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ARS MAGNA or
The Rules of Algebra GIROLAMO CARDANO Translated and Edited by T. RICHARD WITMER With a Foreword by Oystein Ore
DOVER PUBLICATIONS, INC. New York
Copyright Copyright © 1968 by The Massachusetts Institute of Technology. All rights reserved under Pan American and International Copyright Conventions. Published in Canada by General Publishing Company, Ltd., 30 Lesmill Road, Don Mills, Toronto, Ontario. Published in the United Kingdom by Constable and Company, Ltd., 3 The Lanchesters, 162-164 Fulham Palace Road, London W6 9ER.
Bibliographical Note This Dover edition, first published in 1993, is an unabridged republication of the edition published by The MIT Press in 1968 under the title The Great Art or The Rules if Algebra. It was translated and edited from the 1545 edition of Artis maguac, sive de regillis algebraic is. Lib. U/lUS. Qui & tot ius operis de aritlunetica, quod opus Peifectlllll inscripsit, est in ordine decimus with additions from the 1570 and 1663 editions. This Dover edition is published by special arrangement with The MIT Press, 55 Hayward Street, Cambridge, Massachusetts 02142.
Library of Congress Cataloging-in-Publication Data Cardano, Girolamo, 1501-1576. lArs magna. Liber l. English) Ars magna, or, The rules of algebra / Girolamo Cardano translated and edited by T. Richard Witmer ; with a foreword by Oystein Ore. p. cm. Originally published: The great art, or The rules of algebra. Cambridge, Mass. : M.I.T. Press, 1968, which was translated and edited from the 1545 ed. of Ars magna, liber unus, with additions from the 1570 and 1663 eds. Includes bibliographical references and index. ISBN 0-486-67811-3 (pbk.) l. Algebra-Early works to 1800. I. Witmer, T. Richard, 1909II. Title. III. Title: Ars magna. IV. Title: Rules of algebra. QAl54.8.C3713 1993 512.9'4-dc20 93-34446 CIP
Manufactured in the United States of America Dover Publications, Inc., 31 East 2nd Street, Mineola, N.Y. 11501
Table
FOREWORD
of Contents
by Oystein Ore
xv
PREFACE
The Great Art, or The Rules
Vll
of Algebra
by Girolamo Cardano ApPENDIX
Portions of Euclid's Elements Cited by Cardano INDEX
262 265
Foreword It has often been pointed out that three of the greatest masterpieces of science created during the Rinascimento appeared in print almost simultaneously: Copernicus, De Revolutionibus Orbium Coelestium (1543) ; Vesalius, De Fabrica Humani Corporis (1543), and finally Girolamo Cardano, Artis Magnae Sive de Regulis Algebraicis (1545). But while the two first works have been readily available in magnificent editions and excellent translations, Cardano's Ars Magna has remained relatively obscure, its material confined to early and now rare Latin editions. The Ars Magna has always been highly praised as a milestone in th