BY
DAVID EUGENE SMITH
AND
LOUIS CHARLES KARPINSKI

BOSTON AND LONDON
GINN AND COMPANY, PUBLISHERS
1911

COPYRIGHT, 1911, BY DAVID EUGENE SMITH
AND LOUIS CHARLES KARPINSKI
ALL RIGHTS RESERVED
811.7

The AthenÆum Press
GINN AND COMPANY · PROPRIETORS
BOSTON · U.S.A.

PREFACE

So familiar are we with the numerals that bear the misleading name of Arabic, and so extensive is their use in Europe and the Americas, that it is difficult for us to realize that their general acceptance in the transactions of commerce is a matter of only the last four centuries, and that they are unknown to a very large part of the human race to-day. It seems strange that such a labor-saving device should have struggled for nearly a thousand years after its system of place value was perfected before it replaced such crude notations as the one that the Roman conqueror made substantially universal in Europe. Such, however, is the case, and there is probably no one who has not at least some slight passing interest in the story of this struggle. To the mathematician and the student of civilization the interest is generally a deep one; to the teacher of the elements of knowledge the interest may be less marked, but nevertheless it is real; and even the business man who makes daily use of the curious symbols by which we express the numbers of commerce, cannot fail to have some appreciation for the story of the rise and progress of these tools of his trade.

This story has often been told in part, but it is a long time since any effort has been made to bring together the fragmentary narrations and to set forth the general problem of the origin and development of these numerals. In this little work we have attempted to state the history of these forms in small compass, to place before the student materials for the investigation of the problems involved, and to express as clearly as possible the results of the labors of scholars who have studied the subject in different parts of the world. We have had no theory to exploit, for the history of mathematics has seen too much of this tendency already, but as far as possible we have weighed the testimony and have set forth what seem to be the reasonable conclusions from the evidence at hand.

To facilitate the work of students an index has been prepared which we hope may be serviceable. In this the names of authors appear only when some use has been made of their opinions or when their works are first mentioned in full in a footnote.

If this work shall show more clearly the value of our number system, and shall make the study of mathematics seem more real to the teacher and student, and shall offer material for interesting some pupil more fully in his work with numbers, the authors will feel that the considerable labor involved in its preparation has not been in vain.

We desire to acknowledge our especial indebtedness to Professor Alexander Ziwet for reading all the proof, as well as for the digest of a Russian work, to Professor Clarence L. Meader for Sanskrit transliterations, and to Mr. Steven T. Byington for Arabic transliterations and the scheme of pronunciation of Oriental names, and also our indebtedness to other scholars in Oriental learning for information.

DAVID EUGENE SMITH

LOUIS CHARLES KARPINSKI

CONTENTS

PRONUNCIATION OF ORIENTAL NAMES

(S) = in Sanskrit names and words; (A) = in Arabic names and words.

b, d, f, g, h, j, l, m, n, p, sh (A), t, th (A), v, w, x, z, as in English.

a, (S) like u in but: thus pandit, pronounced pundit. (A) like a in ask or in man. a, as in father.

c, (S) like ch in church (Italian c in cento).

?, ?, ?, ?, (S) d, n, sh, t, made with the tip of the tongue turned up and back into the dome of the palate. ?, ?, ?, ?, (A) d, s, t, z, made with the tongue spread so that the sounds are produced largely against the side teeth. Europeans commonly pronounce ?, ?, ?, ?, ?, both (S) and (A), as simple d, n, sh (S) or s (A), t, z. ? (A), like th in this.

e, (S) as in they. (A) as in bed.

g, (A) a voiced consonant formed below the vocal cords; its sound is compared by some to a g, by others to a guttural r; in Arabic words adopted into English it is represented by gh (e.g. ghoul), less often r (e.g. razzia).

h preceded by b, c, t, ?, etc. does not form a single sound with these letters, but is a more or less distinct h sound following them; cf. the sounds in abhor, boathook, etc., or, more accurately for (S), the "bhoys" etc. of Irish brogue. h (A) retains its consonant sound at the end of a word. ?, (A) an unvoiced consonant formed below the vocal cords; its sound is sometimes compared to German hard ch, and may be represented by an h as strong as possible. In Arabic words adopted into English it is represented by h, e.g. in sahib, hakeem. ? (S) is final consonant h, like final h (A).

i, as in pin. i, as in pique.

k, as in kick.

kh, (A) the hard ch of Scotch loch, German ach, especially of German as pronounced by the Swiss.

?, ?, (S) like French final m or n, nasalizing the preceding vowel.

?, see ?. Ñ, like ng in singing.

o, (S) as in so. (A) as in obey.

q, (A) like k (or c) in cook; further back in the mouth than in kick.

r, (S) English r, smooth and untrilled. (A) stronger. ?, (S) r used as vowel, as in apron when pronounced aprn and not apern; modern Hindus say ri, hence our amrita, Krishna, for a-m?ta, K???a.

s, as in same. ?, see ?. s, (S) English sh (German sch).

?, see ?.

u, as in put. u, as in rule.

y, as in you.

?, see ?.

', (A) a sound kindred to the spiritus lenis (that is, to our ears, the mere distinct separation of a vowel from the preceding sound, as at the beginning of a word in German) and to ?. The ' is a very distinct sound in Arabic, but is more nearly represented by the spiritus lenis than by any sound that we can produce without much special training. That is, it should be treated as silent, but the sounds that precede and follow it should not run together. In Arabic words adopted into English it is treated as silent, e.g. in Arab, amber, Caaba ('Arab, 'anbar, ka'abah).

(A) A final long vowel is shortened before al ('l) or ibn (whose i is then silent).

Accent: (S) as if Latin; in determining the place of the accent ? and ? count as consonants, but h after another consonant does not. (A), on the last syllable that contains a long vowel or a vowel followed by two consonants, except that a final long vowel is not ordinarily accented; if there is no long vowel nor two consecutive consonants, the accent falls on the first syllable. The words al and ibn are never accented.