Origins of mathematical words: a comprehensive dictionary of Latin, Greek, and Arabic roots

369 Pages·2013·3.61 MB·English

by  Anthony Lo Bello

Origins of Mathematical Words
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Origins of
Mathematical
Words
A Comprehensive Dictionary of Latin, Greek, and Arabic Roots
Anthony Lo Bello
The Johns Hopkins University Press
Baltimore
© 2013 Th e Johns Hopkins University Press
All rights reserved. Published 2013
Printed in the United States of America on acid- free paper
2 4 6 8 9 7 5 3 1
Th e Johns Hopkins University Press
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Library of Congress Cataloging- in- Publication Data
Lo Bello, Anthony, 1947–
Origins of mathematical words : a comprehensive dictionary of Latin, Greek,
and Arabic roots / by Anthony Lo Bello.
pages cm
Includes bibliographical references.
ISBN- 13: 978- 1- 4214- 1098- 2 (pbk. : alk. paper)
ISBN- 10: 1- 4214- 1098- 2 (pbk. : alk. paper)
ISBN- 13: 978- 1- 4214- 1099- 9 (electronic)
ISBN- 10: 1- 4214- 1099- 0 (electronic)
1. Mathematics– Terminology. I. Title.
QA41.3.B45 2013
510.1'4–dc23 2013005022
A cata log record for this book is available from the British Library.
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Contents
Preface vii
A 1 N 220
B 42 O 227
C 50 P 233
D 102 Q 264
E 118 R 269
F 145 S 283
G 151 T 309
H 158 U 335
I 170 V 339
J 189 W 344
K 190 X 344
L 191 Y 344
M 198 Z 345
Bibliography 346
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Preface

This is a book about words, mathematical words, how they
are made and how they are used. If one admits the proverb that life
without literature is death, then one must agree that the correct
formation and use of words is essential for any literature, whether
mathematical or otherwise.

If the way in which men express their thoughts is slipshod and
mean, it will be very difficult for their thoughts themselves to
escape being the same. (Henry Alford, A Plea for the Queen’s
English: Stray Notes on Speaking and Spelling, tenth thousand,
Alexander Strahan publisher, London and New York, 1866,
pp. 5–6)

In October 2008, Trevor Lipscombe, at the time editor-in-
chief of the Johns Hopkins University Press, suggested to me that I
undertake to write what he called a discursive etymological dictionary of
mathematical words whose origins were in Greek, Latin, or Arabic, that
is to say, in those languages that I have studied sufficiently so as to be
able to comment on the derivations of words that proceeded from
them.
There are other dictionaries of mathematical words. That of
James and James (Mathematics Dictionary, van Nostrand Reinhold, New
York, 1959) is justly famous, but it is not an etymological dictionary,
so the reader will find little in these pages that might already have
been discovered in theirs. The valuable work of Schwartzman (The
Words of Mathematics, Mathematical Association of America, 1994)
vii
may be consulted with benefit by anyone who looks into this book,
and such an investigator will notice the ways in which I differ from
my learned colleague: I have retained the Greek and Arabic alphabets
to avoid the dark and doubtful consequences of transliteration, I have
sat in judgment on the correctness of the words I explain, and I have
used my license to be discursive to discuss not only the function of
mathematics in liberal education but also English usage among
mathematicians and their colleagues in the learned world. Since the
majority of mathematicians earn their living on the faculties of
colleges and universities, I have further commented on the use of
words and the style of prose to be found nowadays in these
establishments, and which mathematicians for the most part have
adopted in their bureaucratic activities such as committee reports,
minutes, departmental newsletters, and discussions about
mathematics education and curriculum.
Although Herodotus assures us that mathematics, like Egypt,
was the gift of the Nile, the Egyptian language had no influence on
subsequent mathematical vocabulary. Neither did the inhabitants of
Mesopotamia employ any word that survives in modern
mathematical usage. The Greeks, as the word mathematics itself
testifies, were the people responsible for developing our subject as
the system of consecutive thought as we know it today, and it is to
their language that the earliest mathematical words still in use are to
be traced. As mathematics is a Greek word, so the earliest mathematical
vocabulary was Greek. The mathematical vocabulary of the Greeks
has for two thousand years been the common patrimony of our
science. It was among the Greeks that the principle ars gratia artis was
first applied to mathematics; it is a principle on which the chief of the
philosophes commented disapprovingly in the book in which he
introduced Newton to the continent:

viii
…Tous les arts sont à peu près dans ce cas; il y a un point, passé
lequel les recherches ne sont plus que pour la curiosité: ces
verities ingénieuses et inutiles ressemblent à des étoiles qui,
places trop loin de nous, ne nous donnent point de claret.
(Voltaire, Lettres philosophiques, ou Lettres anglaises, Éditions Garnier
Frères, Paris, 1964, vingt-quatrième lettre, p. 139)

…This is very nearly the case with most of the arts: there is a
certain point beyond which all researches serve to no other
purpose than merely to delight an inquisitive mind. Those
ingenious and useless truths may be compared to stars which, by
being placed at too great a distance, cannot afford us the least
light. (Translation found in the Harvard Classics, Easton Press
Millennium Edition, vol. 34, French and English Philosophers,
p. 162)

During the period of the Roman Empire, some of the Greek
mathematical literature was translated into the Latin tongue, although
the most common practice was to study the subject in the language in
which it was written and even to travel to Greece to do so, as Horace
(Epistiolarum liber II 2, 41–45) testified:

Romae nutriri mihi contigit atque doceri,
Iratus Grais quantum nocuisset Achilles.
Adiecere bonae paulo plus artis Athenae,
Scilicet ut vellem curvo dinoscere rectum
Atque inter silvas Academi quaerere verum.

It was my Fortune to be bred and taught
At Rome, what Woes enrag’d Achilles wrought
To Greece: kind Athens yet improv’d my Parts
With some small Tincture of ingenuous Arts,
To learn a right Line from a Curve, and rove
In search of Wisdom through the museful Grove.
(Translation by Francis)

The chief early Latin translation of a Greek mathematical text was
the edition by Boëthius of the Elements of Euclid, accomplished in the
late fifth century A.D., shortly after the fall of Rome. Boëthius
ix