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    IF the knowledge of the subject under consideration varied directly as the number of text-books on that subject, there is no doubt that elementary trigonometry would be running very high for the first place among school-books. The law of the survival of the fittest, in its manifold forms, is appropriate for text-books, if for anything, and it is perhaps good that this is so, as we should soon be flooded out by their excessive number. Of late, however, books for beginners on this branch of mathematics have been of a high standard of excellence, and the one before us is no exception. The joint authors are well known for their school books on algebra, and their great experience in teaching has given them a real insight into “how to teach.” To briefly enumerate the points which the authors name as special to this book, we may commence by saying that only those elementary parts have been handled which do not require the use of infinite series and imaginary quantities. Special prominence is given to examples, &c. on easy identities and equations, to enable the beginner to thoroughly master the fundamental properties of trigonometrical ratios. The subject of radian or circular measure is with advantage referred to later. Logarithms are fully dealt with, and special attention has been given to the exposition of problems on heights and distances. The examples in all chapters are numerous and typical. This book can safely be recommended to beginners, and it may, besides imparting to them a sound elementary knowledge of the subject, ingraft an intelligent interest for more advanced study.

    Elementary Trigonometry.

    By H. S. Hall S. R. Knight (London: Macmillan and Co., 1893.)

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