The Number Concept

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Number Concept, The

The Project Gutenberg EBook of The Number Concept, by Levi Leonard Conant This eBook is for the use of anyone anywhere at no cost and with almost no restrictions whatsoever. You may copy it, give it away or re-use it under the terms of the Project Gutenberg License included with this eBook or online at www.gutenberg.net
Title: The Number Concept Its Origin and Development
Author: Levi Leonard Conant
Release Date: August 5, 2005 [EBook #16449]
Language: English
Character set encoding: ISO-8859-1
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[*Transcriber's Note: The following errors found in the original have been left as is.
Chapter I
, 14th paragraph: drop double quote before 'It is said';
Chapter IV
, 1st paragraph: 'so similar than' read 'so similar that';
Chapter IV
, table of Hebrew numerals (near footnote 144): insert comma after 'shemoneh';
Chapter V
, table of Tahuatan numerals (near footnote 201): 'tahi,' read 'tahi.'; Same table: ' 20,000. tufa' read '200,000. tufa';
Chapter VI
, table of Bagrimma numerals (near footnote 259): 'marta = 5 + 2' read 'marta = 5 + 3'; Same table: 'do-so = [5] + 3' read 'do-so = [5] + 4';
Chapter VII
, table of Nahuatl numerals (near footnote 365): '90-10' read '80-10'; In paragraph following that table: '+ (15 + 4) × 400 × 800' read '(15 + 4) × 20 × 400 × 8000 + (15 + 4) × 400 × 8000'; In text of footnote 297: 'II. I. p. 179' read 'II. i. p. 179'; *]
THE MACMILLAN COMPANY NEW YORK · BOSTON · CHICAGO · DALLAS ATLANTA · SAN FRANCISCO

MACMILLAN & CO., LIMITED LONDON · BOMBAY · CALCUTTA MELBOURNE

THE MACMILLAN COMPANY OF CANADA, LIMITED TORONTO

THE NUMBER CONCEPT

ITS ORIGIN AND DEVELOPMENT

BY LEVI LEONARD CONANT, PH.D. ASSOCIATE PROFESSOR OF MATHEMATICS IN THE WORCESTER POLYTECHNIC INSTITUTE

New York MACMILLAN AND CO. AND LONDON 1931

COPYRIGHT, 1896, BY THE MACMILLAN COMPANY.

COPYRIGHT, 1924, BY EMMA B. CONANT.

All rights reserved--no part of this book may be reproduced in any form without permission in writing from the publisher.

Set up and electrotyped. Published July, 1896.

Norwood Press J.S. Cushing Co.--Berwick & Smith Co. Norwood, Mass., U.S.A.

PREFACE.
In the selection of authorities which have been consulted in the preparation of this work, and to which reference is made in the following pages, great care has been taken. Original sources have been drawn upon in the majority of cases, and nearly all of these are the most recent attainable. Whenever it has not been possible to cite original and recent works, the author has quoted only such as are most standard and trustworthy. In the choice of orthography of proper names and numeral words, the forms have, in almost all cases, been written as they were found, with no attempt to reduce them to a systematic English basis. In many instances this would have been quite impossible; and, even if possible, it would have been altogether unimportant. Hence the forms, whether German, French, Italian, Spanish, or Danish in their transcription, are left unchanged. Diacritical marks are omitted, however, since the proper key could hardly be furnished in a work of this kind.
With the above exceptions, this study will, it is hoped, be found to be quite complete; and as the subject here investigated has never before been treated in any thorough and comprehensive manner, it is hoped that this book may be found helpful. The collections of numeral systems illustrating the use of the binary, the quinary, and other number systems, are, taken together, believed to be the most extensive now existing in any language. Only the cardinal numerals have been considered. The ordinals present no marked peculiarities which would, in a work of this kind, render a separate discussion necessary. Accordingly they have, though with some reluctance, been omitted entirely.
Sincere thanks are due to those who have assisted the author in the preparation of his materials. Especial acknowledgment should be made to Horatio Hale, Dr. D.G. Brinton, Frank Hamilton Cushing, and Dr. A.F. Chamberlain.
WORCESTER, MASS., Nov. 12, 1895.

CONTENTS.
Chapter I.
Counting 1
Chapter II.
Number System Limits 21
Chapter III.
Origin of Number Words 37
Chapter IV.
Origin of Number Words (_continued_) 74
Chapter V.
Miscellaneous Number Bases 100
Chapter VI.
The Quinary System 134
Chapter VII.
The Vigesimal System 176 * * * * * Index 211

THE NUMBER CONCEPT: ITS ORIGIN AND DEVELOPMENT.
CHAPTER I.
COUNTING.
Among the speculative questions which arise in connection with the study of arithmetic from a historical standpoint, the origin of number is one that has provoked much lively discussion, and has led to a great amount of learned research among the primitive and savage languages of the human race. A few simple considerations will, however, show that such research must necessarily leave this question entirely unsettled, and will indicate clearly that it is, from the very nature of things, a question to which no definite and final answer can be given.
Among the barbarous tribes