Sources and Studies in the History of Mathematics and Physical Sciences Dominique Raynaud A Critical Edition of Ibn al-Haytham’s On the Shape of the Eclipse The First Experimental Study of the Camera Obscura Sources and Studies in the History of Mathematics and Physical Sciences Series editor Jed Buchwald Associate editors J.L Berggren J Lützen J Renn Advisory Board C Fraser T Sauer A Shapiro Sources and Studies in the History of Mathematics and Physical Sciences was inaugurated as two series in 1975 with the publication in Studies of Otto Neugebauer’s seminal three-volume History of Ancient Mathematical Astronomy, which remains the central history of the subject This publication was followed the next year in Sources by Gerald Toomer’s transcription, translation (from the Arabic), and commentary of Diocles on Burning Mirrors The two series were eventually amalgamated under a single editorial board led originally by Martin Klein (d 2009) and Gerald Toomer, respectively two of the foremost historians of modern and ancient physical science The goal of the joint series, as of its two predecessors, is to publish probing histories and thorough editions of technical developments in mathematics and physics, broadly construed Its scope covers all relevant work from pre-classical antiquity through the last century, ranging from Babylonian mathematics to the scientific correspondence of H A Lorentz Books in this series will interest scholars in the history of mathematics and physics, mathematicians, physicists, engineers, and anyone who seeks to understand the historical underpinnings of the modern physical sciences More information about this series at http://www.springer.com/series/4142 Dominique Raynaud A Critical Edition of Ibn al-Haytham’s On the Shape of the Eclipse The First Experimental Study of the Camera Obscura 123 Dominique Raynaud PPL Université Grenoble Alpes Grenoble Cedex France ISSN 2196-8810 ISSN 2196-8829 (electronic) Sources and Studies in the History of Mathematics and Physical Sciences ISBN 978-3-319-47990-3 ISBN 978-3-319-47991-0 (eBook) DOI 10.1007/978-3-319-47991-0 Library of Congress Control Number: 2016954711 © Springer International Publishing AG 2016 This work is subject to copyright All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed The use of general descriptive names, registered names, trademarks, service marks, etc in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made Printed on acid-free paper This Springer imprint is published by Springer Nature The registered company is Springer International Publishing AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland Table of Contents Acknowledgments x Introduction 1 A Key Milestone in the History of Optics 2 Ibn al-Haytham’s Legacy Chapter This Edition The Need for a Critical Edition Wiedemann’s Translation Naẓīf’s Study 10 Sabra’s Comment 13 Codicological and Stemmatological Notes 14 Authorship and Date 14 The Manuscripts 16 The Stemma of the Text 18 The Stemma of Diagrams 19 Editorial Procedures 20 Scientific Vocabulary 20 Spelling Variants 22 Punctuation 22 Diacritical Marks 23 Tips on Reading 23 General Outline of the Treatise 23 Reading the Diagrams 25 vi On the Shape of the Eclipse Transliteration 26 Sigla 27 Chapter Arabic Text and Translation 29 The Observations 30 Effect of the Size of the Aperture on the the Image of the Sun 30 Different Observations in the Case of the Moon 32 Principles of the Demonstration 33 Rectilinear Propagation of Light; Homothety 33 Point-Analysis of the Image 35 Geometric Construction 40 Relation Between the Distance and Size of the Aperture 42 Distinction of the Convex and Concave Faces of the Crescent 45 Analysis of the Image of the Convex Face 46 Geometric Construction 46 A Lemma 49 Application of the Lemma 51 The Archimedean Analysis 54 Analysis of the Image of the Concave Face 60 Effect of the Size of the Aperture on the Image of the Concave Face 62 Effect of the Distance on the Image of the Concave Face 63 Condition for the Image to Appear Crescent-Shaped or Circular 66 Geometric Demonstration 67 Analysis of the Image in the Case of the Moon 74 Conditions for the Image of the Moon to be Crescent-Shaped 74 Material Impossibility for these Conditions to be Fulfilled 75 Conclusion 78 Chapter Ibn al-Haytham’s Method 79 Ibn al-Haytham’s Predecessors 79 Pseudo-Aristotle 79 Al-Kindī 82 Table of Contents vii Pseudo-Euclid 84 Al-Khujandī 87 Uṭārid al-Ḥāsib 89 The Archimedean Analysis 90 The Point Analysis of Light 91 Ibn al-Haytham’s Experimental Method 95 Ibn al-Haytham’s Device 97 Purposes of the Camera Obscura 97 Shape of the Camera Obscura 98 Walls 98 Verticality 99 Movability 99 Parallelism 100 Aperture 100 Dimensions of the Camera Obscura 101 Depth of the Darkroom 101 Size of the Aperture 102 Evaluating Ibn al-Haytham’s Device 104 Stigmatism in Geometrical Optics 105 Stigmatism in Wave Optics 106 Diffraction 108 Sharpness of an Image 108 Optimal Size of the Aperture 110 Chapter Ibn al-Haytham’s Optical Analysis 113 Conditions for an Image to be Seen in the Darkroom 113 Image Inversion 114 Outline of the Demonstration 116 Mathematical Relationships 117 The Crescent-Shaped Image 122 The Circular Image 122 The Rounding of the Image 129 Stability of these Conditions 129 viii On the Shape of the Eclipse The Image as a Function of the Size of the Aperture 130 R < r 135 r 136 Flattening 138 Special Cases 140 The Image as a Function of the Focal Distance 142 General Case 142 R Flattening 143 Special Cases 144 The Image as a Function of the Shape of the Aperture 145 Graphic Simulation 145 Transformation of the Image 146 The Image as a Function of the Light Source 148 Geometry 148 Proto-Photometry 150 Center 153 Edge 154 Tip 156 Conclusion 159 Appendix A Tentative Dating of On the Shape of the Eclipse 161 The Status of Scientific Diagrams 161 The Eclipses to Be Surveyed 164 The Magnitude of the Eclipse 166 The Occultation Angle 168 The Geometry of the Eclipse Image 171 Location Known 171 Location Unknown 175 Images in Vertical Distortion 175 Images in Full Distortion 176 Discussion 180 Table of Contents ix Conclusion 181 References 187 Index Nominum 205 Index Rerum 213 Arabic-English Glossary 225 Table of Figures 239 Plates 245 Plates Da Vinci (ca 1490) 247 Gemma Frisius (1545) Danti (1573) Santbech (1561) Schwenter (1636) Plate 3.1B The History of the Camera Obscura Kircher (1646) 248 On the Shape of the Eclipse Kircher (1646) Kircher (1646) Zahn (1685) Mersenne (1651) Chérubin D’Orléans (1671) Plate 3.1C The History of the Camera Obscura Plates 249 Baisiu (ca 1300) Da Vinci (1489) Kepler (July 10, 1600) Maurolico (1543) Kepler (1604) Plate 3.2 Explanations of the Formation of the Image Kepler (1604) 250 On the Shape of the Eclipse R1 R2 S Plate 3.3 The Image through the Aperture Gnomon: in Rayy-Bīrūnī (R1), in RayyMarrā̄kushī̄ (R2), and in Samarkand (S) Plate 4.1 Point Analysis of a Crescent-Shaped Image Plates 251 0.02 0.06 0.09 0.18 0.36 0.54 0.73 0.91 1.09 1.27 1.45 1.63 Plate 4.2 The Solar Disc as the Square Aperture Increases 252 On the Shape of the Eclipse 0.02 0.06 0.09 0.18 0.36 0.54 0.73 0.91 1.09 1.27 1.45 1.63 Plate 4.3 The Solar Disc as the Triangular Aperture Increases Plates 253 0.02 0.06 0.09 0.18 0.36 0.54 0.73 0.91 1.09 1.27 1.45 1.63 Plate 4.4 The Solar Crescent as the Circular Aperture Increases 254 On the Shape of the Eclipse Plate 4.5 Scheiner’s Helioscope Plates A B Plate 4.6 Images Obtained through the Helioscope Plate 4.7 Point Analysis of a Circular Image 255 C ‫‪On the Shape of the Eclipse‬‬ ‫ص‬ ‫ص‬ ‫ظ‬ ‫م‬ ‫ق‬ ‫ل‬ ‫ع‬ ‫ج‬ ‫ه‬ ‫ث‬ ‫ن‬ ‫ي‬ ‫ك‬ ‫و‬ ‫ا‬ ‫س‬ ‫د‬ ‫ب‬ ‫ط‬ ‫ح‬ ‫ف‬ ‫خ‬ ‫‪256‬‬ ‫ش‬ ‫ت‬ ‫ب‬ ‫د‬ ‫ا ك‬ ‫م‬ ‫ح‬ ‫ز‬ ‫ل‬ ‫ه‬ ‫ن ط‬ ‫ج‬ ‫ظ‬ ‫ق‬ ‫ع‬ ‫ص‬ ‫ل‬ ‫م‬ ‫ن‬ ‫ي‬ ‫و‬ ‫خ‬ ‫ر‬ ‫غ‬ ‫ف‬ ‫ت‬ ‫ض‬ ‫ك‬ ‫ه‬ ‫ز‬ ‫ط‬ ‫ح‬ ‫ش‬ ‫ا‬ ‫ج‬ ‫س‬ ‫د‬ ‫ب‬ ‫‪Plate App1 MS F Fā̄tiḥ 3439‬‬ ‫‪Plates‬‬ ‫‪257‬‬ ‫ظ‬ ‫ق‬ ‫ع‬ ‫ث‬ ‫ل‬ ‫ن‬ ‫م‬ ‫ك‬ ‫ي‬ ‫ف‬ ‫ه‬ ‫ط‬ ‫ز‬ ‫و‬ ‫س‬ ‫ت‬ ‫ص‬ ‫ن‬ ‫ا‬ ‫د‬ ‫ح‬ ‫ش‬ ‫خ‬ ‫ج‬ ‫ب‬ ‫ك‬ ‫ه‬ ‫ش‬ ‫ق‬ ‫ف ع‬ ‫ر‬ ‫ب‬ ‫د‬ ‫ت‬ ‫ا‬ ‫م‬ ‫ز‬ ‫ح‬ ‫ك‬ ‫ط‬ ‫ن‬ ‫ل‬ ‫ه‬ ‫خ‬ ‫م‬ ‫ج‬ ‫ظ‬ ‫ذ‬ ‫ه‬ ‫ق‬ ‫ل‬ ‫غ‬ ‫م‬ ‫ن‬ ‫ي‬ ‫و‬ ‫ض‬ ‫خ‬ ‫ر‬ ‫ع‬ ‫ف‬ ‫ج‬ ‫س‬ ‫ث‬ ‫ك‬ ‫ص‬ ‫ط‬ ‫ز‬ ‫ا‬ ‫د‬ ‫ح‬ ‫ب‬ ‫ش‬ ‫ت‬ ‫‪Plate App2 MS B Bodleian Arch Seld A32‬‬ ‫‪258‬‬ ‫‪On the Shape of the Eclipse‬‬ ‫ظ‬ ‫ق‬ ‫ل‬ ‫ع‬ ‫ث‬ ‫ه‬ ‫ن‬ ‫ي‬ ‫م‬ ‫ج‬ ‫ط‬ ‫ك‬ ‫و‬ ‫ص‬ ‫س‬ ‫ز‬ ‫د‬ ‫ب‬ ‫ح‬ ‫ف‬ ‫خ‬ ‫ا‬ ‫ش‬ ‫ت‬ ‫ك‬ ‫ه‬ ‫ش‬ ‫ع‬ ‫ر‬ ‫ب‬ ‫د‬ ‫ص‬ ‫ن‬ ‫ف‬ ‫ق‬ ‫م‬ ‫ت‬ ‫ا‬ ‫خ‬ ‫م‬ ‫ك‬ ‫ز‬ ‫ح‬ ‫ط‬ ‫ن‬ ‫ل‬ ‫ه‬ ‫ج‬ ‫ظ‬ ‫ع‬ ‫ق‬ ‫ذ‬ ‫ل‬ ‫م‬ ‫خ‬ ‫ه‬ ‫غ‬ ‫ن‬ ‫ي‬ ‫و‬ ‫ث‬ ‫ض‬ ‫ك‬ ‫ز‬ ‫ح‬ ‫ف‬ ‫ر‬ ‫ط‬ ‫ش‬ ‫ج‬ ‫ص‬ ‫س‬ ‫ا‬ ‫د‬ ‫ب‬ ‫ت‬ ‫‪Plate App3 MS P St Petersburg B1030‬‬ ‫‪Plates‬‬ ‫‪259‬‬ ‫ظ‬ ‫ق‬ ‫ل‬ ‫ع‬ ‫ث‬ ‫ن‬ ‫ي‬ ‫م‬ ‫ص‬ ‫ه‬ ‫ج‬ ‫ط‬ ‫و‬ ‫ك‬ ‫خ‬ ‫س‬ ‫ز‬ ‫ح‬ ‫ف‬ ‫ا‬ ‫د‬ ‫ب‬ ‫ش‬ ‫ت‬ ‫ك‬ ‫ه‬ ‫ش‬ ‫ف ع‬ ‫ر‬ ‫ب‬ ‫م‬ ‫ص‬ ‫ن‬ ‫ق‬ ‫ت‬ ‫ا ك‬ ‫ح‬ ‫ج‬ ‫خ‬ ‫م‬ ‫ز‬ ‫ل‬ ‫ن‬ ‫ط‬ ‫ه‬ ‫ظ‬ ‫ق‬ ‫ه‬ ‫ل‬ ‫ع‬ ‫ن‬ ‫ض‬ ‫ث‬ ‫م‬ ‫ي‬ ‫و‬ ‫ف‬ ‫ك‬ ‫خ‬ ‫ر‬ ‫ش‬ ‫ت‬ ‫ص‬ ‫ط‬ ‫ز‬ ‫ح‬ ‫ا‬ ‫ج‬ ‫س‬ ‫د‬ ‫ب‬ ‫‪Plate App4 MS O India Office 1270‬‬ ‫‪260‬‬ ‫‪On the Shape of the Eclipse‬‬ ‫ظ‬ ‫ع‬ ‫و‬ ‫م‬ ‫خ‬ ‫ق‬ ‫ل‬ ‫ن‬ ‫ي‬ ‫ص‬ ‫ه‬ ‫ث‬ ‫ز‬ ‫ك‬ ‫ف‬ ‫ح‬ ‫ج‬ ‫س‬ ‫د‬ ‫ط‬ ‫ش‬ ‫ت‬ ‫ب‬ ‫ه ش‬ ‫ك‬ ‫م‬ ‫د‬ ‫ف ع‬ ‫ق‬ ‫ن‬ ‫ظ‬ ‫م‬ ‫خ‬ ‫ر‬ ‫ت‬ ‫ا ك‬ ‫ح‬ ‫ز‬ ‫ب‬ ‫ل‬ ‫ن‬ ‫ه‬ ‫ط‬ ‫خ‬ ‫م‬ ‫ع‬ ‫ا‬ ‫ق‬ ‫ل‬ ‫ن‬ ‫ي‬ ‫و‬ ‫ذ‬ ‫ص‬ ‫ث‬ ‫ه‬ ‫ك‬ ‫ف‬ ‫ت‬ ‫ز‬ ‫ط‬ ‫ح‬ ‫ج‬ ‫ا‬ ‫س‬ ‫د‬ ‫ش‬ ‫ب‬ ‫‪Plate App5 MS L India Office 461‬‬ ‫‪Plates‬‬ ‫‪261‬‬ ‫ظ‬ ‫ق‬ ‫ل‬ ‫ع‬ ‫ث‬ ‫ن‬ ‫ه‬ ‫ي‬ ‫م‬ ‫ك‬ ‫و‬ ‫ف‬ ‫ط‬ ‫ز‬ ‫ج‬ ‫ح‬ ‫خ‬ ‫ب‬ ‫ه‬ ‫ش‬ ‫ف ع‬ ‫ر‬ ‫ك‬ ‫ب‬ ‫د‬ ‫ن‬ ‫ص‬ ‫ق‬ ‫ت‬ ‫ا‬ ‫خ‬ ‫م‬ ‫س‬ ‫ا‬ ‫د‬ ‫ش‬ ‫ت‬ ‫ص‬ ‫م‬ ‫ك‬ ‫ح‬ ‫ز‬ ‫ن‬ ‫ل‬ ‫ه‬ ‫ط‬ ‫ج‬ ‫ظ‬ ‫ق‬ ‫ذ‬ ‫ل‬ ‫ع‬ ‫ن‬ ‫ي‬ ‫غ‬ ‫ض‬ ‫ث‬ ‫ه‬ ‫م‬ ‫و‬ ‫ف‬ ‫ك‬ ‫خ‬ ‫ر‬ ‫ت‬ ‫ش‬ ‫ز‬ ‫ط‬ ‫ح‬ ‫ص‬ ‫ج‬ ‫س‬ ‫ا‬ ‫د‬ ‫ب‬ ‫‪Plate App6 Edited Diagrams‬‬ ... Springer International Publishing AG 2016 D Raynaud, A Critical Edition of Ibn al- Haytham’s On the Shape of the Eclipse, Sources and Studies in the History of Mathematics and Physical Sciences,... twenty-year long controversy between Abdelhamid I Sabra and Roshdi Rashed on whether we should or should not identify Abū Al ibn al- Ḥasan ibn al- Ḥasan ibn al- Haytham (the mathematician) with Muḥammad... the Shape of the Eclipse needs to be established A first response is given by the way all manuscripts are titled: al asan ibn al- Ḥasan ibn al- Haytham’s Epistle on the Shape of the Eclipse. ” The