Sources and Studies in the History of Mathematics and Physical Sciences Editorial Board J.Z. Buchwald J. Liitzen G.J. Toomer Advisory Board P.J. Davis T. Hawkins A.E. Shapiro D. Whiteside Springer Science+Business Media, LLC
Sources and Studies in the History of Mathematics and Physical Sciences K. Andersen Brook Taylor's Work on Linear Perspective I. CannonlS. Dostrovsky The Evolution of Dynamics: Vibration Theory from 1681 to 1142 B. ChandlerlW. Magnus The History of Combinatorial Group Theory A.I. Dale A History of Inverse Probability: From Thomas Bayes to Karl Pearson, Second Edition A.I. Dale Pierre-Simon Laplace, Philosophical Essay on Probabilities, Translated from the fifth French edition of 1825, with Notes by the Translator p.i. Federico Descartes on Polyhedra: A Study of the De Solidorum Elementis B.R. Goldstein The Astronomy of Levi ben Gerson (1288-1344) H.H. Goldstine A History of Numerical Analysis from the 16th through the 19th Century H.H. Goldstine A History of the Calculus of Variations from the 11th through the 19th Century G. GraBhoff The History of Ptolemy's Star Catalogue A. W. Grootendorst Jan de Witt's Elementa Curvarum Linearum, Liber Primus T. Hawkins The Emergence of the Theory of Lie Groups: An Essay in the History of Mathematics 1869-1926 A. Hermann, K. von Meyenn, VE Weisskopf (Eds.) Wolfgang Pauli: Scientific Correspondence I: 1919-1929 c.c. HeydelE. Seneta I.J. Bienayme: Statistical Theory Anticipated I.P. Hogendijk IbnAI-Haytham's Completion of the Conics A. Jones (Ed.) Pappus of Alexandria, Book 7 of the Collection Continued after Index
Jan de Witt's Elementa Curvarum Linearum, Liber Primus Text, Translation, Introduction, and Commentary by Albert W. Grootendorst With the Help of Miente Bakker With 150 Illustrations ~, T Springer
Albert W. Grootendorst Department of Mathematics (Emeritus) Delft University Aardbeistraat II The Hague 2564 TW The Netherlands Sources and Studies Editor Gerald 1. Toomer 2800 South Ocean Boulevard, 21 F Boca Raton, FI... 33432 USA Library of Congress Cataloging-in-Publication Data Witt. Johan de, 1625-1672. [Elementa curvarum linearum-liber primus. English.] Jan de Witt's "elementa curvarum: / text, translation, introduction, and commentary by Albert W. Grootendorst with the help of Miente Bakker. p. cm. - (Sources and studies in the history of mathematics and physical sciences) Includes bibliographical references and index. ISBN 978-1-4612-7056-0 ISBN 978-1-4612-1238-6 (ebook) DOI 10.1007/978-1-4612-1238-6 1. Geometry, Analytic-Early works ta 1800. 1. Grootendorst. A. W. II. Bakker, Miente. III. Title. IV. Series. QA551.W7613 2000 516--dc21 99-053565 Printed on acid-free paper. 2000 Springer Science+Business Mettia New York Originally published by Springer-Verlag New Yodl:,!nc.in 2000 Softcover reprint of the hardcover l st editian 2000 AII rights reserved. This wark may not be translated or copied in whole ar in part without the written permis sion of the publisher (Springer Science+Business Media. LLC), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use of general descriptive names. trade names. trademalks, etc., in this publication, even if the former are not especiaily identified, is not to be taken as a sign that such names, as understood by the Trade Marks and Merchandise Marks Act, may accordingly be used freely by anyone. Production managed by Terry Komak; manufacturing supervised by Joe Quatela. Photocomposed copy prepared from the author's LATEX files. ISBN 978-1-4612-7056-0 9 8 7 6 5 4 3 2 1
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Jan de Witt (1625-1672) Adriaen Hanneman (1601-1671) pinxit. Source: Museum Boijmans Van Beuningen, Rotterdam
Preface The present book is a translation into English of Elernenta CU'f'Varurn Linearurn-Liber Prirnus, written in Latin, by the Dutch statesman and mathematician Jan de Witt (1625-1672). Together with its sequel, Elernenta CU'f'Varurn Linearurn-Liber Secundus, it constitutes the first textbook on Analytic Geometry, based on the ideas of Descartes, as laid down in his Geornetrie of 1637. The first edition of de Witt's work appeared in 1659 and this translation is its first translation into English. For more details the reader is referred to the Introduction. Apart from this translation and this introduction, the present work contains an extensive summary, annotations to the translation, and two appendices on the role of the conics in Greek mathematics. The translation has been made from the second edition, printed by the Blaeu Company in Amsterdam in 1684. In 1997 the translator published a translation into Dutch of the same work, likewise supplied with an introduction, a summary, notes, and two appendices. This edition appeared as a publication of the Stichting Mathematisch Centrum Amsterdam. The present translation, however, is a direct translation of the Latin text. The rest of this work is an English version of the introduction, the summary, the notes, and the appendices, based on the Dutch original. Of course, I am greatly indebted to several people who advised me during the process of translating. In the first place I thank my friend and colleague Dr. Miente Bakker whose critical mind and great skill in the field of text processing have substantially contributed to this publication.
viii Preface A number of colleagues have read parts of the manuscript. They are: Dr. J.J. Schoorl, who checked the Introduction and to whom I owe a considerable increase of my knowledge of English grammar; Dr. Adrian Rice, who read the whole translation and the annotations to this translation; Dr. Anke van Zanten and her husband, Prof. A.J. van Zanten, who read the appendices; and Mrs. M. Lange and her husband, Dr. E. Lange, who checked the translation of de Witt's letter to van Schooten. Of course I am fully responsible for the remaining errors. I would also like to thank Dr. J.P. Hogendijk, who introduced me to Dr. Rice. Many thanks also to Tobias Baanders, who drew the fine figures illustrating the text. I am also grateful to the Management of Stichting Mathematisch Centrum in Amsterdam for giving their permission for this translation. Finally I thank Springer-Verlag for the publication of this edition, especially Dr. Catriona Byrne and Dr. Thomas von Foerster, for their initiative and constant cooperation, the production editor Ms. Terry Kornak, and the copy editor Ms. Julia Brainin for the meticulous way they read and corrected the proofs. The Hague, April 2000 A.W. Grootendorst
Contents Preface vii 1 Introduction 1 2 Summary 15 3 Latin text and translation 37 4 Annotations to the translation 217 Appendices A Application of areas 263 B The conic sections in Apollonius 275 References 285 Index 289
Albert Grootendorst (*1924) studied mathematics at Leiden University, where he obtained his Ph.D. for a dissertation on Theta-series in relativequadratic number fields (1959); his supervisor was Professor H.D. Kloosterman. From 1952 to 1956 he was a teacher at a grammar school in the Hague. From 1956 to 1989 he was attached to Delft University of Technology as a member of the scientific staff, a lecturer, and a full professor, respectively. In cooperation with his colleague Professor B. Meulenbeld he wrote a textbook on analysis in three volumes. He also translated a number of seventeenth-century mathematical texts from Latin into Dutch and into English, and wrote a number of articles on the history of mathematics. With Professor W.C. Waterhouse and Dr. C. Greitzer he revised Clarke's translation of Disquisitiones Arithmeticae by C.F. GauB. His main research interests are Greek mathematics and seventeenth-century mathematics.