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.


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.