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Origins of Mathematical Words This Page Intentionally Left Blank Origins of Mathematical Words a Comprehensive Dictionary of Latin, Greek, and Arabic Roots Origins of Mathematical Words This page intentionally left blank 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 2715 North Charles Street Baltimore, Mary land 21218- 4363 w w w . p r e s s . j h u . e d u 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. Special discounts are available for bulk purchases of this book. For more information, please contact Special Sales at 410- 516- 6936 or [email protected]. Th e Johns Hopkins University Press uses environmentally friendly book materials, including recycled text paper that is composed of at least 30 percent post- consumer waste, whenever possible. 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 This page intentionally left blank 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 transliterated rather than translated some of the Greek technical terms, such as basis, diameter, gnomon, isosceles, orthogonal, parallel, parallelogram, rhomboid, rhombus, scalene, and trapezia; other transliterations of his did not survive the passage of time, for example, aethimata (postulates) amblygonium (obtuse-angled), oxygonium (acute-angled), and cynas etnyas (common notions or axioms). Other Greek terms he actually translated into Latin, thereby producing the ancestors of our current English words: acutus, aequiangulus, aequilaterus, aequus, alternus, angulus, circulus, circumferens, componens, contactus , describere, dividere, exterior, extremus, figura, incidere, infinitus, interior, linea, magnitudo, multilaterus, multiplicare, obtusus, perpendicularis, planus, portio, proportio, punctum, quadrilaterus, recta (right), rectiangulus, rectilineus, secans, sectio, sector, semicirculus, spatium, subtendere, superficies (surface), supplementum, tangens, trilaterus, vertex. When the conquests of Islam brought the Arabs into contact with the Byzantine Empire, the caliph requested manuscripts of scientific knowledge from the emperor at Constantinople, and the text of Euclid was introduced to the Muslims. The translations of the Greek texts into the Arabic language were the productions of learned authorities, among whom may be mentioned al-Hajjaj and Ishaq, the translators of Euclid. The following introduction to the commentary of al-Nayrizi (died circa 922) on Euclid’s Elements tells how this was done: In the name of Allah, the compassionate, the merciful! Praise be unto Allah, Lord of the worlds, and may Allah be gracious unto Mohammed and unto his family, all of them. This is the abridgment of the book of Euclid on the study of the Elements preliminary to the study of plane geometry, just as the study of the letters of the alphabet, which are the elements of composition, are preliminary to composition. This is the book which Yahya bin Khalid bin Barmak ordered to be translated from the Roman tongue [that is, Greek] into the Arabic tongue at the hands of al-Hajjaj bin Yusuf Matar. And when Allah brought into his caliphate the Imam Mamun Abdullah bin Harun, the Commander of the Faithful, who x delighted in learning and was enthusiastic about wisdom, who was close to scholars and beneficent unto them, al-Hajjaj bin Yusuf saw that he could find favor with him by correcting this book, by summing it up, and by abbreviating it. And so there was left nothing superfluous in it that he did not make succinct, nor any flaw that he did not fix, nor any defect that he did not set aright and rectify, until he had corrected it, made it certain, summed it up, and abbreviated it for people of understanding, discrimination, and learning, without his having changed any of its meaning at all. And he left the earlier edition as it stood for the public.
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