Fibonacci’s Liber Abaci: A Translation into Modern English of Leonardo Pisano’s Book of Calculation

634 Pages·2002·20.62 MB·English

by  Laurence Sigler (auth.)

Sources and Studies
in the History of Mathematics and
Physical Sciences
Editorial Board
1.Z. Buchwald 1. Llitzen G.J. Toomer
Advisory Board
P.J. Davis T. Hawkins
A.E. Shapiro D. Whiteside
Springer Science+Business Media, LLC
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Springer
Laurence Sigler (deceased)
Mathematics
Bucknell University
Lewisburg, PA 17837
Sources and Studies Editor:
Gerald J. Toomer
2800 South Ocean Boulevard, 21 F
Boca Raton, FL 33432
USA
Library of Congress Cataloging-in-Publication Data
Fibonacci, Leonardo, ca. 1170-ca. 1240
[Liber abaci. English]
Fibonacci's Liber abaci : a translation into modem English of Leonardo Pisano's Book
of calculation / [translated by] Laurence Sigler
p. cm.-(Source and studies in the history ofmathematics and physical sciences)
Includes bibliographical references.
1. Mathematics, Medieval. 2. Mathematics-Early Works to 1800. I. Sigler, L.E.
II. Title III. Sources and studies in the history of mathematics and physical sciences.
QA32 .F4713 2002
51O-de21
ISBN 978-0-387-40737-1 ISBN 978-1-4613-0079-3 (eBook)
DOI 1O.1007/978-1-4613-0079-3 2001057722
Printed on aeid-free paper.
First softeover printing, 2003
© 2002 Springer Science+Busiess Media New York
Originally published by Springer-Verlag New York, Ine in 2002
AII rights reserved. This work may not be translated or copied in whole or 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. lJse in connection with any form ofinformation storage and retrieval, electronic
adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed
is forbidden. The use in this publication of trade names, trademarks, service marks, and similar terms, even
if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are
subject to proprietary rights.
9 8 7 6 5 4 3 2 I SPIN 10953310
Typesetting: Pages created by the author using a Springer TEX macro paekage.
www.springer-ny.com
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Contents
I Introduction 1
II rebiL icabA 31
1 Here snigeB the First Chapter 71
2 nO the Multiplication of elohW Numbers 32
3 nO the Addition of elohW Numbers 93
4 nO the Subtraction of resseL Numbers morf Greater srebmuN 54
5 nO the snoisiviD fo Integral Numbers 94
6 nO the Multiplication fo Integral Numbers htiw Fractions 77
7 nO the Addition dna Subtraction and noisiviD fO Numbers
with Fractions dna the Reduction of lareveS Parts to
a elgniS Part 99
8 nO gnidniF ehT eulaV of esidnahcreM yb the Principal Method 721
9 nO the Barter of esidnahcreM and ralimiS sgnihT 971
01 nO seinapmoC dna Their srebmeM 312
11 nO the gniyollA of seinoM 722
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21 Here snigeB Chapter evlewT 952
31 nO the Method Elchataym and woH with It ylraeN llA
Problems of Mathematics erA devloS 744
41 nO gnidniF Square dna cibuC Roots, and no the ,noitacilpitluM
,noisiviD and Subtraction of Them, and nO the Treatment
of slaimoniB and semotopA and their stooR 984
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Part I
Introduction
L. Sigler, Fibonacci's Liber Abaci
© Springer-Verlag New York, Inc. 2002
Liber abaci is one of the most important books on mathematics of the
Middle Ages. Its effect was enormous in disseminating the Hindu number sys
temandthemethodsofalgebrathroughout Europe. Thisis thefirst translation
of the Latin manuscript of Liber abaci into a modern language. It is hoped
that itsavailability to historians, mathematicians, and the publicingeneral will
make a contribution to their knowledge of this part of our cultural heritage.
Mathematics and science are, after all, as much a part ofour culture as litera
ture, art, and music. It is as important for a person to know about the classics
ofmathematics and science as it is to know about the classics ofliterature and
art.
Leonardo Pisano, known today to mathematicians and scientists over the
world by the name Fibonacci, was a citizen ofthe maritime city-state of Pisa
from 1170untilafter1240. ThiswasthetimeoftheCrusades,ofstrongpolitical
conflicts between the Emperor Frederick IIofthe Holy Roman Empire and the
Papacy; it was also the time of the religious fervor of St. Francis of Assisi.
The Italian maritime states of Pisa, Genoa, Venice and Amalfi were locked in
intensetrade rivalry throughout theMediterraneanworld, includingByzantium
and the Muslim countries.
Leonardo was instructed in mathematics as a youth in Bugia, a trading
enclave established by the city of Pisa and located on the Barbary Coast of
Africa in the Western Muslim Empire. He continued to develop as a mathe
matician by traveling on business and studying in such places as Egypt, Syria,
Provence, and Byzantium. He developed contacts with scientists throughout
the Mediterranean world. He became proficient in Euclid's Elements, and the
Greek mathematical methodofdefinition, theorem, and proof. Helearned from
the Arabic scientists the Hindu numbers and their place system, and the al
gorithms for the arithmetic operations. He also learned the method ofalgebra
principallyfound in theworkofal-KhwarizmI[K]. Through hisstudyand travel
and learned disputations with world scientists, he became a very superior cre
ative mathematician. He participated in the academiccourtofFrederickII who
sought out and recognized great scholars of the thirteenth century. Leonardo
with his scientific knowledge saw clearly the advantages of the useful mathe
matics known to the Muslim scientists, principally their Hindu numerals and
decimal place system, their calculating algorithms, and their algebra. Knowl
edge of the Hindu numerals began to reach Europe in the second half of the
tenth century through the Arabs by wayofSpain, however their usage was still
not a general practice at Leonardo's time. Leonardo resolved to write his en
cyclopedic work, Liber abaci, to bring to the Italian people the world's best
mathematics in a usable form.
Calculation has been an activity of mankind since ancient times. It was
facilitated by various mechanical devices that by Greek and Roman times had
developed into the abacus. The best known form consists of a wooden frame
strung with wires on which are mounted beads for counters. The efficiency of
this abacus isattestedtobyitssurvivaland use insome partsoftheworldeven
today. There were also early forms of the abacus consisting oftables of wood