The Number Concept

Number Concept, The

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Title: The Number Concept Its Origin and Development
Author: Levi Leonard Conant
Release Date: August 5, 2005 [EBook #16449]
Language: English
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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
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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