REVIEWS 161 



A Comparative Study of the Early Treatisei Introducing into Europe the 

 Hindu Art of Reckoning. By Suzan Rose Benedict. [Pp. vi + 126.] 

 (Concord, N. H. : The Rumford Press, 1914.) 



This work is a thesis submitted in partial fulfilment of the requirements for the 

 degree of Doctor of Philosophy in the University of Michigan in 1914, and consists 

 of a very laborious and useful contribution to our knowledge of the development 

 of mathematics from the Dark Ages to the Renaissance. This development is not 

 nearly so thoroughly treated in even the best histories of mathematics as it should 

 be, and the most important contributions are in periodical literature. Hence the 

 need of such works as the present one. "As a first step," says Miss Benedict 

 (p. 2), " it seemed advisable to find the arithmetics of this period which have been 

 published, and to make a bibliography which may perhaps save valuable time for 

 some later study. Accordingly, a systematic search has been made, and all the 

 treatises found, unless dealing exclusively with abacus reckoning, have been noted. 

 There is included in this bibliography, where it has been possible to find such 

 information, the name and date of the treatise, a few words concerning the author, 

 the library where the manuscript may be found, and the journal or monograph in 

 which it is published. There is added to this a brief account of the contents, the 

 approximate length, and, in the case of Latin works, the words of the beginning 

 and end." The bibliography (pp. 4-22) extends from Brahmagupta to Peurbach. 

 The scope of this work has had to be limited to a discussion of the fundamental 

 operations upon integers, numeration, addition, subtraction, mediation, duplation, 

 multiplication, and division (pp. 23-116). It is, perhaps, unfortunate that German 

 works should have modified the spelling of English so much that " Lewi " appears 

 for " Levi." Miss Benedict finds (p. 117) that " it is impossible to conclude that 

 China contributed to the mathematical knowledge of India," that " the suggestion 

 of Greek influence need hardly be considered,'' and that "among the Hindus, 

 mathematics was developed not as a subject of value in itself, but as an aid to 

 religious ceremonies or business transactions." I think that her second result 

 may be doubted. Philip E. B. Jourdain. 



Theory of Errors and Least Squares : A Text-book for College Students and 

 Research Workers. By Le Roy D. Weld, M.S., Professor of Physics 

 in Coe College. [Pp. xiv+190.] (New York : The Macmillan Co.; 

 London : Macmillan & Co., Ltd., 1916. Price 5s. 6d. net.) 



This is a very simply written and practical text-book on the theory of the 

 distribution of errors, which is of such great importance in all the natural sciences. 

 The chapters deal with measurement, its nature and inaccuracies ; the occurrence 

 and general properties of errors ; probabilities ; the error equation and the 

 principle of least squares, in which Gauss's deduction of the error equation is 

 given in preference to that of Hagen ; the adjustment of indirect observations, 

 with illustrations from various sciences; empirical formulae; weighted observa- 

 tions; precision and the probable error. An appendix contains supplementary 

 notes chiefly of a mathematical nature, together with a collection of important 

 definitions and theorems for convenient reference. 



The reading of this book inspires us with the lively desire that at least the 

 elementary questions of the theory of errors should be included in all elementary 

 courses of mathematics. A good place for this theory would be just after where 

 probabilities are treated in most books on what is called in schools " higher 

 algebra." Philip E. B. Jourdain. 



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