*The Hindu-Arabic numerals*(Ginn and Company, Boston, 1911). We present below the Preface written by the authors and short extracts from two reviews. The first review is by Joseph Vance McKelvey and appears in the

*Bulletin of the American Mathematical Society*

**21**(4) (1915), 202-203. The second is by Florian Cajori and appears in

*Science, New Series*

**35**(900) (1912), 501-504.

**Preface to The Hindu-Arabic numerals.**So familiar are we with the numerals that bear the misleading name of Arabic, and so extensive is their use in Europe and the Americas, that it is difficult for us to realize that their general acceptance in the transactions of commerce is a matter of only the last four centuries, and that they are unknown to a very large part of the human race to-day. It seems strange that such a labour-saving device should have struggled for nearly a thousand years after its system of place value was perfected before it replaced such crude notations as the one that the Roman conqueror made substantially universal in Europe. Such, however, is the case, and there is probably no one who has not at least some slight passing interest in the story of this struggle. To the mathematician and the student of civilization the interest is generally a deep one; to the teacher of the elements of knowledge the interest may be less marked, but nevertheless it is real; and even the business man who makes daily use of the curious symbols by which we express the numbers of commerce, cannot fail to have some appreciation for the story of the rise and progress of these tools of his trade.

This story has often been told in part, but it is a long time since any effort has been made to bring together the fragmentary narrations and to set forth the general problem of the origin and development of these numerals. In this little work we have attempted to state the history of these forms in small compass, to place before the student materials for the investigation of the problems involved, and to express as clearly as possible the results of the labours of scholars who have studied the subject in different parts of the world. We have had no theory to exploit, for the history of mathematics has seen too much of this tendency already, but as far as possible we have weighed the testimony and have set forth what seem to be the reasonable conclusions from the evidence at hand.

To facilitate the work of students an index has been prepared which we hope may be serviceable. In this the names of authors appear only when some use has been made of their opinions or when their works are first mentioned in full in a footnote.

If this work shall show more clearly the value of our number system, and shall make the study of mathematics seem more real to the teacher and student, and shall offer material for interesting some pupil more fully in his work with numbers, the authors will feel that the considerable labour involved in its preparation has not been in vain.

We desire to acknowledge our especial indebtedness to Professor Alexander Ziwet for reading all the proof, as well as for the digest of a Russian work, to Professor Clarence L Meader for Sanskrit transliterations, and to Mr Steven T Byington for Arabic transliterations and the scheme of pronunciation of Oriental names, and also our indebtedness to other scholars in Oriental learning for information.

**Review of The Hindu-Arabic numerals (1911) by: Joseph Vance McKelvey.**

*Bulletin of the American Mathematical Society***21**(4) (1915), 202-203.The origin and development of our present number system is probably given as little thought as anything that is so commonly known and used. For persons who are not interested in things mathematical, as well as for those who are thus interested, The Hindu-Arabic Numerals furnishes information that is by no means current. The authors have given in concise form the history of the characters that every school boy of modern days learns to use in computation. Beginning with an account of the early ideas about these characters, the writers go on with the details of place value, the symbol zero, and the actual physical forms by which the numbers have been represented at various times. In chapter 5 is begun the account of their introduction into Europe. This westward aggression seems to have been very slow at first because the new numerals did not appeal to the traders and were regarded as a sort of novelty by educators. The complete acceptance of this really wonderful system finally took place in the sixteenth and seventeenth centuries.

**Review of The Hindu-Arabic numerals (1911) by: Florian Cajori.**

*Science, New Series***35**(900) (1912), 501-504.This book gives in compact form a readable and carefully prepared account of the numerous researches which have been made in the endeavour to trace the origin and development of the Hindu-Arabic numerals. Teachers of mathematics will welcome it, while students specializing in the history of mathematics will derive great help from the many bibliographical references to other publications on this subject. Like the arithmetician Tonstall the authors read everything in every language and spent much time in licking what they found into shape 'ad ursi exemplum', as the bear does her cubs. But it would not be a correct statement, were we to convey the idea that the book does not embody original research. In several cases the authors have been able to correct mistakes of earlier writers and to add results of their own research. In a few instances this history appears to us in-complete and defective. ... The authors very properly give much attention to the study of routes of commercial travel. There is every reason to believe that the migrations of the numerals took place along commercial routes. The authors con-sider the possibility of an early influence of China upon India; they speak of trade routes and the interchange of thought by land and sea, between countries bordering on the Mediterranean and far-off India. They even point out early relations of Greece with China. In view of these careful studies it is singular that practically nothing should be said on the intercourse which did or did not exist between Babylonia and India during the centuries immediately preceding and following the beginning of the Christian era. They ignored a question which lies at the root of present-day speculations on the earliest traces of the principle of local value and the symbolism for zero.