9780306815805_FM.qxd 8/22/07 10:38 AM Page i THE ARCHIMEDES CODEX 9780306815805_FM.qxd 8/22/07 10:38 AM Page ii 9780306815805_FM.qxd 8/22/07 10:38 AM Page iii THE ARCHIMEDES CODEX How a Medieval Prayer Book Is Revealing the True Genius of Antiquity’s Greatest Scientist REVIEL NETZ WILLIAM NOEL Da Capo Press A Member of the Perseus Books Group 9780306815805_FM.qxd 8/22/07 10:38 AM Page iv Many of the designations used by manufacturers and sellers to distinguish their products are claimed as trademarks.Where those designations appear in this book and Da Capo Press was aware of a trademark claim, the designations have been printed in initial capital letters. Copyright © 2007 by Reviel Netz and William Noel All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of the publisher. Printed in the United States of America. Production Services by Chris Grison for Outbox Creative Partners Set in 11.5 point Bembo by Outbox Creative Partners Cataloging-in-Publication data for this book is available from the Library of Congress. First Da Capo Press edition 2007 First published in Great Britain in 2007 by Weidenfeld & Nicholson. ISBN-10 0–306–81580–X ISBN-13 978–0–306–81580–5 Published by Da Capo Press A Member of the Perseus Books Group www.dacapopress.com Da Capo Press books are available at special discounts for bulk purchases in the United States by corporations, institutions, and other organizations. For more information, please contact the Special Markets Department at the Perseus Books Group, 2300 Chestnut Street, Suite 200, Philadelphia, PA 19103, or call (800) 255-1514, or e-mail [email protected]. 1 2 3 4 5 6 7 8 9—10 09 08 07 9780306815805_FM.qxd 8/22/07 10:38 AM Page v Contents List of Illustrations vii Preface 1 1 Archimedes in America 3 2 Archimedes in Syracuse 27 3 The Great Race, Part 1: Before the Palimpsest 65 4 Visual Science 87 5 The Great Race, Part II:The History of the Palimpsest 117 6 Archimedes’ Method, 1999, or The Making of Science 139 7 The Critical Path 159 8 Archimedes’ Method, 2001, or Infinity Unveiled 183 9 The Digital Palimpsest 205 10 The Stomachion, 2003, or Archimedes at Play 233 11 New Light on an Old Subject 261 Epilogue:“The Vast Book of the Universe” 281 Acknowledgements 295 Further Reading 299 Index 305 v 9780306815805_FM.qxd 8/22/07 10:38 AM Page vi 9780306815805_FM.qxd 8/22/07 10:38 AM Page vii List of Illustrations 1a The Archimedes Palimpsest. (John Dean) 1b The Archimedes Palimpsest open. (John Dean) 2a The Euryalus fortress, Syracuse, Sicily. (John Dean) 2b Hagia Sophia, Constantinople (Istanbul). (John Dean) 3 A medieval scribe. (Walters Art Museum) 4a Constantinople (Istanbul). (John Dean) 4b The Monastery of St. Sabas, Palestine. (John Dean) 4c Leaf of the Palimpsest, Cambridge University Library. (Cambridge University Library) 5a Abigail Quandt, Senior Conservator of Manuscripts and Rare Books at the Walters Art Museum. (The Archimedes Palimpsest Project) 5b Conserving the Palimpsest. (The Archimedes Palimpsest Project) 5c Disbinding the Palimpsest. (The Archimedes Palimpsest Project) 6a Heiberg’s photograph of folio 57r of the Archimedes Palimpsest, Rochester Institute of Technology, Johns Hopkins University. (The Archimedes Palimpsest Project) 6b An illustration in H. Omont’s 1929 publication of Greek manuscripts in the Bibliothèque Nationale. (The Archimedes Palimpsest Project) 6c Folio 57r of the Archimedes Palimpsest as it is now. RIT and JHU. (Copyright: Owner of the Archimedes Palimpsest) 6d An X-ray Fluorescence image of folio 57r. SLAC. (Copyright: Owner of the Archimedes Palimpsest) 7a A detail of the Archimedes Palimpsest before it was disbound. (The Archimedes Palimpsest Project) vii 9780306815805_FM.qxd 8/22/07 10:38 AM Page viii THE ARCHIMEDES CODEX 7b The Palimpsest in normal light. It is very difficult to discern any undertext. RIT and JHU (Copyright: Owner of the Archimedes Palimpsest) 7c An early experiment, this is a highly processed image of the same area. RIT and JHU (Copyright: Owner of the Archimedes Palimpsest) 8a Setting up a leaf of the Palimpsest to be imaged. (The Archimedes Palimpsest Project) 8b Roger Easton, Professor of Imaging Science at the Rochester Institute of Technology. (John Dean) 8c Bill Christens-Barry of Equipoise Imaging LLC. (John Dean) 8d Keith Knox, Chief Scientist at the Boeing Corporation, Maui. (John Dean) 9 Diagram to Archimedes’ Spiral Lines proposition 21, in ultra- violet light. RIT and JHU. (Copyright: Owner of the Archimedes Palimpsest) 10a A detail of the Palimpsest in normal light. RIT and JHU. (copyright: Owner of the Archimedes Palimpsest) 10b The same page in pseudocolor. RIT and JHU. (Copyright: Owner of the Archimedes Palimpsest) 11a Reviel Netz has annotated this ultraviolet image in green. (The Archimedes Palimpsest Project) 11b Nigel Wilson. (The Archimedes Palimpsest Project) 12a Will Noel and Reviel Netz study a leaf of the Archimedes Palimpsest. (John Dean) 12b A pseudocolor image of the Hyperides text in the Palimpsest. RIT and JHU. (Copyright: Owner of the Archimedes Palimpsest) 12c A detail of the third unique text in the manuscript in natural light. RIT and JHU. (Copyright: Owner of the Archimedes Palimpsest) 12d A pseudocolor image of the same detail as 12c, with the word “Aristotle” circled. RIT and JHU. (Copyright: Owner of the Archimedes Palimpsest) viii 9780306815805_FM.qxd 8/22/07 10:38 AM Page ix LIST OF ILLUSTRATIONS 13a Bob Morton,Abigail Quandt, and Gene Hall. (The Archimedes Palimpsest Project) 13b EDAX scan. (The Archimedes Palimpsest Project) 13c Outside Beamline 6-2 at the Stanford Linear Accelerator Center. (The Archimedes Palimpsest Project) 14a A leaf of the Archimedes Palimpsest in the beam at SLAC. (The Archimedes Palimpsest Project) 14b Uwe Bergmann, Reviel Netz and Will Noel. (The Archimedes Palimpsest Project) 15a Abigail Quandt inserts a forgery into the beam at SLAC. (The Archimedes Palimpsest Project) 15b A regular image of one half of a forged page. RIT and JHU. (Copyright: Owner of the Archimedes Palimpsest) 15c An “iron map” of the same page, taken at SLAC. SLAC. (Copyright: Owner of the Archimedes Palimpsest) 16a Uwe Bergmann,Abigail Quandt, Keith Knox, Reviel Netz and Roger Easton at SLAC. (The Archimedes Palimpsest Project) 16b A detail of folio 1v of the Palimpsest, taken in normal light. RIT and JHU. (Copyright: Owner of the Archimedes Palimpsest) 16c An “iron map” revealing the colophon of the scribe of the prayer book. SLAC. (Copyright: Owner of the Archimedes Palimpsest) Endpapers: front The Archimedes Palimpsest, folios 16v–17r in natural light; back The Archimedes Palimpsest, folios 16v–17r processed to reveal the text of Archimedes’ On Floating Bodies. ix 9780306815805_FM.qxd 8/22/07 10:38 AM Page x 9780306815805_FM.qxd 8/22/07 10:38 AM Page xi This book is dedicated to Lynn, to Maya, Darya, and Tamara, and to Ioannes Myronas 9780306815805_FM.qxd 8/22/07 10:38 AM Page xii 9780306815805_FM.qxd 8/22/07 10:38 AM Page 1 Preface icetas Choniates, the brother of the Archbishop of Athens, wit- Nnessed the greatest calamity that ever befell the world of learning. In April 1204, Christian soldiers on a mission to liberate Jerusalem stopped short of their goal and sacked Constantinople, the richest city in Europe. Nicetas gave an eyewitness account of the carnage.The sumptuous treasure of the great church of Hagia Sophia (Holy Wisdom) was broken into bits and distributed among the sol- diers. Mules were led to the very sanctuary of the church to carry the loot away.A harlot, a worker of incantations and poisonings, sat in the seat of the Patriarch and danced and sang an obscene song.The sol- diers captured and raped the nuns who were consecrated to God. “Oh, immortal God,” cried Nicetas, “how great were the afflictions of the men.”The obscene realities of medieval warfare crashed upon Constantinople, and the hub of a great empire was shattered. The looted city had many more books than people. It was the first time that Constantinople had fallen in the 874 years since Constantine the Great, Emperor of Rome founded it in AD 330. Its inhabitants still considered themselves Romans, and the city held the literary treasures of the ancient world as its inheritance. Among the treasures were treatises by the greatest mathematician of the ancient world and one of the greatest thinkers who had ever lived. He approximated the value of pi, he developed the theory of centers of gravity, and he made steps toward the development of the calculus 1,800 years before Newton and Leibniz. His name was Archimedes. Unlike hundreds of thousands of books that were destroyed during the fall of the city,three books containing Archimedes’ texts survived. 1 9780306815805_FM.qxd 8/22/07 10:38 AM Page 2 THE ARCHIMEDES CODEX Of the three books, the first to disappear was Codex B; it was last heard of in the Pope’s library in Viterbo, north of Rome, in 1311. Next to disappear was Codex A; it was last recorded in the library of an Italian humanist in 1564. It was through copies of these books that Renaissance masters such as Leonardo da Vinci and Galileo knew the works of Archimedes. But Leonardo, Galileo, Newton and Leibniz knew nothing about the third book. It contained two extraordinary texts by Archimedes that were not in Codices A and B. Next to texts such as these, Leonardo’s mathematics look like child’s play.