. Zinner, Deutsche und niederländische astronomische Instrumente, 112.

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Fig. 18 Diagram of the organum ptolomei in Vienna, Österreichische Nationalbibliothek MS 5418, f. 182r. Reproduced by permission of Österreichische Nationalbibliothek, Vienna.

Fig. 19 Diagram from Vienna, Österreichische Nationalbibliothek MS 5258, f. 81r. Reproduced by permission of Österreichische Nationalbibliothek, Vienna.

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lines to straight lines: he himself says that he read about the instrument in the works of an ‘antiquus compositor’.10 So, by the middle of the fifteenth century, there are several different instruments, using the same geometry, some of which are shaped like ships, others that are not. Some of these texts about them are listed by Zinner under the short title ‘organum ptolomei ad multas prouincias’, but that heading conceals a group of loosely related texts rather than a homogeneous set of copies of a single text. To further complicate things, there are instruments not called organum ptolomei in the manuscripts, but which use the same geometry as the objects that are given that name.11 The confusion in the manuscript tradition is also shown by an instrument illustrated in a manuscript copied in the area around Vienna in the late fifteenth and early sixteenth centuries, now in the library of Lund University.12 The manuscript includes texts about, and diagrams relating to, a number of instruments, including, on f. 44v, a Regiomontanus-type dial that has been given the title Naviculum Ptolomei (figure 20). Above the diagram are a few sentences explaining how to use the instrument to tell the time. This diagram, in the second part of the manuscript, probably dates to the late fifteenth or early sixteenth century, indicating that at this date the new form of universal rectilinear dial might still be given the name of the ship-shaped dial that had preceded it. At the same time, the ship-shaped organum ptolomei might or might not be given that name in the manuscripts describing it. This group of manuscripts highlights a problem with the cataloguing of manuscripts about astronomical instruments: since so many of them begin with something like ‘Describe a circle abcd . . .’, classifying

10

Zinner, Deutsche und niederländische astronomische Instrumente, 112. Some instruments are called organum ptolomei in the text (for example, Munich, Bayerische Staatsbibliothek MS Lat. 19690, f. 79r; Brussels, Bibliothèque Royale MS 2962–2978, f. 29r; Yale Medical-Historical Library, MS24, f. 268r; and Vienna, Österreichische Nationalbibliothek, MS 5258, f. 80r. Others are not given that name (for example, Yale Medical-Historical Library MS 24, f. 446r; Vienna, Österreichische Nationalbibliothek, MS 5228, f. 36r; and Yale Medical-Historical Library MS 24, f. 202r. For information on these manuscripts, see Halm and Laubmann, Catalogus codicum latinorum, vol. II pt. 3, 269; Calcoen, Inventaire des manuscrits scientifiques, vol. 1, 57–61; Faye and Bond, Supplement, 57–8; Österreichische Akademie der Wissenschaften, Tabulae codicum manu scriptorum, vol. 4, 65 and 77. 12 The manuscript is available online at http://www1.ub.lu.se/externt/apps/lauren tius/volumes.cfm?title=Mh_47 (accessed 22 February 2008). See also Severino, “An Unknown Manuscript of Gnomonics.” 11


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Fig. 20 Lund University Library, MS 47, f. 44v. Reproduced by permission of Universitetsbiblioteket, Lund University.

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such texts by incipit allows very different works to be wrongly grouped together. Similarly, classifying the texts by the name they give to the instrument they describe would be misleading, since the names are not fixed. Some texts describe an inscribed plate with the latitude lines traced out as arcs, by the plumb-bob being attached to a slider on a rotating rule. Others describe an inscribed plate with the latitude lines traced as parallel lines. On these, the plumb-bob is to be suspended on either a folding arm riveted to the plate at the top of the latitude/ date grid, or on a slider moving horizontally along a bar which in turn slides vertically on runners placed either side of the latitude/date grid. The writer of one of the texts explains that there are two ways of suspending the plumb-bob. One, described first, involves making a little folding arm, attached at the top of the instrument; the second has a straight ruler sliding in two parallel vertical tracks, applied to the instrument either side of the latitude/date scale.13 In short, the design of dial that is now most common—the so-called Regiomontanus dial, printed first in his Kalendarium of 1474 (figure 21), complete with a folding arm attached to the page of the book—was not yet the standard way of making a universal rectilinear dial. The texts listed by Zinner as ‘organum ptolomei ad multas prouincias . . .’ are a nebulous group, describing several different physical forms of the instrument under the same name. Other texts describe the same instruments, but without calling them organum ptolomei. One such text, despite being written in the same practical terms as those texts describing a particular physical form of the instrument, includes no details about the composition of the object, describing only its geometry.14 It describes, in very practical terms, how to divide the scales, but does not say whether the latitude lines are straight or curved, and does not describe how the suspension point of the plumbbob is supposed to move over the latitude/date grid. The text is illustrated with a diagram (figure 22). To make sense of this confusing group of texts and instruments, I distinguish between practical and physical information. Practical information includes details like painting the numbers in a different colour

13 14

New Haven, Yale Medical-Historical Library, MS 24, ff. 268v–270v. Yale MS 24, ff. 446–448.


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Fig. 21 Regiomontanus’ printed version of the instrument sometimes known as the organum ptolomei, but titled by him ‘general horary quadrant.’ Reproduced by permission of University of Chicago Library.

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Fig. 22 Diagram from Yale MS 24, f. 448r, showing the geometry of the organum ptolomei, but not its physical form. Reproduced by permission of Yale University, Harvey Cushing / John Hay Whitney Medical Library.


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so that they are more visible,15 or using a triangle of paper to transfer the divisions from one part of the instrument to another.16 But, ultimately, such practical instructions need not be about actually making a three-dimensional physical object. By contrast, physical information tells the reader how to make a real instrument, by specifying how to make a folding arm from which to suspend the plumb-bob,17 or telling the reader that it is best to use a sheet of wood or ivory to make the instrument.18 So, a text about the organum ptolomei might give very detailed practical information about drawing an object, without giving physical information about how to translate this geometrical object into a usable sundial. Indeed, given the variety of physical forms of dial which all go under the name, it seems as though organum ptolomei refers not to any instrument at all—but to the geometry by which instruments can be made. If an organum ptolomei can be made on paper, as a geometrical object, but need not be a physical instrument, what, then, would the point of it be? In his work on the organum ptolomei, Andres Stiborius explains that understanding of many astronomical instruments relies on the theory of astronomy: Also almost unlimited [kinds of ] instruments depend on this knowledge of the primum mobile: the astrolabe, saphea, organum ptolomei, meteoroscope, armillary, torquetum, rectangulum, equatorium, compasses, quadrants, and many others of this sort.19

In light of this, a role for the geometrical objects called organum ptolomei becomes clear, alongside the physical objects made according to the same geometry: they are practical despite existing only on paper, because the understanding of geometry and astronomy described by Stiborius can be gained by either a geometrical diagram or a physical object. It is often assumed that instrument treatises are somehow simply both practical and physical, but from the evidence of organum ptolomei it seems that things are not that simple: we must look closely

15

Yale MS 24, f. 269r: bonum esset quintos fieri colore distinctio ab aliis. Yale MS 24, f. 447r: dein applica quadrantem de carta . . . 17 Yale MS 24, f. 212r: fiat brachiolum duarum iuncturarum eiusdem longitudinis; et per clauiculum sibi inuicem constrictarum non faciliter a se moueatur . . . 18 Yale MS 24, f. 269r: Et fiat istud horologium in quadrato lingo vel lamina . . . 19 Stiborius, “Uiri Mathematici,” ab3v: “Pendent item ex hac primi mobilis scientia instrumenta pene infinita. Astrolabium: saphea: organum Ptoloaemei: metheoroscopion: armilae: toquetum: rectangulis: aequatoria: compassi: quadrantes: & alia id genus multa.” 16

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Fig. 23A Fig. 23 The division of the bead and mast scales according to the navicula geometry and the division of the bead and mast scales according to the organum ptolomei and Regiomontanus dial geometry (figure 23B).


Fig. 23B

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at the texts and the instruments. Moreover, we must look closely at the relationship between both texts and instruments, and the geometry according to which they are made. Returning to the development of the new versions of the organum ptolomei, the relationship between these instruments and the navicula now appears more clearly. Some version of a text, probably the exemplar construction, describing the navicula dial became available to scribes in the area that is now Germany and Austria. They rewrote the text, redrew the diagrams, and called it the organum ptolomei. A couple of decades later, variant versions of the instrument appear, at first just in the textual tradition, and in the mid fifteenth century the geometry changed again: the arcs traced out by a tilting ruler were replaced by straight lines over which a plumb-bob was suspended by various means, such as a folding arm, or a sliding bar with a sliding cursor. Looking more closely at the geometrical changes made to the navicula and the organum ptolomei through this process of revision and reinvention, we see that the organum ptolomei and related instruments have been made according to a simpler geometry than is specified by the navicula manuscripts and was used to make the surviving English medieval dials. The construction of this group of instruments is based on a projection of the celestial sphere resulting in parallel hour lines (as for all so-called rectilinear dials). All of the fifteenth-century navicula texts and instruments use the same geometry—previously called the Bodley construction, after MS Bodley 68, which contains a copy of one version of the instructions for this—which I will refer to as the ‘navicula’ geometry. This construction involves the use of auxiliary arcs to slightly warp the scales, resulting in slightly different divisions of the scales at the bottom (for the mast) and side (for the bead) of the front of the instrument (figure 23). In contrast, the organum ptolomei manuscripts and the Regiomontanus dial use a simplified geometry, which does not involve the use of auxiliary arcs, and divides the scales directly on the circle. The diagram (in figure 23B) shows this construction, used for both the mast and bead scales. However, this simplification of the construction of the mast and bead scales produces only a limited difference between the two constructions—Jan Kragten has calculated the following values for the divisions, for a maximum solar declination of 24 degrees:20

20

Kragten, The Little Ship of Venice.


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degrees from centre line to the . . . first line

second line

third line

fourth line

fifth line

sixth line

Bead/Mast scale of the organum ptolomei and Regiomontanus dial geometry

6.04

11.73

16.71

20.62

23.13

24.00

Bead scale of the navicula geometry

6.48

12.43

17.36

21.09

23.29

24.00

Mast scale of the navicula geometry

5.49

10.94

15.99

20.19

23.00

24.00

The largest difference between the two methods is about three-quarters of a degree, a difference that—in conjunction with very accurate measurements of a surviving instrument—could be useful in allowing scholars to determine whether it has been made according to the simplified organum ptolomei geometry, or the English navicula construction. However, in terms of actually using the dial, the thickness of the thread of the plumb-bob, and the inaccuracy involved in setting the mast and the bead, quickly render these differences of half a degree or so almost negligible. A more important difference between the two constructions is that they use a different length of mast—the construction geometry used is as follows: • For latitude L, the position of the corresponding division on the latitude scale on a navicula or organum ptolomei is constructed by extending the line at angle L as far as the tangent to the circumference of the circle outside the 12 o’ clock line. • The divisions marked on this line are then transferred to the centre of the instrument, or to a ruler which is pivoted at the centre of the circle.21 • For a Regiomontanus dial the construction is similar, except that the line extended at angle L is extended only as far as the 12 o’ clock line. The two sets of latitude divisions are related by a factor linked to the maximum declination of the sun, marked as D on the diagram in figure 24, which is usually given as 24 or 23.5 degrees in texts on the construction of the navicula. 21

In the organum ptolomei ita sit manuscripts the divisions are constructed by a slightly different method, but it yields identical divisions.

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Fig. 24 Diagram showing the geometry of the construction of mast scales according to the navicula and organum ptolomei geometries.


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However, the earliest texts on the organum ptolomei, with incipit ‘organum ptolomei ita sit . . .’ seem to have become corrupted, and angle D is 30 degrees, because of the way that the circle is divided in the earliest stages of the text. This indicates a link to the group B navicula text: Navicula, group B22 Afterwards the quarter circle AB is divided first into three parts, and each of these thirds into another three, and there will be 9 divisions, and any of these may be divided again into two parts, and again into five parts, and there will be 90 degrees, of which from A to B the maximum declination of the sun is selected, that is 23 and a half degrees, and point F is marked there. Similarly from A towards D, and that is point G Organum ptolomei ita sit23 Then whichever quarter is divided into three equal parts, and they will be the signs, and whichever sign [is divided] into 30 degree[s], indeed according to which it serves. Then put the ruler over the beginning of one sign before B and over the end of another after B and lead a line which connects on either side of circumference ABCD, and on the [point of ] contact of this line and the diameter BD, make point G.

If the source for the organum ptolomei text had lost a line or two— the lines explaining that the thirds should be further subdivided and these subdivisions used to mark the maximum solar declination of the sun—then this explains why it has this slightly strange value of D=30 degrees. This value of D means that an organum ptolomei will have hour lines that are slightly smaller than those on a navicula, for the same size mast (or vice versa: the mast will be too long on an instrument with the same size hour lines). This is confirmed by the diagrams illustrating the text, which have D as 30 degrees, indicating that the diagram was redrawn following the corrupt text, rather than being copied independently from the text. There is further evidence in the organum ptolomei manuscripts for the corruption of their source text. The organum ptolomei ita sit texts, for example, do not explain how to divide the bead scale at the right-hand side of the instrument, or even that there should be a scale on the right-hand side, and give truncated instructions for what one can do with the instrument: measure the length of the day and tell the

22 23

Appendix 5, p. 229, line 14, p. 231, line 1. Appendix 9, p. 269, line 4, p. 271, line 4.

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time. The instructions for measuring the length of the day are accurate enough—this operation does not require the scale on the right-hand side of the instrument—but those for telling the time are unusual, and would not have worked:24 When truly you wish to know the completed hours of the day, put the foot of the mast over the degree of the sun or the present day, and raise the organum with its pinnulis towards the sun, so that the rays of the sun cross through their pinholes. And the indicator will drop over as many whole hour lines as will be the hour from the rising of the sun, or from the beginning of the day, reckoned by the preceding discovery. And if it were before midday, you will count from the start of the day towards noon; if truly after midday, in the other direction.

These instructions miss out a vital stage. To set up the organum ptolomei for use, it is necessary, after setting the slider to the correct latitude, to pull the thread across to the (missing) scale on the right-hand side, and to slide the bead until it lies over the 12 o’clock line. Without this stage, the readings given by the instrument could be inaccurate by many hours, which would probably have frustrated anyone who tried to make and use the instrument. So, in short, the geometrical inaccuracies of the instrument described in the organum ptolomei ita sit manuscripts, due to textual corruption, would have rendered it almost useless. Authors of the various manuscripts that Zinner classified under the heading organum ptolomei ad multas prouincias sometimes complained about the corruption of the text, and it is likely that the variation between these resulted from their attempts to rewrite the text. For example, one copy of a text describing the organum ptolomei (in Yale MS 24, f. 268v) is prefaced by a statement that the various other texts about it are confusing and incorrect.25 Among manuscripts describing the organum ptolomei, most retain the construction of the hour lines with angle D=30 degrees. Only three manuscripts have D equal to the maximum solar declination (Munich BSB, MS Lat 19690; Vienna ANL, MS 5228; Yale MS 24), and all of these post-date the redesign of the organum ptolomei in the

24

Appendix 9, p. 274, line 20, p. 275, line 5. Yale MS 24, f. 268v: “Organum ptholomei ad multas prouincias in canone proprio vt ab ipso componitum est satis obscurum breuitate exhibetur propter quod diuersi canones feruntur a pluribus. Hic hicque sequitur plus lucide composicion eius edocet licet subscriptibus par sit tibi nec ex illo hoc ex aliis varietur instrumentum canonibus quare in sua forma et veritate permaneat. Explicit prefacio.” 25

Fig. 25 The British Museum dial, as recorded in the register on its acquisition in 1893. Reproduced by permission of the Trustees of the British Museum.

the navicula and the organum ptolomei 111

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mid fifteenth century, and the reworking of texts about the instrument. It therefore seems increasingly likely that the rewriting of the text was at least partly motivated by the corruption of existing works available. Because of these geometrical problems with the organum ptolomei ita sit text, it should be possible to identify instruments that have been made from these instructions by measuring the angle according to which their mast scale has been constructed. However, no surviving instruments of which I am currently aware have angle D equal to 30 degrees rather than to the maximum solar declination of 23.5 or 24 degrees. A now-lost German instrument might have been an organum ptolomei made according to the instructions in the organum ptolomei ita sit texts, but all that remains of it is a small sketch in the British Museum accessions register (figure 25). This instrument, along with several others, was bought by the British Museum from the Spitzer collection sale on June 16th 1893 for 30 francs. The collection from which it was acquired was amassed by Frédéric Spitzer, who was born in Vienna in 1815 and moved to Paris in 1852. When he died on 23rd April 1890, there followed the sale of the century.26 A de-luxe catalogue containing descriptions of every item, and pictures of many of them, was produced. Unfortunately, the ship-shaped dial was not illustrated among the mathematical instruments, but is described in detail:27 No 153—Horomètre Astrolabe en Cuivre. Cologne (1581) L’un de ses côtés de l’appareil forme horomètre, l’autre, astrolabe incomplet à cause d’un évidement circulaire pratiqué dans le disque qui constituerait le dos de l’astrolabe; cette dernière partie renferme la moitié des excentriques et la moitié de l’échelle altimètre. L’autre, outre sa gradatuation en heures, porte une graduation qui correspond aux differentes époques de l’année, et avec les divisions de laquelle on fait coïncider l’extrémité d’une regle mobile, graduée, munie d’un curseur, qui peut tourner, à l’interieur de l’instrument, autour du centre. Deux plaques de cuivre, normales au plan de l’appareil, sont rivées a deux renforts symmétriques et percées de trous qui se correspondent; elles peuven servir de pinnules d’alidade. Grand axe de l’appareil (avec l’anneau): 0m, 171.—Largeur maxima: m 0 , 083.

26

The auction catalogue described it as the ‘plus grande vente du siècle’. See Moliner, Catalogue des objets d’art et de la haute curiosité, vol. 2, xxi. 27 Spitzer, La collection Spitzer, 115.


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Fig. 26 A dial dated 1527, and inscribed with the name Roger Brechte, in the collections of the Museum of the History of Science, Oxford (inv. no. 26323). Reproduced by permission of the Museum of the History of Science, Oxford.

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This description confirms the more tentative evidence from the sketch in showing that this instrument probably only had one scale on the front—for setting the tilt of the mast—as seen in the diagrams and text of the organum ptolomei ita sit manuscripts. However, because it was destroyed in the Second World War bombing of London, it is impossible to say with any certainty what the geometrical construction of the instrument was.28 David King has identified an instrument in the collections of the Museum of the History of Science, Oxford, as including an organum ptolomei among its engraved scales (figure 26). This has angle D equal to 24 degrees—if it is an organum ptolomei, then it was made according to the later, corrected, instructions. Returning to the navicula, the ratio between hour lines and latitude divisions discussed above—important for the geometrical accuracy of the device—has been considered by David King in his discussion of one of the surviving fifteenth-century English instruments, now kept in Geneva. Although otherwise made according to the navicula geometry, it has a mast that is slightly too short, with the latitude divisions that one would expect to find on a Regiomontanus dial rather than on a navicula. Despite the fact that there is only one such instrument, compared with four instruments and a group of manuscripts showing or describing the slightly longer mast, King decides that this is the “standard” type of navicula, from which the “modified” type (with the longer mast) developed:29 Nobody could have conceived the ‘modified’ version without being fully cognizant of, or himself having invented, the ‘standard’ version.

Noticing the similarity between the mast length of the so-called “standard” navicula and the central line on the grid of a Regiomontanus dial, King proposes a new, more complicated, way of telling the time with the instrument that compensates for the approximations inherent in the design of the navicula.30

28 Georg Hartmann, drew a ship-shaped dial in around 1527. The description and diagrams are in Weimar Herzogin Anna Amalia Bibliothek, Cod. Fol. Max 29, ff. 62r, 63r, 63v. On this instrument, see pp. 123–7. 29 King, “14th-century England or 9th-century Baghdad,” 208. 30 King, “14th-century England or 9th-century Baghdad,” 212–213.


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Fig. 27 Diagram showing the relative positions of the 60-degree line on the Regiomontanus dial (R), the navicula (N) and the Geneva navicula (G).

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In order to better understand King’s argument, the diagram in figure 27 is helpful. It superimposes the relative mast lengths and of the navicula, the Regiomontanus dial, and the Geneva navicula. The line and arcs at the top of the diagram are drawn to scale to be the right size for an instrument with hour lines of the width shown at the bottom of the diagram. The lower arc, labelled G, indicates the track of the 60 degrees latitude point on the mast of the Geneva navicula; the upper arc, labelled N, indicates the same track for the navicula mast according to the manuscript geometry and the other surviving instruments. The triangle shows the latitude/date grid for a Regiomontanus dial of the same size, and the line labelled R shows the 60-degree line of this grid. From this, it is easier to see the problem King is trying to solve with a modified modus operandi: the arc of the 60-degree point on the mast of the Geneva navicula drops below the 60-degree line of the Regiomontanus dial, and is therefore accurate only at the centre of its arc, while the arc of the navicula mast is more accurate at the outer points of its arc.31 Having decided that that the simpler geometry must have come before the more complex, King says: I shall be at liberty to reconstruct its modus operandi, since this is necessarily not the same as that described in the medieval English texts. These present a ‘modified’ manifestation of the same instrument.32

To be fair to Prof. King, there is some evidence that people used the navicula according to his proposed modified method, although it dates from several centuries after he assumes the modus operandi to have been used. A surviving instrument in the collections of the Whipple Museum of the History of Science, inscribed with the date 1620, has a scale scratched on the back of the mast which corrects for the inaccuracy at the solstices (marked at the outer ends of the scale).33 Likewise, in his 1646 description of an instrument he calls columba, Athanasius Kircher ends his account of how to use the instrument with an explanation that it is necessary to raise the slider by a degree or two when the mast is tilted, to correct for the error due to the tilt of the mast.34 However, both of these are seventeenth-century sources, and

31 The accuracy of the Regiomontanus dial is shown in Findlay, “Proof of the accuracy of the capuchin and Regiomontanus dials.” 32 King, “14th-century England or 9th-century Baghdad,” 208. 33 See pp. 129 and 134–7 for the Whipple dial. 34 See p. 141 for Kircher’s columba dial.


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both relate to a dial made according to a geometry based on that of the Regiomontanus dial, and described in Oronce Finé’s Protomathesis in 1532, and not a medieval English instrument made according to the navicula geometry.35 In addition, it is not clear how much difference the shorter mast on the Geneva navicula would have made, anyway. The maximum difference due to the different mast lengths is at sunrise and sunset, at which time the mast is at its maximum tilt, and when the slider is further up the mast. Even at these times and places, the difference in the position of the bead would only be a few millimetres, a difference that in using the instrument is itself to be measured with a small bead whose diameter is at least a millimetre or two. King acknowledges this in his discussion, saying that: We are dealing here with instruments small enough to be held in the palm of one’s hand, on which the divisions on the various scales are rather crudely marked . . . Since the instruments are so small, this does not necessarily mean that properly-executed examples of the two kinds would in practice yield noticeably different results.36

There is, however, no evidence that this difference was of concern to the medieval instrument makers and users, or to the people who copied the texts on the navicula. With either type of mast, the navicula can tell the time to within 20 minutes fairly easily, and this was good enough for its medieval users. The instrument approximated the exact time, but then so did clocks, scratch dials on the sides of churches, and methods based on the length of a man’s shadow.37 In the fifteenth century, there just was not any practical concern with differences of 5 minutes here and there in using a portable sundial. However, there is perhaps a more serious problem with King’s argument that needs addressing. His assumption is always that the “standard” and “modified” naviculae were deliberate developments, and he does not consider the possibility that the Geneva navicula has a different mast length by accident. Of the sixteen manuscripts considered here, two have been published, one in Latin by Robert Gunther,

35 See pp. 128–131 for Oronce Finé’s description of a ship-shaped dial, the source for both the Whipple navicula, and Kircher’s description of the columba dial. 36 King, “14th-century England or 9th-century Baghdad,” 224, note 2. 37 See Dohrn-van Rossum, History of the hour, on clocks and their impact on medieval life.

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and one in Middle English by Derek Price,38 and it was these two editions that formed the textual basis of King’s discussion of the navicula. Unfortunately, however, as I have outlined above, Robert T. Gunther’s edition of BL1 missed out a page of the text along with the diagram showing the construction of the hour lines and latitude divisions for the mast.39 To make a navicula, the accompanying text instructs, one chooses the size of the latitude line scale on the mast, and locates the relevant divisions on the upper part of the diagram.40 Then one is supposed to choose the corresponding line on the lower diagram in order to mark the hour lines. On the diagram there are three sets of hour line divisions, and four sets of latitude divisions. The shortest of the sets of latitude divisions is used only in the construction of the diagram. When making an instrument from the templates, the second shortest set of latitude divisions on the upper diagram is used with the shortest of the sets of hour line divisions on the lower diagram. It would have been very easy to choose the wrong set of latitude divisions, especially if a craftsman were working from a set of templates that were separated from the text describing them, like those in CUL. There, the diagrams are labelled simply, with the mast scale described as “instrument guiding the mast of the navicula”41 and the bead scale as “instrument directing the thread with bead”42 The latitude scale diagram is labelled similarly simply, but next to the hour lines diagram there is a little more information, explaining the relationship between the two diagrams.43 Nonetheless, it is easy to see how if someone were working from templates, especially if he had copied or borrowed them rather than constructing them himself, it would be very easy to choose a set of latitude divisions for the mast that are one step too small on the diagram, by assuming that the smallest set of hour line divisions go with the shortest of the lines for the latitude divisions on the mast. The two examples discussed here, that of the corruption and reinvention of the organum ptolomei, and of the shorter mast being used

38 Gunther, Early science in Oxford, vol. 2, 38–51; and Price, “The little ship of Venice.” 39 See p. 72 for this diagram. 40 Appendix 1, p. 179, lines 17ff. 41 Instrumentum regens malum navculae. 42 Instrumentum dirigens filum cum nodulo. 43 CUL, f. 192r, “f.k. equalis .a.h. diuisa rite| mensurans dat aliarum linearum| latitudinis sic .f.m. equalis| est .a.g. et proportio|naliter diuisa| sic .f.q. equalis| .a.p. et rite| diuisa”.


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for the Geneva navicula, provide a caution against the overuse of mathematical arguments and algebraic analysis in the study of medieval astronomical instruments. In the cases discussed above, the occurrence of textual corruption or a simple mistake can explain changes to the mathematical features of instruments, and understanding of these changes requires close engagement with the manuscripts and instruments. Mathematical analysis of a medieval instrument may have value, but it must always be kept firmly rooted in the historical context in which it was made and used, and used only in conjunction with careful historical study of the texts and the instruments. Modern mathematical treatment of medieval instruments is perhaps rather like modernising all of Chaucer’s spelling so that a particular word is always spelt the same way, for the benefit of a reader who does not read Middle English. But modern English, like modern mathematics, has a complicated relationship to its medieval equivalent, and the presentation of a medieval geometrical instrument in modern algebraic notation should be seen as a translation, just as presentation of one of Chaucer’s works in modern English would be. And this translation should always note where there are mismatches between medieval and modern concepts, words and ideas. It should note where the mathematical treatment departs from the evidence and moves into conjecture; it should explain how and why a certain theorem or proposition is used. In short, modern mathematical treatment of medieval instruments should be honest about its relationship with the medieval evidence if it is to provide insight into the geometry of medieval instruments.44

44 See Burnett, “Editorial,” who discusses the problems of working with pre-modern mathematical texts: “In mathematics, unlike other subjects, two levels of ‘translation’ are required: the literal translation and the ‘translation’ into modern notation . . . If the first level is omitted, there is a real danger of misrepresenting the original author, or at least losing many of the nuances of his mathematical culture.”

CHAPTER EIGHT

HOW SIXTEENTH-CENTURY BOOKS REDEFINED A MEDIEVAL SUNDIAL Despite their disagreement on many aspects of the navicula’s development, construction and use, a point on which almost all authors agree is that of the rarity of the instrument. Hester Higton writes “Perhaps the most uncommon form of these aristocratic dials was the navicula de venetiis which was produced during the late Middle Ages” and “The first mention in print of this unusual dial was in Oronce Finé’s comprehensive work on sundials, De Solaribus Horologiis et Quadrantibus, published in Paris in 1560.”1 Higton, in common with most other scholars who have written about the navicula, recognises that interest in the instrument continued after its late-medieval heyday, suggesting that “Finé’s book may have rejuvenated interest in this form of dial.”2 However, since Higton’s study was published, the wealth of new manuscript material described above has come to light. Given the variations between these manuscript copies, and the vagaries of the survival of medieval material, it is very likely that they represent only a fraction of the texts circulating in the late Middle Ages. Their links to the practical geometry traditions, borrowing material from geometric texts3 and including more information than simply how to make or use a navicula, indicate that the manuscripts can be seen as treatises teaching geometry and astronomy as well describing a particular type of dial. In short, the navicula was more common in fifteenth-century England than has usually been thought. Of course, to own a brass sundial would have been a luxury available only to those with a certain amount of wealth, but there is no way to tell how many of these dials were made out of wood and sold cheaply but have not survived where the brass ones have.

1

Higton, Sundials: An Illustrated History, 26. Higton, Sundials: An Illustrated History, 26. 3 One of the manuscript texts on the navicula (in BL2) includes material taken word-for-word from the surveying sections of a geometrical treatise: the quadrans vetus perhaps written by Robertus Anglicus. See Hahn, Medieval mensuration, for discussion about and an edition of the quadrans vetus text. 2

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In light of this, it is of interest to discover why its modern reputation is that of a curious and rare object, a collectable thing. A related issue (discussed in the previous chapter) is that of the navicula’s relation to goemetrically similar dials: the organum ptolomei and the so-called Regiomontanus dial, which became popular following publication of a description and image of it in the Kalendarium of Johannes Regiomontanus. Both dials use the same geometry, and are linked by many twentieth-century scholars, but there is currently no evidence that the Regiomontanus dial was known in fifteenth-century England. Instead, the organum ptolomei and the Regiomontanus dial derived from the English navicula. So why have scholars tended to believe that the navicula is a rare variant form of the more numerous Regiomontanus dial, and not look for (and find) the wealth of medieval manuscript evidence to the contrary? This final section seeks to address these issues by considering the post-medieval history of the navicula. In contrast to those scholars who have focussed on the invention and development of the navicula, I will look at its disappearance. By tracking how it stopped being a relatively common instrument, I hope to shed light both on this particular dial, as well as to show some more general developments in books on sundials and the role of illustrations in these works. By considering the few appearances of the navicula in books and collections from c. 1500 to c. 1900, it is clear that after c. 1600 it is considered primarily as a curiosity, a geometrical exercise, or an object for a private or museum collection.4 Therefore, since the navicula was common in fifteenthcentury England, this change in the status of the navicula should be located in the sixteenth century. Then, I look at its non-appearance in some of the most popular sixteenth-century books on sundials, in comparison with its close cousin, the Regiomontanus dial. The role of illustrations in these printed dialling books will be examined, and in the case of the navicula I will argue that print was probably ultimately involved in the demise of this English instrument. This then led to its redefinition as a rare object, a definition that modern scholars have tended to take at face value based on the comparative rarity of the instrument now. 4

Material on the history of collections of scientific instruments is in Impey and MacGregor, The Origins of Museums; Leopold, “Collecting instruments in protestant Europe before 1800;” and Turner, “From mathematical practice to the history of science.”

how 16th-century books redefined a medieval sundial 123 The ship-shaped dial in print and in collections Only one manuscript on the navicula is currently known to have been copied in the sixteenth century: AS, transcribed and translated in Appendix 6, which was probably copied in c. 1535, based on the handwriting and references in the texts. Roughly contemporary with this, in 1527, Nuremburg instrument maker Georg Hartmann included a navis among the instruments in a manuscript about different types of sundials. This work set out the geometrical basis for the construction of dials, and then briefly described and illustrated a range of different types of dial (figure 28). These illustrations look very similar to the medieval English naviculae, and there is a clear link to that tradition in the design of the dial as well as in the inclusion on the back of the shadow square, unequal hours diagram, and list of the dates on which the sun enters each sign of the zodiac (with slightly different values than are seen on the medieval English instruments). However, this instrument uses the simpler geometry of the organum ptolomei, with the construction lines, just still visible on the page, confirming evidence from measuring the positions of points on the bead and mast scale that this instrument was drawn without the use of auxilliary arcs. It has the shorter mast of the organum ptolomei, with the latitude scale divisions made along an extension of the 12 o’clock line, as on the Regiomontanus-type dials.5 It therefore seems likely that Hartmann was working from manuscripts describing the organum ptolomei geometry, but that he may also have had a diagram or instrument that showed the standard design of navicula.6 A few years later, the ship-shaped dial is first described and illustrated in print, in Oronce Finé’s 1532 book Protomathesis.7 Eight years before the publication of his description of the instrument, Finé made

5 Georg Hartmann, “Compositiones horologiorum et aliorum instrumentorum,” in Herzogin Anna Amalia Library, Weimar, MS Fol. Max 29, ff. 13r–72v. A discussion of Hartmann’s role in creating a market for printed paper instruments is found in chapter 3 of Suzanne Karr Schmidt, “Art—A User’s Guide.” 6 In this section I use navicula only to refer to dials that have been made according to the medieval English navicula geometry. Other instruments are referred to either by the names given to them by the authors writing about them, or simply as shipshaped dial. 7 For Finé’s works, see Hilliard and Poulle, Oronce Finé et l’Horloge Planetaire; and Ross, “Oronce Finé’s printed works,” 83.

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Fig. 28 Diagrams from Weimar, Anna Amalia Library, MS Fol Max 29, ff. 62v, 63r, 63v. Reproduced by permission of Herzogin Anna Amalia Bibliothek, Weimar.

how 16th-century books redefined a medieval sundial 125

Fig. 28A

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Fig. 28B


Fig. 28C

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his own ship-shaped dial out of ivory (figure 29). This ship-shaped dial, made from ivory, is signed ‘Orontii F’ and dated 1524. It has been linked to king Francis I because of the presence of the crown and salamander on the mast, and is made according to the same geometry as the discussion of a ‘dial in the shape of a ship’ described in Finé’s Protomathesis (1532), which was republished in 1560 as De solaribus horologiis et quadrantibus libri quatuor.8 Finé describes the simplified version of the geometry—omitting the auxiliary arcs used in the navicula construction geometry, and using a slightly shorter mast. This links it to the organum ptolomei manuscripts, and suggests that Finé’s main source was one of these texts.9 Finé’s royal patron Francis I encouraged scholarship and teaching, and built up a huge library at Fontainebleau. During the early sixteenth century scholars were visiting various European countries on his behalf to buy manuscripts and look at education in other countries.10 Oronce Finé was himself influential in the Collège Royale in Paris11 and is known to have met many visiting scholars, including John Dee.12 Therefore, it is easy to imagine how manuscripts from the area around Vienna, perhaps along with instruments, came to Finé’s notice. The link between two geometrically very similar instruments was made explicit by Finé, in his headings for the descriptions of the two dials “To draw on a quadrangular plane yet another universal rectilinear dial”13 and “To convert that same dial which the preceding [section] treats into the form of a ship, which is of greater utility indeed.”14 Thus Finé’s titles explicitly describe the ship-shaped dial as a variant form of the preceding dial (the Regiomontanus dial), rather than as an important instrument in its own right.

8

On Finé’s books, see Marr, The Worlds of Oronce Finé. The relationship between Finé and Hartmann is unclear. And may not have been direct. 10 For the history of the Bibliothèque Nationale and its constituent collections, see Deslisle, Le Cabinet des Manuscrits, vol. 1. 11 Margolin, “L’Enseignement des mathématiques.” 12 For information on John Dee’s travels around Europe, see Sherman, John Dee. 13 “Aliud insuper horologium vniversale, rectilineum, super quadrangulo plano delineare”: Finé, De solaribus horologiis, 184. 14 “Idem quod antecedens tradidit horologium, in formam navis, amplioris quidem vtilitatis, conuertere”: Finé, De solaribus horologiis, 187. Finé thinks that the shipshaped dial is of greater utility because of the shadow square and unequal hours diagram found on the back (see Finé, De solaribus horologiis, 187). 9

how 16th-century books redefined a medieval sundial 129 Finé explains how to use the dial, in six sections, covering timekeeping and measurement of latitude as well as how to measure the heights of towers. The following lists the contents as summarised in the margins of the 1560 edition of Finé’s text: 1. Firstly, to observe the time in equal hours with the nauis 2. To ascertain the time of rising and setting of the sun, as well as the semi arc of the day [the length of the day] 3. So that the unknown latitude of a place, or the height of the pole, may be sought for 4. To compute the altitude of the sun above the horizon 5. To investigate the unequal hour in the daytime 6. About measuring the length of things

Most striking about Finé’s description, though, is the diagrams, which show the whole instrument (figure 30). They overlay the construction lines on an image of the completed instrument, showing the sliding cursor separately from the instrument, perhaps in order that the scale on the mast can be seen clearly by someone wishing to make a dial. Although the construction lines are not needed when using the instrument, most of them are shown so as not to obscure important parts of the scales, indicating perhaps that as well as clarifying the text on the construction of the instrument, the diagrams were intended to be copied.15 An object kept at the Whipple Museum of the History of Science gives evidence that the diagrams were indeed copied in order to produce an instrument (figure 31). This is an exact copy of the illustration in Finé’s book, of the same size and with the same decorative features as the diagrams in the 1560 edition of Finé’s work. The only difference is that the mast on the actual instrument is slightly wider (10mm) than that on the instrument illustrated in the text (8mm), and the numbering of the unequal hours diagram is slightly different. It is signed SF and dated 1620, and it has been suggested that that ‘SF’ might be Samuel Foster of Emmanuel College, Cambridge, and the Royal Society, London.16 However, the evidence is extremely thin:

15 Gingerich, “Astronomical instruments with moving parts,” argues in the case of books on equatoria that some of the diagrams of this instrument of planetary motion were intended to be copied rather than cut out. He points out that copies of Apianus’ Instrument Buch included a separate set of the diagrams on heavy paper to allow their assembly, and that around ¼ of surviving copies have these plates present. 16 Bryden, Catalogue 6: Sundials and Related Instruments, suggests that “SF” might be Samuel Foster, on whom see Venn and Venn, Alumni Cantabrigensis, vol. 1 pt. 2, 163.

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Fig. 29A Fig. 29 Ship-shaped dial in the Museo Poldi Pezzoli, Milan (inv. no. 4277, reproduced in Brusa (1980)). This instrument is made of ivory, and signed “Opus Orontii F.” Reproduced by permission of Museo Poldi Pezzoli, Milan.


Fig. 29B

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Fig. 30A Fig. 30 Finé’s printed version of the dial shaped like a ship, from Finé (1560), 184 and 187. Reproduced by permission of the Whipple Library, University of Cambridge.


Fig. 30B

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Fig. 31A Fig. 31 The Whipple ship-shaped dial, inv. no. 731. It is called the “Whipple” dial to distinguish it from another instrument in the collections of the same museum, which will be referred to as the “Cambridge” dial. Reproduced by permission of the Whipple Museum of the History of Science, University of Cambridge.


Fig. 31B

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the initials ‘SF’ aren’t unusual enough that this suggestion should be regarded as anything more than speculation. A second latitude scale has at some point been added to the back of the mast by a less proficient hand than the one who engraved the other scales and divisions (figure 32). The roughly engraved scale on the back of the mast gives the positions of the slider at the equinoxes, to correct for the fact that the mast traces out arcs rather than the parallel lines on a Regiomontanus-type dial.17 If the maximum solar declination is 24 degrees, then the latitude position at the equinox should be: l' = l/(cos 24)

where l is the latitude position at the solstice. Measuring the position of the latitude marks on the Whipple instrument confirms that they are in the expected places for this ‘correction’ of the scale.18 This alteration of the instrument indicates that it was at some point owned by someone with enough mathematical skill to mark on the corrected latitude values. However, the Whipple navicula provides the only clear evidence of anyone having used Finé’s account of the dial shaped like a ship to actually make an instrument. Finé’s influence on sixteenth-century mathematics was considerable, even though other authors had perhaps eclipsed him by the end of that century,19 so it is perhaps surprising that there is only limited evidence that scholars read and used his account of this instrument. After the mid-sixteenth century, references to the ship dial in English sources are few and far between. It seems almost as if a oncecommon instrument had simply disappeared. There appeared a brief reference to the ‘astronomer’s shippe’ in Robert Recorde’s Castle of Knowledge, published in 1556:20 Although there be many and wonderfull instruments wittily deuised for practise in Astronomy, as the Astrolabe, the Plaine sphere, the Saphey, the Quadrante of diuers sortes, the Chylynder, Ptolome his rules,

17 See chapter 7. For discussion of the diffuculties of analysing medieval instruments algebraically. 18 The mark for 40 degrees latitude is 26mm from the pivot (it should be at 25.2mm), 50 degrees is at 36.5mm (36.7mm) and 60 degrees is at 51mm (52.0mm). 19 For more detail on Finé’s influence on sixteenth-century English mathematicians, see Heninger, “Oronce Finé and English textbooks.” 20 Recorde, The Castle of Knowledge, 27.


Fig. 32 Numbers of the scale on the back of the mast and from the latitude scale on the front of the mast on the Whipple dial. Reproduced by permission of the Whipple Museum of the History of Science, University of Cambridge.

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chapter eight Hipparchus rules, Tunsteds rules, the Albion, the Torquete, the Astronomers staffe, the Astronomers ringe, the Astronomers ship, & a great number more, which hereafter in tyme you may know, yet all these are but parts or (at the most) diuers representations of the Sphere.

Robert Recorde (c. 1510–1558), physician and polymath, had been educated at Oxford and Cambridge. He was interested in a wide range of subjects including geometry, astrology and astronomical instruments, along with antiquities, histories and chronicles.21 He was a prominent member of society, and was appointed to an office of the Royal Mint in 1549. In 1556 Recorde published The Castle of Knowledge, dedicating it to Queen Mary. Recorde’s books were part of the growing number of texts concerned with improving the level of knowledge of scientific and technical knowledge among Tudor Englishmen, with emphasis on practical applications. Recorde explicitly drew on (and improved on) the work of previous scholars; among those he singled out as authorities were Oronce Finé and Sacrobosco. He complained that few works by medieval English writers were read widely, listing Robert Grosseteste, Michael Scot, John Baconthorpe, William Batecumbe, Simon Tunsteed and Richard of Wallingford as among those deserving attention.22 This patriotic aspect of Recorde was picked up by John Dee who explained that Recorde had written his earlier Ground of Artes “for very loue to Commonweale . . . [with] as greate affection as any man to helpe my countre men”.23 Recorde’s concern with English material and learning meant that he wrote in the vernacular, suggesting English equivalents for Latin and Greek terms where none existed already.24 Recorde’s mention of the astronomer’s ship occurs with a list of instruments, related to the sphere, which starts with common objects such as the astrolabe, sphere and quadrant. Later in the list, many of the items are unusual, uncommon, and specifically English. Recorde specifies Tunsteed’s rules, invented in the fourteenth century by the Oxford mathematician Simon Tunsteed, and the Albion, described by Richard Wallingford, Abbot of St Albans.25 The instruments in the latter half 21 Kaplan, Robert Recorde, 4. Recorde’s annotations in a manuscript now in Corpus Christi College, Cambridge, show that he could read Anglo-Saxon, see MacKisack, Medieval History in the Tudor Age, 25. 22 Recorde, The Castle of Knowledge, 98–9. 23 Recorde, The Ground of Arts, back of title page. 24 “Robert Recorde”, in Gillespie, Dictionary of Scientific Biography. 25 For analysis of the significance and popularity of the Albion and manuscript and printed texts on it, see North, Richard of Wallingford, especially “The Place of Albion in the History of the Equatorium”, vol. 2, 249–286.

how 16th-century books redefined a medieval sundial 139 of the list typically survive only in a few manuscripts and a handful of physical examples; in some cases no instruments are extant. Many of them are strongly linked to England or to Englishmen. In this context, the reference to the “Astronomers shippe” reads as if Recorde is treating it more as a mathematical curiosity than as a common instrument. In light of Recorde’s interest in antiquarianism, his patriotism, and his concern with English authors and material, his interest in the navicula is understandable. He states in the Castle of Knowledge that he has written another book, titled the Gate of Knowledge, containing details of the construction of various astronomical instruments, including the quadrant. But because this text has not survived, and may never have been printed, it is not currently possible to find out whether Recorde included the “Astronomers shippe” in this book and so not possible to determine with certainty the place it held in his work.26 John Dee, friend of Robert Recorde, had connections with many of the most prominent mathematicians in Europe. After getting his MA at Cambridge in 1548 he travelled to Louvain, where he met people including Gemma Frisius and Gerard Mercator, and then to Paris, where he met Oronce Finé.27 He assembled a very large library, which he made accessible to scholars.28 Dee collected titles covering virtually every aspect of classical, medieval and renaissance learning, with a particular focus on scientific and historical manuscripts and books. Dee’s interest in dialling is shown by his ownership of a number of texts on dials, and by evidence that students went to him for lessons on the subject: “[August 8th 1579] John Elmeston, student of Oxford, cam to me for dialling.”29 His book collecting began at Cambridge in the 1540s, and he acquired manuscripts from various sources including

26 Slightly later in the sixteenth century another English author mentions the ship dial. John Blagrave, who in 1585 published a book titled the Mathematical Jewel. The full title of the work lists all the instruments that Blagrave’s new instrument is better than: “The mathematical iewel, shewing the making, and most excellent vse of a singuler instrument so called: in that it performeth with wonderfull dexterite, whatsoeuer is to be done, either by quadrant, ship, circle, cylinder, ring, dyall, horoscope, astrolabe, sphere, globe, or any such like heretofore deuised: yea or by most tables commonly extant: and that generally to all places from pole to pole”. In his 1609 book on dialling, Blagrave does not mention the ship-dial, but nor does he mention any other portable dials, concentrating instead on the myriad ways of dividing a dial on a flat or curved surface. See Blagrave, The Mathematical Iewel, and Blagrave, The Art of Dialling. 27 Sherman, John Dee, 5. 28 Roberts and Watson, John Dee’s Library Catalogue. 29 Halliwell, “The private library of Dr. J.D.” 6.

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some of the newly dissolved religious houses and college libraries. In his catalogue of September 6th 1583, Dee listed around 3,000 books and 1,000 manuscripts, including: M186 “Groβhed Roberti Lincolniensis Episcopi, de luci, de iridis cum multis aliorus tractatibus, circiter 34 pergamento 4o [added later]a thik boke, with a labell”30

This has been identified by Roberts and Watson as manuscript DI, which contains a group A text on the construction of the navicula. Thus, John Dee owned one manuscript with a text on the navicula in it. He is, moreover, known to have been interested in dialling as an application of mathematics and especially geometry. In his Mathematical Preface of 1570 Dee explained some of the virtues of studying dialling, with reference to the teaching and understanding of geometry and astronomy: By the demonstratiue delineation of these Dialls, of all sortes, requireth good skill, both of Astronomie, and Geometrie Elementall, Spaericall, Phaenomenall, and Conikall.31

Evidence from the marginal notes in some of the surviving medieval manuscripts shows that Oxford students were among those reading navicula texts. John Chaunteler, studied for a BA and MA at Oxford, and signed his name in BL1.32 After holding various church positions, he ended up as Chancellor of Chichester in 1573.33 In 1589 Nicholas and Renauld Smythe read BL2, which contains a text on the use of the navicula, and complained about being unable to read the handwriting.34 Renauld can be identified as a student at University College, Oxford from 1588, and is perhaps the same Renauld who studied at Gray’s Inn in 1585. Another reader of MS Bodley 607 was Thomas Lowe, who matriculated at Broadgates Hall, Oxford, in 1594. Finally, Hugh Ramsdon received the same manuscript from an unknown person in partial settlement of some unspecified debt. He matriculated at Magdalen Hall, Oxford, in 1607 and received his MA in 1615 before returning to Yorkshire to take up appointments as rector and vicar.

30

“M186” in Roberts and Watson, John Dee’s Library Catalogue. Dee, “Preface,” dii. 32 BL1, f. iiv. 33 Biographical details for this paragraph taken from Emden, Biographical Register; and Foster, Alumni Oxoniensis. 34 BL2, f. iir. 31

how 16th-century books redefined a medieval sundial 141 The final piece of evidence for interest in the ship-shaped dial in the sixteenth century is difficult to interpret: it is the British Museum instrument, apparently made by Arscenius in 1581. It was, however, lost in the Second World War bombing of London, so detailed discussion of it is not currently possible. However, as outlined in chapter 7 and illustrated in figure 25, from the surviving sketch of the instrument it seems to have been an organum ptolomei, made according to the corrupted manuscripts with the bead scale missing, rather than according to one of the corrected versions of the geometry.35 In the seventeenth century, along with the Whipple dial, inscribed 1620 and copied from diagrams in Finé’s book, there is further evidence that Finé’s account of the dial shaped like a ship was used as a source, albeit for a book rather than for an instrument. In 1646 the Jesuit polymath and priest, Athanasius Kircher, published his Ars magna lucis et umbrae. It considers subjects relating to light and shadows, including a description of sundials: some plain, some decorative; some evidently real, some apparently relating to imagined instruments. Many of the instruments described are also shown in one of the fold-out copperplate illustrations. In the section on portable dials, Kircher includes a description of the construction and use of a dial he calls the columba, saying that his source for this is Oronce Finé’s 1560 De solaribus horologiis.36 The imagery of his illustration is striking, and helps to explain why Kircher has renamed the instrument columba. There is little in the text or diagram to confirm whether or not Kircher had among his sources an instrument as well as the text and illustrations from Oronce Finé’s book. Descriptions of the Musaeum Kircherianum published after Kircher’s death list several mathematical instruments in this great collection, which included a large armillary sphere, some astrolabes, and two quadrants, but nothing that might be identified as a ship-shaped dial.37 In the illustration of the columba the geometry of the instrument is overlaid on the image of the dove; the motto, the shield shape and three fleur-de-lys point to an emblematic or heraldic meaning for the 35 Mention is sometimes made of a navicula supposed to have been in the collections of the Science Museum, London, but now lost. However, there is no trace in the available documentation of there ever having been a ship-shaped dial at that museum, and it must be assumed that this was originally a mistake for the now-lost British Musuem instrument. 36 Kircher, Ars magna lucis et umbrae, 507. 37 de Sepibus, “De instrumentis mathematicis.”

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Fig. 33 Kircher’s columba dial, from his Ars magna lucis et umbrae (1646), facing page 506 in most copies of the book, but wrongly placed at page 560 in this copy. Reproduced by permission of the Whipple Library, University of Cambridge.

how 16th-century books redefined a medieval sundial 143 image. The quadrants in the four corners look more “real” than does the columba, the central instrument on the page. But the pedum pastoralis (the mast) is shown as a physical component, rather than just as a geometrical construction, and the line running through the sights on the dove’s head and tail indicates that they are to be placed at the same height. This arrangement is essential if the instrument is to function accurately. So it isn’t simply the case that this is an “unreal” instrument.38 Kircher’s illustration of the columba contains several levels of emblematic meaning. The Greek motto at the bottom of the illustration reads peristera pamphilos39 or ‘dove [of] pamphilos’. Since Pope Innocent X (pope 1644–1655) came from the powerful Pamphili family, and his arms consist of a dove carrying an olive branch under three fleur-de-lys it is clear that this illustration should be linked to him.40 So in the section on the columba Kircher is not only giving the reader information about a particular sundial, but also making a strong statement of allegiance to the new pope. His motivation for doing so may specifically be linked to the insecurity of his position in 1646. Kircher had strong links with the previous pope and his family, the Barberini, who had fallen dramatically from favour following the election of Innocent X.41 The imagery of sundials was often connected with their owners’ ability to measure time, and hence to influence the timing of events. The power to determine the time was associated with temporal power. Hence, many sundials included coats of arms or emblems related to specific rulers.42 In this case, there are further meanings to be drawn

38 Kircher represented “real” instruments in emblematic ways. For comparison, see Severino, “Ars magna lucis et umbrae,” and Monaco, “Quattro tavole sciateriche.” Mario Biagioli shows, in the case of Scheiner and Galileo’s observations of sunspots, that the geometric and representative functions of a diagram cannot easily be separated. See Biagioli, “Picturing objects in the making.” 39 The stem of the “T” is missing but the ligature between S and E indicates that the T should be there. 40 Many illustrations in the Ars Magna are linked to the Pope or to the Holy Roman Emperor by using their emblems of the dove and eagle. The sciatericon discussed above is a particularly clear example. 41 M. Ott, “Pope Innocent X.” 42 In the seventeenth century there was increasing concern with accuracy of time measurement, especially in the church (both protestant and catholic). The measurement of time was associated with good government and the orderly and virtuous life. See Dohrn-van Rossum, History of the Hour, 156 and 260–75. On the impact of clocks and time measurement in Europe, see also Landes, Revolution in Time.

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from the way the sundial is depicted. In the columba diagram, the geometry of the columba and the pope’s arms are contained within the main construction circle. This circle has at the top a 3-branched cross, very much in the style of those found on orbs which make up the regalia of a ruler. Such orbs were used in emblem books of the time to represent the world. The columba diagram could, therefore, be read as an indication of the pope’s influence over both time and space. A more specific reading would connect to Pope Innocent X’s political concerns in the closing years of the bloody Thirty Years War and with the Jesuit order’s geographical concerns, linked to their worldwide mission.43 The Latin motto Spes unica pacis suggests that the pope, and through him the Catholic church, is the one hope of peace for Europe.44 In this context the renaming of the ship-dial as columba starts to make sense. Far from being simply a reworking of material about a sundial, Kircher’s account is a strong political statement of allegiance to Pope Innocent X. His intended seventeenth-century readership would have understood the multiple meanings of his account more readily than his modern readers do. Naming the dial columba in this context gives a double meaning to what could at first sight look like a simple description of a sundial. Moving into the eighteenth century, there is an isolated piece of evidence for interest in the navicula in its the presence of an instrument in the collection of John Wilson. Wilson (1719–1783) was a gentleman-antiquarian resident at Broomhead Hall near Sheffield. He was educated at Sheffield and Chesterfield grammar schools before returning to run the family estates on the death of his father.45 Wilson collected manuscripts and books: But his attention was not confined to the collecting of charters and other manuscripts. He improved the library which had been collected by his grandfather the vicar of Sheffield, by the addition of many choice printed

43

Gorman, “The angel and the compass.” See Preimesberger, “Bilder des Papsttums vor und nach 1648.” Pope Innocent X himself made use of this double imagery of the dove to show both his family allegiance and as an image of peace. When he added a lantern to the church S Ivo alla Sapienza in Rome, he used the image of the dove on the outside to refer to his family, the Pamphili, and on the inside to refer to the holy spirit. See Connors, “S. Ivo alla Sapienza.” 45 This and other biographical material from Hunter, Hunter’s Hallamshire, which draws on the collection, family records and his personal contact with John Wilson’s youngest son William Wilson, who inherited the books and objects on John’s death. 44

how 16th-century books redefined a medieval sundial 145 volumes; he formed a cabinet of coins of considerable value; and he had a little museum consisting of rare prints, a few paintings, and other objects natural and artificial, ancient and modern, of different degrees of curiosity and value.46

However, Wilson was not among the first rank of wealthy gentleman collectors and scholars. Hunter explains: He collected some things which were scarcely worth preservation . . . he arranged and composed nothing, saving his early study of Hallamshire, and a genealogical account of his own family.47

Among Wilson’s collection was the fifteenth-century navicula now in the Musée d’Histoire des Sciences in Geneva.48 Appearing as part of an average gentlemanly collection, the navicula was probably among the “objects natural and artificial” in John Wilson’s cabinet. However, Wilson shows little interest in timekeeping specifically; his concerns related more strongly to local history and genealogy than to geometry and dialling.49 As discussed earlier, John Wilson’s navicula is very similar to one illustrated in the Gentleman’s Magazine in 1787 following correspondence from W.B. of Colchester on December 6th of the previous year. At the end of 1786, when W.B. was writing to the Gentleman’s Magazine from Colchester, the Geneva navicula was probably in Sheffield, part of the estate of John Wilson, who had died 4 years previously. Although W.B. is at present unidentified, it is clear from his account of the ‘ancient sundial’ and the statement that readers could have one made for themselves from the diagrams, that his interest in the navicula was focussed on the gentlemanly study of geometry, and on an interest in antiquities.50 It is also noteworthy that the author does not name the instrument, and does not call the “middle, or upright piece” the mast, indicating that he had not read any of the texts describing the instrument, in which the standard terminology of ‘mast’ and ‘navicula’ was used.

46

Hunter, Hunter’s Hallamshire, 276. Hunter, Hunter’s Hallamshire, 276. 48 This navicula was sold at Sotheby’s, London, on 25th February 1993 by Wilson’s descendants who still had it in their collection. 49 For more general discussion of eighteenth-century antiquaries in England, see Sweet, “Antiquaries and antiquities in eighteenth-century England.” 50 For other instruments illustrated in the Gentleman’s Magazine, see Delehar, “Illustrations of scientific instruments.” 47

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Fig. 34A Fig. 34 The Cambridge dial, in the collections of the Whipple Museum of the History of Science (inv. no. 5902). Reproduced by permission of the Whipple Museum of the History of Science, University of Cambridge.


Fig. 34B

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The final piece of evidence for antiquarian interest in the navicula before c. 1900 is an instrument dating from the late eighteenth or early nineteenth century, recently acquired by the Whipple Museum of the History of Science, Cambridge (figure 34). This instrument does not show the decorative features of the diagrams published in the Gentleman’s Magazine, so it was probably not made by copying them as W.B. had suggested.51 In addition, the towns on the back of the Cambridge navicula are unusual compared to those listed on other instruments and in texts. They include European cities and trade centres, whereas the earlier instruments only have English towns on them, and they are placed on the back of the body of the instrument rather than on the back of the mast. Nonetheless, this instrument shows some features that are specified in the text of medieval manuscripts on the navicula—most notably the presence of crosses at the top of the hour lines—so it is likely that an interested scholar made this instrument in the early nineteenth century, according to instructions in one of the medieval manuscript texts. This would also account for the somewhat primitive engraving on the dial, and the slightly idiosyncratic layout of the scales and numbers. By the eighteenth and nineteenth centuries the navicula was being collected and studied as an interesting rarity, a curiosity, a historical relic. This shift from the common and useful to the rare and curious therefore seems to have occurred in the sixteenth century, when interest in the navicula was focussed on the collection and study of manuscripts, based around informal networks of scholars, some of whom were based in the universities, and some of whom were outside the academic institutions. Members of a diverse group of men interested in the history and antiquities of England,52 Robert Recorde and John Dee, are linked to the instrument, although there is very little evidence for the nature of their engagement with the navicula. Considering Oronce Finé’s contemporary influence it is surprising that there

51 The sale catalogue suggests: “The form was reproduced in the Gentleman’s Magazine of 1787 (as discussed by Delehar), with the recommendation that the illustrations were “particular in the delineation . . . that any of your readers . . . might have one made . . . as correct as the original.” See Tesseract Catalogue 56. 52 Discussion of many of the key sixteenth-century English antiquaries, their collections and priorities, is in MacKisack, Medieval history in the Tudor age.” The concern with studying specifically English things was linked to the religious reforms instituted by Henry VIII and Elizabeth I, and to identifying English precedent for this controversial move.

how 16th-century books redefined a medieval sundial 149 is only limited evidence, in the form of the Whipple instrument and Kircher’s columbia dial, that others used his descriptions of the dial shaped like a ship. This unusual state of affairs is all the more striking considering the increasing popularity of books on dialling throughout the sixteenth century. The non-appearance of the ship-shaped dial in sixteenth-century books on dialling In the late fifteenth and sixteenth centuries there was a rapid increase in publications on practical geometry. These books were not necessarily aimed at practitioners of, for example, surveying, but were probably printed to meet the evolving upper classes’ interest in mathematical subjects.53 In line with the focus of medieval practical geometry texts, it seems that the purpose of the sixteenth-century dialling texts was as much to teach geometry and astronomy as to teach the construction and use of sundials. This was, for example, the aim of Oronce Finé’s Protomathesis: to place the descriptions of sundials into a strongly geometrical framework.54 The printed practical geometries and instrument texts are richly illustrated and many have volvelles among their diagrams. Owen Gingerich has argued that it is with the rise of printing that paper instruments become common, giving examples from texts on the equatorium, which shows planetary motions.55 An early publication including details of a dial related to the navicula is Regiomontanus’ Kalendarium. This starts as a standard astronomical calendar text, including details of saints days and moon phases. Towards the end, Regiomontanus gives details of a few instruments for telling the time in equal and unequal hours, starting with a horary quadrant. The illustration, included at the end of the book rather than in the body of the text, accurately lays out the scales of the instrument, and the text specifies that it can be used as an instrument in the back of the book:

53 54 55

See, for example, Hill, “Juglers or Schollers?” See Eagleton, “Oronce Finé’s sundials.” Gingerich, “Astronomical instruments with moving parts,” 63.

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chapter eight By the horary quadrant put into this book, you will easily discern the hours of day in whatever place, if you have previously examined the functions of the parts of the instrument.56

Although the text explains how to use this diagram as an instrument, it would have been awkward to do so, being at the back of the book, rather than in line with the text. Another possibility, however, is the functioning of the diagram as a paper instrument once it had been pasted onto board or wood. The next section describes the dial usually known as the Regiomontanus dial, which can be used for any latitude between 30 and 60 degrees. Like the quadrant, this dial is illustrated by a diagram inserted on a separate page at the back of the book.57 This picture functions in a similar way to that of the quadrant: it can be traced, copied or cut out, or used as an instrument just as it is, thanks to the folding metal arm fixed to the page. This metal arm is attached to the page in many surviving copies of the Kalendarium and is found in various editions of the book. In the 1476 copy printed in Venice, now to be found at the Museum of the History of Science in Oxford, the folding arm is present, but someone has also scratched lines into the surface of the page. These lines trace the geometry of the construction of this dial: the circles and straight lines that are described in the text of the book. So the owner of this book has used this diagram to help understand the geometry, scoring lines onto the diagram at the back of the book rather than drawing his own dial. In this case a dual use—understanding the geometry and using the diagram as a paper instrument—is suggested by a single extant diagram. In the early sixteenth century several other German texts including sections on dialling became popular, including Sebastian Münster’s 1531 Horologiographia. On page 25 of this book begins a section on the Regiomontanus dial, titled: The construction of a horary quadrant, which can be used in any region whose latitude doesn’t exceed 30 or 66 degrees.58

56 “Per quadratum horarium huic libello insertum horas dierum in quauis habitatione facile discernes si prius officia partium instrumenti perspexeris.” Regiomontanus, Kalendarium, 49. 57 See p. 101 for the image. 58 “Fabricatio horarii quadranti, quo in quauis habitatione, quae 66 & 30 gradum in latitudine non excedat, uti possis Caput V.”

how 16th-century books redefined a medieval sundial 151 This section details the construction of the dial, and includes two illustrations of it (figure 35). The first contains the construction letters referring to the instructions in the text, and includes the main construction lines and circles so that the reader can follow and understand the details in the accompanying paragraphs. The second diagram is a large, accurate image of the finished dial, giving full detail of the latitude and date grid (unlike the first diagram) and more clearly marked zodiac calendars at the right and top of the instrument, for setting the date. Everything needed to understand the construction and make a dial with compasses and a straight edge is in the first diagram, so the second one must have served some other purpose: to be copied. This image of a finished dial could have been traced, copied or cut out, just like the illustrations in the Regiomontanus book. Because the diagrams are in the body of the text, it is perhaps more likely that the illustration was to be copied, rather than cut out.59 Many of the other illustrations in Münster’s book have the same character: quadrants to be copied and a plumbline added; scales for a cylinder dial that can be traced and wrapped round an appropriate piece of wood. The text appearing with the description of the Regiomontanus dial specifies that you need to make a moveable arm attached above the latitude and date scale, which would enable someone copying the diagram to finish the instrument off and make a usable sundial. Later in the sixteenth century a very influential dialling text was published: Christopher Clavius’ Gnominces (1581) describes fixed and portable dials, and includes diagrams for most of them. In common with earlier texts, some instruments are illustrated with two diagrams, one showing the construction details, and one showing the finished instrument. In the section on the horary quadrant, Clavius uses the following illustrations (figure 36). This pair of diagrams probably have a similar function to those in Münster’s book: one is to explain the detail of the construction, the other shows the complete instrument, perhaps so that it could be copied to have a functional instrument without having to work through the complex geometry. Clavius has a section on the Regiomontanus dial on page 638 of his book. It includes a diagram of the instrument that is very similar to that in Oronce Finé’s 1532 Protomathesis. As in Finé’s illustration,

59 Some illustrations in Münster’s other works were woodcuts cut by Hans Holbein the Younger. See Koegler, “Hans Holbeins d.J. Holzschnitte.”

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Fig. 35A Fig. 35 Diagrams of the Regiomontanus dial from Münster (1532), 29 and 30. Reproduced by permission of the Whipple Library, University of Cambridge.


Fig. 35B

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Fig. 36A Fig. 36 Diagrams of quadrants, from Clavius (1581), 647 and 648. Reproduced by permission of the Whipple Library, University of Cambridge.


Fig. 36B

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Clavius shows the jointed arm separately so that it does not obscure the scales of the dial, and would allow the dial to be copied as with other diagrams in the book (figures 37 and 38). Interestingly, Clavius acknowledges Finé as an authority on dialling and refers directly to his work on dialling in the section on the Regiomontanus dial, mentioning an error in his treatment of the dial: Moreover, in the construction of this latter zodiac, Oronce, whom almost all men follow, rambled.60

That Clavius refers to Finé directly, and discusses an error in his treatment of the Regiomontanus dial while acknowledging him as an expert, shows the status of the earlier author.61 It also suggests that, since Clavius writes about the Regiomontanus dial without even mentioning the existence of a variant form in the shape of a ship, explicitly linked to it by Finé, the dial shaped like a ship was not important to Clavius. Perhaps he didn’t know what it was, didn’t realise that Finé had simplified the geometry and overstated the relationship between the dials, or just didn’t feel any need to include this dial, which looked like it was based on the Regiomontanus dial, in his otherwise comprehensive treatment of gnomonics. It isn’t that Clavius didn’t include any variant forms, because he does include the Capuchin dial, a single-latitude version of the Regiomontanus dial, later in his book. Nor is it that he didn’t know about it, as it immediately follows the Regiomontanus dial in Finé’s book, which Clavius evidently knew well. The influence of Regiomontanus, Münster and Clavius was considerable in sixteenth-century Europe. In his study of the education of mathematicians in England, Mordechai Feingold analyses the textbooks they used and shows that these three were among the most read authors.62 More generally, books on dialling were dominated by continental authors during the sixteenth century, and many such books were imported into England.63 In addition, works by these authors

60 Clavius, Gnomonices Libri Octo, 637: “In constructione porrò posterioris huius Zodiaci hallucinatus est Orontius, quem ferè omnes sequuntur.” Other authors took great joy in finding error in Finé’s work: his attempts to square the circle were attacked by his contemporaries. See “Oronce Finé” in Gillespie, Dictionary of scientific biography. 61 Kircher also mentions this error when writing about the columba dial in his Ars magna. 62 Feingold, The Mathematicians’ Apprenticeship. 63 Roberts, “Importing books for Oxford.”


Fig. 37 Oronce Finé’s diagram showing the construction of the Regiomontanus dial (from Finé (1560), 179). Reproduced by permission of the Whipple Library, University of Cambridge.

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Fig. 38 Clavius’ diagram of the same instrument, showing many of the same features, including the jointed arm drawn off to one side of the instrument (from Clavius (1581), 628). Reproduced by permission of the Whipple Library, University of Cambridge.

how 16th-century books redefined a medieval sundial 159 appear in surviving sixteenth-century booklists,64 including those of people as diverse as Sir Edward Dering, first Baronet of Kent, in whose collection were several works by Finé,65 and a range of Oxford scholars with much more modest collections of books, including Thomas Carpenter, scholar, and James Reynolds, scholar, both of whom died in 1577, and both of whose libraries contained Münster’s Horologiographia.66 The audience for printed books was, perhaps inevitably, narrower than the potential interest in a portable sundial. The expense of producing these richly illustrated dialling books was significant; Guillaume Cavellat, publisher of Oronce Finé’s 1560 De solaribus horologiis, complains about the cost of producing woodblock and copperplate illustrations and the risk of plagiarism. Cavellat also kept stocks of books with the imprint date left blank, to be completed later so as to give the purchaser the impression of having the latest edition.67 Presumably he was not alone among printers in having these economic concerns. So, if the illustrations in these mathematical books could be copied to make instruments, it is possible that the woodblock images of instruments were also used to print single-sheet copies of instruments like the Regiomontanus dial. These could be sold with the books, or separately, allowing a wider diffusion of information about and use of this dial than might have been the case if information about it was limited to books. Indeed, in sixteenth-century Germany there was a significant trade in single-sheet woodcuts, many of which showed portraits, religious images, coats of arms or pictures of strange phenomena, whether celestial or terrestrial. And in 1550s Nuremberg, there were 10 bookshops operated by woodblock cutters, indicating the popularity of these woodcut illustrations. A wider audience saw and owned singleleaf images than had access to books, which were much more expen-

64 Most modern editions of these booklists leave out the instruments that are described alongside the books. An excellent exception to this is Leedham-Green, Books in Cambridge Inventories, especially vol. 2, 824–5. 65 Fehrenbach and Leedham-Green, Private Libraries in Renaissance England, vol. 1, 175, 219 and 221 (PLRE4.58, 4.301 and 4.312). 66 Fehrenbach and Leedham-Green, Private Libraries in Renaissance England, vol. 5, 33 (PLRE 116.56). 67 Pantin, “Les problèmes de l’édition des livres scientifiques,” and de Renzi, Instruments in Print. On the challenges of printing mathematical diagrams and formulae in general, see Rider, “Early modern mathematics in print.”

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sive, and sometimes a single image would appear as both a book illustration and as a single-leaf.68 By their very nature, the single leaf prints have suffered disproportionately from damage or loss, so it is suspected that many more prints circulated than the number of surviving examples would now suggest. Among these single-leaf prints are images of instruments, of the kind found in instrument books, and surviving examples include sundials by Georg Hartmann (1551), and scales for a cylinder dial by Phillipp Apian (1567).69 These single-sheet printed instruments would have been relatively cheap to produce, and provided an easy way for people to own a paper instrument: simply buy a printed sheet, mount it on a piece of wood or wrap it around a cylinder and add a gnomon. In light of the existence of single-sheet woodcuts of instruments that circulated as well as the books, and the evidence that many such instruments were illustrated in books in ways that meant that they might be copied to make a working instrument, the popularity of the Regiomontanus dial might have been due to the fact that it was easy to print, and easy to cut or copy out to make a dial quickly and cheaply. The editions of Regiomontanus Kalendarium fitted with a metal cursor support this claim: once a publisher had produced the woodcut and the metal pieces to rivet on to the page it would have been easy to produce and sell single sheet instruments as well as the books, in order to recoup some of the costs of having the woodcut block cut. From studies of Italy, France and England, it is clear that there, too, printed instruments were gaining popularity during the sixteenth-century.70 No matter how clear a diagram of a navicula or a ship-shaped organum ptolomei, it requires two moving parts as well as a cursor, whereas the Regiomontanus dial needs only one part and a jointed arm. Given the similarity of the Regiomontanus dial and the navicula and shipshaped organum ptolomei in many practical and geometrical respects, it may be that the marginally more complex physical construction of the navicula weighed against it in sixteenth-century printed books, and this started a feedback loop that then increased the popularity of the Regiomontanus dial, influencing future authors in their choice of dials when they prepared new books. 68

“Introduction” in Strauss, The German Single-Leaf Woodcut, 1550–1600, 2. Strauss, The German Single-Leaf Woodcut, 1500–1550, 82 and 258. 70 See Bryden, “The Instrument-Maker and the Printer,” and Turner, “Paper, Print, and Mathematics.” 69

how 16th-century books redefined a medieval sundial 161 In his 1564 book on sundials drawing on Münster and Finé, Jean Bullant provides evidence that this was, indeed, the case. He describes how to make and use the Regiomontanus dial, including two illustrations of the instrument (one showing the geometry and one showing the finished instrument). He then discusses a variant form of it, beginning: The description of the following dial is the same as the foresaid one, except that this description of the dial or instrument is made of two pieces, on one of those pieces, that is the larger (which is almost like the mater of the astrolabe) is described only the scale of height, and the horizon line. And the other piece is put and fixed to the first, and is attached at the centre of it, so that it can be moved and turned from one part and from another, on which are described the hours, whether before or after midday, and also the meridional zodiac, at the right of this plate, joining the line of 12 hours of midday.71

This dial is shown in three illustrations (figures 39 and 40). Bullant brought the shadow square and unequal hours diagram from the back of Finé’s instrument, onto the front—thus making it one-sided and more suitable for printing. In place of a fragile narrow mast, he has made the instrument out of two rotating plates, and instead of a sliding cursor, Bullant suggests using a folding metal arm like that on the Regiomontanus dial. If, as Bullant says, the only difference between the Regiomontanus dial and its ship-shaped variant is that the former is in one piece, whereas the latter is in two pieces, then the simplicity of the Regiomontanus dial weighs in its favour. Once a woodcut had been prepared, offprints could be sold along with the books describing dials. This potential—to make an instrument by copying or cutting out an illustration, to use a woodcut illustration to make a paper instrument by pasting it to a sheet of wood or metal and attaching a cursor—was built into the illustrations in sixteenth-century dialling books. The 71 Bullant, Horologiographie, 102: “La description de l’horloge suiuante est conforme à la deuant dite, sinon qu’en ceste description l’horloge ou instrument est fait de deux pieces, en l’vne desquelles pieces, assauoir la plus grande (qui est quasi comme la mere de l’astrolabe) est descrit seulement l’eschelle de hauteur, & la ligne de l’horizon. Et l’autre piece set met & applique sur la premiere, & est attachee sur le centre d’icelle, en sorte qu’elle puisse estre demenee & tournee d’vne part & d’autre, en laquelle sont descrites les heures tant de deuant que d’apres midi, & aussi le zodiac meridien, à la dextre d’icelle table ioignant la ligne de 12 heures du midi”. Diagrams of the universal rectilinear dial are on pp. 99 and 101; diagrams of the ship-shaped dial on pp. 106–7.

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Fig. 39A Fig. 39

Diagram showing the geometry of the dial, from Bullant (1564), 106.


Fig. 40

Bullant’s diagrams of the parts of the instrument, from Bullant (1564), 107.

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influence of these printed illustrations, the growing popularity of the Regiomontanus dial, and of German dialling texts more generally, may explain why, despite Finé’s influence on many European authors, the dial shaped like a ship was not described or even mentioned in later dialling texts. The influence of continental instrument makers and authors in the sixteenth century, and Regiomontanus’ enormous posthumous influence and reputation, in Germany and across Europe,72 meant that after 1600 the navicula was redefined as a rarity, a curiosity, an object for a gentlemanly or museum collection, and its place as a practical and useful instrument was taken by other dials, especially the Regiomontanus dial. The popularity of continental dialling texts, the influence of print and the possibility of producing instruments from the woodcut diagrams in sundial books had overtaken the English instrument and manuscript tradition, even in England.

72

Pantin, “New philosophy and old prejudices.”

APPENDIX ONE

GROUP A NAVICULA MANUSCRIPTS BL1: Oxford, Bodleian Library, MS Bodley 681 This manuscript is a collection of Latin and English texts, on parchment, probably written in the early fifteenth century in England. Probably made up of what were originally three separate manuscripts, the book now contains: I 1 2

[f. 1r] John of Maidston on the annulus, for calendrical calculations [f. 13r] Chaucer’s Treatise on the Astrolabe

3

[f. 26r] Another treatise on the construction of the astrolabe, with diagrams and tables. On f. 34r is a note “anno domini 1403” in a hand that was added hardly later than the text was copied

4

[f. 35r] Treatise on the construction of the navicula, followed by a table of latitudes [f. 42v] Diagrams including the back of an astrolabe (f. 42v), the construction diagrams for the navicula (ff. 43v, 44rv, 45r), a lunar volvelle (f. 46r), a sinecal quadrant (f. 48r) and mathematical tables (f. 47r).

II

III 5

This text was owned by a variety of people during the 200 years between its composition and its acquisition by the Bodleian. The early fifteenthcentury copyist is anonymous, but later in the century the manuscript belonged to John Enderby of Louth, and later still in the same century to the abbot of Coldingham. In the early sixteenth century it was the property of John Chaunteler of Oxford2 and was probably received by the Bodleian in 1605. A note on f. 48v suggests that the manuscript was bound on June 27th 1550:

1 2

Madan and Craster, Summary catalogue, 228–9. Ownership notes on f. ii.

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appendix one Thys byke made the 27 day of June in the forth yeare of the reyne of kyng Edward the vith be the grace of god kyng of yngleond france & yrelond defendor of feyth and justle in prime heade of the spyrytuality & temporalite <whych> nessyte that I Jhon

However, it is difficult to know which, if any, of the owners mentioned in the paragraph above would have owned the navicula text, since it could have been acquired from a different source and bound with the other texts in 1550. DI: Oxford, Bodleian Library, MS Digby 983 MS Digby 98 consists of a number of texts on paper and parchment, collected and copied by Peter Partriche while he was at Oxford in the early fifteenth century. Some sections date from earlier centuries and were presumably incorporated into the manuscript by Partriche at the same time as he copied the bulk of its contents: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

[f. 4r] Treatise on genera by Robert Allyngtone [f. 7v] On gerunds and supines [f. 11r] Massa Compoti by Alexander de Villa Dei [f. 21v] Treatise on algorism [f. 30r] On roots [f. 31r] Treatise on algorism [f. 31v] On multiplication [f. 32r] Names of the fixed stars, after Symonem Suthray [f. 33v] Tables [f. 34r] Arithmetical questions [f. 41r] John of Maidstone on the annulus, for calendrical calculations [f. 49r] Walter Burley on comets [f. 61v] Short work on comets [f. 71v] A note from St Augustine, on the digestion of food [f. 72r] The prophecies of Merlin [f. 75v] On the construction of the navicula [f. 78r] Part of Euclid’s Elements (manuscript of the twelfth century) [f. 86r] Part of Boethius’ Arithmetic (manuscript of the twelfth century) [f. 78r] ‘Contra opinionem ponentem quadratum continuum componi et non quadratis’ 20 [f. 86r] Simon Bredon on Boethius’ Arithmetic

3

Hunt, Watson and Macray, Digby manuscripts, 109–113 and 53–5 of the notes.

group a navicula manuscripts 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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[f. 118r] John Peckham on perspective [f. 128r] Notes on Euclid’s Elements [f. 130v] Propositions 1–6 of the first book of Euclid’s Elements [f. 132r] Simon Bredon Theorica Planetarum [f. 145v] Robert Grosseteste Practica Astrolabii [f. 148v] On the composition and use of the quadrant and cylinder [f. 152r] On the rays of the sun in a crystal sphere filled with water [f. 152v] Robert Grosseteste on light [f. 154r] Robert Grosseteste on colour [f. 154r] Robert Grosseteste on the rainbow [f. 155v] Robert Grosseteste on potency and action [f. 156r] Robert Grosseteste on the airs [f. 158r] Robert Grosseteste on the sphere [f. 162r] On the composition of the quadrant, with Oxford tables (manuscript of the thirteenth century) [f. 166r] On the composition of the cylinder, for the latitude of Oxford (manuscript of the thirteenth century) [f. 168r] Robert Grosseteste on the sphere (manuscript of the thirteenth century) [f. 171r] Sacrobosco on the sphere (manuscript of the thirteenth century) [f. 177r] The Franciscan rule [f. 177v] The Franciscan testament [ff. 178v, 180r] Two letters [f. 179v] A letter from the reign of Henry IV [f. 179v] a petition from the reign of Henry IV [f. 181r] Excerpts from Hildegard of Bingen, book 1, chapter 5 [ff. 181v, 182r, 199v, 214r, 224r] Prices paid for threshing wheat [f. 183v] A letter to Bishop Robert Chetyngdone [f. 184r] On the revocation of the statute Contra Provisoires in 1398 [f. 185r] Blasphemous declaration by the Prior of Clerkenwell [f. 185v] On favour and indulgence [f. 186r] Hildegard of Bingen Pentachronon [f. 194r] Verses against the greed of monks [f. 194r] Satirical verses against monks [f. 195r] Satire of the council at London in 1382, and in praise of Wycliff [f. 196r] Part of a treatise against friars [f. 198r] Part of a disputation, against the Jews [f. 200r] The determination of master John Whitehead of Scotland on the preceding material against friars [f. 208r] The determination of the same on confession and absolution [f. 216r] Elements of civil law [f. 225r] Mirror of St Edmund [f. 255v] The twelve articles of the faith [f. 257r] Medical recipes for wounds, taken from the Surgery of Walter Brit

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Peter Partriche studied at Oxford in the early fifteenth century, receiving his MA by 1414 and DTh by 1421. He was at times a controversial figure: there are suggestions that he had converted fellow students to Wycliffism while at Oxford, and later in his life he was attacked in his stall at Lincoln cathedral on 28th June 1435, during a dispute between dean Macworth and the chapter of Lincoln.4 That this volume was copied and collected by him is shown by his signature in articles 11, 19, 20, 26, 30, 33 and 56 in the list above. On f. 1v there is a table of contents in Partriche’s hand, showing the contents of his collection. After his death on 10th January 1451, Partriche gave some of his manuscripts to the then recently founded All Soul’s College, Oxford, and to Lincoln Cathedral. This manuscript is not among those identified as being bequeathed to either institution, but there is evidence that it remained in Lincoln. Accounts relating to Gravely Place, a house in the Minster Yard at Lincoln, were added to the volume, and there is a note on f. 197v by William Maydwell, who is perhaps the Lincoln man of that name who died in 1555.5 From Lincoln the manuscript passed to the library of John Dee. He probably acquired it in 1556 and it appears as M186 in his library catalogue of 1583:6 Großhed Roberti Lincolniensis Episcopi, de luci, de indis, cum multis aliorus tractatibus, circiter 34 pergameno 4o (added later) a thik boke, with a labell

Later in his life, Dee had to sell parts of his library in order to pay his living costs, and the bulk of his books and manuscripts were disposed of in 1625–6. MS Digby 98 was probably disposed of before this date, as it was in the library of Thomas Allen by 1622. Since Allen and Dee were friends, it is likely the Dee gave or sold the manuscript to him in the early seventeenth century. It appears as Allen’s number 19 in the

4

Emden, Biographical register, 1430–1. Mare and Barker-Benfield (eds), Manuscripts at Oxford, 120, and Lincolnshire Archive Commission, Dean and Chapter wills 2, f. 162v. 6 “M186” in Roberts and Watson, John Dee’s library catalogue. 5

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quarto section of his catalogue.7 On his death in 1632 Allen bequeathed most of his manuscripts to Kenelm Digby, who had them rebound and numbered, giving MS Digby 98 the identifier “A136”. Soon after this, Digby bequeathed his manuscript collection to the Bodleian Library. PH1: London, Royal College of Physicians, MS 3588 This manuscript is a collection of astronomical texts linked to the Augustinian Priory at Thurgarton, Nottinghamshire. The contents are: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26

[f. 1*] Notorial attestation of c. 1500 [f. 1r] Table of the altitude of the sun [f. 2r] Section II.36 of Chaucer’s Treatise on the Astrolabe9 [f. 2v] A note about equal and unequal hours [f. 2v] Star lists [f. 5v] On the natures of the planets [f. 6r] More on the planets [f. 16r] Table of the sun [f. 19r] On the construction of the navicula (the group B text) [f. 21r] On the construction of the navicula (the group A text) [f. 24v] Miscellaneous notes, along with diagrams for the group B navicula text [f. 28r] Table showing which planet rules each hour of the day [f. 28v] A note about weights and measures [f. 29r] A table of zodiac signs [f. 29v] Miscellaneous notes [f. 30r] On the signs of the zodiac [f. 37r] On the construction of the astrolabe [f. 46v] A star list [f. 47v] On the 12 signs of the zodiac [f. 48r] On the natures of stars [f. 49r] On the state of the moon [f. 50r] On birth and infirmity [f. 50v] On the disposition of the year [f. 51r] On the solid sphere [f. 73r] Table of altitudes and latitudes [f. 74r] Astronomical notes and calculations

7 Hunt, Watson and Macray, Digby manuscripts, 169, edited from Oxford, Bodleian Library, MS Wood F26 part I. 8 Ker, Medieval manuscripts in British libraries, vol. 1, 207–9. 9 Eagleton, “A previously unnoticed fragment.”

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27 [f. 75r] A star list 28 [f. 76r] Profatius on the quadrant 29 [f. 98r] Prognostications based on the day, month and sign (in a sixteenthcentury hand)

The link to Thurgarton is suggested by its presence in tables giving the latitude of towns on f. 24r, by calculations for the latitude of Thurgarton on f. 25r, and by a note “T” in the solar altitude table on f. 75v next to the latitude of Thurgarton. The manuscript also appears in a fifteenth-century list of Thurgarton books, MS Sloane 3548, which was, until recently, thought to have been a booklist of some unknown friary, perhaps the Benedictine order.10 An erased ex libris inscription at the bottom of f. 26r can be partially deciphered as “Liber Roberti {. . .} canonici de Thurgarton.”11 Superimposed in the gap is “Maycotte”, also in a medieval hand. An interesting feature of MS RCP 358 is that it is probably written by the same scribe as compiled the booklist and copied many of the texts in MS Sloane 3548. This could mean that the booklist is of a personal collection of books and booklets, although if this is the case it is a rather large number of texts for a single person to own, and it seems more likely to be the books of the institution, or a subset of them. On a single folio, at the end of the MS Sloane 3548 are almost 50 entries in no particular order, one of which describes manuscript PH1.12 MS RCP 358 is indexed with white and blue threads at the start of the most important texts in the volume, allowing a reader to go straight to the right section for their needs. Other evidence that this manuscript was much used is given by the many marginal notes, annotations and additions, which indicate not only that the canons owned texts on astronomical instruments, but also that they owned instruments. For example, on f. 75r, under a list of stars and their coordinates, is the following note indicating that they had an astrolabe: cauda leonis . alacab . alhabZe . deneblagedi . mekar non sunt in mago astrolabio

After the dissolution of the monasteries the manuscript presumably passed into private ownership, and the later text (ff. 98 to 119, an

10 11 12

Bressie, “MS Sloane 3548, Folio 158.” Webber and Watson, The libraries of the Augustinian Canons, 415. Webber and Watson, The libraries of the Augustinian Canons, 419.


171

astrological text in a sixteenth-century hand) added to the collection. However, little is known of the history of this manuscript or its owners between 1513 (the last dated annotation) and the 1928 catalogue of the manuscripts of the Royal College of Physicians in which it is described by DW Singer.13 PH2: London, Royal College of Physicians, MS 38414 This manuscript, copied in the late fifteenth or early sixteenth century, includes a variety of astronomical and astrological texts. The manuscript is all in the same hand and little annotated. On the basis of the writing and contents, it can best be dated to c. 1500. Nothing is currently known of its provenance before it was catalogued in 1928.15 In English 1 [f. 1r] 16 questions, the first on thunder and lightning, the last on shooting stars 2 [f. 4r] On significators 3 [f. 6r] 12 chapters on the secrets of astronomy 4 [f. 9v] 12 considerations on judging from the stars 5 [f. 13v] Astrological tables, with an introduction 6 [f. 25v] On knowing at what time of the year to do things 7 [f. 25v] Of the part of water in many things 8 [f. 26r] Haly on the beams of the planets 9 [f. 27r] On diagnosing from urine 10 [f. 28r] Messahalla on eclipses 11 [f. 30v] On the election of times for journeys 12 [f. 37r] Albumasar on the revolutions of the world 13 [f. 48r] Sacrobosco de Sphaera 14 [f. 54r] What an astronomer should know 15 [f. 57r] On the 12 signs 16 [f. 60r] On the figures of the 12 signs 17 [f. 61v] On nativities 18 [f. 70r] On the nativities of children 19 [f. 72r] Canons on the sun and moon 20 [f. 75r] To know the state of a sick man 21 [f. 78r] On the planets and seasons

13 14 15

“MS 358” in Singer, Descriptive catalogue. Ker, Medieval manuscripts in British libraries, vol. 1, 212–5. “MS 384” in Singer, Descriptive catalogue.

172 22 23 24 25

appendix one [f. 85r] Hippocrates on life and death [f. 86r] How to find the 7 planets [f. 87r] The Ephemerides of Regiomontanus [f. 93r] Tables of the moon and planets

In Latin 26 [f. 99r] De urina non visa 27 [f. 102r] Ptolemy on the significances of the 7 planets 28 [f. 103v] Zael on the significance of the planets 29 [f. 103v] Zael on conjunctions 30 [f. 104r] On the firmament 31 [f. 108r] Ptolemy on nativities 32 [f. 111r] On the use of the navicula 33 [f. 111v] Messahalla on the heavens and stars 34 [f. 112r] Tables of the 12 signs 35 [f. 112v] Lines on the ruler of things 36 [f. 112v] Centilogium Bethemii

TO1: Cambridge, Trinity College, MS O.5.2616 This manuscript is a collection, on parchment and almost all in English, of astronomical and astrological texts. It was probably compiled by someone for their personal use, and is in a single hand throughout. The contents are as follows: 1 2 3 4 5 6 7 8 9 10 11 12 13

[f. 1r] An English version of Alkabicius’ Liber Introductoris [f. 28r] An incomplete treatise on medical astrology by William English [f. 37v] Another text by William English [f. 42r] Albumasar’s Flores [f. 58r] The Elections of Zael [f. 70v] The Domes of Astronomy [f. 90r] 127 Aphorisms on astrology, in English [f. 93v] Centiloquium, attributed to Ptolemy, in English [f. 98v] Note on bloodletting [f. 99r] Text on comets, largely an English paraphrase of Ptolemy [f. 100r] A note on the leap year [f. 100r] Astrological note on recovering from sickness [f. 100r] Albumasar’s Elections, in English

16 James, Western manuscripts in the library of Trinity College, and Rand Schmidt, The authorship of the Equatorie of the Planetis, 186–91.

group a navicula manuscripts 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

173

[f. 109v] On the positions of Saturn [f. 110v] Interpretations from Messahalla’s Book of Interrogations [f. 111r] A text on significators [f. 111v] Dorotheus on the occult [f. 111v] Predictions based on the air [f. 112r] On the significance of the conjunction of Saturn and Jupiter [f. 112v] A second chapter on the conjunction of Saturn and Jupiter [f. 113r] On sowing seeds in different seasons [f. 114r] On planting trees [f. 115r] On the construction of the navicula [f. 118r] An English translation of Analdo di Negro’s Theorica Planetarum [f. 146r] Translation of part of John Ashenden’s Summa iudicialis [f. 162v] Haly on deciding the Lord of the year [f. 164r] Richard of Wallingford’s Exafrenon [f. 174v] Zael’s Book of Interrogations [f. 177v] Messahalla’s de significatione planetarum (in Latin) [f. 179r] Tables for Oxford

The manuscript contains references which date it to the last quarter of the fourteenth century. On ff. 112v–113r a reference to John Ashenden’s prediction of an eclipse of the moon indicates the text was written after this date and the same folio also contains a prophecy for 1405. The script is anglicana, and consistent with the dates in the text. Most of the manuscripts in Trinity class O were presented to the College by Roger Gale in 1738, whose father had probably acquired it by 1697.17 The major sources for Gale’s library were the libraries of Patrick Young and John Dee. Kari Anne Rand Schmidt examines the question of provenance for this manuscript,18 concluding that this manuscript is an unlikely choice for a puritan theologian (John Owen, through whose collection the Young manuscripts passed before being acquired by Gale), but nor is there any evidence in Dee’s library catalogues to suggest that he owned it.

17 18

Rand Schmidt, The authorship of the Equatorie of the Planetis, 203–6. Rand Schmidt, The authorship of the Equatorie of the Planetis, 204–5.

174

appendix one WO: Oxford, Bodleian Library, MS Wood D8

This manuscript, on paper, in a somewhat messy hand, was copied by Thomas Ponteshyde, rector of Blisland in Cornwall.19 He copied the texts in the last quarter of the fifteenth century, and one of the entries (a text on horse medicine) was completed on May 10th 1485.20 The entry for WO in the Bodleian Library’s Summary catalogue is extremely abbreviated,21 but full details of the manuscript’s contents are given in Edward Bernard’s 1697 Catalogi librorum manuscriptorum Angliae et Hiberniae:22 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

19 20 21 22

‘Themata epistolarum et evangeliorum pro toto anno’ The effects and influence of the moon in the 12 signs Tables of the planets The course of the moon The natures and complexions of the 7 planets On the 12 signs On days for bleeding On the hours of the planets On the sexes of the signs On 32 dangerous days Verses on the compotus Verses on phlebotomy Calendrical tables Table of the 5 moveable feasts On the quality of the year, in English On the longitude and latitude of kingdoms and towns Canons on the new calendar On the nature, motions and effects of the planets Sphere of Phythagoras William Burley on comets [f. 48v] Canons by Nicholas of Lynn on the tables of William Rede Sacrobosco de Sphaera [f. 86r] On the form and use of the navicula On male and female constellations The number of blood spots of Christ, in English

Keiser, “Practical books for the gentleman,” on 476. Note on f. 128r. Madan and Craster, Summary catalogue, vol. 2 pt. 2, 1185. Bernard, Catalogi librorum, 366.

group a navicula manuscripts 26 27 28 29 30 31 32 33 34 35 36 37 38

175

[f. 93r] Walter Britt, Theorica planetarum On horse medicine, in English On lunations Practica astrolabii Practica geometriae The new calendar, with a table of signs The hours of the planets Table for Easter in leap years Gregory of Huntingdon, Imago mundi [f. 182v] Regule algorismi Herbarium, in English John of Burgundy on the plague, in English On diverse medicines

Transcription and translation This transcription is based on BL1, the text printed by Robert T. Gunther. However, because his edition is incomplete—most notably because he missed out a page of the text along with one of the diagrams—I have re-transcribed the base text, with contractions silently expanded, and noted the variants from it witnessed by the other manuscripts of the main group A text, based on my transcriptions and, in the case of TO1, the transcription printed in Rand Schmidt (1993), 207–12. one {.}etter illegible two {. .}tters illegible more than two {. . .}s illegible <editorial insertion> \scribal insertion/ 23 d constructionem nauicule de ve-|neciis24 tria ad minus sunt instru-|menta valde necessaria. Que sic25 fi-|ant. Capias circinum et disiunge| pedes ad mensuram dimidij pedis| et pungas .3.26 puncta fideliter in trian-|gulum in .3. laminis de auricalco sig|nando27 ipsa28 puncta cum .3. litteris .A.B.C. Deinde po-|nas pedem vnum circini in 23 24 25 26 27 28

Text starts DI f. 76v, PH1 f. 21r, PH2 f. 111r, TO1 f. 121r de veneciis] omitted DI sic] omitted DI .3.] tria tria PH1 signando] signynge or markinge TO1 ipsa] ea DI

176

appendix one

Fig. 41

Oxford, Bodleian Library, MS Bodley 68, f. 38v. © Bodleian Library, University of Oxford.


177

puncto29 .A. et cum altero pede| describe arcum a puncto .B. vsque in punctum .C. hoc in| 3. laminis facto; redeas ad primam. et a punctis .B.| C. protrahe lineas ad punctum .A. et sic habes .6. par-|tem circuli. Tunc diuidas arcum .B.C. in .60. gradus30 e-|quales. de quibus .24tus. gradus ab angulo31 .B. atque omnes| alij ab ipso vsque in angulum .C. habebunt lineas suas| vsque in32 centrum .A.; de ceteris gradibus vsque ad primam| lineam que est linea declinacionis sufficit quod 5tus. gradus| habeat lineam suam ad centrum .A. hoc facto; erige line-|am per angulos rectos33 a medio puncto lineae .A.B. vsque| in punctum .C. deinde pone pedem vnum circini immobilem| in puncto .A. et alium pedem in pede illius linee ortogo-|naliter erecte et protrahe arcum modicum vsque in lineam| declinacionis. super cuius contactum34 erigas ortogonaliter| aliam lineam cum arcu suo vt prius. Et sic de aliis quot| volueris pro nauiculis maioribus vel minoribus. Et| sic habes declinacionem solis et gradus latitudinum| sufficientes pro tota terra bone habitacionis. Qui vo-|luerit plures gradus addere pro remocioribus terre partibus;| addat in nomine domini.|
ost hoc35 sequitur de aliis instrumentis pro figuris sig-|norum prius inceptis. In quibus facies lineam a cen-|tro A per medium arcus BC vsque ad terminum lami-|ne que vocetur linea equinoctialis. Tunc capias cum| circino declinacionem36 solis videlicet spacium .24. graduum| de priori instrumentum. et punctues eam37 fideliter in vtraque| parte equinoctialis in arcubus istorum. Que puncta vocen-|tur puncta solsticialia. super que puncta facies lineam oc-|cultam ab vna parte laminis in aliam. et sic habes in equi-|noctiali duas intersectiones38 que signentur cum litteris| D.E. Tunc ponas pedem vnum circini in puncto .D.| et cum altero pede formes semicirculum ab vno pun-|cto solsticiali vsque in aliud.39 Omnibus hiis in vtroque in-|strumento factis; capias vnum istorum per quod philum cum| nodulo regetur. et pone vnum pedem in puncto .E. et| moueas alterum pedem vsque ad vlteriorem partem 29 30 31 32 33 34 35 36 37 38 39

puncto] confito DI gradus] partes DI partyes TO1 angulo] angle or corner TO1 in] ad DI rectos] riõte or euene TO1 contactum] contact or touchinge TO1 post hoc] hoc facto DI post hec PH1 declinacionem] declinacioun or bowinge TO1 punctues eam] poynte hit or pricke hit TO1 intersectiones] intersecciouns or entrekittinges TO1 aliud] aliam PH1

178

appendix one

semicir-|culi. cum quo pede ducas circumferenciam ab vna parte oc|culte linee vsque in aliam. Adhuc pedibus circini non mo-|tis; capias aliud40 instrumentum per quod malum nauicu-|le regetur. et pone vnum pedem circini in vno puncto| solsticiali et cum alio pede facias41 punctum pro centro in| linea occulta. in quo centro pones pedem vnum immo-|bilem et cum altero pede deduces arcum a puncto solstici-|ali vsque in equinoctialem. Et sub eadem forma facies| consimilem arcum in parte altera. Tunc isti42 arcus cum| exteriori linea circumferenciali alterius instrumenti di-|vidantur in .6. partes equales. Quarum due partes iux-| ta solsticia diuidantur in .3. partes equales. Omnes ali-|e partes diuidantur in .6. partes equales. hoc facto; omnes| iste diuisiones vtriusque instrumenti ducantur interius| vsque in semicirculum cum regula versus centrum .D.| Deinde ducantur cum regula et gnomone a semicir-|culo in arcu .B.C. hoc modo. Confirmes regulam super| laminam extra arcum .B.C. cum duobus forpicibus ita| vt vnum latus gnomonis concordet regule. et al-|iud; equinoctiali. Tunc moueas gnomonem super re-|gulam per notas in semicirculo. et notes eas in arcu| predicto et hoc cum occultis lineis interius vt postea| poteris eas cum regula a centro .A. apercius notare43| exterius. Iste figure zodiaci facte sunt secundum formam| astrolabij. et non quadrantis. In quadrante quilibet| gradus tenet locum proprium secundum quod distat44 ab equi-|noctiali. In astrolabio 4 gradus cardinales te-|nent sua propria loca et non plures. sicut hic in istis| figuris. alii gradus extrahuntur a locis suis. vi-|delicet in figura mali trahuntur interius versus equinoc-|tialem. In figura phili et noduli trahuntur exterius versus puncta solsticialia. quod prouenit ex magnitu-|dine paralellorum iuxta equinoctialem.|
ost hoc facies vnam vel duas figuras pro line-|is45 horariis inueniendis46 hoc modo. Ponas pedem vnum circini in centro .A. primi instrumenti. mouendo| alterum pedem quousque recte fuerit in pede breuioris| linee latitudinum. per47 quam mensuram describes super48 li-|neam rectam semicirculum in dorso eiusdem instrumenti.| deinde ducito lineam a centro in

40 41 42 43 44 45 46 47 48

aliud] illud PH1 facias] facies PH1 isti] iste DI notare] note hem or marke hem TO1 distat] diuersith or is in fernesse TO1 lineis] liniis DI horariis inueniendis] inueniendis horareis PH1 per] super DI super] omitted TO1


179

medium punctum .f. Tunc| vterque arcus in vtraque parte .F. diuidatur in .6. partes49 vi-|delicet in .6. horas equales. quarum .4. prime diuidantur| in .3. partes equales, .v.50 diuidatur in .2. partes equales.| et .6. non diuidatur. Tunc omnes iste diuisiones simul51| trahantur cum rectis lineis ab vna parte in aliam. et sic| habebis in semidiametro veram disposicionem linearum| horariarum pro nauicula illius quantitatis. Iterum redeas ad| primum instrumentum et pone pedem circini in centro .A.| vt prius. et moueas alterum pedem quousque recte fuerit in| pede maioris linee latitudinum. deinde pedibus circini| non motis. pone vnum pedem in puncto .f. et vbi alter| pes intersecat primam lineam, fac ibi punctum. et ab vno| puncto in aliud trahas lineam. super quam lineam capias| lineas horarias pro maiori nauicula. Eodem52 modo facies| de .3. et .4. linea latitudinum. Pro 5 et aliis maio-|ribus lineis. facias aliam figuram vt prius. ita53 vt queli-|bet linea latitudinum habeat in istis figuris lineam sibi| conformem maxima linea solummodo excepta.| um volueris nauiculam componere.54 primo elige ti-|bi55 lineam latitudinem ad quantitatem nauicule tue com-|petentem. deinde capias cum circino distanciam56 pedis eius| a centro .A. per quam mensuram describes principalem naui-|cule circulum. relinquens spacium modicum extra pro figu-|ris signorum. Per cuius centrum ab vna parte in aliam| deduces lineam equinoctialem. et ab eodem centro per medi-|um semicirculi deduces57 lineam perpendicularem que erit| linea hore .6. Et sic habes in circulo 3 intersectiones| in quibus facies 3 puncta equinoctialia. tunc redeas ad| lineam latitudinum et capias subtiliter quantitatem arcus| eius que est declinacio solis et punctues eam sexies in pre-|dicto circulo. videlicet in vtraque parte .3. punctorum equinoc-|tialium. Que puncta vocentur puncta solsticialia. super| que puncta trahes duas lineas.58 videlicet vnam in parte| posteriori pro hora .12. noctis; aliam in parte anteriori pro| hora .12. die. Tunc capias instrumentum factum pro regimine| phili et noduli. super quod compones nauiculam ita vt con-|cordent centrum cum

49 50 51 52 53 54 55 56 57 58

partes] partes equales PH1 .v.] vna TO1 but Price (1960) corrects this to .5. simul] omitted TO1 eodem] eadem DI ita] omitted DI componere] compowne or make TO1 elige tibi] tibi erige PH1 distanciam] distaunce or fernesse TO1 deduces] deduces deduces DI lineas] omitted DI TO1

180

appendix one

centro equinoctialis cum equinoctiali.| solsticia cum solsticialibus. et sic59 simul teneantur60 cum du-|obus forpicibus quousque fideliter extraxeris cum regula versus| centrum nauicule. figuram signorum ab vna lamina in| aliam. hoc facto;61 disiungas laminam illam a nauicula et| coniungas aliam et notes62 figuram illius in parte infer-|iori pro gubernacione mali per omnia vt prius. Postea fa-|cies duas lineas63 occultas ab vna parte nauicule| in aliam. videlicet in vtraque parte equinoctialis64 vnam. ab ea| equedistantes. In quibus notabis lineas horarias65| sic. Queres in semicirculum prius factis lineam huic| nauicule conformem in cuius contactu super maximam| semicirculi lineam. que est in nauicula linea hore .6.| pone pedem circini. mouendo alterum pedem quousque recte| fuerit in proxima intersecctione. quam punctues quater in| lineis occultis. videlicet in vtraque parte linee hore .6.| Eodem modo facias66 de omnibus aliis quousque perfeceris. Tunc super| ista puncta trahas lineas pro horis longiores. pro aliis| breuiores. vt hore67 per aliis melius videantur. Latitu-| dines similiter de linea latitudinum transferantur in ma-|lum. Aures cum foraminibus equedistent omni modo ab equinoctia|li. et sic eleuentur supra puncta solsticialia vt non im-|pediant philum. malum similiter in equinoctio ab vtroque| puncto solsticiali; equedistet68 omni modo.69| n70 hoc instrumento nauicule.71 due zodiaci figure72 ad| minus73 sunt necessarie. videlicet vno in ymo pro gu-|bernacione mali.

59

sic] sicut PH1 sic simul teneantur]teneas sic simul DI I schal holde thus TO1 61 hoc facto] and than TO1 62 notes] note thou or marke TO1 63 lineas] laminas DI 64 equinoctialis] equinoxiali PH1 65 horarias] horarum PH1 66 facias] facies PH1 67 hore] the latitudes of houres TO1 68 equedistet] euen distaunt or yliche fer TO1 69 DI text stops here WO and PH2 start here. Forma de noua instrumenta Nauicula dicto pro horis equalibus vbicumque in tota terra inueniendis inserted in PH2 Forma noue nauicule pro horis equalibus vbicumque pro tota terra inueniendis inserted in PH1 The forme of the newe instrument that is seide a schippe for euen houres oueral in al the erthe to be founden inserted in TO1 title de nauicula and text orma de nouo Instrumento nauicula dicto pro horis equalibus vbicumque in tota inueniendis inserted in WO 70 Space not left for initial I but guide letter faintly visible in margin BL1 71 nauicule] omitted WO 72 zodiaci figure] figure zodiaci PH2 WO 73 ad minus] omitted PH2 60


181

altera74 in parte anteriori75 pro gubernacio-|ne phili et noduli.76 vtraque figura .6. continet signa.77| quodlibet signum .30. continet gradus. per partes eius-|dem signi equaliter diuidendos. Extremi gradus78 hu-|ius figure dant79 solsticia. medius80 vero equinoctia. In| longioribus lineis a summo vsque deorsum perpendiculariter| protractis cum crucibus in summatibus earum signatis ho-|re inicium habent et finem. Ex istis81 lineis tres sunt| punctuate vt cicius videatur82 quota sit linea ab vna| parte vel ab alia. quarum media ab83 vtraque parte semper| est sexta.84 vtraque aliarum duarum85 a parte propiori est ter-|cia. et a parte remociori est nona. Breuiores linee86| intercepte87 horas diuidunt in partes binas vel trinas.| per gradus latitudinum88 in malo. aptare poteris instru-|mentum ad quamcumque volueris regionem. Cum89 volu|eris horam diei inueniere.90 primo videas quod .12. signa| sint in kalendario tuo fideliter posita.91 deinde videas| distantiam solis ab equinoctio92 vel solsticio in signo et| gradu. et ibidem ponas malum.

74

altera] alter WO anteriori] anteriori versus dextram PH2 76 noduli. vtraque figura] noduli et tunc semper operandum est cum dextera manu. et continue versus eandem partem capiendo lumine solis. et tertia figura sit in parte posteriori posita ad quacumque volueris partem aptare poteris instrumentum. vtraque figura PH1 noduli Et tunc semper operandum est cum manu dextera et semper versus eandem partem capiendum est lumine solis Et si figure tertia sit in parte posteriori posita ad quam volueris partem poteris aptare instrumentum. figura ista PH2 knott. & than euermore it is for to worche with the riõt hond & euermore toward the same partie it is to take the liõte of the sunne. And õif the thrid figure be putt in the hynder partie. thou may schape the instrument to what partie thou wolt// This figure TO1 noduli Et tunc semper operandum cum dextera manu et continue versus eandem partie capiendum est lumine solis Et si 3a figura sit in parte posteriori posita ad quamcumque volueris partem aptare poteris instrumentum. Figura ista WO 77 signa] signum WO 78 extremi gradus] extremitates PH2 WO extremitees TO1 79 dant] aut PH2 80 medius] medium WO 81 istis] hiis PH1 82 vt cicius videatur] videatur vt cicius PH2 that it be seen TO1 vt circinis videatur WO 83 ab] ex PH2 84 sexta] hora sexta PH1 85 aliarum duarum] aliarum linearum duarum PH1 86 linee] linea WO 87 intercepte] omitted PH2 88 latitudinum] etiam WO 89 cum] cum autem PH2 cum ergo WO 90 horam diei inueniere] horam diei inuenire PH1 hora inuenire PH2 91 posita] ponita WO 92 equinoctio] equinoxiali WO 75

182

appendix one

deinde teneas phi-|lum super consimilem gradum videlicet super lineam circularem| super quam gradus ille habet vel haberet si esset ibidem | suum contactum circumducendo cauillam in summitate ma-|li quousque nodulus recte fuerit super lineam hore duodeci-|me. Et tunc93 capiendum est lumen solis versus eandem| partem in qua parasti nodulum. ita vt94 lux95 appareat| in foramine vel in linea transuersa alterius tabule| et nodulus in primo visu ostendet tibi96 horam vel ho-|re particulam.97 Si98 longitudines dierum cognoscere vo-|lueris videlicet ab ortu solis in99 occasum; ponas philum| super lineam. vel inter lineas100 ita equedistantem101 vt non| obliquet eas.102 et habes orizontem. Et per103 orizontem104| horis105 \cum/106 particulis107 ex vtraque parte recte108 dupplicatis;109 habebis110| diei ac noctis quantitatem vbicumque fueris in tota terra.111| Et si112 per mutacionem loci nodulus

93

tunc] omitted WO vt] quod PH1 95 lux] lumen solis WO 96 tibi] omitted PH1 97 hore particulam] hore quantitatem PH2 eius partem WO 98 si] si insuper WO 99 in] vsque ad PH2 vsque in WO 100 lineas] lineas horarum PH1 lineas horarum WO text stops here (truncated by removal of page from the manuscript) TO1 101 ita equedistantem vt] equedistantes ita quod WO 102 eas.] eas. vel earum aliquam WO 103 et per] et super PH1 per PH2 104 orizontem] orizontem si PH2 105 horis]horas PH2 106 cum] added in darker ink, in a small neat hand BL1 107 cum particulis] et earum partibus WO 108 recte] omitted WO 109 dupplicatis] duplicatis duplicatis PH2 110 habebis] habebitur WO 111 quantitatem vbicumque fueris in tota terra.] quantitas. Et si fueris in regione aliqua cuius latitudo est tibi ignota considera cum posueris malum. et nodulum super gradum signi in quo est sol secundum modum supradictum. Si in meridie alicuius diei solis lumine veraciter accepto nodulus attingat ad lineam 12e hore in nauicula. Si vero non attingat eleuatur cursor in malo quousque nodulus recte ceciderit super dictam lineam et gradus ille super quem cadit cursor in malo ostendet tibi latitudinem regionem illius. computando gradus a centro nauicule. et tunc signum est quod regio illa magis borialis est qua regio prior quia polus super oryzontem est eleuacion. Si vero vt prius presupposita solar radii accepcione vera nodulus excedat lineam hore 12e deprimetur cursor in malo donec nodulus accedat ad lineam predicte hore et gradus in malo super quem cadit cursor. ostendet tibi latitudine regionis. Et isto modo vlteriori verificandi et regendi hoc in instrumentum vti nocte est cum quis condit versus australum et priori qu’ ad septentrionem accedere cupimus. Et directe versus orientem ac occidentem tendendo id est modus operandi cum instrumento sicut cum quolibet alio replaces ending in WO and also forms the ending of EM 112 si] omitted PH2 94


183

non attingat113 lineam| suam in hora duodecima; ligetur cursor mali in maio-|ri latitudine. videlicet remocius a centro nauicule et| si excedat; ponatur cursor in minori latitudine114| versus centrum. vbi incipiendum est latitudines com| putare per quinque et quinque. et postea per gradus secundum quod| ibidem apparent. Item non assuescas mouere malum115 per| partem eius superiorem. sed per116 inferiorem, ne nimio117 labore| peroretur in axe.| Quo die mensis sol intrat in signum.118 |

Menses. Dies.

1 11

2 10

3 12

4 12

5 13

6 13

7 15

8 15

9 15

10 15

11 14

12 13

<S>i volueris119 horam noctis inuenire oportet quod habeas| in kalendario tuo cum predictis signis signa oppo-|sita. Et in quolibet signo nomen alicuius stelle no-|tabilis in loco longitudinis sue fideliter scriptum cum| gradibus sue latitudinis et hoc per gradus zodiaci. Et vtrum stella sit septentrionalis vel meridionalis. Et tunc| agendum est cum stella sicut cum sole si esset ibidem. et sic| habebis horam stelle. Et si gnadir solis sit in eadem lon-|gitudine cum stella; eadem est hora solis et stelle. quia| sol et gnadir eius licet in diuersis emisperiis semper con-|similes describunt horas. Si gnadir solis precedat in| kalendario videas per quot dies computando .15. dies pro hora.| et quociens inuenieris .15. tociens addas120 horam vnam cum| diebus remanentibus horis stelle. et habebis horam solis.| Et si stella precedat gnadir solis; tociens minuas| horam vnam cum diebus remanentibus de horis stelle. Et| sic iterum habebis horam solis.| <S>ol motu proprio121 equalem cursum agens in circulo suo| ecentrico et inequalem in zodiaco. raptu fir-|mamenti circa axem mundi .365. per annum describit| paralellos. Qui paralelli inequales sunt in magni-|tudine et inequaliter distant abinuicem et ab equinoc-|tiali. Et cum centra eorum semper habeant 113

attingat] attingat nodulum PH2 latitudine] latitudine videlicet PH2 115 mouere malum] malum mouere PH2 116 per] omitted PH1 per partem eius PH2 117 nimio] nimie huius PH2 118 Quo die mensis . . . signum] title and table are across the bottom of ff. 22v and 23r PH1 table, with latitudes and other notes present in PH2: 119 volueris] vis PH1 120 addas] adde PH1 121 motu proprio] motu suo proprio PH1 114

184

appendix one

eandem inequa-|litatem a centro mundi et abinuicem super axem mundi.| oportet quod per eleuacionem et depressionem axis inequaliter| eleuentur et deprimantur et inequliter ab orizonte inter-|secentur. Et licet .24. hore in istis circulus sint equa-|liter distintte tamen122 in perpendiclari altitudine inequa-|liter distant abinuicem et ab orizonte sub et supra.| Ex quibus inequalibus prouenit quod dies artificiales no-|ctibus suis sint inequales et sibi inuicem et inequali-|ter crescant et decrescant videlicet iuxta equinoctium| velocius et iuxta solsticium tardius. Et quanto latitu-|do terre proclinior; tanto dierum inequalitas maior.| Et vbi latitudo nulla; ibi semper equalitas maxi|ma. et tamen123 altitudo meridiana diuersa. Et vbi| latitudo maxima. ibi dies longissima cum consimili noc-|te. longitudinem tocius anni habentes. | Ista tabula sequens docet eleuacionem poli in ciuita-|tibus.~~~~~ 125 Gradus.Minuta124

Alexandria. Ierusalem. Toletum. Roma Marcillia. Cremona Lugdun’. Parisius Constantinop’. London’. Cantuaria. Leicestria. Colcestria. Eboracus

31 32 40 41 44 45 45 48 56 51 51 52 56 54

Oxonia. Berwicus.

52 56

122

50 55 40 40 36 50

dicitur 49 gradus125 minuta 34

anthonius askam doctor astrologe dicit 55 51 gradus 30 minuta 50

tamen] tum PH1 tamen] tum PH1 124 Table titled Tabula latitudinis regionum et ciuitatum ab equinoctiali et longitudinis earum ab occidente and includes some 70 places PH1 table follows data on date of entry of the sun into each zodiac sign PH2 125 These notes all made in later hands. 123


185

For the construction of the navicula de venetiis, at least three instruments are very necessary. And they are made as follows. Take a pair of compasses and separate the feet to the measure of half a foot, and faithfully prick three points in a triangle on three sheets of latten, marking these points with three letters, ABC. Then put one foot of the compasses on point A and with the other foot describe an arc from point B up to point C. This being done on the three sheets, you return to the first, and produce lines from points B and C to point A, and thus you have a sixth part of a circle. Then divide the arc BC into 60 equal parts,126 of which the 24th degree from the angle B, and all the others from there all the way to angle C, have their own lines all the way to the centre A. Concerning the other degrees as far as the first line, which is the declination line, it is sufficient that the fifth degrees have their own lines to the centre A. This being done erect a line at right angles from the centre point of the line AB all the way to point C, then put the fixed foot of a pair of compasses on point A and the other foot on the foot of this orthogonally erected line, and extend a small arc as far as the declination line, above which point of contact you orthogonally erect another line, with its arc, as before. And thus from the others, as many as you wish, for larger or smaller naviculae. And so you have the declination of the sun and the degree of latitude sufficient for all the earth [that is] good for habitation. He who wishes to add more degrees for remoter lands and regions, adds [them] in the name of the Lord. After this it follows concerning the other instruments for the figures of the signs, begun earlier. On which you will make a line, which is called the equinoctial line, from the centre A through the middle of arc BC all the way to the edge of the sheet. Then you take, with the compasses, the declination of the sun, that is the interval127 of 24 degrees on the previous instrument, and prick it faithfully on each part of the equinoctial [line] on this arc, which points are called the solsticial points. Above these points, you make a hidden line from one side of the sheet to the other, and thus you have on the equinoctial two intersections which are marked with letters DE. Then you put one foot of the compasses on point D and with the other foot make a semicircle from one solsticial point all the way to the other. All this

126 Although gradus might be translated as ‘degree’, ‘part’ is used here. Manuscripts DI and TO1 give this reading. 127 I.e. the ‘interval’ or space between the feet of the compasses.

186

appendix one

being done on both instruments, you take the one of those by which the thread with the bead is ruled, and put one foot on point E, and move the other foot all the way to the furthest part of the semicircle. With that foot lead a circumference from one part of the hidden line as far as to the other. The feet of the compasses having not yet moved, you take the other instrument, by which the mast of the navicula is ruled, and put one foot of the compasses on the solsticial point, and with the other foot make a point about the centre on the occult line, in which centre you place one immovable foot, and with the other foot lead an arc from the solsticial point all the way to the equinoctial. And in the same way128 you make a similar arc on the other side. Then this arc, with the outer circumferential line of the other instrument, is divided into six equal parts. Of which the two parts near the solstice are divided into three equal parts. All other parts are divided into six equal parts. This being done, all those divisions of each instrument are led inside the semicircle with the ruler, towards centre D. Then they are led with the ruler and gnomon from the semicircle to arc BC in this way. You secure the ruler over the sheet outside arc BC with two tongs, so that one side of the gnomon agrees with the ruler, and the other with the equinoctial. Then you move the gnomon above the ruler, through the marks on the semicircle, and record them on the foresaid arc, this inside the hidden lines, so afterwards you can clearly record the same outside with the ruler from the centre A. These zodiac figures are made following the form of the astrolabe, and not the quadrant. On the quadrant any degree has its own place, according to its distance from the equinoctial. On the astrolabe the four cardinal degrees have their proper places and no more, just as here in these figures. The other degrees are removed from their place, that is on the figure of the mast, they are drawn inside towards the equinoctial. On the figure of the thread and bead, they are drawn outwards towards the solsticial point, which comes from the size of the zodiac near the equinoxes. After this, you make one or two figures for finding the hour lines, in this way. You put one foot of the compasses on centre A of the first instrument, the second foot being moved until it is right on the foot of the short line of latitude, by which measure you will describe a semicircle above a straight line on the back of the same instrument. Then lead a line from the centre to the midpoint F. Then each arc on each part of F is divided into six parts, that is into six equal hours, of which 128

Literally, ‘under the same form’.


187

the first four are divided into three equal parts, the fifth is divided into two equal parts, and the sixth is not divided. Then all these divisions are drawn similarly with straight lines from one part to the other, and so you will have on the semidiameter the right arrangement of hour lines for a navicula of this size. Again you return to the first instrument and put the foot of the compasses on centre A, as earlier, and move the other foot until it is right on the foot of the long line of latitude. Then without moving the feet of the compasses, put one foot on point F and where the other foot cuts the first line, make a mark there; and from one point to the other draw a line, on which line you take the hour lines for the larger navicula. Do [this] in the same way for the third and fourth latitude line. For the fifth and other longer lines, make another figure as earlier, so that each latitude line has on that figure its matching line, except the longest line. When you want to make a navicula, first choose your latitude line, agreeing with the size of your navicula; then take, with the compasses, the distance of the foot of it from centre A. By that measure you describe the principal circle of the navicula, leaving a small space outside it for the figure of the signs. Through the centre of which, lead the equinoctial line from one part to the other, and from this centre through the middle of the semicircle lead a perpendicular line, which will be the six o’clock line. And so you have three intersections on the circle on which you make three equinoctial points. Then return to the latitude line and accurately take the quantity of its arc, which is the declination of the sun, and prick it six times on the foresaid circle, that is, on each side of the three equinoctial points, which points are called solsticial points. Over which points you draw two lines, that is to say one in the latter part for 12 o’clock at night, the other in the former part for 12 o’clock in the day. You then take the instrument made for setting the thread and bead, above which you place the navicula so that it agrees: centre with centre, equinox with equinox, solstice with solstice. And so it is likewise held with the two tongs until you faithfully transfer the figure of the signs, with a ruler towards the centre of the navicula, from one sheet onto the other. This being done, you separate that sheet from the navicula and join the other [to it], and mark the figure of it on the lower part for the governance of the mast, through all [points] as before. Afterwards make two hidden lines from one part of the navicula to the other, that is on each side of the equinoctial, equidistant from it, on which you mark the hour lines, as follows. You will seek, on the semicircle made earlier, the line corresponding to to

188

appendix one

this navicula. On the point of contact of which, on the largest line of the semicircle (which is the six o’clock line on the navicula), you put the foot of the compasses, the other foot being moved until it is right on the next intersection, which you prick four times on the hidden lines, that is in each part of the six o’clock line. You do [this] in the same way for all the others, until you finish. Then you draw long lines over those points for the hours, over the others short [lines], so by them the hours can easily be seen. Similarly transfer the latitudes from the latitude line onto the mast. Sights with pinholes [are] equidistant in every way from the equinoctial, and are raised above the solsticial points so that they do not hinder the thread. Similarly, the mast [is] on the equinoctial, equidistant from each of the solsticial points, in this way. On this, the navicula instrument, at least two zodiac figures are necessary, that is to say one at the bottom for the setting of the mast, the other on the foremost part for the setting of the thread and bead. Each figure contains six signs, of which each sign contains 30 degrees, the same sign is divided equally into parts. The outermostmost parts of this figure give the solstices, the middle truly the equinoxes. On the longer lines, perpendicularly extended all the way downwards, with a cross at the top of each, the marked hours have a beginning and end. Out of these lines, three are pointed so that it is easily seen how much the line is from one part or the other; of which [lines] the middle from either side is always six o’clock; of the other two, the one from the nearer side is terce, and from the farther side is nones. The short lines between the hours divide [them] into two or three parts. By the degrees of latitude on the mast, the instrument can be adjusted to whatever region you want. When you want to find the time of day, you first look at [in] which 12 signs in your calendar are truly positioned, then look at the distance of the sun from the equinox or solstice in sign and degree, and put the mast in that very place. Then you hold the thread over the same degree, that is to say over the curved line above which that degree has or would have if it were touching it in that place, [and] move [it] about the fixed point at the top of the mast until the bead is right over the 12 o’clock line. And then the light of the sun is taken, towards the same part in which you prepared the bead, so that the light appears in the hole or on the


189

transveral line on the other panel,129 and the bead will at first sight show to you the hour or part of the hour. If you want to know the length of the day, that is to say from sunrise to sunset, you put the thread on the line or equidistantly between lines, so they are not oblique, and consider the horizon.130 And you will have the quantity of the day an night, by means of the horizon the hours and the small parts from each side, correctly doubled, wherever you may be in the whole world. And if, by alteration of the position of the bead,131 it does not touch its 12 o’clock line, fix the cursor of the mast at a larger latitude, that is to say further from the centre of the navicula. And if it exceeds it, the cursor is placed on a smaller latitude, towards the centre, where the latitudes begin to be reckoned by 5 and 5, and afterwards by the degree following that very place [where] they appear. Similarly, were you not accustomed to move the mast by its upper part, but by the lower, [it is] not too great an effort [for] it to be raised completely on the axis. Which day of the month the sun enters a sign.

Month Day

1 11

2 10

3 12

4 12

5 13

6 13

7 15

8 15

9 15

10 15

11 14

12 13

If you want to find the hour at night, is necessary that you have in your calendar, with the foresaid signs, the signs placed opposite [them]. And in whichever sign the name of any notable star in its longitude position [is] faithfully recorded with degrees of its latitude, and this by degrees of the zodiac, [and] of each star, be it northerly or southerly. And then it should proceed with the star, just as with the sun if it was in that place, and so you will have the star time. And if the nadir of the sun is in the same longitude as the star, this is the sun and star time, because the sun and its nadir, although in opposite hemispheres, always describe the time similarly. If the nadir of the sun precedes [the longitude of the star] in the calendar, you may see by how many days, and 15 days per hour are reckoned, and as often as you find 15, you

129

The flat part at right angles to the instrument. i.e.: hold the instrument so that the sights are parallel with the horizon, and the thread hangs parallel to the hour lines, indicating the point of sunrise and/or sunset. 131 The beginning of this section is missing. Compare with text in appendices 2 and 3. 130

190

appendix one

add one hour that many times, with the remaining day the star time, and you will have the sun time. And if the [longitude of the] star precedes [that of] the nadir of the sun, you take away by as many times one hour, with the remaining day the star time. And so again you will have the sun time. The sun in [its] proper movement—evenly driven around in its eccentric orbit, and unevenly in the zodiac, distributed across the firmament—describes divisions around the axis of the world 365 times a year. These divisions of the zodiac are unequal in magnitude and unequal distances from each other and from the equinoctial, while the centre of each is always at an unequal distance from the centre of the world and mutually from the axis of the world. To divide the horizon between them it is necessary to elevate and depress the irregularity, by raising up and suppressing the unequal axes. And that circle has 24 equally separated hours, although they are unequally spaced in altitude, each above and below the horizon: for this inequality produces artificial days, whose nights are unequal, and in turn from their irregular risings and settings one may see that near the equinox they are fast and near the solstice slow. And the value of latitude of a region can be deduced; so great is the inequality of the daylight. And where latitude is zero; [there] is always maximal equality, nevertheless the meridional altitude is limited. And where latitude is greatest, there the days are longest, with a similar length of night the whole year long. The following table shows the elevation of the pole in cities~~~~~~ degree minute

Alexandria Jerusalem Toledo Rome Marseilles Cremona Lyons Paris Constantinople London Canterbury Leicester Colchester York Oxford Berwick

31 32 40 41 44 45 56 48 56 51 51 52 56 54 52 56

50 55 40 It is said [to be] 49 degrees 40 36 50 Anthony Askam, doctor of astrology, says 55 51 degrees 30 minutes 50

APPENDIX TWO

GROUP A NAVICULA MANUSCRIPTS EM: Cambridge, Emmanuel College, MS 361 This manuscript consists of a number of previously unassociated parts, which have at some point been bound together. The first part is on vellum, and the second on paper, and between the two is a booklet of paper of a different size, containing the navicula text: I 1 2

[f. 1r] Macer on the power of plants [f. 36v] Secontur minuitiones, with miscellaneous remedies

3

[f. 41r] On the construction of the navicula, on smaller leaves in a different hand

1 2 3 4

[f. 1r] On the astrolabe, with diagrams [f. 14r] Astronomical tables and canons [f. 52r] Sacrobosco on the sphere [f. 60r] Further tables and canons

Ib II

The booklet containing the navicula text was previously kept folded, and the outside leaves are therefore somewhat damaged and difficult to read. It was copied in the late fifteenth or early sixteenth century. Apart from an ownership note at the top of one of the pages, there is no evidence for the provenance of this booklet, or when it was bound with the other works in the collection. Transcription and translation This text is transcribed separately since it is substantially different to those above, while clearly being based on a group A text. EM has

1 James, Descriptive catalogue of the western manuscripts in the library of Emmanuel College, 37.

192

appendix two

undergone significant alteration so that the instructions describe how to use a navicula marked with the calendar months rather than the zodiac months. Analysis of the contents of group A texts shows that EM is closest to WO, since both share a distinctive ending, explaining that the navicula can be used all over the world. Therefore, although WO is included in the transcription in appendix 1, its variant readings have been noted, where relevant, in the transcription of the ending of EM, below. Contractions have been silently expanded. one {.}etter illegible two {. .}tters illegible more than two {. . .}s illegible <editorial insertion> \scribal insertion/ Instrumentum pro horis diei comprendis in tota terra habitabilis Nauicula| duas continet figuras zodiaci vnam pro gubernacione mali in pede|nauicule signatam Alia pro gubernacione noduli in dextera parte lo|catam vlterius continet ii lineas perpendiularis protracta {n}tfigure|tenus cruce signatas quarum prima versus dexteram p{artem} na|uicule est linea merediei et voco dexteram partem nauicule illam que|obietur lateri dextri respiciti|

prima linea a linea merediei designant 2 horam 3 4 5 6 7 8 9 10 {11}

primam post 2am meridie 3am 4am 5am 6am 7am 8am 9am 10am {11am}

{11am} {horam} {10am} 9am 8am 7am 6am 5am {4am} {3am} {2am} {1am}

12 linea et prima versus sinistram est linea medie noctis s{. . .} fio{. . .}| {. .}rtea a lineis cruce signatis Alie breuiores line{.} interceptis| horas diuidunt in partes duas vel in tres vt vna linea intercepta horam| diuidit in duas partes 2e linee intercepte horam diuidunt in partes| tres / Figura zodiaci in extremitate mali diuiditur in 12 signa| {spacium} signo-


Fig. 42

193

Emmanuel College, Cambridge, MS 36, f. 41r. By permission of the Master and Fellows of Emmanuel College, Cambridge.

194

appendix two

rum diuidatur {in} spacia paruua quorum quodlibet spacium continet| duas gradus extremis 4 figure circa solticia videlicet gemini et cancro| sagittario et capricorno quodlibet istorum in .4. diuidit in 3 spa|cia spacio continentem 10 grados vlterius sub illa figura zodiaci {. .}|cuantur .12. menses scripte in 2 ordinibus quelibet menses diui|ditur in .6. spacia spacio continentem 5 dies Si mensis habuerit 30 dies| Si mensis habuerit 31 dies tunc vltimum spacium continebit 6 dies Si |mensis habuerit 28 dies tunc vltimum spacium continebit 3 dies Si mensis| habuerit dies tunc vltimum spacium continebit 4 dies Julius situatur in extre|mitatis figure mensium et habet in tria spacia quorum vnum est in ordinem| superiori et 2o alia spacia in ordine inferiori et quodlibet illorum spaciorum| continet 10 dies December situatur in alia extremitatis figure| mensium et habet vnum spacium in ordine inferiori et 2o spacia in or|dine superiori spacio continent 10 dies| Vlterius continet illa nauicula aliam figuram zodiaci in eius dextera parte| in quo 6 signa habuerunt ibi computari descendendo videlicet ista cancer leo virgo| libra scorpio sagittarius Alia 6 sunt computari ascendendo videlicet| capricornus aquarius piscis aries Taurus gemini Quodlibet signum| diuiditur in 6 spacia spacio continent 2 gradus extremis 4 signis| circa solsticia videlicet gemini et cancro Sagittario et capricorno que| diuiduntur in tria spacia spacio continentem 10 gradus Extremitates| tam illius figure zodiaci tam alterius dant solsticia medium equinoctia| Pro situacione cursoris est notandur que diuisiones in malo sunt gradus| latitudinum ciuitatum Latitudo ciui{. .}tis est distancia senith| ab equinocciali Senith est punctus directe supra ponitus capitibus| nostris/ Cursor super malum per tot gradus distabit a centro| nauiculae quot sunt gradus nauicule in latitudine ciuitatis Conuenio conuenienter| ponam tabulam latitudinis ciuitatum Anglis quas latitudines secundum| diuersos reperi inscriptis incipiendo a ciuitatibus borialibus|

Villa Sancti Johannis Berwyk Eboracus lyncolnia leycestria Norhampton herfordia Cestria Oxonia

58 0 56 50 53 40 53 10 52 50 52 50 52 50 52 10 51 40

Colchestri Villa Sancti Albani Cantuaria London’ Exon’ Wyntonia

51 40 51 38 51 33 51 34 51 50 50 15


195

Cum volueris horam diei inueniere| si menses sint inscripte pone| pede ita que media linea eius| concordet cum die menses et tunc filum extensum super mediam lineam pedis| mali ostendet gradum solis et tunc est situacion pedis mali pro tali| die Si menses non fuerint scripte in pede nauis oportet attenderes| ad gradum in quo sol est iuxta kalendarem nouum et tunc ponas pedem na|uis ita que media linea eius concordet directe cum gradu sol vel situ|acion pedis pro tali die deseruiet Deinde teneas filum super cen|silem gradum in figura zodiaci a parte dextera videlicet super lineam circu|larem circumducendo cauillam in summitate mali quousque nodulus fuerit| directe super lineam merediei et tunc capiendum est lumen solis| versus eandem partem versus quam parasti nodulum ita vt lumine sol| aparet in vtraque foramine et capud nodulum ostendet tibi horam et eius| parte transactam Si autem totum ortum solis scire desideras ponas| filum super lineam vel inter lineas eque distantes ita que non obli|quet ipsos vel earum partes et patebit tibi pro quo sol oritur|et occiditur et hore cum particulis ab illo loco vsque ad lineam meridiei de|monstrat medietate diei quibus duplicatis patebit| quantitas diei et noctis| Si2 fueris in altera regionem3 cuius latitudo est tibi ignota considera cum| posueris malum et nodulum super gradum4 in quo est sol secundum modum supra| dictum si in meredie alicuius diei solis lumine veraciter acceptes5 no|dulus attinget ad lineam hore 12e in nauiculam6 Si vero non| attingat eleuetur7 cursor in malo quousque nodulo directe8| ceciderit super dictam lineam. gradus9 super quem cadit cursor| in malo ostendet tibi latitudinem regionis illius computando gradus| a centro nauicule et tunc signam est que regio illa magis borialis est qua| regio prior quia polus super orizontem est eleuando10 Si vero vt| prius presupposita solaris radii acceptacionem11 vera nodulus| excedat lineam

2

From here onwards variant readings from WO are noted since the ending of these two copies is similar and distinctive. Si] Et si WO 3 altera regionem] regione aliqua WO 4 gradum] gradum signi WO 5 acceptes] accepto WO 6 nauiculam] nauicula WO 7 eleuetur] eleuatur WO 8 nodulo directe] nodulus recte WO 9 lineam. gradus] lineam et gradus ille WO 10 eleuando] eleuacion WO 11 acceptacionem] acceptacione WO

196

appendix two

hore 12e deprimetur cursor in malo quosque12| nodulus accedat ad lineam predicte hore et gradus in malo super quem| cadit cursor ostendet tibi latitudinem regionis et illo modo13 verificandi| et regendi hoc instrumentum vti nocte est cum quis tendet14 versus australem et priori siue15 ad septentrionem accedere cupimus Sed16 directe versus orientem| vel17 occidentem tendendo id est modus operandi cum hoc instrumento sicut cum quolibet alio|18

12 13 14 15 16 17 18

quousque] donec WO illo modo] isto modo ulteriori WO tendet] condit WO sum] qu’ WO Sed] Et WO vel] ac WO immediately following is: Versus de nominibus .5. portus Anglie .1. .2. .3. .4. .5.DouerSandwyc’HastyngRyyFryg marenēt .i. wych


197

By [this] instrument you take the hour of the day in all the habitable earth. The navicula contains [two] zodiac figures, one for setting the mast, marked at the foot of the navicula, the other for setting the bead, placed on the right side. Furthermore, it contains in that place perpendicular lines extended as far as the figure, [and] marked with a cross, of which the first towards the right-hand side of the navicula is the midday line, and I call the right side of the navicula that which will be falling.19 The right side is considered,

first line from the midday line marks 2nd 3rd the 4th 5th 6th 7th 8th 9th 10th 11th

first hour, after midday 2nd 3rd the 4th 5th 6th 7th 8th 9th 10th 11th

11th 10th 9th 8th 7th 6th 5th 4th 3rd 2nd 1st

hour

the 12 line, and the first [one] towards the left is the midnight line [s{. . .}fio{. . .} {. . .}tea] to the lines marked with a cross. Other, shorter, lines between the hours, divide [them] into two or three parts, so that one line between the hours divides [them] into two parts, the second line between the hour divides [it] into three parts. The zodiac figure on the end of the mast is divided into 12 signs. The area of the signs is divided into small spaces, any of which spaces contains two degrees, the outer four figures, around the solstices, that is Gemini and Cancer, Sagittarius and Capricorn, each of these four is divided into three spaces, [each] space containing 10 degrees. Further, under that zodiac figure [. . cuantur] the 12 months are written in two rows, each month divided into six spaces, [each] space containing five days, if the month has 30 days. If the month has 31 days then the last space will contain six days. If the month has 28 days then the last space will contain three days. If the month has days then the last space will contain four days. July is is situated at the end of the

19

i.e., in use, the left hand side of the instrument is pointed at the sun.

198

appendix two

figure of the months and has three spaces, of which one space is in the upper row and the two others are in the lower row, and each one of these spaces contains 10 days. December is situated at the other end of the figure of months, and has one space in the lower row and two spaces in the upper row, [each] space containing 10 days. Further, the navicula contains another zodiac figure on its right side in which the six signs were there to be reckoned descending, that is to say that Cancer, Leo, Virgo, Libra, Scorpio, Sagittarius, [and] the other six are to be reckoned ascending, that is Capricorn, Aquarius, Pisces, Aries, Taurus, Gemini. Each sign is divided into six spaces, [each] space containing two degrees, the outer four signs, near the solstices, that is Gemini and Cancer, Sagittarius and Capricorn, which are divided into three spaces, [each] space containing 10 degrees. So the ends of this zodiac figure, just as much as the former, give the solstices, the middle the equinoxes. For the positioning of the cursor, it is noted that the divisions on the mast are degrees of latitudes of cities. The latitude of a city is the distance from the zenith to the equinoctial. The zenith is the point positioned directly above our heads. The cursor on the mast will be distant from the centre of the navicula by as many degrees as there are degrees in the latitude of the city, [which] I bring conveniently together. I set down a table of latitude of English cities, whose latitudes following diverse [sources] you find written, starting with northern cities.

Perth Berwick York Lincoln Leicester Northampton Hereford Chester Oxford

58 0 56 50 53 40 53 10 52 50 52 50 52 50 52 10 51 40

Colchester St Albans Canterbury London Exeter Winchester

51 40 51 38 51 33 51 34 51 50 50 15

When you want to find the unknown time of day: if the months are inscribed, place the foot according to the middle of its line, agreeing with the day of the month, and then the thread is stretched over the middle line of the foot of the mast, showing the degree of the sun, and then [this] is the position of the foot of the mast for such a day. If the months were not inscribed at the foot [of the mast] of the


199

navicula, it is proper that you pay attention to the degree in which the sun is according to the new calendar, and then put the foot of the ship, so that its middle line or the position of the foot [of the mast] agrees directly with the degree of the sun, it will serve for such a day. You then hold the thread above the reckonable degree of the zodiac figure on the right hand side, that is over the circular line, moving [it] about the fixed-point at the top of the mast, until the bead is directly over the midday line. And then the light of the sun will be taken, towards the same part in which you prepared the bead, so that the light of the sun appears in both the pinholes, and the top [of the] bead shows you the hour and its completed part. However, if you want to know the time of sunrise,20 you put the thread over the line, or equidistant between lines, so that it is not oblique to them or their parts, and when the sun rises and sets will be known to you. And the hour with the small parts from this place to the midday line shows half the day, which, doubled, will show the quantity of the day and night. If you were in another region whose latitude [is] unknown to you, look when you have positioned the mast and bead above the degree in which the sun is, following the foresaid method. If at midday of any day, you receive the light of the sun truly, the bead will touch the 12 o’clock line on the navicula. If it really does not touch [the 12 o’clock line], the cursor is raised on the mast until the bead falls directly over the said line, the degree above which the cursor falls on the mast shows you the latitude of this region, the degrees being reckoned from the centre of the navicula. And then it is noted in which more northerly region is [that] earlier region, because the pole is elevated above the horizon. However if, as earlier, [after] the aforesupposed taking of the rays of the sun, the bead truly exceeds the 12 o’clock line, the cursor will be dropped on the mast so that the bead approaches the foresaid hour line, and the degree on the mast until the bead approaches the line, the foresaid hour and degree on the mast over which the cursor falls show you the latitude of the region. And by this verified and directed method, this instrument is to be used at night, with which it will extend towards the south, and beyond, or [if] we want to approach the north. But also reaching straight towards the east or west: this is the way of operating with this instrument, just as with any other. 20

This translation leaves out ‘totum’.

APPENDIX THREE

GROUP A NAVICULA MANUSCRIPTS BL2: Oxford, Bodleian Library, MS Bodley 607 Written in the early fifteenth century, on parchment and in Latin, MS Bodley 607 is still in a contemporary English binding.1 The binding has holes in the front and back covers that are 43mm in diameter and covered with leather flaps, presumably to hold something that is no longer there. The contents of this manuscript are: 1 2 3 4 5 6 7 8 9 10

[f. v] On the dispositions of men, some leaves lost [f. 1r] A treatise on chiromancy [f. 3r] A treatise on physiognomy [f. 16r] On the use of the navicula [f. 19r] A verse and prose compotus [f. 24r] Algorismus integrum [f. 45r] Sacrobosco on the sphere [f. 63r] An alchemical treatise by Roger Bacon [f. 72v] Aristotle on bodies [f. 73r] An ecclesiastical compotus

Although it is not known exactly when this work was written, or by whom, there are notes indicating that on 25th December 1589 the book was in the possession of a Nicholas Smythe, who notes the difficulty that he and his friends had in reading the handwriting. Around the same time a Renauld Smythe also owned it, but little else is known of the volume’s provenance until it reached the Bodleian in 1603–4.

1

Madan and Craster, Summary catalogue, vol. 2, pt. 1, pp. 187–8.

202

appendix three RA: Oxford, Bodleian Library, MS Rawlinson D248

This text is small (octavo) and is a collection of texts in various fifteenth-century hands. The contents are as follows:2 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

[f. 1r] 15 signs of the day of judgement, from St Jerome [f. 1v] On divine judgement [f. 1v] Four verses on the wounds of Christ [f. 2r] On the use of the navicula, with table of latitudes of towns [f. 5r] Prophecies of Merlin, the Sibyls, and others ‘de Scotia’, in French [f. 6r] Notes on Aristotle on comets [f. 9r] “En autre maner et plus legier poies asmelier chescristaus et autrez” [f. 9v] 41 verses “non vives sino [falso] crimine” [f. 10v] explicato praenomium apud viros usitatorum [f. 11r] Verses on the world, following the letters of the alphabet [f. 11v] Notes in the colours of urines, in Latin and English [f. 12v] “De inutilibus anni diebus” [f. 13v] On the aspects of planets [f. 14r] On Brutus in England [f. 14v] Prophecies of Gilda

Transcription and translation The text describing the use of the navicula contained in manuscripts BL2 and RA is much longer and more detailed than the version in the text of manuscripts like BL1. It is therefore transcribed separately here, with BL2 as the base text, and RA’s variants noted. Contractions have been silently expanded. one {.}etter illegible two {. .}tters illegible more than two {. . .}s illegible <editorial insertion> \scribal insertion/

2

Macray, Catalogi codicum manuscriptorum, 110.


Fig. 43

203

Oxford, Bodleian Library, MS Bodley 607, f. 16r. © Bodleian Library, University of Oxford.

204

appendix three

Forma de nouo instrumento3 nauicula dicit4| pro horis equalibus vbicumque in tota terra inueniendis5 In| hoc instrumento due figure zodiaci6 necessarie sunt videlicet vna| in ymo pro gubernacione mali altera in parte anteriori7| pro gubernacione fili et noduli et tunc semper operandum8 | cum dextra manu et continue versus eandem partem capiendum est lumine| solis Figura ista continet 129 signa. quodlibet signum 30 continet| gradus10 partes eiusdem signi equaliter diuidentes. extre-|ma huius figure dant solsticia medium equinoctia.| superiores ante linea vsque deorsum perpendiculariter protracte11| cum crucibus siue punctis in summitatibus earum signate inicium| hore designant.12 Pro13 gradibus eciam in malo aptare| poteris instrumentum ad quamqumque volueris regionem. Cum| igitur volueris horam diei inuenire primo videas quod 12 sunt| signa in zodiaco nauicule qui quidem zodiacus diuiditur| per .6. spacia et in quolibet spacio ponuntur duo signa quorum| vtrumque14 equaliter distat a primis punctis cancri et| capricorni sicut alterum eorundem et dies erunt equalis lon|gitudinis cum sol fuerit in vno illorum signorum sicut erunt| cum sol fuerit sub altero eorundem et eciam equalis breuitatis| et eciam equalis altitudinis et equales ascensiones habebit sol in| illis signis et ideo cum sol fuerit in aliquo illorum15 signorum que16 po|nuntur in eodem spacio zodiaci nauicule17 tunc pes| mali diebus gubernari per illa puncta que18 directe po|nuntur sub illis signis inter lineas circumferenciales ita| tum quod quando dies elongantur pes mali diebus successiem| abmoueri a primo puncto capricorni versus

3 4 5 6 7

instrumento] instrumento que vocatur RA dicit] que docet RA inueniendis] inueniendis est RA zodiaci] sodiaci RA forms of ‘zodiac’ spelt as ‘sociac’ throughout mali, altera in parte anteriori pro gubernacione] omitted, scribe has inserted //

RA 8 9 10 11 12 13 14 15 16 17 18

operandum] operandum est RA 12] 21 RA gradus] gradus per RA protracte] protracti RA designant] designant et finem RA pro] per RA vtrumque] vtraque RA fuerit in aliquo illorum] fuerit sub in aliquo istorum RA que] qui RA nauicule] nauiculi RA que] qui RA


205

primum punctum cancri| et in dierum abreuiacione e contra scilicet19 a primo puncto cancri| versus primum punctum capricorni sub illa condicione que| sub20 quocumque puncto inter lineas cicumferenciales maneat| per .5 dies preter quam21 sub punctis que ponuntur sub| spaciis extremis quorum vnum est spacium geminorum| et cancri. 22 aliud est spacium sagittarii et capricorni sub| nullo enim illorum spaciorum23 ponuntur in tria puncta| igitur sub quolibet eorum24 manebit pes mali per 12orum dies| simul 25 in ascensu solis et per tot in descensu eiusdem| Si igitur vis26 scire quota sit hora diei videas in quo signo est sol et in quo gradu27 et tunc pone pedem mali| sub eodem signo et sub eodem gradu in nauicula quia vt dictum| est sub quolibet signo ponuntur 6 puncta corespondenciam| 30 gradibus in illo signo ita que quilibet punctus corespondeat 5e gradibus et sic si sol esset in primo gradu alicuius signi tunc po|nendus esset pes mali28 in primo puncto sub eodem signo| et sic de inceps29 de singulis signis et sic30 cum posueris pedem| mali in suo loco debito pro illo31 gradu tunc pone| filum supra punctum in dextero latere nauicule corespon|dentem illi puncto sub quo ponitur32 pes mali et| remoueatur nodulus siue33 margarita quousque stet directe| super34 lineam hore 12e vel lineam meridionalem quo idem| est et tunc capiendum est lumine solis35 versus eandem partem| ad quam traxeris36 filum in dirigendo nodulum itaque| lumine solis intret per ambo37 foramina in sinistro extremo| et appereant38 in foraminibus alterius extremi tunc respicias| super quam

19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38

e contra scilicet] a quo scilicet RA sub] simul RA quam] qua RA cancri] cancri et RA illorum spaciorum] spaciorum illorum RA eorum] omitted RA per 12orum dies simul] per decem simul dies RA igitur vis] ergo vis RA gradu] gradu illius signi RA mali] male RA de inceps] omitted RA et sic] tunc RA illo] isto RA ponitur] ponatur RA siue] cum RA super] supra RA capiendum est lumine solis] capiendum lumine solis est RA quam traxeris] qua traxisti RA ambo] omitted RA appereant] aperiat RA

206

appendix three

lineam vel inter39 quas lineas cadit nodulus| vel margarita et scies40 horam vel partem hore que sitam41 in| qua sumus Eciam si longitudines dierum scire volueris| videlicet ab ortu solis vsque ad occasum pone filum directe| super aliam42 lineam horarum ita que non cancellet vel| intersecet aliam43 illarum vel si non poteris ponere filium| illo modo tunc pone filum inter alias44 2as lineas horarum| ita que non magis apropinquet alicui linea horarum secundum vnam| partem quam secundum aliam45 et tunc sub vna parte videlicet sub dextera| habebis horas medietatis noctis.46 Ad cognoscendum| latitudinem alicuius regionis ignotam videndum est sub quo signo| et gradu est sol et ponendus est pes mali sub| eodem signo et gradu in eodem die tunc capiendum est| lumine solis in alta meridie per foramina sicut dictum| est prius et si filum cadat directe super gradum corespondentem gradum solis in dextro latere tunc gradus mali super quo47| ponitur cursor ostendet tibi veram latitudinem illius patrie si| vero filum non cadat directem48 super illum gradum in dextro| latere tunc non habes eius latitudinem Si vero| filum non attingat gradum in dextro latere corespondentem| gradum49 solis tunc eleuetur cursor. quousque filum tangat| illum gradum. si autem excedat gradum in dextro latere| tunc deprimatur cursor50 donec filum cadat directem51 super| predictum gradum et tunc gradus in malo super quam52 cadit| cursor ostendet tibi latitudinem illius patrie in qua es componendo| gradus a centro nauicule / Ad sciendum quota sit hora| planetarum primo inuenias altitudinem solis in meridie illius| diei in quo es siue53 que patet

39

RA looks like ncio scies] scias RA 41 sitam] site RA 42 aliam] aliqua RA 43 aliam] aliqua RA 44 alias] aliquas RA 45 aliam] aliquam aliquam RA 46 horas medietatis noctis] horas mediatis diei et ex alia parte versus sinistram parte habebis horas medietatis noctis RA the scribe of BL2 probably missed a line out when copying 47 quo] que RA 48 cadat directem] cadit directe RA 49 gradum] gradui RA 50 cursor] omitted RA 51 directem] dircē [could easily be directem as well as directe] RA 52 quam] que RA 53 siue] secundum RA 40


207

in nouo kalendare54 qua| inuenta pone filum super consimilem gradum in circum|ferencia quadrantis vt patet in dorso nauicule tunc| amoueatur margarita sursum vel deorsum donec| veniat ad lineam meridianam que est vltima linea| arcnalium versus dextram deinde capiat lumine| solare55 per ambo foramina et margarita ostendet quota| fuerit hora planete scilicet vtrum sit56 2a 3a vel 4ta| et sic de aliis vnum si nodulus ante57 primam lineam58| arcnalem sit59 versus sinistram tunc est prima hora| si inter primam et 2am60 est 2a hora et prima de aliis| quousque margarita proueniat61 ad lineam 6am que est linea| meridiana quia tunc habetur hora 6a et hora 7a62 inci|piet esset ab eodem instanti63 et opposito modo operandem est| post nonam vnum64 si nodulus fuerit intro lineam meridio|nalem65 et lineam 5am est .7. horam66 si inter 5am et 4am tunc| est 8a. hora et ita de aliis vnum notandum que in quolibet| die artificiali sunt 12 hore planetarum primarie quacumque longa| vel breuis fuerit illa dies67 et consimiliter68 est de quacumque | nocte69 siue longa siue breui70 Si altitudinem meridianam71| velis scire sic est operandum72 primo respicias gradum solis gu|bernantem pedem mali corespondentem diei in quo es et ponas| margaritam super vltimam73 in summitate cruciatam ita| que cancellet gradum consimilem et corespondentem gradum pedis| mali quo facto maneat margarita et moueatur| pes mali ad tantum gradum trans lineam mediam crucialem | tunc eleuetur dextra pars nauis74

54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74

kalendare] calendario RA solare] solar’ [could be solarem]? RA sit] omitted RA ante] ante ante RA lineam] omitted RA sit] omitted RA 2am] 2am tunc RA proueniat] prouenerit RA 7a] alia RA instanti] isti RA vnum] vie RA lineam meridionalem] meridianam RA et lineam 5am est .7. horam] quinta tunc est media hora RA breuis fuerit illa dies] fuerit breuis dies illa RA consimiliter] similiter RA nocte] nate RA breui] breue RA meridianam] meredianem RA sic est operandum] sic operandum est RA vltimam] vltimam lineam RA nauis] maius [sic] RA

208

appendix three

quousque margarita| cadat super vltimam crucialem versus sinistram75 ostendentem| mediam horam noctis tunc margarita cadente super illam| lineam notetur gradus ex altera parte nauis super| quem76 cadit linea et ille gradus ostendet tibi altitudinem| meridianam etc.:77| Pro mensuracione rerum altitudinum secundum omnem diuisionem| et primo siue longitudinem est primitus notandur que si sit accessibilis| oportet respicere altitudinem rei per ambo foramina vno oculo et accedere| ad rem vel recedere a rem in tantum perpendiculum cadat super| lineam mediam scale idest super 12ia gradum deinde accipe altitudinem| oculi tui vsque ad plantam pedis et tantum accipias retro| te et quanta est altitudo oculi tui ad terram et nota locum| deinde mensura quot sunt pedes inter notam et fundamentum| turris vel alterius rei mensurande et habebis altitudinem eius|Si ante turris sit inaccessibilis vide summitatem eius per ambo| foramina et respice numerum punctorum vmbre recte sicut| prius et pone signum d. in loco in quo stas in hora consi|deracionis. consequenter elonga te a turri vel apropinqua secundum lineam| rectam et iterum respice altitudinem et quere numerum punc|torum vmbre recte ad hunc locum in quo 2o stabis et| pone signum in illo loco C. et mensura quot sunt pe|des inter illa 2o signa C.D. et retine illud postea| abstrahe numerum minorem vmbre recte de maiori et seruetur differentia deinde distantam inter 2o loca multiplicata per 12 et| productum diuide per differenciam prius acceptam et illi quo exierit| adde quantitem tue altitudinis et quo exibit est altitudo| turris. Quod si steteris in valle et altitudinem turris vel me|tiri considera primo altitudinem montis per 2as staciones secundam formam| prius dictam deinde considera altitudinem turris et montis simul per modum| predictam et remoue altitudinem montis de altitudine tocius aggregati| et residuum est altitudo turris. Sequitur iam 2a pars de men|suratione siue latitudinem cum scala facta primo in vno terris plani| et respice alterum terminum plani per ambo foramina tenendo| conum quadrantis siue nauis iuxta oculum tunc perspecto| termino plani mensurandi accipiatur numerus punctorum| vmbre verse et per 12 multiplica quantitem ab oculo tuo vsque| ad pedem. productum diuide per numerum punctorum vmbre| verse prius accepte et exibit quantitas latitudinis| plani. Sequitur iam 3a pars

75 76 77

sinistram] sinistram partem RA quem] que RA et sic] omitted, text stops here and restarts at point indicated below RA


209

de mensuracione siue profunditum si vis| igitur putei rotundi profunditatem metiri ab vno latere| putei respite cum scala terminum oppositi lateris in profundo| putei et notetur quantitatis diametri lateris putei| deinde accipiatur numerus punctorum vmbre et multiplica| quantitatem diametri latitudinis putei per 12 et productum diuide| per numerum punctorum vmbre recte et exibit profunditas| putei.78 Si volueris mensurare autem 79 rem secundem altitudinem| sic est operandem respice summitatem rei80 per ambo foramina et| notetur gradus super quem cadat linea siue sit in vmbra recta| siue in vmbra versa si super gradum in vmbra recta tunc| talis est proportio magitudinis inequalitis inter altitudinem rei et spa|cium qualis81 proportio magnitudinis inequalitis82 inter 12 et illum83 gradum| super quem84 cadit linea in vmbra recta sed si cadat super| gradum in vmbra versa tunc talis est proportio magnitudinis inequa|litis spacii ad altitudinem rei qualis est inter85 12 et illum gradum| super quam cadit linea in vmbra versa et finis.:.86

78

putei] end of section omitted RA autem] aliquo RA 80 rei] omitted RA 81 qualis] equalis est RA 82 inequalitis] inequalitatum RA 83 illum] istum RA 84 quem] que RA 85 est inter] omitted RA 86 et finis] et c RA Explicit materia de nouo instrumento que vocatur nauicula added in RA along with a table of latitudes titled hoc tabula subscripta est tabula de latitudine ciuitatem qua gubernandem est cursor in malo vt dicitur in canone instrumenti. 79

210

appendix three

The form of the new instrument called ‘navicula’, for discovering equal hours wherever in the whole habitable world. In this instrument two zodiac figures are necessary, that is one at the bottom for the setting of the mast, the other on the foremost part for the setting of the thread and bead. And then it is always operated with the right hand and the light of the sun is continually taken towards the same part. That figure contains 12 signs, each of which contains 30 degrees, the parts of the same sign being equally distributed. The outer [parts] of this figure give the solstices, the middle the equinoxes. Before this is a perpendicular line extended all the way down, with a cross or mark at the top of each, [which] designate the beginning of the hour. Furthermore, [using] the scales on the mast you can adjust the instrument to any region you want. When, therefore, you want to find the hour of the day, first look at which of the 12 are signs in the navicula zodiac [scale], which zodiac is indeed divided by six spaces, and in any such space two signs are placed, each of which is equally far from the first point of Cancer and Capricorn as the other one. And the days will be equally long when the sun is in one of those signs, and so it will be while the sun is under the other one, and indeed of equal shortness. And the sun will also have equal altitudes and equal ascensions in those signs, and therefore when the sun is in any of those signs which are placed in the same space of the navicula zodiac [scale]. Then the foot of the mast is to be set by means of those points, which are placed directly under those signs between the circumferential lines. So thus, when the days are lengthened, the foot of the mast is to be moved on successive days from the first point of capricorn towards the first point of cancer, and in the shortening of days again from the opposite direction, that is from the first point of cancer towards the first point of capricorn. Under this arrangement, it stays under whatever point between the circumferential lines for five days, except under the points which are placed under the outer spaces, of which one is the space of gemini or cancer, [and] the other is the space of sagittarius and capricorn. Indeed, under none of those spaces are three points placed, therefore the foot of the mast will stay under any one of them for 12 days, as in the sun’s ascent, and then through as many of them [i.e. days] during its descent. If, therefore, you want to know what the time of day is, look at what sign the sun is in, and in what degree, and then put the foot of the mast under the same sign and under the same degree on the navicula, because, as it is said, under any one sign are placed six points, corresponding [to] 30 degrees in this sign, so that


211

any one point corresponds to five degrees and so if the sun were in the first degree of any sign, then the foot of the mast should be placed on the first point under the same sign, and so from the start of a single sign. And so, when you have placed the foot of the mast in its proper place for this degree, then put the thread above the point on the right side of the navicula corresponding [to] that point under which the foot of the mast is positioned. And the bead or pearl is moved back until it rests directly over the 12 o’clock line, or the midday line, which is the same. And then the light of the sun is taken towards the same part to which you have pulled the thread, so that the light of the sun enters through both the pinhole sights on the outer left [part], and appears in the holes on the other side. You then conside over which line, or between which lines, the bead or pearl falls, and you will know the sought-for hour or part of hour in which we are. Also, if you want to know the length of the day, that is from the rising of the sun up to [its] setting, put the thread directly over another hour line so that it does not cross or cut another of those, or, if you are not able to place the thread in this way, then put the thread between another two hour lines so that it is not any closer to any hour line according to one part than according to another. And then under one part, that is under the right [side], you will have the hour of midnight. To know the latitude in any unknown regions, it should be seen which sign and degree the sun is in, and the foot of the mast positioned under the same sign and the degree in the same day. Then, at high noon, the light of the sun is taken through the holes, as said earlier, and if the thread falls directly over the position corresponding to the degree of the sun on the right hand side then the degree of the mast, above which the cursor is positioned, shows your true latitude of that part. If however the thread does not fall directly over that degree on the right hand side, then you do not have its latitude. Truly, if the thread does not touch the degree on the right hand side corresponding [to] the degree of the sun, then raise the cursor until the thread touches that degree. But if it exceeds the degree on the right-hand side, then sink the cursor until the thread falls directly over the foresaid degree, and then the degree on the mast, above which the cursor falls, shows you the latitude of that land in which the degree is constructed from the centre of the navicula. To know what the planetary hour is, first find the altitude of the sun at noon on that day in which you are, or which is known in the new

212

appendix three

calendar. Which being known, put the thread over a similar degree on the edge of the quadrant, as is available on the back of the navicula. Then move the pearl is moved up or down until it comes to the noon line, which is the last arc line towards the right. Then take the light of the sun through both holes and the pearl will show what number is the planetary hour, certainly whether it is the second, third or fourth, [or] another one. If the bead is before the first arc line, towards the left, then it is the first hour. If between the first and second, it is the second hour, and so for the others, until the pearl comes to the sixth line, which is the midday line, because then the sixth hour is passed and the seventh hour will begin, being from the same moment, and operating in the opposite way, it is one past noon. If the bead is within the midday line and the fifth line [then] it is the seventh hour, if between the fifth and fourth, then it is the eighth hour, and so for each of the others. It is noted that in any artificial day there are 12 primary planetary hours, however long or short that day is, similarly for whatever night, whether long or short. If you want to know the meridional altitude, this is the operation. First look at the degree of the sun, setting the foot of the mast [on] the corresponding day in which you are, and place the pearl over the furthest [line] crossed at the top so that it crosses a similar degree, and the corresponding degree of the foot of the mast. Which being done, the pearl stays [there], and the foot of the mast is moved to so many degrees across the middle crossed [line]. Then the right-hand part of the ship is raised until the pearl falls over the farthest crossed [line]87 towards the left, showing the middle hour of the night. Then, the pearl falling over that line, the degree from the other part of the ship is noted, above which the line falls, and this degree shows you the meridional altitude, etc. For the measuring of the height of something according to all the divisions, and the first, or length. It is firstly noted that if it is accessible, it is necessary to look at the height of the thing through both sights [with] one eye, and to approach the thing or to go back from the thing by so much [that] the plumbline falls over the middle line of the scale, that is over the 12th degree. Then take the height of your eye to the sole of [your] foot, and take as much backwards [from] you, and that much is the height of your eye from the ground, and mark the

87

Translation assumes scribal error of crucialem for cruciatem.


213

place. Then measure how many feet are between the mark and the base of the tower, or other thing, and you will have its height. If in front of the tower is inaccessible, look at its top through both holes, and look back at the number of points [of the] umbra recta, just as before, and put mark D in the place where you are standing at the time of inspection. Consequently move yourself away from the tower, or draw near, following a straight line, and look again at the height, and seek the number of points [of the] umbra recta from this place in which you stand second, and put a mark in this place C. And measure how many feet are between these two marks CD, and remember that. Afterwards take the smaller number of the umbra recta from the larger and record the difference. Then multiply the distance between the two places by 12, and divide the product by the difference previously learnt, and [to] that which emerges add the quantity of your altitude, and what results is the altitude of the tower. But if you are standing in a hollow and [examine] the height of a tower, or to estimate [it], consider first the height of the hill from two places, following the pattern said before. Then firstly consider the height of the tower and hill, similarly by the foresaid method, and remove the height of the hill from the cumulative height of the whole, and the remainder is the height of the tower. Now follows the second part of measuring, or width. With the scale made first, on flat land, and look at the other boundary of the flat through both holes, holding the apex of the quadrant, or ship, next to the eye. Then, on the observed boundary of the measured flat, the number of points of the umbra versa is taken, and multiply by 12 the quantity from your eye to [your] foot. Divide the product by the number of points of the umbra versa learnt before, and it shows the quantity of the width of the flat. Now follows the third part of measuring, or depth. If you want, therefore, to measure the depth of a round well, from one side of the well look with the scale [at] the edge at the opposite side at the bottom of the well, and the magnitude of the diameter of the side of the well, then the number of points of the umbra is taken, and multiply the quantity of the latitudinal diameter by 12, and divide the product by the number of points of the umbra recta, and it will show the depth of the well. But if you want to measure the height of a thing, or altitude, this is the operation. Look at the top of the thing through both holes, and the degree above which the line falls is recorded, whether it be on the

214

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umbra recta or on the umbra versa. If above a degree on the umbra recta then that much is the proportion of the size of the disparity between the height of the thing, and such a space is proportional to the size of the disparity between 12 and that degree above which the line falls on the umbra recta. But if it falls above a degree on the umbra versa then so much is the proportion of the size of the disparity of the space to the height of the thing, such as it is between 12 and that degree above which the line falls on the umbra versa, and finish.

APPENDIX FOUR

GROUP A STEMMATICS

Construction and usage

BL1 DI PH1 TO1

Usage only

BL2 EM PH2 RA WO

template construction method and use of navicula; with diagrams different to those in TO1 and DI; star time and table of latitudes at end; s. xv 1/4 template construction method; with diagrams different to those in BL1 text; s. xv 1/4 template construction method and use of navicula; no diagrams; star time and table of latitudes at end; s. xv 2/4 template construction method and use of navicula; with diagrams different to those in BL1 text; s. xiv 2/2 use of navicula; detail on measuring heights and depths; no table of latitudes; s. xv 1/4 use of navicula; expanded to include instructions for a navicula with a different calendar scale; s. xv 2/2 use of navicula; does not include star time section; table of latitudes at end; s. xv 4/4 use of navicula; simple treatment of heights and depths; table of latitudes at end; s. xv 1/2 use of navicula; does not include star time section or table of latitudes; s. xv 4/4 (c. 1485)

Despite the variation between copies—both in terms of wording and contents—it is nonetheless clear that all developed from some lost archetype. For example, we can see similarities in the wording of the opening of the section on using the navicula:1 BL1, DI, PH1, PH2, TO1, WO

1

In hoc instrumento nauicule. due zodiaci figure ad minus sunt necessarie. videlicet vno in ymo pro gubernacione mali. altera in parte anteriori pro gubernacione phili et noduli.

DI is omitted here; it has no usage section. See appendices 1–3.

216 EM

BL2, RA

appendix four Instrumentum pro horis diei comprendis in tota terra habitabilis Nauicula duas continet figuras zodiaci vnam pro gubernacione mali in pede nauicule signatam Alia pro gubernacione noduli in dextera parte locatam2 Forma de nouo instrumento nauicula dicit pro horis equalibus vbicumque in tota terra inueniendis In hoc instrumento due figure zodiaci necessarie sunt videlicet vna in ymo pro gubernacione mali altera in parte anteriori pro gubernacione fili et noduli

The following table summarises the contents of the section on the use of the navicula in each of the main subgroups:2

BL1, PH1, PH2, TO1, WO

1. 2. 3. 4.

8.

introduction and explanation of parts of navicula finding the time of day finding the length of the day (truncated in TO1) finding the latitude of a region (opening sentences missing in all copies except WO, not present in TO1) table of the day on which sun enters each sign (present only in PH1, BL1) finding the time by night from the stars (present only in BL1, PH1) an explanation of why time varies with latitude (present only in BL1, PH1) list of towns and their latitudes (present only in PH1, BL1, PH2)

1. 2. 3. 4. 5. 6.

introduction and explanation of parts of navicula list describing the layout of the hour lines list of towns and their latitudes finding the time of day finding the length of the day finding the latitude of a region

5. 6. 7.

EM

BL2 RA

2

1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11.

introduction and explanation of parts of navicula finding the time during the day finding the length of the day finding the latitude of a region finding the planetary or unequal hour finding the midday altitude of the sun finding the height of something (present only in BL2) finding the height of something inaccessible (present only in BL2) finding the depth of something (present only in BL2) finding the height of something list of towns and their latitudes (present only in RA)

The opening lines of this manuscript differ significantly from others in the group; that it is descended from the same source is shown by the significant similarities in other parts of the text, and so it is included here.

group a stemmatics

217

In order to consider the relationships between the manuscripts in a more quantitative way, statistical analysis of the groups A manuscripts was carried out with assistance from Matthew Spencer, of the Department of Biochemistry, University of Cambridge (now at School of Environmental Sciences, University of Liverpool). The analysis used phylogenic methods from evolutionary biology, which have been applied to the reconstruction of many stemmas, for example St. Augustine’s Quaestiones in Heptateuchem,3 Geoffrey Chaucer’s Canterbury Tales,4 and John Lydgate’s Kings of England.5 More recently, it has been used to construct a stemma for the manuscripts of Geoffrey Chaucer’s Treatise on the Astrolabe.6 As expected, copies of the group A text on the construction of the navicula are very closely related; the stemma in figure 44 shows that the four copies of this section (TO1, DI, PH1 and BL1) fall into two pairs: PH1 and BL1, and TO1 and DI. The group A manuscript texts on the use of the navicula were much more divergent, and two different analyses gave slightly different results (these analyses did not include DI since it stops at the end of the construction section). The first method consisted of a word-level analysis of the sections on the use of the navicula. This calculation considered how many times a pair of manuscripts differ in those places where both has a particular word: for example, if one manuscript had nauicula and another nauiculum in a particular place, this would count as a difference. The stemma constructed is in figure 45.7 The second method was to consider the items in each copy: the presence or absence of, say, a statement that you need to set the slider on the mast to your latitude, however it is expressed. Because of the significant variations in wording between some versions of the text on the use of the navicula, this method was expected to be a more reliable indicator of the relations between the texts (figure 46). This indicated that the manuscripts fall into two main subgroups, with PH1 and BL1 close together, likewise TO1 and PH2, and RA and BL2 as developments of the same branch. WO, although close to the largest group, is not closely associated with any manuscript in particular within it, 3

Lee, “Numerical taxonomy revisited”. Barbrook, Howe, Blake and Robinson, “The phylogeny of the Canterbury Tales,” and Spencer et al., “Analysing the order of items.” 5 Mooney et al., “Stemmatic analysis of Lydgate’s “Kings of England.” 6 Eagleton and Spencer, “Copying and conflation.” 7 This stemma was constructed using the same data, but with a newer piece of software: NeighborNet. See Eagleton and Spencer, “Copying and conflation” on the construction of a stemma for Chaucer’s Treatise on the Astrolabe using NeighborNet. 4

218

Fig. 44

appendix four

Stemma of group A manuscripts on the construction of the navicula.

Fig. 45

Stemma of group A manuscripts on the use of the navicula.

group a stemmatics

Fig. 46

Stemma of group A manuscripts on the use of the navicula.

219

220

appendix four

and EM is very different to all copies, thanks to the presence in it of material added to describe a variant type of navicula. The stemmas in figure 46 agrees with the one in figure 45 in its grouping of RA and BL2, although the relationship between them is reversed, with this stemma indicating that BL2 was descended from a text similar to RA, rather than the other way round. WO and EM appear between this branch and the main subgroup (of TO1, PH1, BL1, PH2), which divides pair wise in this stemma, and agrees with the first stemma, based on the construction sections of the text, in placing BL1 and PH1 close together. In order to resolve the apparent contradictions between the two stemmas based on the sections on the use of the navicula, and the possible place of the archetype on these stemmas, close consideration of the variations between the texts was needed. One significant variant is a line missing from BL1 but present in most other group A manuscripts (TO1, PH1, PH2, WO, RA, BL2). For comparison, the table below gives the text from BL1, PH1 and BL2:8 BL1

BL2

PH1

In hoc instrumento nauicule. due zodiaci figure ad minus sunt necessarie. videlicet vno in ymo pro gubernacione mali. altera in parte anteriori pro gubernacione phili et noduli. vtraque figura .6. continet signa. quodlibet signum .30. continet gradus. per partes eiusdem signi equaliter diuidendos. In hoc instrumento due figure zodiaci necessarie sunt videlicet vna in ymo pro gubernacione mali altera in parte anteriori pro gubernacione fili et noduli et tunc semper operandum cum dextra manu et continue versus eandem partem capiendum est lumine solis Figura ista continet 12 signa. quodlibet signum 30 continet gradus partes eiusdem signi equaliter diuidentes. In hoc instrumento nauicule. due zodiaci figure ad minus sunt necessarie. videlicet vno in ymo pro gubernacione mali. altera in parte anteriori pro gubernacione phili et noduli.et tunc semper operandum est cum dextera manu. et continue versus eandem partem capiendo lumine solis. et tertia figura sit in parte posteriori posita ad quacumque volueris partem aptare poteris instrumentum. vtraque figura .6. continet signa. quodlibet signum .30. continet gradus. per partes eiusdem signi equaliter diuidendos.

8 See appendix 1, p. 180, line 21, p. 181, line 3; and appendix 3; p. 204, lines 2–8. All manuscripts except EM and BL1 contain the line, but there are minor variations in the wording. Emphasis added to PH1 transcription.

group a stemmatics

221

This missing line explains which way round to use the navicula, essential because in spite of its symmetrical appearance, the instrument is not symmetrical in use (as you face the instrument the right-hand side is midday, and the left-hand side is midnight). Therefore it is reasonable to assume that this line was in the archetype text, since the instructions do not include all the necessary information without it, and so none of the other surviving manuscripts can be descendents of BL1, as they all contain this line. This agrees with the indications of all three stemmas, which show BL1 at the end of a branch. In order to resolve the question of the copying order of RA and BL2, careful consideration was made of the passages found in BL2 but not RA. One of them, on measuring the height of an accessible tower (one which is not, for example, behind a defensive moat), duplicates a section that is in both BL2 and RA, suggesting that RA was expanded with material from another source, rather than being a summary from a text like BL2. This was confirmed by identification of the source from which the extra sections were taken: the quadrans vetus by Robertus Anglicus. The table below gives the corresponding section in quadrans vetus for just one of the additional sections; the similarity between them is as strong for any of the variant readings in BL2, most of which are witnessed by at least one of the manuscripts used by Nan Hahn in her edition of quadrans vetus.9

BL2

quadrans vetus

respicere altitudinem rei per ambo foramina vno oculo et accedere ad rem vel recedere a rem in tantum perpendiculum cadat super lineam mediam scale idest super 12ia gradum deinde accipe altitudinem oculi tui vsque ad plantam pedis et tantum accipias retro te et quanta est altitudo oculi tui ad terram et nota locum deinde mensura quot sunt pedes inter notam et fundamentum turris vel alterius rei mensurande et habebis altitudinem eius

respice altitudinem rei per ambo foramina uno oculo, et accede ad rem vel recede a re in tantum donec perpendiculum cadat super lineam mediam quadrantis id est super 45 gradum. Deinde accipe altitudinem oculi tui ad terram et nota locum. Deinde mensura quot sunt pedes inter notam et fundamentum turris vel alterius rei mensurande, et habebis altitudinem eius.

9

Hahn, Medieval mensuration, 67, and appendix 3, p. 208, lines 7–13.

222

appendix four

To clear up any remaining doubt that this material was added to the navicula text from the quadrans vetus, excluding the possibility that the text in quadrans vetus came from the navicula text,10 the following phrase is telling: the scribe has removed the description “on which the rivet with the thread is attached” and added “or the ship”:11 BL2

quadrans vetus

through both holes, holding the apex of the quadrant, or ship, next to the eye.

through both holes, holding the apex of the quadrant, on which the rivet with the thread is attached, near the eye

This, combined with the duplication of a section on measuring heights in BL2, suggests that BL2 is an augmented version of a text like RA, with material added from the quadrans vetus. Therefore, the second method, based on the items present or absent in the texts on the use of the navicula, has given a more accurate stemma for this pair. A final piece of evidence allows a tentative suggestion of where on the stemma the archetype might be located. In WO and EM, and in RA and BL2, there appears a section of text missing from all copies of the main subgroup (TO1, PH1, BL1, PH2), but which must have been present in the archetype in some form. These lines are the start of the section on finding your latitude:12

10 The earliest medieval manuscripts of quadrans vetus date from the thirteenth century, whereas the earliest navicula manuscripts date from the late fourteenth century. King “A vetustissimus Arabic treatise on the quadrans vetus” identifies an Arabic manuscript on the quadrans vetus that is older than the medieval texts. 11 Appendix 3, p. 208, lines 30–1, and “per ambo foramina, tenendo conum quadrantis, in quo est clavus cui fi lum annecitur, iuxta oculum”: Hahn, Medieval mensuration, 67. 12 Appendix 1, p. 182, line 13; p. 183, line 7; appendix 2, p. 195, lines 18–23; and appendix 3, p. 206, lines 9–23.

group a stemmatics

223

BL1

EM

BL2

Et si per mutacionem loci nodulus non attingat lineam suam in hora duodecima; ligetur cursor mali in maiori latitudine. videlicet remocius a centro nauicule et si excedat; ponatur cursor in minori latitudine versus centrum. vbi incipiendum est latitudines computare per quinque et quinque. et postea per gradus secundum quod ibidem apparent. Item non assuescas mouere malum per partem eius superiorem. sed per inferiorem, ne nimio labore peroretur in axe.

Si fueris in altera regionem cuius latitudo est tibi ignota considera cum posueris malum et nodulum super gradum in quo est sol secundum modum supra dictum si in meredie alicuius diei solis lumine veraciter acceptes nodulus attinget ad lineam hore 12e in nauiculam Si vero non attingat eleuetur cursor in malo quousque nodulo directe ceciderit super dictam lineam. gradus super quem cadit cursor in malo ostendet tibi latitudinem regionis

Ad cognoscendum latitudinem alicuius regionis ignotam videndum est sub quo signo et gradu est sol et ponendus est pes mali sub eodem signo et gradu in eodem die tunc capiendum est lumine solis in alta meridie per foramina sicut dictum est prius et si filum cadat directe super gradum corespondentem gradum solis in dextro latere tunc gradus mali super quo ponitur cursor ostendet tibi veram latitudinem illius patrie si vero filum non cadat directem super illum gradum in dextro latere tunc non habes eius latitudinem Si vero filum non attingat gradum in dextro latere corespondentem gradum solis tunc eleuetur cursor. quousque filum tangat illum gradum. si autem excedat gradum in dextro latere tunc deprimatur cursor donec filum cadat directem super| predictum gradum et tunc gradus in malo super quam cadit| cursor ostendet tibi latitudinem illius patrie in qua es componendo gradus a centro nauicule

This section is perhaps where there is most variation between the subgroups: after this point the texts diverge more markedly than they do up to this section. WO, EM, RA and BL2 all have a section on finding latitude but fall into two pairs with different wording of it. The PH1, BL1, PH2 subgroup is missing the first part of the section13—telling you 13

It is missing from TO1 because of the loss of a page.

224

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how to set up the navicula to find your latitude—and starts with the part on how to move the cursor up and down if the bead doesn’t lie on the 12 o’clock line when the instrument is correctly set up. A section on finding latitude was probably in the archetype, as all copies of texts on the use of the navicula have some version of it. Without the start of the text it would have been very difficult to follow the instructions unless the user already had a certain amount of knowledge of this or similar instruments. From this, it initially seems likely that either the WO/EM pair or the RA/BL2 pair is closer to the archetype than is the main subgroup. As it has already been indicated that the shorter versions of the usage section are probably closer to the archetype than are the longer versions, then it is likely that WO is very close to the original text. Had the wording of this section in the three subgroups been similar, except for the loss of a few lines, then this would certainly have been the conclusion. But the significant differences in wording between the three versions should urge caution. Texts on the use of the navicula in groups D and E all include a section on finding latitude,14 as do the many texts on the quadrant and the astrolabe, and most practical geometry treatises. And the instructional nature of the prose, and limited technical vocabulary available for treatises on astronomical and timekeeping instruments might account for the apparent similarities between the three versions. Yes, the archetype probably had a section on finding latitude, but it is not easy to tell which of the three versions above is closest to its original wording. It is possible that the archetype could be located between EM and WO on the third stemma (figure 46) (based on items that are present or absent), with a section on finding latitude that looked like the one now found in WO and EM. In this case, the explanation for the existence of the two other versions could be that each branch independently lost the ending of the text, and each reconstructed it according to the material usually found in treatises on astronomical instruments, the PH1, BL1 and PH2 group adding material about telling the time by the stars, and the RA and BL2 group bringing in text on measuring heights and depths, and telling the time in unequal hours. In this case, the

14 Group B texts describe another construction method, and the group C text has been missing since 1838 and its contents are at present unknown.

group a stemmatics

225

loss of the start of the section on finding latitude in PH1, BL1 and PH2 would have to be ascribed to independent copying errors. Perhaps more appealing is the idea that the section on finding latitude was originally closer to that in PH1, BL2 and PH2 (except with the now-missing lines at the beginning telling the user how to set up the instrument) and, after lines were lost, different scribes rewrote the section in different ways, in order to bring back in the necessary instructions. This explanation would account for the fact that it is at this point that the three main subgroups diverge markedly: no material from the ending of BL1 appears in either WO/EM or RA/BL2, except for the latitude table. But even the latitude table is not firm evidence that the three versions of the end of the text are linked. I chapter 4 I argue that the latitude tables in navicula manuscripts, rather than being specifically compiled by the scribe of an early copy of the group A navicula text, are part of a wider tradition, based on several standard versions of the table.15 These tables, in their short, medium and long versions, usually contain the same places and values for latitude and longitude, and were circulated in books of astronomical tables, with quadrant texts, as well as on their own. The tables in navicula manuscripts were probably copied from these sources, so their presence in some but not all of the manuscript copies could indicate little more than the links of all navicula texts to the genre of astronomical instrument texts, and geometrical and astronomical texts more broadly. All of these speculations are, eventually, just that: suggestions for how the texts fit together. None of these stemmas can be seen as a definite representation of the development of the group A construction texts. What is certain, however, given the relationships between the group A manuscripts, and the likely stemmas generated from close analysis of their contents, is that there were many more group A texts than now survive. A conservative estimate based on the branching pattern of the third stemma (from the items present in each version), might be that there were twice as many copies as the nine that now survive. And given the methods used to construct the stemma, and the vagaries of survival of medieval English manuscripts, this is more likely to be an underestimate than an overestimate.

15 On the latitude tables and their links to a standard version of the table that was circulating, see chapter 4.

APPENDIX FIVE

GROUP B NAVICULA MANUSCRIPTS AD: MS Additional 230021 This fifteenth-century parchment manuscript is probably a selection of texts copied from MS Egerton 2622 or from a source common to both. It is in a single, even, hand, and each quire is labelled “1 quaternus” and similar, indicating that the manuscript is complete. The contents are as follows: 1 2 3

[f. 3r] Chaucer’s Treatise on the Astrolabe [f. 29r] on the construction of the navicula [f. 32r] tractatus secundum Galfridum “super Palladium de plantacionibus et insercionibus arborum” [f. 46r] Nicholas Bolard “de generatione, rectificatione et alteratione arborum” [f. 50r] A natural philosophical work

4 5

On f. 2r there is a 1637 table of contents, which says that the navicula text was written by “incerto auctors,” lists the other texts in the manuscript, and states that in 1637 the volume belonged to John Cobbes, of Bury St Edmunds. The manuscript is next known to have been in the possession of Francis Palgrave in December 1842, and then acquired by the British Museum from the collection of M D Turner at auction on 8th June 1859. EG: MS Egerton 26222 This fifteenth-century collection is very closely related to manuscript AD,3 and its contents are as follows:

1

British Museum, Catalogue of additions (1875), 813–4. British Museum, Catalogue of additions (1889), 349–50. 3 Eisner, A treatise on the astrolabe, 53 and 62–3, and Eagleton and Spencer “Copying and conflation” on the relationship between these manuscripts. 2

228 1 2 3 4 5 6 7 8 9 10 11 12 13 14

appendix five [f. 2r] Mnemonic verses on the calendar with explanations in prose [f. 14r] Verse and prose treatise on arithmetic [f. 32v] Sacrobosco on the sphere, last leaf damaged [f. 50r] Chaucer’s Treatise on the Astrolabe [f. 72r] On the construction of the navicula [f. 74r] Treatise on plague [f. 85r] An anonymous natural philosophical work [f. 89r] A treatise on measuring, with diagrams showing the use of a shadow square and quadrant [f. 99r] “tractatus secundum Galfridium [de Vino Salvo] super Palladium de plantacionibus et intersecionibus arborum” [f. 113r] Nicholas Bolard “de generacionibus et modo generandi et plantandi” [f. 117v] Albertus Magnus on Aristotle on comets [f. 136r] Treatise on arithmetic, the prose section of (2) in English [f. 166r] Rules and problems in arithmetic [f. 169v] On the use of the astrolabe

On f. 1r is a table of contents (in a later hand) listing the texts, and there is evidence that in the sixteenth century this volume belonged to Robert Tomsun, Thomas Lowe, John Thackam and Hugh Ramsdon (who received it in partial settlement of a debt). The British Museum acquired it on 17th January 1885 from Captain A Southey. PH1: MS RCP 358 See Appendix 1 for a description of this manuscript. Transcription and translation This text describes the construction of a single navicula (rather than the three templates described in group A texts). The transcription here is based on manuscript PH1, since it contains the only complete version of the work that is currently known; EG and AD stop at line 62, and the variants they witness are included here up to that point in the transcription. Contractions have been silently expanded.

group b navicula manuscripts

229

one {.}etter illegible two {. .}tters illegible more than two {. . .}s illegible <editorial insertion> \scribal insertion/ Ut veraciter et breuiter nauicule composicion habeatur.4 Fiat primo linea| recta in qua ponatur pes circini5 et cum alio pede facias circulum6| ad quantitatem nauiculem7 componende. cuius centrum sit .O. Tunc fa|cias diametrum8 equalum cingentem lineam predictam9 in O puncto.10 cuius| extremitates tangant circulum prefatum.11 et vbi diameter tangit circulum| prefatum12 in sinistra parte notetur punctus per13 .A. vbi vno14 in dextera parte15| notetur punctus per16 .C. et vbi linea primo facta17 circulum in superiori parte| notetur punctus per18 .B. et ex opposito in parte inferiore sit19 punctus .d.| Postea diuidatur .a.b. quarta circuli primo in tres partes20. et qualibet| tercia in alias tres. 21 et erunt diusiones .9.22 et iterum diuidatur qualibet istarum| in duas partes. 23 et iterum qualibet earum24 in .5. partes. et erunt gradus .90.| de quibus ab .a. ad25 .B. sumatur maxima declinatio solis videlicet26| .23. gradus cum dimidio et signetur ibi punctus per27 .F. Similiter ab

4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27

nauicule composicion habeatur] habeatur composicion nauicule AD EG circini] circini immobilis AD EG facias circulum] fiat circulus AD EG nauiculem] nauicule EG facias diametrum] fiat diameter AD EG predictam] priorem AD EG puncto] puncto per angulos rectos AD EG prefatum] omitted AD EG prefatum] omitted AD EG per] omitted AD EG vno] omitted AD EG parte] omitted AD EG per] omitted AD EG facta] facta tangit AD EG per] omitted AD EG sit] notetur AD EG tres partes] duas partes equales AD EG alias tres] illarum in 3 AD EG diuisiones .9.] sex diuisiones AD EG duas partes] 3 partes et erunt 18 diuisiones AD EG et iterum qualibet earum] et quelibet illarum AD EG ad] versus AD EG videlicet] siue AD EG per] omitted AD EG

230

Fig. 47

appendix five

London, Royal College of Physicians, MS 358, f. 19r. Reproduced by permission of the Royal College of Physicians, London.


231

.A. versus| .d. et sit28 punctus .g. Conformaliter sumatur alia29 declinaton a .C.| versus .B. et sit punctus .h. et a .C. versus .d. et sit punctus .I. Deinde| notetur30 a .d. versus .A. et sit punctus .S. et a.d. versus .C. et sit punctus| T. Erunt igitur archus tres videlicet31 .F.G./H.I./et s.t. sibi inuicem| equales. Post hec32 ducatur linea recta33 Ab .F. vsque34 ad .g. et alia35| ab .h. vsque36 ad .I. et secabunt .F.g. et h.I. diametrum .A.C. 37| in duabus punctus equedistantibus ab .O. puncto.38 Ponatur igitur pes| circini imobilis in .o. et39 fiat circulus transiens per puncta40 vbi linee .F.g.| et .h.I. secant diametrum .A.C. qui circulus diuidi debet in .24. partes| equales. et a punctus earum41 eque distantibus a lineis42 .F.G.J.I.| sibi ipsis43 inuicem oppositum ducantur linea recte. et erunt inter illas| duas lineas sit ductas .12. spacia. que dupplicatta sunt| .24. horis diei naturalis corespondencia.44 Et sciendum est quod linea| .H.I. meridiem semper demonstrat. linea vero .F.g. mediam noctem. lineam| et45 inter medie vnam horam ante meridiem. et aliam post meridiem| demonstrat.46 Vlterius pro gradibus mali signandum.47 Erigatur lineam directem48 ab| .A. puncto per quartam diuisam itaque eque distantibus49

28

sit] signetur AD EG alia] eadem AD EG 30 notetur] notetur ead declinacio AD EG 31 tres videlicet] omitted AD EG 32 hec] omitted AD EG 33 recta] omitted AD EG 34 vsque] omitted AD EG 35 alia] omitted AD EG 36 vsque] omitted AD EG 37 et secabunt .f.g. et .h.i. diametrum .a.c.] tunc linea FGHI secabunt AC diameter AD EG 38 puncto] centro AD EG 39 et] tunc AD EG 40 per puncta] omitted AD EG 41 earum] istarum diuisionum AD EG 42 a lineis] omitted AD EG 43 ipsis] omitted AD EG 44 oppositum ducantur linea recte. et erunt inter illas duas lineas sit ductas .12. spacia que duplicata sunt .24. horis diei naturalis corespondencia] sicut sunt puncta AD EG 45 et inter] et linea bd semper .6. horam ante meridiem et post meridiem signat qualibet autem inter AD EG scribe probably missed out a line when copying PH1 46 meridiem demonstrat] signat secundum ordinem quam seruant vt patet faciliter intuenti AD EG 47 signandum] assignando AD EG 48 directem] recta AD EG 49 eque distantibus] equaliter distet AD EG 29

232

appendix five

aliam .O.b. vsque.50 tunc figatur| regulam in o. centro et ducatur ad .5. gradum ab .A. in quarta diuisa. et vbi| regulam tangit lineam erectam ab .A. notetur punctus. Deinde ducatur| regulam ad gradum .10. ab .A. et vbi tangit predictam lineam erectam notetur| punctus. et sit per omnes quintos gradus quousque huius51 .60. gradus vel plures| vel52 pauciores prout placuint. Eodem modo poteris ceteros gradus in eandem| lineam transferre super semper ad quintos gradus in linea erecta fac53 lineas| longiores. tunc ex eadem linea gradus ducantur in malum.54 Postea| vt scribantur55 signa in inferiore parte nauiculem pro gubernacione mali| protrahatur lineam ab .o. per .S. aliqualiter extra circulum magnum. vt continere| valeat gradus et spacia signorum. Similiter56 alia linea fiat ab .o. per .t.| que due dicuntur linea declinacionis. deinde ducatur linea recta| ab .s. ad .T.57 et vbi secat lineam .o.d. sit punctus e58. Tunc super| punctum .e.59 describatur circulus per puncta .s.t. Sed quia signa cum| suis ascensionibus sunt hinc operi noctia. et in circulo directo| absque difficultate magna diuidi non possunt. ideo arce quadam| leni subsequente diuidantur. Ponatur pes circini in puncto| .E. et describatur semicirculem60 per .d. cuius extremitates tangant diametrum| .S.T. ex vtraque parte .E. Tunc ponatur pes circini in fine| eiusdem semicirculi versus .t. et describatur semicirculus magnus per| .s. vsque ad lineam .o.d. Iterum ponatur pes circini in extremitate61| partem semicirculi versus .s. et fiat alius semicirculus per .t. cuius extremi|tates tangant fines semicirculi62 prius facti super lineam .o.d.63 Tunc| circulus obliqus64 ex hiis65 compositus66 diuidatur in .12. partes 50

vsque] omitted AD EG huius] omitted AD EG 52 vel] aut AD EG 53 fac] fiant AD EG 54 tunc ex eadem linea gradus ducantur in malum] omitted AD EG 55 scribantur] inscribantur AD EG 56 similiter] consimiliter AD EG 57 que due dicuntur linea declinacionis. deinde ducatur linea recta ab .s. ad .t.] omitted AD EG 58 e] et AD EG 59 tunc super punctum .e.] tunc ponatur pes circini immobilis in puncto E AD EG 60 semicirculum] semicirculum valde paruus AD EG 61 extremitate] fine AD EG 62 semicirculi] semicirculi magni AD EG 63 .o.d.] od et sit circulus oblongus AD EG 64 obliqus] omitted AD EG 65 hiis] hiis semicirculi AD EG 66 compositus] factus AD EG 51


233

equales. que| sunt .12. signa.67 deinde ab istis porcionibus sic diuisis per regulam| fixam in centro .E. extrahantur signa in circulum directum perintus des|criptum. et vlterius a circulo directo in archum .s.t. 68 hoc modo.| Ponatur regulam super duo puncta opposita in circulo directo| proprinquiora et eque distantia linea .o.d. extense. et vbi| regulam69 tangit70 archum .s.71t. signetur punctus. Eodem modo| fiat per omnes diuisiones circuli directi. et erunt signa diuisa| cum suis ascensionibus in archu .s.72t. deinde extra73 archum .s.74|.t. describantur alii .2°. archus75 vsque ad lineas declinacionis| intercipiendo spacia pro nominibus signorum inscribendorum. Ad huc| extra istos76 archus fiat alius archus cum paruo spacio77 pro gradi|bus signorum inponendorum. Figura78 tunc regulam in centro .o. et a di|uisionibus signatum in archum .s.79t. ducantur linee recte| vsque ad archum exteriorem vlterio iam descriptum. Postea| scribantur nominia signorum in spaciis interceptiis inter istas80 lineas| rectas cingentes archus. ita quod in primo spacio et interiori81| prope punctum .s. scribatur capricornus. in 2°. aquarius. in 3°. pisses. in 4°.| aries. in 5°. taurus.82 in 6° .gemini. Scilicet in83 spacio exteriori| parte .t.84 scribatur cancer. modo contrario. deinde .leo. uirgo. libra.| scorpio. et sagittarius in spaciis ceteris scribantur per ordinem85.| Deinde diuidantur .4. spacia86 equinoctiali propinquiora super| archum exteriorem videlicet quodlibet spacium .in.6. partes equales.| et ducantur diuisiones in paruum spacium interius. quo 67 que sunt 12 signa] incipiendo diuision in altero concursum semicirculorum que erunt 12 signa AD EG 68 archum .s.t.] dyametrum eiusdem AD EG 69 regulam] lineam AD EG 70 tangit] omitted AD EG 71 .s.t.] sdt AD EG 72 .s.t.] sdt AD EG 73 extra] extrahe AD EG 74 .s.t.] sdt AD EG 75 archus] archus super centro O AD EG 76 istos] illos AD EG 77 spacio] spacio .6. AD EG 78 figura] figuratur AD EG 79 .s.t.] sdt AD EG 80 istas] illas AD EG 81 interiori] interiori parte AD EG 82 in 2° aquarius in 3° pisses in 4° aries in 5° taurus] 2° aquarius 3° pisses 4° aries 5° AD EG 83 scilicet in] et in primo AD EG 84 .t.] .t. reuertando AD EG 85 ordinem] ordinem inscribantur AD EG 86 .4. spacia] .4. signorum spacia linea AD EG

234

appendix five

facto| corespondebunt ciulibet signo prius ponito .6.87 parua spacia.| in quorum quodlibet sunt .5. gradus diuidendi. cum operi volueris per| nauiculam. qui deseruient pro mali regiem .5. diebus.88 duo vero| spacia solsticiis proxima diuidendi sunt in 3. partes equales89.| et in qualibet parte sunt .10. gradus signorum suprapositorum. per 10. dies| pro regiem mali seruientes.90 De diuisione signorum in| latere tablule que sit super archum .h.t.i. pro gubernacionem| noduli siue margarite in nauiculam sequitur iam tractare.| Describatur circulus super punctum contactus linearum .o.t. et .h.i. cuius| vna diameter sit .h.i. et altera porcio linea .o.c. extense| Ponatur tunc tunc pes circini immobilis in puncto .C. et| extendatur pes mobilis ad punctum contactus circumferentie dicti circuli .s.| \ad .h./91 et linea .o.t. versus centrum .o. et describatur porcio circuli vsque ad| lineam .h.i. extensam. Et in linea .o.t. signetur punctus tante| distancie a centro prioris circuli quante est .t. ab eodem centro super| quem describatur alia porcio circuli \versus o/92 priori consimilis ex parte op|posita. Istarum vno porcionum extremitates tangant se super lineam| .H.i. extensam diuidantur tunc ille porciones circulorum in| .12. partes equales que sunt .12. signa. et quodlibet signum in .6. partes.| equales partes ea \.4./93 que solsticiis sunt propinquiora. que in .3. partes.| diuidatur. Deinde per omnia sicut/prius extrahe\ban/tur94 signorum diuisiones| a porcionibus signatur \in circulo exteriori/95 in circulum interiorem. et ab illo circulo| in archum .s.d.t. ita hic extremitater diuisiones signate| in dictis porcionibus in circulum descriptum per .h.i. et ab illo in| archum .h.t.i. et sit diuiduntur signa in latere predicto.

87

prius ponito .6.] superius posito sive AD EG diuidendi. cum operi volueris per nauiculam. qui deseruient pro mali regiem .5. diebus] secundum estimacionem diuidendi AD EG 89 equales] equales diuidenda AD EG 90 seruientes.] seruientes et c. text stops here AD EG 91 added at beginning of line, as a correction to the text PH1 92 added above line of text PH1 93 added above line of text PH1 94 added above line of text PH1 95 added in margin PH1 88


235

Ad sciendum intersitum sol in signa quolibet mense Sol Arietem in marcio. intrat Taurum in aprili. Geminos .in. maio. Cancrum in junio. Leonem. in. julio. Virginem. in. aug’. Libram in sept’. Scorp’ in oct’. Sagittarium in neuembē. Capric’ in decē. Aquarius in jan’. Pisces in feb’rum.

12 11 13 13 14 15 14 14 13 12 11 10

2 20 1 12 22 2 18 21 13 13 10 3

12 12 13 13 15 15 15 15 13 13 11 10

8 2 7 18 4 8 0 3 19 5 16 9

12 12 13 14 15 15 15 15 14 13 11 10

14 8 13 10 10 14 6 9 1 11 22 15

12 12 13 14 15 15 15 15 14 13 12 10

20 14 19 6 16 20 12 15 7 17 4 21

di

ho

di

ho

di

ho

di

ho

in anno bi sextili

anno primo post bi sext’

anno 2° post bi sext’

anno 3° post bi sext’

Equinoctium Solsticium Equinoct’ Solstic’

236

appendix five

To truly and quickly have the construction of the navicula. First make a straight line on which the foot of a pair of compasses is placed, and with the other foot make a circle about the size of the navicula to be constructed, whose centre is O. Then make equal diameters on point O, surrounding the foresaid line, whose ends touch the foresaid circle, and where the diameter touches the foresaid circle on the left hand side, point A is marked. Point C is marked where one [is] on the right hand side, and point B is marked where the foresaid line touches the upper part of the circle, and point D is opposite on the lower part. Afterwards the quarter circle AB is divided first into three parts, and each of these thirds into another three, and there will be 9 divisions, and any of these may be divided again into two parts, and again into five parts, and there will be 90 degrees, of which from A to B the maximum declination of the sun is selected, that is 23 and a half degrees, and point F is marked there. Similarly from A towards D, and that is point G. Likewise select another declination from C towards B and it is point H, and from C towards D and it is point I. Then it is inscribed from D towards A and it is point S, and from D towards C and it is point T. Therefore, there will be three arcs, that is FG HI and ST, each equal to one another. After this straight lines are led from F as far as G and another from H as far as I and FG and HI will divide the diameter AC at two points equidistant from point O. Then the fixed foot of a pair of compasses is put on O and a circle is made crossing through the points where the lines FG and HI cut the diameter AC, which circle is to be divided into 24 equal parts, and from each of those points equidistant from the lines FGHI, each mutually opposite to themselves, straight lines are led, and between those two extended lines there will be 12 spaces, which are doubled, corresponding to the 24 hours of the natural day. And it should be known that the line HI always represents midday, the line FG truly [represents] midnight, and in the middle between [them], one hour before midday, and another [one hour] after midday. Further, the degrees on the mast will be marked. Raise a straight line from point A, divided into four, so that each is equidistant from OB. Then a ruler is fixed on centre O and it is led to five degrees from A in that divided quarter, and where the ruler touches the straight line erected from A a point is marked. Then the ruler is led to 10 degrees from A and where it touches the foresaid erected line a point is marked, and it is [done] through every five degrees until 60 degrees of that [quarter] or more or less, just as pleases. In the same way you


237

will be able to transfer the other degrees onto the same line, always above to five degrees on the erected line. Make long lines, then from each line the degrees are led onto the mast. Afterwards, the signs are inscribed on the lower part of the navicula. For setting the mast, a line is extended from O through S just like another outside the large circle, so that it is able to contain the degrees and spaces of the signs. Similarly another line is made from O through T, which two are called declination lines, then the straight line is led from S to T, and where it cuts the line OD is point E. Then above point E a circle is described through points ST. But because the signs with their ascensions are here worked at night, and cannot be divided directly on the circle without great difficulty, therefore a certain auxilliary arc may subsequently be divided. The foot of the compasses is placed on point E and a semicircle is described through D, whose ends touch the diameter ST outside each side of E. Then the foot of the compasses is placed at the end of the same semicircle towards T, and a large semicircle is described through S as far as line OD. Again the foot of the compasses is placed on the outer part of the semicircle towards S and another semicircle is made through T whose ends touch the ends of the semicircle made earlier above the line OD. Then the oblique circle constructed from it is divided into 12 equal parts, which are the 12 signs. Then from those parts the signs, thus divided [using] a ruler fixed on centre E, are drawn out on the guide circle, skillfully described. And further, from the circle directly onto arc ST in this way: the ruler is placed over two nearer points directly opposite on the circle and equidistant from the extended line OD. And where the ruler touches the arc ST a point is marked. In the same way, this is done through all the divisions of the guide circle, and there will be signs divided with their ascensions on arc ST, then outside arc ST another two arcs are described as far as the declination lines, interrupted by spaces for the names of the signs to be inscribed. To this point, outside those arcs, another arc is made with a small space for the degrees of the signs to be assigned. Then a ruler is fixed on centre O and straight lines are led from the divisions marked on arc ST as far as the outer arc, now described further. Afterwards the names of the signs are written in the spaces between those straight lines, surrounding the arcs, so that in the first space and on the inside, near point S, Capricorn is written, in the second Aquarius, in the third Pisces, in the fourth Aries, in the fifth Taurus, in the sixth Gemini. Know that in the outer space [near] T Cancer is written, then, in

238

appendix five

the opposite direction, Leo, Virgo, Libra, Scorpio, and Sagittarius are written in the other spaces in order. Then the 4 spaces nearer the equinoctial are divided above the outer arc, that is each space [divided] into 6 equal parts, and the divisions are led within the small spaces. Which being done, they correspond [with] any sign previously put into the six small spaces, into each of which are divided five degrees, when you want to use by the navicula, which will serve to rule the mast for five days. The two spaces nearest the solstices are truly divided into three equal parts, and in each part there are 10 degrees of the signs above, serving to rule the mast for 10 days. Of the division of the signs. On the side plate which is above arc HTI, for setting of the bead or pearl on the navicula: [it] now follows to treat [this]. Describe a circle above the point of contact of the lines OT and HI, of which one diameter is HI and the other part the extended line OC. Then the fixed foot of the compasses is placed on point C and the mobile foot is extended to the point of contact of the circumference of the said circle, S to H, and the line OT towards centre O. And part of a circle is described as far as the extended line HI. And on line OT a point is marked, of the same distance to the centre of the previous circle as is T from the same centre, above which another part of the previous circle is similarly described, from the opposite part. Concerning one of those, the extremes of the part touch it above the extended line HI. Then this part of the circle is divided into 12 equal parts, which are the 12 signs, and each sign into six equal parts, of which the four nearer the solstices are divided into three parts. Then by all [this], just as before, the divisions of the signs are drawn out from the designated parts in the outer circle into the inner circle. And from this circle on the arc SDT so that the outermost divisions are marked in the said part of the circle described through HI, and from that on the arc HTI, and the signs are divided on the foresaid side.


239

To know the sun’s entrance in the signs in any month The sun enters . . .

Aries in March Taurus in April Gemini in May Cancer in June Leo in July Virgo in August Libra in September Scorpio in October Sagittarius in November Capricorn in December Aquarius in January Pisces in February

12 11 13 13 14 15 14 14 13

2 20 1 12 22 2 18 21 13

12 12 13 13 15 15 15 15 13

8 2 7 18 4 8 0 3 19

12 12 13 14 15 15 15 15 14

14 8 13 10 10 14 6 9 1

12 12 13 14 15 15 15 15 14

20 Equinox 14 19 6 Solstice 16 20 12 Equinox 15 7

12

13

13

5

13

11

13

17 Solstice

11 10

10 3

11 10

16 9

11 10

22 15

12 10

4 21

day hour day hour day hour day hour in a bissextile year

the first the second the third year after year after year after a bissextile a bissextile a bissextile {year} {year} {year}

APPENDIX SIX

THE GROUP C NAVICULA MANUSCRIPT TO2: Trinity O.8.161 This manuscript contained: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26

A calendar A table of eclipses of the sun, 1415–1462 A table of eclipses of the moon, 1406–1462 On eclipses Planetary calendar, with canon On the effect of the moon in the 12 signs [*f. 1r] A short work on lunations [*] Daniel on the interpretation of dreams [*f. 21v] Two treatises on physiognomy [*f. 26r, 34v] A treatise on chiromancy by Master Roderick Majoricus [*f. 41v] A treatise on physiognomy by the same [*f. 51r] Grosseteste on the sphere [*f. 57r] Sacrobosco de Sphaera [*f. 63r] Work on geometry and measuring, with drawings of buildings [*f. 54r] A treatise on chiromancy, with diagrams [*f. 75v] On male and female constellations [*f. 96v] On the hours of planets and their effects [*f. 105r] Walter Brit’s Theorica Planetarum [*] William Rede’s tables, and the canons on them [*f. 122r] Walter Burley on Aristotle on comets [*f. 145r] Richard of Wallingford on the construction of the rectangulus John Slape on the construction of the nauis, quadrant and cylinder The same on the construction of the astrolabe On the use of the astrolabe, with diagrams Three figurae for the construction of the navicula Canon on the calendar which is at the start of the book

The items starred are now in London, British Library, MS Egerton 847, and the folio references for that manuscript are given in square brackets. The other parts have never been found since the manuscript’s

1

James, Western manuscripts in the library of Trinity College.

242

appendix six

theft from Trinity College, Cambridge, in 1838. James2 suggests that they are in MS Egerton 824 (formerly Trinity College, Cambridge, MS O.7.17) but Roberts and Watson have pointed out that the contents don’t match those missing from Trinity O.8.16 and that the manuscript is the wrong size.3 This manuscript first appears in Thomas Allen’s 1622 catalogue of his manuscript library, as number 19 in the octavo section of the catalogue. Unlike the majority of his manuscripts it did not pass via Kenelm Digby into the Bodleian Library in the mid seventeenth century, but was instead acquired by John, Duke of Lauderdale for his private library. On Duke Lauderdale’s death on 24th August 1682 his library passed to his son, Charles, who sold it off in pieces to pay for his lengthy litigation with the Duchess (John’s wife) about his father’s estate. Towards the end of January 1692, part of the Lauderdale manuscript collection was sold off by auction at Tom’s coffee house, by J. Bullord. Several of the manuscripts in the catalogue contain scientific and medical texts, including copies of Chaucer’s Treatise on the Astrolabe and other instrument treatises, and among the books sold was one containing:4 71

2 3 4

Lib MSS in Pergam in 4yo. Quo continentur: 1. Novum Calendarum, cum Eclipsibus ~&d & cum canone eorundem. 2. Kalendarium Planetarum; cujus Canon est in fine Libri. 3. De efficacia Lunae in 12 Signis, cum Domibus Planetarum, Tabula Lunae & Planetarum. 4. Tract. de Lunationibus. 5. Interpretatione Somniorum Dametis [sic]. 6. Physiognomia Aristotelis. Item alius Tractatus Physiognomiae. 7. Chiromantia. Roderici. Item Physiognomia Ejusdem. 8. Tract. Geometrice, Altimetriae, Planimetriae, &c. 9. Tract. Lincoln. de Sphaera. 10. Tractatus communis de Sphaera. 11. Tractatus de Chiromantia cum Manibus & signis depictis. 12. De Constellationibus Fortunae Virorum & Foeminarum. 13. De Horis Planetarum & Effectibus eorundem. 14. Tractatibus M. Walt. Brytte de Theorica Planetarum. 15. Canones super Tabulas Reed, cum Tabulis Ejusdem. 16. Tractatus Burley super Libros Meteorum. 17. Composition Instrumenti Rectangulum vocati. 18. Practica

James, Western manuscripts in the library of Trinity College. Roberts and Watson, John Dee’s library catalogue, 176. Scott, Laing and Thomson, The Bannatyne miscellany, vol. 2, 156.

the group c navicula manuscript

243

Iohannis Slape de Compositione Navis, Quadrantis, & Chilindri. 19. Compositio Astrolabii cum figuris Ejusdem. 20. Practica Ejusdem. 21. Sphaera Pythagorae, cum Nominibus Calculatis. 22. De Membris Astrolabii, &c. 23. Figura Astrolabii & Rethe ejusdem. 24. Tres Figurae pro Navicula. 25. Canon Calendarii Planetarum.

Presumably, the manuscript was bought by John Gale, as it, along with many others in the Trinity College class O, came to the College in 1738 with the bequest of Roger Gale (see also the description of Trinity O.5.26 in Appendix 1). In 1838, 100 years after the manuscript arrived at Trinity College, Cambridge, it was discovered to be missing. Although he always denied it, going as far as to print a pamphlet in his defence,5 the theft was eventually pinned onto James Orchard Halliwell-Phillips. Halliwell (he added Phillips to his name later) began residence as an undergraduate at Trinity College in 1837.6 He was quickly given access to the College manuscripts, and catalogued some of the class O manuscripts. In March and April 1838 a check of the library found 17 or 18 to be missing, and at around the same time Halliwell transferred to Jesus College. In late 1839 Halliwell was in debt, and was forced to sell his manuscript collection of some 300 volumes to settle his bills. He prepared a catalogue titled A catalogue of scientific manuscripts in the possession of J. O. Halliwell, Esq. and began by offering them for sale privately to people and institutions including the British Museum and his old tutor, George Peacock, who had now become Dean of Ely. Peacock declined to buy the collection, and also declined to keep a sample manuscript that Halliwell had sent with the offer letter. The 1839 catalogue of Halliwell’s manuscript collection indicates that MS O.8.16 had already been broken up by this time, since only part of the manuscript is listed.7 The other parts—including the treatise on the navicula—do not appear in the rest of the catalogue, suggesting that either Halliwell had decided to keep them, or that he had already disposed of them, whether by gift or sale. In 1840 Halliwell left Cambridge without a degree, and the manuscript collection was to be auctioned at Sotheby’s on 27th June 1840,

5

Halliwell, Statement in answer to reports. Winstanley, “Halliwell-Phillips and the Trinity College library.” 7 Halliwell, Catalogue of scientific manuscripts, no. 41. These parts of MS O.8.16 are now in London, British Library, MS Egerton 847. 6

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appendix six

following a sale of his printed books earlier in the same month. The sales were poorly attended, and in the end the manuscript sale was cancelled. The catalogue lists 162 manuscripts, not including the navicula text, but including the parts of Trinity O.8.16 listed in the 1839 catalogue.8 Because he hadn’t managed to sell the manuscripts at auction, Halliwell passed them all on to a London bookseller, Rodd, who broke up the collection and sold them. The British Museum bought the part of Trinity O.8.16 included in the catalogues, noticed that it was among those taken from Trinity College, and alerted the College. This is now MS Egerton 847 (bearing Halliwell’s library number 47) and has stayed in the British Library. Trinity College managed to recover 7 or 8 other manuscripts from Rodd, but other texts were never found, including the “Practica Iohannis Slape de Compositione Navis, Quadrantis, & Chilindri.”9 Nor was the missing part of Trinity O.8.16 auctioned with the rest of Halliwell’s library at Sotheby’s on 1st to 4th July 1889.10 A survey of manuscript catalogues reveals no obvious candidates for the missing half of Trinity O.8.16. John North studied the manuscripts of Richard of Wallingford’s Rectangulus (a text also in the missing part of O.8.16), and concluded that the missing Trinity College copy was not among them.11 It seems that this part of the manuscript may have either been destroyed or disposed of, although the hope remains that it is perhaps in a private collection somewhere.

8

Halliwell, Catalogue of a collection of scientific and historical manuscripts, no.

137. 9 10 11

Winstanley, “Halliwell-Phillips and the Trinity College library.” Halliwell, Catalogue of the important library of the late J. O. Halliwell-Phillips. North, Richard of Wallingford, especially vol. 1.

APPENDIX SEVEN

THE GROUP D NAVICULA MANUSCRIPT D: MS Aberdeen University 1231 This miscellany, containing texts in English and Latin, contains: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

1

[f. 1r] Moralised tales [f. 10r, 39rv] Eight questions and answers about liturgical practice [f. 10v] Chaucer’s Treatise on the Astrolabe [f. 31r] Seneca on the four virtues [f. 38v] Horoscope of Henry VII, born 28th Jan 1457, added later [f. 40r] Diagram of a quadrant [f. 41r] Table of the length of daylight [f. 41v] Table of latitudes and longitudes [f. 42r] Text on making a quadrant [f. 44v] Diagram of a quadrant [f. 44v] On the composition of the nauis [f. 47r] Calendar, September-December only [f. 51r] The kings of England [f. 51v] Short verses, including King Arthur and the operations of the months [f. 52r] Table of numbers: cardinal, ordinal, etc. [f. 52v] Table of a great cycle [f. 54r] Annals from year 1 to the death of King Henry I [f. 58v] Table of epacts and concurrents [f. 58v] Mnemonic verses [f. 60r] Table of a great cycle 1437–1968 [f. 61v] Verses on the compotus [f. 62r] The 32 dangerous days and the 7 days for taking blood [f. 63r] Multiplication square [f. 63v] Table of wheat and loaves of bread [f. 65r] Luni-solar volvelle [f. 66r] Text on making a sundial, Latin and English versions [f. 68v] Numbers in mirror-writing [f. 69r] Planetary tables [f. 70v] Table of a great cycle 1386–1917 [f. 71r] Table of the sign of the zodiac in each month

Ker, Medieval manuscripts in British libraries, vol. 2, 4–11.

246 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63

appendix seven [f. 71v] Text and diagrams of solar and lunar eclipses [f. 72v] Weather prognostications [f. 73v] Compass rose diagrams [f. 74r] Volvelle with the signs and months [f. 77r] The complexions of the seasons [f. 78r] Astrological calendar [f. 84r] Cicio Janus and other mnemonic verses [f. 85v] A zodiac man, with explanatory text [f. 87r] “Secundum vsum romanum Triplex est stilus dictaminis. scilicet spondaicus . . .” [f. 87v] Form of an inventory [f. 88r] Seven formulary letters [f. 95r] On the compotus and calendar [f. 116v] Fourteen formulary letters [f. 120v] “Clerici accusati . . .” [f. 121r] “Be it knownen to all crysten men that I am kyng of all kynges . . .” and reply dated 1441 [f. 121v] Invitations to meetings [f. 122r] On the art of writing [f. 131v] Religious verses [f. 132v] Texts relating to St Ursula [f. 136v] “O monachi diabolici pensate quid est . . .” [f. 138r] Hermetic prophecies [f. 138v] Verses on errors and vices [f. 139r] Political verse [f. 140v] Table showing the descent of Henry VI from St Louis [f. 141v] The influences of the planets [f. 145v] Tables of measurement [f. 146v] Verses against women [f. 149v] Divination from dice throwing [f. 153r] Health and bloodletting, and good and dangerous days for it [f. 154v] Prognostications from wind and sun in the 12 days before Christmas [f. 155r] Stanzas on the years of a great cycle starting in 1140 [f. 158v] Table of the names of Christian kings [f. 159v] Charms against fleas, rats and mice, added later

References within the texts indicate that this manuscript can best be dated to c. 1440, and it is linked by dialect to the area around Chester. There are several main hands, one of which is linked to the Augustinian convent of Warrington by a note on f. 72v. Later, the manuscript was owned by William Fitton (note on f. 98v) from Gawsworth, Cheshire, and was given to Aberdeen University Library in 1723 by Robery Barclay of Urry (donation note on f. 8v).

the group d navicula manuscript

247

Transcription and translation The text here is transcribed from the only copy of the group D text that is currently known: AB. Contractions have been silently expanded. one {.}etter illegible two {. .}tters illegible more than two {. . .}s illegible <editorial insertion> \scribal insertion/ Composicio Nauis| irst make acercle and diuide hym by .A.C. and .B.D. diametres| and þe centre or þo myd poynt of þo cercle be called .O. and .A.B. quarter| {. . .} þo ferth part of þo serkle be deuidyd in to .90. degres of þo whik 90| degres fro A toward B take þo most and grettest declinacion of þo sonne| þat is .20. and .3. degres and ahalf degre and make þer f poynt On þo same| wyse be don fro b. toward .A and merk þer .q. poynt Item also fro B| toward c. and mark r. poynt. þen fro C. toward .b. on þo to syde and| toward .d. on þo todyr syde be .ii. poyntis markyd .h. and .I. Also fro .d.| toward .c. and fro .d. toward A. be .s. and .t. poyntis Also fro A toward .d.| be markyd g poynt and þen þer arches þese bowes .A.f. and .A.g. .b.q. and| .b.r. c.h. and .c.I. d.s. and d.t. schal be equall’ ywon elyke quantite Then| Fro .o. be .q. draw out alyne on lenghe And fro A be anoþer lyne draw| Ortogonal wyse and þer as þis lyne cuttys or towchis .o.q. lyne be markyd| .k. poynt. Also fro .o. be .r. on þo same wyse be extend or drawen out| a.ryõt lyne and fror.C. be anoþer lyne drawen ortogonal wyse and where þay| kut or touch be markyd poynt v. Also fro .o. be .s. be anoþer lyne extend| and fro c. be anoþer ortogonal wyse and where þay kut or touche be markyd X| poynt On þo same wyse bedon fro .o. be t. and fro A. and þo poynt of þer cuttyng| be .y. and þen þese lynys k.y. and .vx.2 sal be elyke distaunt elyke far| Fro .b.d. diametre Also be arewlar put on .o. centre and alle þe degres of| .A.B. quarter betwix A and q. be markyd in A.k lyne and þes lynys schal be corespondent| schewand þo latitudys of contres Afterward be þy compas take þo quantite þo| lengh of A k lyne upon .o.k lyne and where þo mouablefote of þo compas| cuttis .o.k. lyne be markyd .z. poynt and

2

.k.y. and .v.x.] probably an error for .k.x. and .v.y.

248

Fig. 48

appendix seven

Aberdeen University Library, MS 123, f. 44v. Reproduced by permission of the University of Aberdeen.


249

þen schal .o.z. lyne be equal elyke| long to .A.k. lyne. This þus don. on þo same wyse drawe alle þe. degres of A.k. lyne in .o.k lyne. þen þo vnmouable fote of þo compas beand| in .o. lede about þo mouable fote be z and make hym cut þes lynys o.v.| .c.x. and o.y. and þe poynt of þo cuttyng of o.v. be cald .l. þe poynt of| cuttyng of .o.x. be P. and þo poynt of cuttyng be P M. of o.y. be| M. and þis cercle .z.l.p.m. schal be circulus articus þe artike cercle| þen fro k to .v. draw aryght lyne and if þy diuision aforn be wele don| or truly made. þat forseyd lyne schal touche þo cercle of z.l.p.m.| in þo poynt where o.b. lyne extend or reryd up and þe same cercle of| .z.l.p.m. touchis or metys þe poynt of þis touchyng be E. On| þo same wyse fro x. to .y. draw anoþer ryõt lyne. and it scal cut .a.d.| lyne extend in þo poynt where .o.d. lyne cutis p.m. porcioun of z.l.p.m.| cercle and þe poynt of þat touchyng be .N. þen alle þe degres markyd {upon} | .o.z. be led about be þy compas þe same wyse or þo porcions of z.l.p.m| cercle upon þo lynys oz. o.l. o.p. o m.o.e. and o.n. Now after al þat| draw aryõt lyne fro F. to .g. and anoþer fro .h. to .I. and þer lynys f.g.| and .h.I. salle cut A.c. diametre in to partis poyntis beand elyk dista{nt}| elyke far fro o. þo centre þe myd poynt put þen þo vnmouable fote of þy compas in .o. and make acercle to þo quantite of þo forsayd cuttyngis of Fg. and h.i.| whilk sercle schal be deuided in to xxtiiiii equal or euyn partis and fro þo| poynt of þo diuisiouns of þo partyngis. beand elyke far to lynys of .f.g.| and .h.i. and to þam selue oppoundyng be drawyn ryõt lynys. and be twen þes| lynes ryõt drawen schal be xii. spacis. whilk spacis doubled ar corespondent| ar answeryng .to xxtiiiii owres of þe day naturel and of þo lynys so draw’| h.I. lyne euermore schewys and sygnifies none or mydday .Fg. schewys| mydnyght and .b.d. euer more .vi. of þo clok befor non and after þe toþer entermene| lynys sum tyme an oure before noun and afterward anoþer oure after non betokyns| as in þo figure truly made playnly it apperys.| de diuisione signorum| Afterward be made diuisions of sygnys on þis wyse Vpon epoynt| be descryued acercle be .k.v. poyntes and k.v. lyne sal be on of his dia|meters. And þe todyr diameter schal be aporcioun of .o.e. lyn extendid Bot| for. þe signys wit þare assensyons. are nesessary to þis werk .and in a direct| cercylle wit owtyn grete difficulte þay may not be discryuyd or diui|did þer for diuid þam wit þis crafte folowand. Opon .e. centre descriue| a lytylle cercle whas semydiameter or. halfdiameter .be a porcion of oe.| lyn. extend qwylke is be twyx .e. and þe poynte of hys towchynge of õl.| cord and apon þe poynte o þe

250

appendix seven

towchynge of þe forsayd lytylle cercle in| e.k. lyn descriue a porcion of a cercle be v. of qwylk porcion þe extremi|tes. salle towch o.e. lyn extend .On þe same. wis on þe poynte of towchyng| of þe same litille cercle in e.v. lyn be discriuyd a lyke porcion of a cercle| be k. poynte and þe extremites of þes porcions salle touch þam selfe opon .o.| e. lyn extend diuid þen þes forsayd porcions in to twelfe euyn| partys qwylke are twelfe signys and ylke a signe in to sex partys outtake| þe foure signis þat are neste þe solstices whylke foure salle be diuidid in| to thre euyn partys. þen fro þere porcions þus deuidid be a reulere| festynd in e. centre. draw oute þe signs and þare diuisions. in to| þe direct cercle descriuyd opon .e. centre be kv poyntis and ferþer so| fro þat direct cercle in to k.v. arch .o þis wys lay þi reular opon þe| poynt be and e lyke far to o.e. lyn extendid qwylke poyntis are agayns| {. . .}þer loky{nge} in þe direct cercle and in þe syd taward k and qwere þe reulere| {t}ouchys b.k. and .v. arch be markyd a poynte and do euyn o þe sam.| {w}yse be alle þe diuisions of þe direct cercle on aþer syd of k.v. arch| {. . .}þe signys salle be diuidid wit þare assensions in k v arch festyn.| {. . .{ {þ}i reulere in o. centre and fro þe diuisions markyd in k v arch| be drawn ryõt lynys to o centre if þe lyst or elle un to þey cut alle þo| arches schewyng þe degres of latitudys on þat syd þen wit owten k.v arche descriue| oþer to arches of what quantite þe lyst and in þo spacis betwene takyn diuyde be þe| inicial lynys of þo sygnys wryte þe namys of þe signys so þat in þo fyrst inder| parti toward v. poynt be wretyn capricornus in þo second aquarius in þo thryd| pyssis in þo .4. Aries in þo fyft taurus in þo .vi. gemini Then in þo fyrst utter or owtward space toward .x. x be wretyn Capricornus. þen aquarius. pisses aries Taurus gemini in þo todyr spacis be wretyn be ordyr And þis is þo inscripcoun| of þo sygnes in þo neþer party of þo schip for gouernans of þo maste| de diuisione signorum in latere| Now it follwys forþermore of þo diuision of signes in þo syde of þe table| whilk is upon .h.c.I. arch for þo gouernyng of þo perle or þe margaryt in þo schip| vpon þo poynt of tuchyng of .o.c. and .h.I. lyns descryue acercyl whos on diameter| schal be .h.I. and þo toþer schal be aporcioun of .e.c. lyne extend Put þen þe| vnmouable fote of þe compas in c poynt and extend þe mouable fote to þo| poynt of tuchyng of circumference of þo forsayd serkylle and of .o.c. lyne toward| o centre and descriue acentre aporcioun of acercyl to it come to h.I. lyne extend| and þen in o.c. lyne be markyd apoynt beand euyn elyke fare fro þe centre of| þo fyrst cercle as is c. poynt fro þa same centre upon whilk poynt| be descriued anoþer porcyon of acercle lyke to todyr porcyoun on þo


251

toþer part| And þen þe extremites of þes porcyons salle touch hemself upon .h.I.| lyne extende if þe dyuision be wele made. deinde þen þo diuisiones of| cercles in to xii. euyn partis whilk ar þo .xii. signes and diuyde ylke signe| in to sex partis owt take þa .iiii. signes whilk ar ner þo solsticies þo| whilk schal be deuyde in to .3. partis: þen on alle wyse as afore is drawn| owt diuisions of signes fro þo forsayd porcyons in to an Inder mor| cercle and fro þat sercle in to k.v. and .y.x. arches so her be dw drawn| owt þe diuisyons markyd in þer forsayd porcyons in to þo cercle d{. . .}| be .h.i. and from þat sercle in to .h. {. . .} .c. I. arch and þus ar had þe si{gnes}| diuidyd in þo syde of þo schip| de diuisione signorum et mensium| And now folwys it of diuisioun of signis and monethis whylk oght| to be wretyn in þo quadraunt and þe chilinder make fyrst acercle nat lyke| to þo cercle last afore. but to3 þo cercle of þo todyr ende of þo table þat is for| to say on þo todyr syde and dyuyde þis cercle in to xii. signes and ylk| asigne in to sex or .iii. partis and for þo poyntis beand contrary or agayn| lokyng on to oþer draw ryõt lynys and note or mark þe poyntis of towchyng| upon y x arch and þen put arewlar upon o centre and be þo poyntys| be ryõt lynys extendid. deuidyng þe space depicte or ordand alouly| to þo signes in þa ende of þo fyrst figure and as afore is don wryte| þo namys of þo sygnes in þer places and þer diuisyons schal be distunt| fro þe toþer diuisions for þes ar not wit ascensyons| de inscripcione mensium per kalendarium| Now it folows of inscripcioun of monethis in þo figure whilk| inscripcioun schal be wroght be þo newe calendar made of frere Ion| Somer And fyrst of þo moneth of Ianuary. loke in þo forsayd lakendar4| in what signe and what degre of þo signe is þo sonne in þo fyrst day| of Ianuare and þen lay þy rewlar festynd in o to þat degre in þo signes| last wretyn or markyd þat is to say to þo xxi degre of capricorne. and in| þo space ordand to þo monthys be mad alang lyne be tokenyng begyn|nyng of Ianuare Then loke in quat degre of þat signe þe sone schal be| in þo .v. day of þat moneth and fro þat degre þat is to say þe xxv degre by a| rewlar layd on hym in þo forsayd space or place be markyd anoþer lyne| schorter þen þo toþer lyne afore markyd And þus do forth be alle þo dayes| of monethis þat ar distaunt be .v. And if þer be mo dayes þen 30. in| amoneth þen lete þo last space stand for 4 dayes and þus schal þou haue| {. . .} monethis truly wretyn in þe fygure. Etc.

3 4

inserted above line of text lakendar] probably an error for kalendar

252

appendix seven The composition of the navicula

First make a circle, and divide it with diameters AC and BD, and [let] the centre or the mid point of the circle be called O, and [let] the quarter AB, the fourth part of the circle, be divided into 90 degrees, of which 90 degrees, from A to B, take the maximum and largest declination of the sun, that is 23 and a half degrees, and mark point F there. In the same way [let it] be done from B towards A, and mark point Q there. Item also from B towards C, [and] mark point R [there]. Then from C towards B on the other side, and towards D on the other side [let there] be two points marked H and I. Also from D towards C, and from D towards A [let there] be points S and T. Also from A toward D [let] point G be marked, and then these arcs, the bows AF and AG, BQ and BR, CH and CI, DS and DT will be equal, with the same quantity. Then from O to Q draw a line one length, and from A [let there] be another line drawn orthogonally, and there where this line cuts or touches line OQ [let] point K be marked. Also from O to R, in the same way, [let] a straight line be extended or drawn out, and from C [let] another line be drawn orthogonally, and where they cut or touch [let] point V be marked. Also from O to S [let] there be another extended line, and from C [let there] be another, orthogonally, and where they cut or touch, [let] point X be marked. In the same way, [let it] be done from O to T, and from A and the point of their cutting to Y, and then these lines KY and VX will be equally distant, equally far from diameter BD. Also [let] a ruler be placed on centre O and [let] all the degrees of quarter AB, between A and Q, be marked on line AK, and these lines will [be] equivalent, showing the latitudes of countries. Afterwards, take the quantity of the length of line AK with your pair of compasses, on line OK, and where the moveable foot of the compasses cuts line OK [let] point Z be marked, and then line OZ will be equal, the same length as line AK. This thus done, in the same way draw all the degrees of line AK on line OK. Then, the immobile foot of the compasses being on O, lead the moveable foot around to Z and make it cut lines OB, CX and OY, and [let] the point of the cutting of OB be called L, the point of cutting of OX be P, and the point of cutting of OY be M, and this circle ZLPM will be circulus articus, the arctic circle, then from K to V draw a straight line, and if the division done before was well done,


253

or truly made, that foresaid line will touch the circle of ZLPM on the point where line OB [is] extended or erected, and [where] the same circle ZLPM touches or meets, [let] the point of this touching be E. In the same way draw another straight line from X to Y, and it will cut extended line AD on the point where line OD cuts the PM part of circle ZLPM, and [let] the point of that touching be N. Then [let] all the degrees marked on OZ be led round with your compasses in the same way, or the parts of circle ZLPM onto the lines OZ, OL, OP, OM, OE and ON. Now after all that, draw a straight line from F to G and another from H to I, and the lines FG and HI will cut diameter AC on two points, equidistant [or] equally far from O, the centre [or] the mid point. Then place the immobile foot of your compasses on O and make a circle, the quantity of the foresaid cuttings of FG and HI, which circle will be divided into 24 equal or even parts, and from the point of the divisions of the parts, being equally far from the lines of FG and HI, and their opposites, [let there] be drawn straight lines, and between these drawn straight lines will be 12 spaces, which spaces [are] double, corresponding or answering to the 24 hours of the natural day, and of the lines drawn, line HI always shows and signifies noon or midday, FG shows midnight and BD always 6 o’clock before noon and after. The other intermediate lines, some [represent the] time an hour before noon and afterwards; another represents an hour after noon, as appears clearly in the figure, [if] correctly made. Of the division of the signs Afterwards the divisions of the signs are made in this way. On point E [let] there be described a circle to points K [and] B, and line KB will be one of its diameters. And the other diameter will be a part of the extended line OE. But for the signs with their ascensions, [they] are necessary for this work, and on a guide circle they may not be described or divided without great difficulty, therefore divide them with this following method. On centre E describe a little circle whose semidiameter or half diameter is a part of the extended line OE, which is between E and the point of its touching of chord ZL. And upon the point of touching of the foresaid little circle on line EK, describe a part of a circle to V, the outsides of which part will touch the extended line OE. In the same way, on the point of touching of the same little circle

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on line EV, [let there] be described a similar part of a circle to point K, and the outsides of these parts will touch each other on the extended line OE. Then these foresaid parts are divided into 12 even parts, which are the twelve signs, and each take a sign into six parts, except the four signs that are nearest the solstices, which four will be divided into three even parts. Then from these parts thus divided, [let] a ruler be fastened on centre E, [and] draw out the signs and their divisions onto the guide circle described on centre E to points KV, and further, from that guide circle onto arc KV, in this way: lay your ruler on the points being equally far from extended line OE, which points are again [. . .] there, looking on the guide circle and on the side towards K, and where the ruler touches BK and arc V [let] there be marked a point, and do again in the same way, [so that] all the divisions of the guide circle are on the other side of arc KV [. . .] The signs will be divided with their ascensions on arc KV, fasten your ruler on centre O and from the divisions marked on arc KV, [let] straight lines be drawn to centre O, if you like, or else until they cut all the arcs showing the degrees of latitude on that side, then, outside arc KV, describe another two arcs of what quantity you like, and in the spaces between the initial lines of the signs write the names of the signs so that in the first inner part towards V, [let] Capricorn be written, in the second Aquarius, in the third Pisces, in the fourth Aries, in the fifth Taurus, in the sixth Gemini. Then in the first lower or outer space towards X [let] Capricorn be written, then Aquarius, Pisces, Aries, Taurus, Gemini, in the other spaces [let] the others be written. And this is the inscription of the signs on the lower part of the ship for setting of the mast. Of the division of signs on the side Now there follows, furthermore, the division of the signs on the side of the plate, which is upon arch HCI for the setting of the pearl or the margaryt on the ship. Upon the point of touching of lines OC and HI, describe a circle, one diameter of which will be HI and the other will be a part of the extended line EC. Then place the immobile foot of the compasses on point C and extend the moveable foot to the point of touching of the circumference of the foresaid circle and of line OC towards centre O, and describe part of a circle as far as the extended line HI. And then on line OC [let there] be marked a point, being even [or] equally far from the centre of the first circle, as is point C from


255

the same centre. Upon which point [let] another part of a circle be described, similar to the other portion on the other part. And then the outsides of these parts will touch each other on the extended line HI if the division is well made. Deinde then [make] the divisions of circles into 12 equal parts, which are the 12 signs, and divide each sign into 6 parts, apart from the 4 signs which are nearest the solstices, which will be divided into 3 parts. Then in the same way as before the divisions of the signs are drawn out from the foresaid parts onto the innermost circle, and from that circle onto arcs KV and YX, and so here the divisions marked on the foresaid parts are drawn onto the circle [d . . .] to HI and from that circle onto H[. . .], arc CI and thus the signs are divided on the side of the ship. Of the division of the signs and the months And now there follows the division of the signs and months, which should be written on the quadrant and the cylinder. First make a circle not like the circle made just before, but [like] the circle of the other end of the plate, that is to say on the other side, and divide this circle into 12 signs, and each sign into six or three parts. And for the points, being contrary, or looking at one another, draw straight lines and note or mark the point of touching upon arc YX, and then put a ruler upon centre O, and [let] straight lines be extended to the points, dividing the space, dedicated or ordered along to the signs on the end of the first figure, as was done before. Write the names of the signs in their places, and their divisions will be distant from the other divisions, for these are not with ascensions. Of the inscription of months by the calendar Now there follows the inscription of the months in the figure, which inscription will be done according to the new calendar made by brother John Somer. And first of the month of January: look in the foresaid calendar at what sign and degree of the sign the sun is in on the first day of January, and then lay your ruler fastened on O to that degree in the signs written or marked before, that is to say to the 21st degree of Capricorn. And in the space dedicated to the months [let] a long line be made, representing the beginning of January. Then find in what

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degree of that sign the sun will be in the fifth day of that month, and from that degree, that is to say the 25th degree, with a ruler laid on it in the foresaid space or place [let] another line be marked, shorter than the other line marked before. And do thus for all the days of months that are distant by five, and if there are more days than 30 in a month, then let the last space stand for four days, and thus you will have [. . .] the months, truly written in the figure, etc.

APPENDIX EIGHT

THE GROUP E NAVICULA TEXT E: MS Ashmole 1881 This quarto collection of texts contains five parts, written in different hands. The first part was probably copied c. 1535, since the work preceding that on the navicula discusses the planets in that year. I 1 2

[f. 2r] An astrological work on the airs and stars [f. 97r] Libellus de Usu Naviculae2

3

A sixteenth-century treatise on astrology, anonymous

4

Predictions for 1597–1602, Rev. Richard Napier

5

An astrological work, transcribed by Elias Ashmole

6

Balemyne De Sigillis Planetarum, perhaps dedicated to an amanuensis by Ashmole

II III IV V

Transcription and translation The text here is transcribed from the only copy of the group E text currently known: AS.3 Contractions have been silently expanded. one {.}etter illegible two {. .}tters illegible more than two {. . .}s illegible <editorial insertion> \scribal insertion/

1

Black, Manuscripts bequeathed unto the university by Sir Elias Ashmole, 150. Black, Manuscripts bequeathed unto the university by Sir Elias Ashmole, 150, has the erroneous statement “sive instrumenti cujusdam meteorologici” after the title. 3 I am grateful to the Cambridge Latin Therapy Group for their help with the translation of this text. See Eagleton et al., Instruments of translation. 2

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Libellus de usu naviculae.| Quamquam varia sunt instrumenta, ex quibus certitudo horarum dignoscitur,| ortus item et occasus solis, longitudines et brevitates dierum ac noctium| et id geminae alia. verum ex omnibus nullum mihi videtur instrumentum quod tot| regionibus deservit et tantas secum affert comoditates vt navicula quoniera| eius versum et utilitates succinctiori modo quo fieri potuit tua dominales in | explicauimus. Atque vt res ipsa dilusidior evaderet totum hoc instrumentum| in 7 capitula distinximus et capitulorum epitomas prout inferius patet| subiunximus.| Capitulorum epitome.| 1: Primum caput quomodo in omnibus fere regionibus per naviculam horae sunt investigandes| 2: Caput 2m. de tempore quo ~ singulis diebus oritur et occidit.| 3: Caput 3m de quantitate diei et noctis.| 4: Caput 4m de latitudine cuiuscumque regionis invenienda.| 5: caput .5. quomodo horae inequales sive horae planetarum perscrutandae sunt| 6: Caput .6. de altitudinibus et profunditatibus rerum mensurandis.| 7: Caput 7. de introitu solis in principia signorum| Caput primum quomodo in omnibus fere regionibus| per naviculam horae possunt inveniri.| Si horam vulgarem per instrumentum naviculae cognoscere velis oportet vt| primo latus infernum ipsius cursoris super gradum altitudinis poli tuae regionis| collocetur (cursorem autem appello armillam parvam malo adherentem quae nunc| sursum nunc deorsum, pro vt tibi libuerit, moveri possit) Constituto cursore super| gradum altitudinis poli in ipso malo consitutum notatum, convenit vt liniolae quae in| pede ipsius mali reperitur. ad gradum loci solis in zodiaco extendatur, deinde| filum protrahito. vsque ad gradum solis. in zodiaco qui in dextro navis latere depin|gitur; et vnionem sive margaritam filo adherentem super gradum ~ in illo zodiaco.| laterali opponas. Postremo facie nauis ad te versa levum naviculae castellum| versus solem irradiantem elevato (.levum autem naviculae castellum dicitur quod| in leva tenetur manu dum facies naviculae ad te versus statuatur. Cum| igitur levum navis castellum ad radios solares elevatum habeas et filo libere pendente| ipsum tam diu instrumentum sursum deorsum moveto, donec radii solares| vtraque castellorum foramina penetraverint. Nam tunc vnio sive margarita| fili horam propositam tibi certissime denunciabit.| Caput secundum de tempore quo ~ singulis| diebus oritur et occidit.| Cursorem super gradum elevationis poli tuae regionis constituito. pedeque mali| opposito ad gradum ~ in zodiaco si filum cum lineis horariis paralelum pendire| facias ad situm ipsius fili, ortum et occasum ~ apertissime perspicies.| Caput tertium de quantitate diei et noctis.| Cognito tempore situli capite supe-

the group e navicula text

259

Fig. 49 Oxford, Bodleian Library, MS Ashmole 188, f. 97r. Reproduced by permission of the Bodleian Library, University of Oxford.

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riori declaratum est quo ~ occidit| illud idem tempus duplicato et proveniet productio diei longitu{di}|nam verissime declarabit. Exi causa. cum ~ 24. gradum H devolui{tur}| in regione cuius elevatio est 52: si filum cum lineis horariis paralel{um}| pendeat, tempus quo ~ occidit erit hora octaua. hoc scilicet \igitur/ tempus| scilicet horas octo duplicabis. et productum scilicet hora: 16: erit longitudi{ne}| diei artificialis in regione cuius elevatio est 52: inquodque dum sol| 24 gradum ~ dilabitur. Et se eandem diei quantitatem a 24: h{orae}| recte subtraxero. quod remanet erit ipsa longitudo noctis videlicet| horae :8: Si quantitas diei fuerit hora :16: longitudo noctis erit 8: horarum| Nam vbi 16: horas a 24 horis subtraxeris risiduae erunt 8 horam| hactenus de hors quae ad ad navis faciem attinent.| Caput 4m. de latitudine cuiuscumque regionis inveniendo| In naviculae dorso quartam circuli partem in 90: gradus diuiso| reperies. cuius ad miniculo. latitudines cuiuscumque regionis igno{ta}| hoc modo perscrutari possis. Quum ~ lineam attigerit meridianam dors{um}| naviculae ad te conversum habeas. et levuum castellum solem versus erigitur| donec radii solares utraque castellorum foramina transierint: tunc| enim filum libere pendens. gradum altitudinis solis in ipsa quarta| circuli parte quae in 90: gradus diuiditur ostendet hoc parte.| Cognita ~ altitudine. meridionalem declinationem solis (modo in| signo boriali fuerit) ab eadem .s. altitudine meridionali subducito| at si ~ sub signo meridionale \devolvatur/ fuerit, tunc solis declinatio altitudi{ne}| eius meridionali apponenda est et quod inde conficitur a 90: gradibus| semper est anferendum est. remanens cuius poli altitudinem| sive latitudinem regionum indicabit.| Caput quintum quomodo horae inequales id est horae plane| tarum inveniuntur|Altitudinem ~ meridionalem (vt in proximo capite declaratum est)| accipias. filumque per ipsum gradum meridianae altitudinis extendas| quo fixa moveatur. vnionem sive margaritam ad lineam horae sextam| moveas, et deinde instrumento versus solem erecto, quae radii solar{es}| vtraque castellorum foramina penetraverint vnio sive margarita| horam inaequalem quaesitam ostendet.


261

A little book on the use of the navicula Although there are various instruments from which the certainty of the hours may be known, the rising and setting of the sun likewise, the length and shortness of the days and nights, and other things of double nature. However, out of all of them, there seems to me to be no instrument which serves so many regions and brings with it so many uses as the navicula, because of its back and its utility, [and] we have explained below the efficient manner in which it can be made your domain. And that this matter may be clearly explained, we have divided all this instrument into 7 chapters, and have added summaries of the chapters, just as it appears below. Chapter summaries: 1 the first chapter: how in almost any region the time is found by means of the navicula 2 second chapter: on the time at which the sun rises and sets on particular days 3 third chapter: on the length of day and night 4 fourth chapter: on discovering the latitude of whichever region 5 fifth chapter: how the unequal hours or planetary hours are examined 6 sixth chapter: on measuring the height and depth of things 7 seventh chapter: on the position of the sun in the principal signs

First chapter. How in almost4 all regions the hours can be found by means of the navicula If you want to know the common time by means of the navicula instrument, it is necessary first to place the lower edge of the cursor over the degree of altitude of the pole5 of your region (I call “cursor” the little ring attached to the mast which may be moved up or down as you like). With the cursor placed over the degree of altitude of the pole marked on that mast, so fits the little line which is found at the foot of the mast, to be extended to the degree of the sun’s position in

4

Because of the tilting mast on the navicula, it can only be used easily at latitudes between 30 and 60 degrees. As this area includes most of Europe, it was probably not a practical limitation for most users. 5 The ‘altitude of the pole’ gives the value of latitude of a place.

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the zodiac, then pull the thread as far as the degree of the sun in the zodiac, which is depicted on the right-hand side of the ship, and place the vnio or bead6 attached to the thread over the degree of the sun in that zodiac on the other side. Finally with the face of the ship7 turned towards you raise the left castle of the navicula towards the shining sun (that castle of the navicula is called ‘left’ which is held in the left hand while the face of the navicula is positioned towards you[)]. So when you are holding the left castle of the ship raised to the rays of the sun, and with the thread hanging freely, so move the instrument further up and down until the rays of the sun have entered both holes of the castles. For then the unio or pearl of the thread will most surely show you the sought-after time. Second chapter on the time at which the sun rises and sets on particular days Position the cursor over the degree of elevation of the pole in your region, the foot of the mast having been placed opposite to the degree of the sun in the zodiac. If you make the thread hang parallel with the hour lines, by the position of the string you will clearly see the rising and setting of the sun. Third chapter on the quantity of day and night Local time being known, as revealed in the chapter above, is where the sun sets, double that same time and the increase in the length of the day, for instance, will be truly declared. Because when the sun descends 24 degrees [in] Cancer in a region whose elevation is 52, if the thread hangs parallel with the hour lines, the time at which the sun sets will be 8 o’clock. Then you will double this time, that is 8 hours,

6 Margarita is here translated as ‘bead’ rather than the more literal ‘pearl’. In other medieval and early modern texts on astronomical instruments the bead on a plumbline is called margarita although it usually refers to a metal bead rather than a pearl. See ‘margarita’, in Howlett (ed.), Dictionary of Medieval Latin, fascicule VI. Vnio is the name for a large single pearl, and so has here been left in Latin in the translation. As with margarita, it is unlikely that this should be taken to indicate that astronomical instruments were jewel-encrusted in the sixteenth century! 7 navis and navicula are here distinguished, although both are used as names for the instrument in the fifteenth and sixteenth centuries. See pp. 4–5.


263

and the product, that is 16 hours, will be the length of the artificial day in a region whose elevation is 52 degrees and in each as long as the sun is falling [through] 24 degrees [of] Cancer. And I correctly subtract the same quantity of day from 24 hours, what remains will be [itself] the length of the night, namely eight hours. If the quantity of the day is 16 hours, the length of the night will be eight hours. For when you subtract 16 hours from 24 hours the remainder will be eight hours; this is enough regarding the hours which pertain to the front of the ship. Fourth chapter on the latitude of any unknown region On the back of the navicula you find a quarter circle divided into 90 degrees with the aid of which you can examine the latitude or of any unknown region in this way. When the sun touches the meridian line, you hold the back of the navicula turned towards you, and the left castle is raised towards the sun, until the rays of the sun pass through each of the holes of the castles: for then, the thread hanging freely, shows on this side the degree of altitude of the sun on that quarter circle itself, which is divided into 90 degrees. With the meridional altitude of the sun known, subtract the meridional declination of the sun, provided that it was in a northern sign, from the same meridional altitude, but if the sun was beneath a southern sign, then the declination of the sun is to be added to its meridional altitude, and what is produced thence is always to be subtracted from 90 degrees, of which [what] remains shall indicate the altitude or latitude of the pole of these regions. Fifth chapter: How the unequal hours, that is planetary hours, can be found Take the meridional altitude of the sun, as was revealed in the previous chapter, and extend the thread from the fixed end whence it is moved, across the degree of the meridian altitude line. Move the unionem or pearl to the 6 o’clock line, and then with the instrument raised towards the sun, so that the rays of the sun pass through the holes on each castle, the unionem or pearl shows the sought after unequal hours.

APPENDIX NINE

ORGANUM PTOLOMEI ITA SIT . . . V1: Vienna, Austrian National Library, MS 54181 This manuscript contains several texts on instruments, and dates from the first half of the fifteenth century. A colophon on f. 24v reading “Explicit composition quadrantis profatii iudei 1434” gives an earliest possible date for the copying of the manuscript. 1. [f. 1r] Profatius Judaeus Compositio novi quadrantis et de utilitate eiusdem 2. [f. 80r] G. Marchionis, Tractatus de quadrante eiusque usu et utilitatibus 3. [f. 111r] Tractate de compositione quadrantis, inc: Geometrie due sunt partes 4. [f. 146r] Illustrated text on the cylinder dial, followed by other dials 5. [f. 180r] Organum Ptolomei text, with diagram 6. [f. 182v] Other texts on instruments, including the quadrant, cylinder, and rules 7. [f. 209r] On the Achaz dial 8. [f. 213r] Text on the geometrical square V2: Vienna, Austrian National Library, MS 53032 This manuscript is very closely related to V1, and it contains many of the same texts, in the same order. Other texts have been added, so although the copy of the organum ptolomei text in this manuscript is very similar to that in V1, with a similar diagram, they perhaps derive

1 Österreichische Akademie der Wissenschaften, Tabulae codicum manu scriptorum, vol. 4, 121. 2 Österreichische Akademie der Wissenschaften, Tabulae codicum manu scriptorum, vol. 4, 93.

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from a common source rather than V2 having been copied from V1. The manuscript’s handwriting suggests a date of the early sixteenth century for the codex, which is supported by a colophon on f.359v reading “Explicit utilitatis Albionis Anno 1520 10 kalends februm.” 1. [f. 1r] Tractatus de motu ambitus et polygonii 2. [f. 11r] Johannesde Chinemve Commentarius in demonstrationes Archimedis 3. [f. 22r] blank leaves 4. [f. 27r] Propositiones tredecim de doctrina sinuum 5. [f. 87r] Jordanus de Nemore, Arithmetica 6. [f. 107r] Georg Peurbach, Theorica Planetarum 7. [f. 130r] Profatius Judaeus De compositione novi quadrantis et de eiusdem utilitatibus 8. [f. 199v] G. Marchionis Tractatus de compositione quadrantis incurvati et eiusdem usu 9. [f. 228r] Text on the cylinder dial 10. [f. 242r] Text on a dial in a concave sphere 11. [f. 253v] Organum Ptolomei text, with diagram 12. [f. 182v] Other texts on instruments, including the quadrant, cylinder, and rules 13. [f. 209r] On the Achaz dial 14. [f. 213r] Text on the geometrical square 15. [f. 291r] Richard of Wallingford, Albion 16. [f. 347v] Text on the saphea 17. [f. 352r] Richard of Wallingford, Albion (continuted) Y: Yale Medical-Historical Library, MS 253 This manucript, probably copied in the mid-fifteenth century, consists of a collection of astronomical and mathematical texts. The manuscript parts are bound with a 1482 edition of Euclid’s Elements, and calculations for the year 1425 (on f. 73r) suggest that the manuscript may have been copied before the printed book was added to the volume.

3

Faye and Bond, Supplement, 59.

organum ptolomei ita sit . . . 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19.

267

[f. 1r] De virga visoria [f. 56r] Franco de Polonia, Compositio et usus torqueti [f, 65r] De gallaxia [f. 68v] Beda, De planetis [f. 73r] Calculations for the year 1425 [f. 73v] Beda, De natura rerum [f. 74r] On weather and the calendar [f. 84v] Johannes Symonis de Zalandria Speculum planetarum [f. 92r] Organum Ptolomei text [f. 93v] Johannes de Lineriis, Canones tabularum [f. 102v] Compositio quadrantis [f. 108r] De compositione et utilitatibus astrolabi [f. 115r] On cylindrical clocks [f. 117r] Petrus Peregrinus de Maricourt Epistola de magnete [f. 120r] Instructions for making a church clock [f. 125r] Instructions for building an organ [f. 127r] De compositione clavicordii [f. 128r] Gerardus Cremonensis Theorica planetarum Euclid, Elementa Geometriae (Venice, Ratdolt: 1482) M: Munich Bayerische Staatbibliothek MS Lat 241054

This manuscript is linked to the astronomical teaching at the University of Vienna.5 The manuscript was probably copied in the earaly sixteenth-century, perhaps soon after the works by Stiborius were composed, and around the time that the 1514 tables added at the back of the volume were printed. 1. [f. 1v] De instrumento astronomico Abion et de utilitatibus eius 2. [f. 52v] Compositio armilararum cum additione Tegernseensis cuiusdam 3. [f. 58r] Ueber den Sonnenring als Stundenzeiger 4. [f. 59r] Bonus de Latis De annulo astronomico 5. [f. 65v] Erklärung des Instrumentes der nachthorne und (der) quadranten 4 5

Halm and Laubmann, Catalogus codicum latinorum, vol. II pt. 4, 119. Hayton, Astrologers and astrology in Vienna.

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6. [f. 67v] Organum Ptolomei text 7. [f. 69r] Andreas Stiborius Canones Saphee 8. [f. 85r] Andreas Stiborius Canones super instrumenti utilis quod organum Ptolomei vocant 9. [f. 89r] Johannes de Sacrobosco Sphaera 10. 1514 Tanstetter ed. of Tabula eclipsium Magistri Georgii Peurbachii. Tabulae Primi Mobilis Joannis de Monteregio. Salzburg Saint Peter’s Library Inc 8006 I have been unable to examine this manuscript since it was sold on an unknown date to an unknown buyer, and is no longer in the library.7 According to the available description of the volume, it was copied during the fifteenth century, in several hands, and includes some of the same texts, in the same order, as manuscript Y. Despite the close correspondence between the works, their order, and folio numbers, it is unlikely that this is identical with manuscript Y. For example, this manuscript has Alfraganus on the mansions of the moon (ff. 75v–79v), tables of the planets and the moon (ff. 80r–82r), a work on the Jacob staff (ff. 82v–84r), Johannes Simon Speculum planetarum (ff. 84v–90v) and the organum ptolomei text (ff. 91r–93v, illustrated with a diagram). Manuscript Y has in the same place notes on weather and the calendar (ff. 74r–84r), Johannes Simon Speculum planetarum (ff. 84v–91v), and the organum ptolomei text (ff. 92r–93v). But manuscript Y is still in its original fifteenth century binding, so these differences are unlikely to be due to twentieth-century alteration of the manuscript, and perhaps instead indicate that the Salzburg manuscript, if still extant, is a very close relative of manuscript Y. 1. 2. 3. 4. 5. 6.

[f. 1r] Virgam visoriam [f. 56r] Composicio Torqueti [f. 60r] De utilitatibus torqueti [f. 65r] De gallaxia et de constellacionibus [f. 68v] Beda De planetis [f. 75v] Alfraganus De mansionibus lune

6 See http://jordanus.ign.uni-muenchen.de/cgi-bin/iccmsm?seite=home&sprache= en (accessed 25 February 2008). 7 Communication of 2nd March 2004, from P. Petrus Eder at the Library.

organum ptolomei ita sit . . . 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19.

269

[f. 80r] Tabula aspectus planetarum ad lunam [f. 82v] Compositio baculi jacob [f. 84v] Johannes Simon de Zelandia Speculum planetarum [f. 91r] Organum Ptolomei text, with diagram [f. 93v] Johannes de Lineriis Canones tabularum [f. 102v] Compositio quadrantis [f. 108r] Compositio astrolabii [f. 109r] Canones ipsius Astrolabii [f. 115r] Johannes Schindel Compositio cylindri [f. 116v] De compositione horararii per Magnetem [f. 120r] De compositione horologii pulsantis [f. 126r] Mensura ad faciendum opus organicum [f. 128r] Theorice planetarum antique Transcription and translation

As explained in chapter 7, texts on the organum ptolomei form a somewhat nebulous group. Here I transcribe one of the texts on the instrument; the one beginning “organum ptolomei its sit. . .”, based on manuscript V1, the earliest copy of the text. Contractions are silently expanded. one {.}etter illegible two {. .}tters illegible more than two {. . .}s illegible <editorial insertion> \scribal insertion/ Incipit compositio Organi ptolomei8| Organum ptolomei ita sit ¶Fiat in lamina circulus| abcd cuius centrum e ¶Qui quadretur duabus dya|metris ac et bd ¶Et dyameter ac ducatur9| ex utraque parte extra circulum aliquantulum ¶Deinde quelibet| quartum10 diuidatur in tres partes equales et erunt signa Et| quodlibet signum .3011 gradus uel

8 Incipit Organum Ptolomei] om. Y Compositio organi Ptolomei mathematicorum principis M 9 ducatur] ducitur Y 10 quelibet quartum] qualibet quartarum M V2 11 .30.] in triginta V2

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Fig. 50 Vienna, Österreichische Nationalbibliothek, MS 5418, f. 180r. Reproduced by permission of Österreichische Nationalbibliothek, Vienna.

organum ptolomei ita sit . . .

271

secundum quod12 apparet ¶Deinde pone| regulam super principium vnius signi ante b et super finem alterius| post b et duc lineam que applicet ex vtraque parte circumferencie| abcd et in contactu huius linee et dyametri bd fac punc|tum g ¶Et secundum quantitatem13 eg fac circulum occultum fg|hk Ita ut f stet14 sub ag15 sub b et c ¶Deinde ponito16 pede17| circini immobili in a et mobili extenso in e circinem18 arcus circuli| usque ad circumferenciam circuli abcd ex utraque sui parte19 que sit lem| ¶Deinde circulum fghk incipiendo20 ab aliqua dyametrorum| diuide in 24 partes equales tunc ponita21 regula super duas proximas| diuisiones circa g trahe similiter lineam ¶Deinde iterum ponita regulam| super alias duas diuisiones immediate sequentes22 trahe terciam lineam23 et sic et 4tam {. .}ciis24 usque ad 13 quam 13am trahes per| punctum k sicut fecisti per g25 quamlibet incipiendo ab inferiori| parte circuli26 abcd et terminando in circulo lem ¶Et hec 13| linee includunt27 12 spacia que spacia horaria vocabuntur et| linee extreme sunt linee meridiane28 ¶Deinde ab a versus b| unam declinacionem solis scilicet 23 gradu 30 minuta que sit ap ¶Item ac| versus b que sit cq ¶Deinde pone regulam super p et q29 et vbi| regula tangit dyametrum bd fac punctum n et secundum quantitatem en duc circulum occultum que30 diuide in 12 partes equales| ab aliqua dyametrorum incipiendo ¶Deinde pone regulam super duo| puncta proxima circa n et vbi regula intersecat circumferenciam| bc fac punctum r ¶Et iterum31 pone regulam super alia duo puncta| proxime sequencia Et vbi regula

12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31

quod] que Y quantitatem] om. Y stet] stat M ag] a et g M ponito] posito Y M V2 pede] b d V2 circinem] circuietur Y V2 sui parte que] parte sui que Y, sui qui M incipiendo] incipito M ponita] posita M V2 circa g trahe . . . diuisiones immediate sequentes] immediate sequenter M terciam lineam] terciam M [. .]iis] [. .]ois Y etc M [ . . .]ciis V2 g] in Y circuli] circuli per M includunt] includent Y linee meridiane] meridiane linee M Deinde pone regulam super p et q] om. M que] quem Y Et iterum] iterum Y M

272

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intersecat32 circulum bc fac| punctum b33 ¶Item ultra dyametrum ac pone regulam super duo| puncta iterum34 proxima et fac signum in circulo c d que sit t35 Item| super duo puncta et in circulo fac signum v36 ¶Erit igitur inter| duo puncta qr signum37 capricorni ¶Et inter rs locus aquarii| ¶Et inter {vt}38 { . . .} locus piscis39 Et inter c t locus arietis| ¶Et inter tv40 locus thauri Et locus geminorum inter vx41| scilicet finem maxime declinacionis secunde quam invenies sicut priorem| ¶Pone igitur regulam super eq et extra circulum bc duc lineolam| quasi produobus uel tribus uel quantis placet spaciis que sit| qy ¶Et similiter duc aliam42 ei equalem que sit xz ¶Deinde secundum| quantitatem ez43 duc arcum zy ¶Et similiter duc alios arcus inter| xz pro signis et eorum gradibus et nominibus ¶Et si placet eciam pro| mensibus ¶Deinde aprincipiis signorum scilicet a notis rstv ad| arcum zy duc similiter lineas inter quas scribe diuisiones et| nomina signorum ¶Alia sex signa transuersim inscribendo et| id pes organi dicitur| Deinde latitudines regionum sic invenies Dum volueris habere44 latitudinem 15 graduum pone regulam super punctum b| Et super finem 30 graduum a d versus a computando| et ubi regula secat dyametrum ac fac signum quia id denotat| latitudinem 15 graduum Et si volueris habere45 latitudinem 30 graduum pone regulam| super punctum b et super finem 60 graduum a d similiter versus a com|putando46 Et vbi regula secat dyametrum ac fac signum quia| ibi est latitudo 30 graduum Et sic semper duplos47

32

regula intersecat] intersecat Y b] s M 34 iterum] om. M 35 proxima et fac signum in circulo c d que sit t] proxima diametro dicta et in circulo fac signum t M 36 Item super duo puncta et in circulo fac signum v] Iterum pone regulam super alia duo puncto proxime sequentia et vbi regula intersecat circulum ibi fac signum v M Item super duo puncta et in circulo fac signum v ultimus punctus signes littera x p’ finis V2 37 qr signum] q et r situs M 38 [vt]] vt Y sc M V2 39 piscis] piscium M 40 tv] t et v M 41 vx] v et x M 42 duc aliam] duc lineolam quasi pro duabus uel tribus uel quantis placet spaciis que sit qv Et similiter duc aliam Y 43 ez] cz V2 44 habere] scire’ Y 45 habere] scire Y 46 computando] computandi Y 47 duplos] duples M 33


273

gradus a d uersus| a et ultra48 per a versus b si opus fuerit pro singulis gradibus| latitudinis inveniendis capiendo| Quibus49 sic habitis malum sic aptabis ¶Recipe cuspidem| quadam50 que sit longa sicut linea media instrumenti apede| eius inclusiue computando per omnes latitudines sursum| usque ad 60 uel plus uel minus secundum quod plures uel pauciores| volueris habere51 latitudines ¶Tamen52 que eciam particula eius quedam| ultra pedem promineat ¶In cuius medio directe53 trahatur vna li|nea sic54 recta in qua linea acentro incipiendo signentur latitudines| eodem penitus55 sicut prius in linea media scilicet. in dyametro ca sunt| signate56 et prout signam57 per incisiones subtiles sicut fiunt| dice vt perpendiculum indica latitudinis illius regionis in qua| fueris possit suspendi ¶Deinde quicquid fuerit extra circulum mbc|dl58 preter pedem59 organi ¶Et similiter quicquid fuerit supra60 arcum le|m totum abscindatur relicto tantum61 circa centrum e quodam spaciolo| vt in eo malus in centro per clauum possit annecti ¶Circa punc|ta eciam m et l62 relinquatur due auricule ad quas possint| due pinnule annecti63 in quarum medio fiant foramina| subtilia per que radius solis poterit sub intraere ¶Et in residuo forma| cuiusdam organi musici relinquatur64| Uerum et65 ipsum nomine ut| credo accepit| Postea annecte malum ad centrum Instrumenti sic caua| malum incipiendo modicum supra e usque ad finem pedis| tam profunde ita ut partes mali non cauate66 et fa|cies instrumenti sint superficies vna ¶Deinde perforando. Instrumentum| et malum in centro e ea67

48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67

ultra] ubi Y Quibus] ciuibus que Y, Quibusdam M quadam] quandam M habere] scire Y Tamen] sic tamen M directe] directem Y sic] om. Y M V2 penitus] positas M signate] signati M signam] signate M circulum mbcdl] circulos abcdlm M pedem] pede M supra] super M V2 tam] tandem M m et l] l et m M ad quas possint due pinnule annecti] annecte M relinquatur] relinque Y relinquetur M Uerum et] Et Y Vnde et M cauate] cauati M ea] eamque M

274

appendix nine

per clauum connectes ita vt malus| in instrumento volui reuoluique possit motu volubili non curte| ¶Uel aliter malus ad organum aptabitur sic ¶Fiat in organo intus| quedam cauerna per modum trianguli cuius triangli caput sit in centro| e et basis eius sit pes trianguli uel arcus yz In quam| cauernam introducatur malus etiam. in centro e iungatur68 cum organo vt| dictum est vt volui reuoluique possit vt dictum est69| Deinde perpendiculo impone margaritam cum stricto| foramine vt non sui sed tui libito moueatur que| margarita quantum ad prius almuri vicem habebit70| Et ipsum perpendiculum malo indica71 tue latitudinis illaquea| ¶Post hoc malo directe72 in linea instrumenti media statuto| trahe almuri perfilum hinc inde Donec directe73 duo puncta| k.74 et g possit attingere75 ¶Et ita organum ptolomei quantum| ad sui composicionem76 pertinet est completum vt patet in figura scripti77 Secuntur vtilitates huius Instrumenti78| Cvm volueris scire arcum seu quantitatem79 diei cuiuslibet| pone pedem mali supra80 gradum solis seu super diem| mensis punctem81 Et dimitte82 perpendiculum mali ut equi|distanter inter lineas horarias dependeat ¶Et vbi almuri faciem organi tetigant ibi est inicium diei punctis83 ¶A quo si versus| lineam meridianam a84 dextris horas computes arcum mediurnum| in venies qui duplicatus totam diem constituet| Cvm vero horas diei transactas scire volueris pone pedem| mali super gradum solis uel diem presentem ¶Et erige85 or|ganum cum pynulis suis versus solem

68

e iungatur] coniungatur M est vt volui et reuoluique possit ut dictum est] om. M 70 prius almuri vicem habebit] presens pro almuri habet M 71 indica] iamdicta Y 72 directe] directo M 73 directe] directem Y 74 k] h Y 75 attingere] iungere Y 76 composicionem] composicion Y 77 figura scripti] figura precedenti Y figura M 78 Secuntur utilitates huius instrumenti] secuntur Y Sequitur usus organi M Secuntur utilitates instrumenti V2 79 quantitatem] quantitatem versus organi Y 80 supra] super Y M 81 punctem] presentem M 82 dimitte] de mitte Y 83 punctis] presentis M 84 a] ad Y 85 erige] erige erignum Y 69


275

ut radius solis| per earum foramina transeat ¶Et super quottam lineam horariam almuri|ceciderit totta86 erit hora ab ortu solis seu ab inicio diei perprece|dentem invento computanto ¶Et si ante meridiem87 fuerit ab inicio| diei versus meridiem computabis ¶Si vero88 post meridiem conuerso89

86 87 88 89

ceciderit totta] inciderit tota Y ceciderit tanta M si ante meridiem] sicu’ meridie Y vero] non Y conuerso] conuerso etc M

276

appendix nine

[Here] begins the composition of the organum ptolomei. The organum Ptolomei is made thus: make a circle ABCD on a plate, whose centre is E, which is quartered by two diameters AC and BD, and diameter AC is led on either side a little bit outside the circle. Then whichever quarter you please is divided into three equal parts, and they will be the signs, and whichever sign [is divided] into 30 degree[s], indeed according to which it serves. Then put the ruler over the beginning of one sign before B and over the end of another after B and lead a line which connects on either side of circumference ABCD, and on the [point of] contact of this line and the diameter BD, make point G. And make a hidden circle FGHK according to the magnitude of EG so that F stays under AG, under B and C. Then you will put the immoveable foot of the pair of compasses on A and you will extend the moveable one to E. The arc of the circle will take a circular course, which is LEM, as far as the circumference of the circle ABCD on either side of it. Then divide the circle FGHK into 24 equal parts, beginning from any of the diameters, then put the ruler over the two nearest divisions around G, [and] similarly lead a line. Then likewise put the ruler over the other two divisions immediately following, [and] draw a third line, and so [on], and the fourth [ . . .] as far as 13, which 13th [line] you will draw through point K it just as you did through G, whichever [of these lines] beginning from the lower part of the circle ABCD, and finishing in the circle LEM. And these 13 lines will enclose 12 spaces, which will be called the spaces of the hours, and the outer lines are the meridional lines. Then from A towards B [take] one declination of the sun, that is 23 degrees 30 minutes, which is AP; likewise AC towards B which is CQ. Then put the ruler over P and Q and where the ruler touches diameter BD make point N, and according to the magnitude of EN lead a hidden circle which you divide into 12 equal parts starting from any diameter. Then put a ruler over the two nearest points around N, and where the ruler cuts the circumference BC make point R; and likewise put the ruler over another two points, the next following, and where the ruler cuts the circle BC, make a point B. Likewise beyond the diameter AC again put the ruler over the two nearest points, and make a mark on circle CD, which is T; likewise over two points, and make a mark V on the circle. Therefore Capricorn will be positioned between the two points QR, and between RS [is] the position of Aquarius, and between VT [is] the position of Pisces, and between CT [is] the position of Aries, and between TV [is] the position of Taurus, and the position of Gemini [is] between VX, that is the end of the next maxi-


277

mum declination which you will find just as before. Therefore put the ruler over EQ and beyond the circle BC lead a small line, as if for two or three spaces (or as many as pleases), which is QV. And similarly lead another equal to it, which is XZ, then following the magnitude of EZ lead an arc ZY. And similarly lead another arc between XZ for the signs and their degrees and names, and indeed, if it pleases, for the months. Then from the beginnings of the signs, that is from marks RSTV to the arc ZY, similarly lead lines, between which you write the divisions and names of the signs. Another six signs will be inscribed transversally, and that is called the foot of the organum. Then you will discover the latitudes of regions, thus: when you want to have the latitude of 15 degrees put the ruler over point B and over the end of 30 degrees counted from D towards A, and where the ruler cuts diameter AC make a mark, because it denotes a latitude of 15 degrees. And if you want to have the latitude of 30 degrees put the ruler over point B and over the end of 60 degrees, similarly counted from D towards A, and where the ruler cuts diameter AC, make a mark, because there is the latitude of 30 degrees. And thus always twice the degrees from D towards A, and beyond through A towards B. If there is need for single degrees of latitude, to be discovered and taken. Which being thus had, the mast will be fitted as follows: you take a certain pointer which is as long as the line of the middle line of the instrument from its foot, counted inclusively through all latitudes up as far as 60, or more or less, according to whether you want to have more or fewer latitudes. And yet, furthermore, a certain little bit of it sticks out beyond the foot, on the middle of which a straight line is thus drawn correctly, on which line, beginning from the center, the latitudes are marked in the same way inside, just as before, on the middle line, that is on diameter CA. They are marked, and as marked by subtle incisions, as they are called, as the plumb-bob can be suspended you reveal the latitude of that region in which you are. Then whatever was made outside the circle MBCDL near the foot of the organum, and similarly whatever was made above the whole arc LEM, the residue will be taken away, so around center E [there is] a certain little space, so that the mast can be fastened on it in the centre with a pin. Indeed around the points M and L there will remain two ears to which two sights can be fixed, in the middle of which fine pinholes will be made, through which the rays of the sun can penetrate. And regarding the residual shape of a certain musical instrument, it is abandoned, and truly I believe it took the name only.

278

appendix nine

Afterwards you fix the mast to the centre of the instrument, thus: you hollow out the mast, beginning a little above E as far as the end of the foot, as deep as the non-hollowed-out parts of the mast, and you will make the surfaces of the instrument one. Then, the instrument and mast being pierced at centre E, you will join them by a pin so that the mast is able to be rolled and revolved on the instrument, the twisting movement not [being] cut short. Or another mast will thus be fitted to the organum, thus: it is made on the organum within a certain hollow, by means of a triangle, the head of which is on centre E, and the base of it is the foot of the triangle, or arc YZ. Into which hollow the mast is brought, and joined on centre E with the organum, as aforesaid, so that it can roll and revolve, as is said. Then you place a margarita with a narrow hole on the plumb-bob, so that it moves not by itself but at your pleasure, which margarita will be the [same] size as before, but will have a pointer. And this plumb-bob indicates your ensnared latitude on the mast. After this, the mast being placed straight on the middle line of the instrument, draw the almuri thence from this position by the thread on either side. While [it is] straight it is able to reach the two points K and G. And thus is finished as much as pertains to the composition of the organum Ptolomei, as is available in the composed figure. The usefulnesses of this instrument follows. When you want to know the arc or the quantity of whichever day, put the foot of the mast over the degree of the sun or the point of the day of the month. And drop the plumb-bob of the mast so that it hangs equidistantly between the hour lines. And where the front of the indicator of the organum touches, there is the point of the start of the day. From which, if towards the meridional line, you count the hours to the right, you will discover the middle arc, which doubled constitutes the whole day. When truly you wish to know the completed hours of the day, put the foot of the mast over the degree of the sun or the present day, and raise the organum with its pinnulis towards the sun, so that the rays of the sun cross through their pinholes. And the indicator will drop over as many whole hour lines as will be the hour from the rising of the sun, or from the beginning of the day, reckoned by the preceding discovery. And if it were before midday, you will count from the start of the day towards noon; if truly after midday, in the other direction.

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INDEX Albion, 138, 266 Alexandria, 45, 46, 48, 184, 190 Allen, Thomas, 29, 168, 169, 242 Annulus, 81, 165, 166 Apian, Phillipp, 3, 23, 160 Aries, first point of, 34, 39, 40, 41, 42, 198, 237, 239, 250, 254, 276 Aristotle, 82, 84, 201, 202, 241 Arscenius, Ferdinand, 141 Astrolabe, 28, 40, 42, 48, 56, 60, 74, 78, 79, 80, 81, 82, 84, 85, 103, 112, 136, 138, 139, 141, 161, 165, 169, 170, 186, 191, 217, 224, 227, 228, 241, 242, 245 Astrology, 78, 80, 83, 84, 85, 138, 171, 172, 190, 246, 257, 267 Astronomy, 1, 4, 5, 37, 39, 42, 44, 46, 48, 49, 65, 74, 78, 79, 80, 81, 82, 83, 84, 85, 86, 90, 91, 98, 103, 119, 121, 129, 136, 138, 139, 140, 149, 169, 170, 171, 172, 191, 222, 224, 225, 262, 266, 267 Augustinian Canons, 47, 57, 78, 79, 80, 169, 170, 246 Austin Friars, 78, 79, 84 Baconthorpe, John, 138 Baghdad, 2, 3, 13, 114, 116, 117 Barclay, Robert, 246 Batecumbe, William, 138 Benedictine Monks, 81, 85, 170 Berwick, 44, 45, 46, 190, 198 Blagrave, John, 3, 23, 139 Book, 5, 6, 29, 36, 43, 48, 49, 70, 73, 77, 80, 81, 82, 100, 121, 122, 123, 129, 138, 139, 140, 141, 144, 149, 150, 151, 156, 159, 160, 161, 164, 167, 168, 169, 170, 173, 174, 201, 225, 241, 242, 244, 261, 266 Booklist, 78, 79, 88, 159, 170 Bredon, Simon, 82, 83, 166, 167 British Museum, 23, 87, 111, 112, 141, 227, 228, 243, 244 Bullant, Jean, 161, 162 Bullord, J., 242 Caerleon, Lewis, 83 Calculate, 1, 37, 40, 42, 56, 74, 82, 106, 217

Calendar, 3, 17, 27, 38, 39, 41, 75, 78, 81, 82, 100, 122, 149, 150, 160, 165, 166, 174, 175, 188, 189, 192, 199, 212, 215, 228, 241, 242, 245, 246, 251, 255, 267, 268 Cambridge, 4, 23, 24, 25, 29, 43, 44, 64, 65, 77, 83, 129, 134, 138, 139, 146, 148, 159, 172, 174, 191, 193, 217, 241, 242, 243, 257 Canterbury, 44, 45, 190, 198, 217 Carpenter, Thomas, 159 Castle of Knowledge, 136, 138, 139 Cavellat, Guillaume, 159 Charite, William, 78, 79 Chaucer, Geoffrey, 28, 48, 78, 79, 80, 84, 86, 119, 165, 169, 217, 227, 228, 242, 245 Chaunteler, John, 81, 140, 165 Chester, 78, 198, 246 Clavius, Christophus, 151, 154, 156, 158 Cobbes, John, 227 Colchester, 13, 44, 45, 145, 190, 198 Coldingham Abbey, Berwickshire, 81, 165 Collection, 7, 12, 13, 17, 20, 36, 47, 77, 81, 82, 83, 84, 88, 112, 113, 114, 116, 122, 123, 128, 134, 141, 144, 145, 146, 148, 159, 164, 165, 168, 169, 170, 171, 172, 173, 191, 202, 227, 242, 243, 244, 257, 266 Collège Royale, Paris, 128 Columba, 116, 117, 141, 142, 143, 144, 156 Constantinople, 45, 47, 190 Construction, 1, 20, 21, 22, 24, 25, 26, 27, 28, 29, 30, 32, 33, 34, 36, 37, 38, 40, 51, 56, 57, 60, 61, 64, 65, 66, 70, 71, 74, 75, 76, 78, 80, 83, 88, 106, 107, 108, 110, 114, 118, 121, 123, 128, 129, 139, 140, 141, 143, 144, 149, 150, 151, 156, 157, 160, 165, 166, 169, 173, 185, 191, 217, 218, 220, 224, 225, 227, 228, 236, 241 exemplar, 28, 29, 30, 32, 33, 34, 36, 37, 38, 40, 56, 57, 84, 95, 106 template, 21, 25, 27, 28, 29, 33, 37, 38, 56, 60, 61, 64, 65, 70, 71, 73, 74, 83, 118, 228

288

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Craft, 5, 27, 33, 73, 76, 79, 249 Craftsmen, 21, 22, 27, 38, 40, 73, 76, 118 Cremona, 45, 184, 190 Cylinder, 44, 80, 82, 139, 151, 160, 167, 241, 255, 265, 266 Day, 17, 26, 27, 36, 37, 41, 85, 90, 109, 110, 129, 149, 150, 165, 169, 170, 174, 187, 188, 189, 190, 197, 198, 199, 202, 210, 211, 212, 216, 236, 238, 239, 245, 246, 249, 251, 253, 255, 256, 261, 262, 263, 278 De Solaribus Horologiis, 121, 128, 141, 159 Declination, 33, 37, 70, 106, 107, 109, 110, 112, 136, 185, 187, 236, 237, 252, 263, 276, 277 Dee, John, 82, 128, 138, 139, 140, 148, 168, 173, 242 Dering, Sir Edward (Baronet of Kent), 159 Diagram, 1, 7, 16, 23, 24, 25, 26, 27, 28, 29, 33, 34, 35, 36, 37, 51, 53, 55, 56, 57, 59, 60, 61, 63, 64, 65, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 79, 80, 81, 83, 85, 95, 96, 97, 98, 100, 102, 103, 106, 107, 108, 109, 114, 115, 116, 118, 123, 124, 128, 129, 141, 143, 144, 145, 148, 149, 150, 151, 152, 154, 156, 157, 158, 159, 160, 161, 162, 164, 165, 168, 169, 171, 175, 178, 180, 181, 185, 186, 187, 188, 191, 194, 197, 198, 199, 204, 210, 215, 216, 220, 228, 241, 245, 246, 249, 251, 253, 255, 256, 265, 266, 268, 269, 278 Dial, 1, 3, 4, 5, 8, 10, 12, 13, 14, 17, 19, 20, 21, 34, 36, 44, 49, 56, 74, 75, 77, 78, 79, 80, 82, 84, 85, 86, 88, 91, 93, 94, 98, 100, 103, 104, 106, 107, 111, 112, 113, 114, 115, 116, 117, 121, 122, 123, 128, 129, 130, 132, 134, 136, 137, 139, 141, 142, 143, 144, 145, 148, 149, 150, 151, 156, 159, 160, 161, 162, 164, 245, 265, 266 Digby, Kenelm, 24, 166, 168, 169, 242 Dreams, 85, 241 Elmeston, John, 139 Enderby, John, 81, 165 Equatorium, 103, 138, 149 Evans, Lewis, 5, 7 Exeter, 12, 13, 16, 43, 44, 45, 46, 198

Figure, 1, 7, 16, 23, 24, 25, 26, 27, 28, 29, 33, 34, 35, 36, 37, 51, 53, 55, 56, 57, 59, 60, 61, 63, 64, 65, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 79, 80, 81, 83, 85, 95, 96, 97, 98, 100, 102, 103, 106, 107, 108, 109, 114, 115, 116, 118, 123, 124, 128, 129, 141, 143, 144, 145, 148, 149, 150, 151, 152, 154, 156, 157, 158, 159, 160, 161, 162, 164, 165, 168, 169, 171, 175, 178, 180, 181, 185, 186, 187, 188, 191, 194, 197, 198, 199, 204, 210, 215, 216, 220, 228, 241, 245, 246, 249, 251, 253, 255, 256, 265, 266, 268, 269, 278 Finé, Oronce, 117, 121, 123, 128, 136, 138, 139, 141, 148, 149, 151, 156, 157, 159 Fitton, William, 246 Florence, 17, 18, 20, 21, 75, 76 Foster, Samuel, 129, 140 Francis I, King of France, 128 Frisius, Gemma, 139 Gale, Roger, 173, 243 Geneva, 12, 13, 14, 16, 20, 21, 22, 39, 42, 43, 114, 115, 116, 117, 119, 145 Gentleman’s Magazine, 13, 16, 20, 21, 39, 42, 145, 148 Geometry, 3, 6, 13, 33, 34, 37, 38, 41, 42, 48, 49, 51, 56, 57, 60, 61, 64, 65, 71, 73, 74, 75, 76, 82, 85, 88, 89, 90, 91, 93, 94, 95, 98, 100, 102, 103, 104, 106, 107, 108, 110, 112, 114, 116, 117, 119, 121, 122, 123, 128, 138, 140, 141, 143, 144, 145, 149, 150, 151, 156, 160, 161, 162, 224, 225, 241, 265, 266 Gnomonices, 156 Greenwich, 10, 12, 13, 16, 20, 21, 38, 39, 42, 49, 77 Grosseteste, Robert, 82, 138, 167, 241 Gunther, Robert T., 2, 7, 23, 24, 25, 28, 29, 40, 60, 70, 74, 117, 118, 175 Halliwell-Phillips, James Orchard, 243, 244 Hartmann, Georg, 114, 123, 128, 160 Hereford, 44, 198 Hour, 1, 5, 7, 12, 13, 16, 17, 20, 21, 25, 26, 27, 28, 36, 37, 38, 41, 57, 61, 70, 71, 72, 73, 75, 76, 85, 93, 95, 106, 109, 110, 114, 116, 117, 118, 123, 128, 129, 143, 148, 149, 150, 161, 169, 174, 175, 186, 187, 188, 189, 190, 196, 197, 199,

index 210, 211, 212, 216, 224, 236, 239, 241, 253, 261, 262, 263, 276, 278 Illustration, 5, 13, 16, 21, 51, 56, 57, 60, 61, 71, 75, 122, 123, 129, 141, 143, 145, 148, 149, 151, 159, 160, 161, 164 Innocent X, Pope, 143, 144 Instrument albion, 138, 266 annulus, 81, 165, 166 astrolabe, 28, 40, 42, 48, 56, 60, 74, 78, 79, 80, 81, 82, 84, 85, 103, 112, 136, 138, 139, 141, 161, 165, 169, 170, 186, 191, 217, 224, 227, 228, 241, 242, 245 columba, 116, 117, 141, 142, 143, 144, 156 cylinder, 44, 80, 82, 139, 151, 160, 167, 241, 255, 265, 266 dial, 1, 3, 12, 13, 20, 21, 34, 36, 44, 49, 74, 78, 79, 80, 84, 85, 86, 88, 93, 94, 98, 100, 103, 104, 106, 107, 111, 112, 113, 114, 115, 116, 117, 121, 122, 123, 128, 129, 130, 132, 134, 136, 137, 139, 141, 142, 144, 148, 149, 150, 151, 156, 159, 160, 161, 162, 164, 265, 266 equatorium, 103, 138, 149 printed, 56, 160 rectilinear dial, 93, 98, 100, 106, 128, 161 sphere, 93, 106, 136, 138, 139, 141, 167, 169, 174, 191, 201, 228, 241, 266 Inventory, 5, 20, 79, 159, 246 Jerusalem, 45, 47, 86, 190 Kalendarium, 75, 100, 122, 149, 150, 160, 242 Kircher, Athanasius, 116, 117, 141, 143, 144 Latitude, 1, 5, 7, 12, 13, 16, 21, 25, 26, 27, 28, 32, 33, 36, 37, 39, 41, 42, 43, 44, 46, 47, 48, 49, 51, 57, 60, 61, 70, 71, 72, 82, 86, 89, 90, 93, 94, 95, 100, 107, 110, 114, 116, 118, 123, 129, 136, 137, 150, 151, 156, 165, 167, 169, 170, 174, 180, 183, 185, 186, 187, 188, 189, 190, 198, 199, 202, 209, 211, 215, 216, 217, 222, 223, 224, 225, 245, 252, 254, 261, 263, 277, 278 Leicester, 44, 45, 78, 79, 190, 198

289

Libelle of Englysche Polycye, 86, 88 Liberal arts, 82, 85, 91 Lincoln, 44, 81, 82, 168, 198, 242 Lincoln Cathedral, 82, 168 London, 10, 12, 23, 25, 43, 44, 45, 46, 47, 114, 129, 141, 145, 167, 168, 169, 170, 171, 190, 194, 198, 227, 230, 241, 242, 243, 244, 262 Louth, 81, 165 Lowe, Thomas, 140, 228 Lyons, 45, 190 Maitland, John (Duke of Lauderdale), 242 Manuscript groups A, 2, 21, 24, 25, 27, 28, 29, 36, 37, 38, 46, 56, 60, 64, 73, 75, 80, 84, 85, 90, 140, 169, 175, 191, 192, 217, 218, 219, 220, 225, 228 B, 24, 28, 33, 34, 38, 57, 60, 109, 169 C, 24, 25, 29, 224 D, 25, 33, 34, 57, 75, 78, 90, 247 E, 25, 36, 257 Manuscripts, 1, 2, 3, 4, 5, 7, 12, 17, 23, 24, 25, 27, 28, 29, 30, 33, 34, 35, 36, 37, 38, 39, 40, 42, 43, 45, 46, 47, 48, 49, 51, 56, 57, 60, 61, 64, 70, 73, 74, 75, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 88, 89, 93, 94, 95, 98, 106, 107, 109, 110, 114, 116, 117, 119, 121, 122, 123, 128, 138, 139, 140, 141, 144, 148, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 182, 185, 191, 193, 201, 202, 216, 217, 218, 219, 220, 221, 222, 225, 227, 228, 235, 241, 242, 243, 244, 245, 246, 257, 265, 266, 267, 268, 269 annotations, 37, 47, 138, 170, 171 Bayerische Staatsbibliothek, Munich MS Lat 19690, 110 MS Lat 24105, 267 MS Lat 24105 (M), 25, 172, 191, 227, 241, 242, 249, 252, 267, 269, 271, 272, 273, 274, 275, 277 Bodleian Library, Oxford MS Ashmole 188 (AS), 5, 24, 25, 36, 123, 257, 259 MS Bodley 607 (BL2), 24, 90, 140, 201, 203 MS Bodley 68 (BL1), 4, 23, 24, 45, 66, 68, 72, 106, 165, 176 MS Digby 98 (DI), 24, 25, 28, 60, 61, 64, 70, 71, 73, 82, 140, 166,

290

index

168, 169, 175, 177, 178, 179, 180, 185, 215, 217 MS Rawlinson D248 (RA), 23, 25, 26, 27, 28, 44, 47, 83, 84, 202, 204, 205, 206, 207, 208, 209, 215, 216, 217, 220, 221, 222, 223, 224, 225 MS Wood D8 (WO), 24, 25, 26, 28, 77, 80, 81, 82, 174, 180, 181, 182, 192, 195, 196, 215, 216, 217, 220, 222, 223, 224, 225 British Library, London MS Additional 23002 (AD), 25, 28, 80, 84, 227, 228, 229, 231, 232, 233, 234, 253 MS Egerton 2622 (EG), 23, 25, 28, 80, 227, 228, 229, 231, 232, 233, 234, 276 Emmanuel College, Cambridge, MS 36, 24, 26, 28, 48, 77, 90, 182, 191, 192, 193, 215, 216, 220, 222, 223, 224, 225 Lund University Library, MS 47, 99 Medical-Historical Library, Yale University MS 24, 98, 100, 102, 103, 110 MS 25, 252, 253, 266, 268, 269, 271, 272, 273, 274, 275 Osterreichische Nationalbibliothek, Vienna MS 5228, 98, 110 MS 5303 (V2), 265 MS 5418 (V1), 96, 265, 270 Royal College of Physicians, London MS 358 (PH1), 169, 230 MS 384 (PH2), 45, 171, 215 St Peters Library, Salzburg, Inc 800, 268 stemma, 218, 219 Trinity College, Cambridge MS O.5.26 (TO1), 4, 23, 25, 73, 172 MS O.8.16 (TO2), 25, 241, 242, 243, 244 University Library, Aberdeen, MS 123 (AB), 25, 33, 34, 35, 39, 51, 52, 56, 57, 71, 75, 78, 80, 84, 109, 185, 236, 247, 248, 252 University Library, Cambridge, MS Ee.III.61 (CUL), 25, 64, 70, 73, 83, 118 Weimar, Anna Amalia Library, MS Fol Max 29, 124 Map, 2, 44, 45, 49, 94 Marseilles, 45, 190

Mathematics, 1, 4, 44, 89, 112, 119, 122, 136, 139, 140, 141, 149, 159, 160, 165, 266 Maydwell, William, 168 Measure, 7, 12, 13, 16, 37, 56, 74, 109, 129, 143, 169, 185, 186, 187, 213, 246 Medici, 17, 20 Medicine, 81, 83, 84, 174, 175 Mercator, Gerard, 139 Merton College, Oxford, 2 Meteorology, 83 Moerbeke, William, 3, 4 Münster, Sebastian, 150, 151, 152, 156, 159, 161 Navicula Gentleman’s Magazine, 13, 16, 20, 21, 39, 42, 145, 148 Instituto e Museo di Storia della Scienza, Florence, 17, 18, 20, 21, 75, 76 Musée d’Histoire des Sciences, Geneva, 12, 13, 14, 16, 20, 21, 22, 39, 42, 43, 114, 115, 116, 117, 119, 145 Museo Poldi Pezzoli, Milan, 130 Museum of the History of Science, Oxford, 12 National Maritime Museum, Greenwich, 10, 12, 13, 16, 20, 21, 38, 39, 42, 49, 77 parts bead, 5, 7, 25, 26, 28, 29, 30, 33, 34, 37, 38, 39, 41, 57, 61, 66, 68, 70, 71, 75, 104, 106, 107, 109, 110, 117, 118, 123, 141, 186, 187, 188, 189, 197, 199, 210, 211, 212, 224, 238, 262 body, 12, 17, 20, 29, 32, 34, 36, 57, 60, 65, 70, 71, 76, 93, 148, 149, 151 cursor, 5, 20, 26, 27, 36, 39, 48, 56, 73, 90, 93, 95, 100, 106, 110, 116, 117, 129, 136, 160, 161, 182, 183, 189, 194, 195, 196, 198, 199, 206, 209, 211, 217, 223, 224, 261, 262 hour lines, 5, 7, 12, 16, 17, 20, 21, 25, 26, 28, 37, 38, 57, 61, 70, 71, 72, 73, 75, 76, 85, 93, 95, 106, 109, 110, 114, 116, 118, 148, 186, 187, 189, 199, 211, 216, 262, 278 mast, 5, 7, 12, 13, 16, 17, 20, 21, 25, 26, 27, 28, 29, 30, 32, 33, 34, 36,

index 37, 38, 39, 41, 48, 49, 51, 57, 61, 66, 68, 70, 71, 73, 75, 76, 81, 90, 95, 104, 106, 107, 108, 109, 110, 112, 114, 116, 117, 118, 123, 128, 129, 136, 137, 143, 145, 148, 161, 186, 187, 188, 189, 197, 198, 199, 210, 211, 212, 217, 236, 237, 238, 254, 261, 262, 277, 278 pinhole sights, 5, 20, 37, 76, 110, 188, 199, 211, 277, 278 plumb-bob, 5, 7, 74, 95, 100, 103, 106, 107, 151, 212, 262, 277, 278 scale, 5, 7, 12, 13, 16, 17, 21, 25, 26, 28, 29, 30, 32, 33, 34, 36, 38, 56, 57, 60, 61, 65, 66, 68, 70, 71, 72, 74, 75, 80, 100, 104, 106, 107, 108, 109, 110, 112, 114, 116, 117, 118, 123, 129, 136, 137, 141, 148, 149, 151, 156, 160, 161, 208, 210, 212, 213, 215, 221 shadow square, 1, 7, 26, 37, 123, 128, 161, 228 unequal hours diagram, 1, 7, 26, 36, 37, 85, 123, 128, 129, 149, 161, 169, 216, 224, 261, 263 standard design, 5, 13, 17, 20, 22, 51, 71, 73, 75, 76, 85, 86, 88, 89, 100, 114, 123 Whipple Museum of the History of Science, Cambridge Cambridge dial, 146 Whipple dial, 116, 117, 129, 134, 136, 137, 141, 146, 148, 149, 257 Newcastle, 44, 46 Night, 27, 36, 90, 187, 189, 190, 199, 212, 216, 237, 261, 262, 263 Northampton, 12, 43, 44, 45, 46, 49, 198 Organum ptolomei, 3, 6, 34, 36, 65, 94, 95, 96, 98, 100, 101, 102, 103, 104, 105, 106, 107, 109, 110, 112, 114, 118, 122, 123, 128, 141, 160, 265, 268, 269, 274, 276 Oxford, 2, 4, 5, 7, 8, 12, 13, 16, 20, 21, 23, 24, 25, 29, 38, 40, 43, 44, 45, 46, 60, 66, 68, 70, 72, 74, 78, 81, 82, 83, 84, 85, 88, 91, 113, 114, 118, 138, 139, 140, 150, 156, 159, 165, 166, 167, 168, 169, 171, 173, 174, 176, 190, 198, 201, 202, 203, 244, 245, 257, 259, 262 Palgrave, Francis, 227 Paris, 45, 46, 73, 112, 121, 128, 139, 190

291

Partriche, Peter, 82, 166, 168 Peacock, George, 243 Peckham, John, 82, 167 Perth, 44, 46, 198 Peter of Muchelney, 3, 85 Peurbach, George, 266 Phillips, James Orchard Halliwell, 243 Ponteshyde, Thomas, 81, 174 Practical geometry, 41, 48, 65, 74, 82, 85, 89, 121, 149, 224 Price, Derek J de Solla, 1, 2, 23, 24, 25, 60, 118, 179 Printed instruments, 56, 159, 160 Protomathesis, 117, 123, 128, 149, 151 Ptolemy, 3, 172 Quadrans Vetus, 37, 80, 89, 121, 221, 222 Quadrant, 13, 48, 56, 61, 65, 74, 78, 80, 82, 85, 89, 103, 138, 139, 141, 143, 149, 150, 151, 165, 167, 170, 186, 212, 213, 222, 224, 225, 228, 241, 245, 255, 265, 266 Ramsdon, Hugh, 140, 228 Recorde, Robert, 136, 138, 139, 148 Rectilinear dial, 106 Regiomontanus dial, 3, 93, 94, 100, 104, 106, 107, 114, 115, 116, 117, 122, 128, 150, 151, 152, 156, 157, 159, 160, 161, 164 Regiomontanus, Johannes, 3, 93, 94, 95, 98, 100, 104, 106, 107, 114, 115, 116, 117, 122, 128, 136, 149, 150, 151, 152, 156, 157, 159, 160, 161, 164, 172 Reynolds, James, 159 Robertus Anglicus, 121, 221 Rodd, Thomas, 244 Rome, 45, 144, 190 Sacrobosco, Johannes, 82, 138, 167, 171, 174, 191, 201, 228, 241, 268 Science Museum, London, 141 Scot, Michael, 138 Sibton Abbey, Suffolk, 12, 38, 77, 78 Slape, John, 29, 80, 241, 243, 244 Smythe, Nicholas, 201 Smythe, Renauld, 140, 201 Solar declination, 33, 37, 70, 106, 107, 109, 110, 112, 136, 185, 187, 236, 237, 252, 263, 276, 277 Somer, John, 3, 75, 83, 251, 255 Southey, Captain A., 228 Spain, 2

292

index

Sphaera, 91, 171, 174, 241, 242, 243, 268 Sphere, 93, 106, 136, 138, 139, 141, 167, 169, 174, 191, 201, 228, 241, 266 Spitzer, Frédéric, 112 St Albans, 3, 138, 198 St Augustine, 79, 82, 166, 217 St Victor, Hugh of, 89 Star, 27, 81, 90, 94, 149, 166, 169, 170, 171, 172, 189, 190, 198, 215, 216, 224, 246, 257, 276 Stiborius, Andreas, 103, 267, 268 Sun, 5, 12, 13, 17, 21, 26, 27, 36, 37, 39, 40, 41, 49, 61, 75, 79, 89, 90, 107, 109, 110, 123, 129, 167, 169, 171, 184, 185, 187, 188, 189, 190, 197, 198, 199, 210, 211, 212, 216, 236, 239, 241, 246, 252, 255, 256, 261, 262, 263, 276, 277, 278 sunrise, 1, 36, 37, 117, 189, 199 sunset, 1, 36, 37, 117, 189 Sundial, 1, 3, 4, 5, 8, 10, 12, 13, 14, 17, 19, 20, 21, 34, 36, 44, 49, 56, 74, 75, 77, 78, 79, 80, 82, 84, 85, 86, 88, 91, 93, 94, 98, 100, 103, 104, 106, 107, 111, 112, 113, 114, 115, 116, 117, 121, 122, 123, 128, 129, 130, 132, 134, 136, 137, 139, 141, 142, 143, 144, 145, 148, 149, 150, 151, 156, 159, 160, 161, 162, 164, 245, 265, 266 Table, 12, 13, 16, 17, 21, 26, 27, 37, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 51, 75, 82, 83, 139, 161, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 183, 190, 191, 198, 202, 209, 215, 216, 220, 221, 225, 227, 228, 241, 245, 246, 250, 251, 267, 268 Templates, 21, 25, 27, 28, 38, 56, 60, 61, 64, 65, 70, 71, 73, 74, 83, 118, 228 Thackam, John, 228 Thurgarton, 57, 79, 80, 169, 170 Time, 1, 2, 5, 7, 21, 22, 26, 27, 28, 36, 37, 39, 40, 41, 42, 43, 44, 47, 60, 81, 82, 84, 85, 89, 90, 91, 98, 110, 114, 117, 129, 143, 144, 145, 149, 166, 168, 171, 187, 188, 189, 190, 198, 199, 201,

210, 213, 215, 216, 217, 224, 243, 253, 261, 262, 267 Toledan tables, 37, 48 Toledo, 45, 46, 190 Tomsun, Robert, 228 Trade, 4, 43, 78, 81, 86, 88, 148, 159 Translation, 3, 23, 24, 25, 26, 34, 84, 119, 123, 173, 175, 185, 191, 199, 202, 228, 257, 262, 269 Treatise on the Astrolabe, 28, 48, 78, 79, 80, 84, 165, 169, 217, 227, 228, 242, 245 Tunsteed, Simon, 138 Uses finding latitude, 223, 224, 225 length of day, 1, 26, 36, 90, 245, 261 telling the time, 7, 26, 27, 36, 37, 81, 90, 91, 110, 114, 149, 224 Venice, 1, 2, 3, 4, 23, 25, 60, 106, 118, 150, 267 Volvelle, 51, 74, 165, 245, 246 W.B., 13, 16, 145, 148 Wallingford, Richard of, 3, 83, 138, 173, 241, 244, 266 Warrington, 78, 246 Whethamstede, John, 3, 85 Wilson, John, 144, 145 Winchester, 13, 16, 43, 44, 46, 198 Year, 1, 2, 5, 16, 27, 40, 41, 42, 78, 123, 144, 145, 165, 169, 171, 172, 173, 174, 175, 190, 243, 245, 246, 257, 266, 267 York, 12, 43, 44, 45, 46, 47, 79, 190, 198, 266 Young, Patrick, 173 Zinner, Ernst, 94, 95, 98, 100, 110 Zodiac, 7, 12, 13, 17, 21, 26, 27, 29, 34, 37, 39, 40, 47, 49, 51, 61, 75, 78, 80, 81, 90, 123, 151, 156, 161, 169, 184, 186, 188, 189, 190, 192, 197, 198, 199, 204, 210, 245, 246, 261, 262

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