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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 thisbook may be reproduced in any formwithout permission in writing fromthe 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 consultedin the preparation of this work, and to whichreference is made in the following pages, great care hasbeen taken. Original sources have been drawn upon inthe majority of cases, and nearly all of these are the mostrecent attainable. Whenever it has not been possible tocite original and recent works, the author has quoted onlysuch as are most standard and trustworthy. In the choiceof orthography of proper names and numeral words, theforms have, in almost all cases, been written as they werefound, with no attempt to reduce them to a systematicEnglish basis. In many instances this would have beenquite impossible; and, even if possible, it would have beenaltogether 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 furnishedin 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 hereinvestigated has never before been treated in any thoroughand comprehensive manner, it is hoped that this book maybe found helpful. The collections of numeral systemsillustrating the use of the binary, the quinary, and othernumber systems, are, taken together, believed to be themost extensive now existing in any language. Only thecardinal numerals have been considered. The ordinalspresent no marked peculiarities which would, in a workof this kind, render a separate discussion necessary. Accordinglythey have, though with some reluctance, beenomitted entirely.
Sincere thanks are due to those who have assisted theauthor in the preparation of his materials. Especialacknowledgment should be made to Horatio Hale, Dr. D. G. Brinton, Frank Hamilton Cushing, and Dr. A. F.Chamberlain.
Worcester, Mass., Nov. 12, 1895.