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

The Number Concept

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