Isaac Newton on Mathematical Certainty and Method Niccol`oGuicciardini The MIT Press Cambridge, Massachusetts London, England c 2009 Massachusetts Institute of Technology All rights reserved. No part of this book may be reproduced in any form by any electronic or mechanical means (including photocopying, recording, or information storage and re- trieval) without permission in writing from the publisher. For information about special quantity discounts, please email special
[email protected] This book was set in Computer Modern by Compomat s.r.l., Configni (RI), Italy. Printed and bound in the United States of America. Library of Congress Cataloging-in-Publication Data Guicciardini, Niccol`o. Isaac Newton on mathematical certainty and method / Niccol`o Guicciardini. p. cm. - (Transformations : studies in the history of science and technology) Includes bibliographical references and index. isbn 978-0-262-01317-8 (hardcover : alk. paper) 1. Newton, Isaac, Sir, 1642–1727—Knowledge-Mathematics. 2. Mathematical analy- sis. 3. Mathematics-History. I. Title. QA29.N4 G85 2009 510-dc22 2008053211 10987654321 Index Abbreviations, xxi Andersen, Kirsti, 9, 140 Abel, Niels H., 40–41 Apagogical proofs (in Barrow’s sense), 177 Accountants, 5, 351 Apollonius, xviii, 15, 56, 63, 80, 81, 91, 105, Acerbi, Fabio, xviii, 83, 86, 88, 102 118, 145, 253, 342, 385 Adams, John C., 248, 307, 340, 348 Archimedes, xiii, 65–66, 145, 342 Affected equations, 136, 154, 156, 158, 162, Aristaeus, 81 166, 167, 179, 193, 194, 212, 231, Aristotelian conception of pure and mixed 345, 355, 356, 376 mathematics, 146, 172 Alchemy, 3, 238, 313, 342 Aristotelian inertia, 235 Algebra speciosa, 339 Aristotelian logic, 23 Algebraic curves, 6, 15, 42, 104, 157, 188 Aristotelian substantial forms and occult Algebraic equations qualities, 297 Newton’s method of resolution, 158–164, Aristotelian textbook tradition, 323 179, 355 Aristotle (pseudo) Problemata Mechanica, to be neglected, 256, 266, 289, 311, 344 4 used in common analysis, 5 Arithmetica speciosa, 298 used in the Principia, 259 Arthur, Richard T.