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.