(1) MR. MERCER possesses a fine conception of how trigonometry should be presented to youths, and his book is admirable and altogether good. The development of the subject is very gradual indeed, and is constantly enforced by means of concrete examples, systematic computations, practical geometry, and by judicious graphs. Thus the first ten chapters are confined to the development of the simple trigonometrical ratios, that is, to the solution and application of right-angled triangles, under all sorts of conditions, such as in problems of elementary surveying, the resolution of vectors, areas, solutions of triangles in general, &c., and later on additional illustrations of right-angled triangles occur in the chapter on traverse tables. Four-figure mathematical tables, including logarithms, are in constant use, and careful attention is paid to arrangement and checking of the numerical work. After this thorough grounding, angles of any magnitude are introduced, and triangles are solved by general formulæ, a useful table of log. haversines being here provided. Then the radian measure of an angle is explained, and the treatment becomes more abstract, the final chapters dealing with multiple and submultiple angles, transformation formul, identities, equations, and inverse notation. Finally, there are two hundred miscellaneous examples grouped in sets of five, and collected answers to the very numerous exercises distributed throughout the book. The author is to be congratulated on having produced a very notable text-book on elementary trigonometry, and one that is worthy of adoption in the secondary, technical, and public schools throughout the country.
(1) Trigonometry for Beginners.
By J. W. Mercer. Pp. xi + 351. (Cambridge: University Press, 1906.) Price 4s.
(2) Trigonometry for Beginners.
By Rev. J. B. Lock J. M. Child. Pp. vii + 195. (London: Macmillan and Co., Ltd., 1906.) Price 2s. 6d.
(3) Geometry: an Elementary Treatise on the Theory and Practice of Euclid.
By S. O. Andrew. Revised edition. Pp. xii + 218. (London: John Murray, 1906.) Price 2s.
(4) Modern Commercial Arithmetic.
Part i. By G. H. Douglas. Pp. 163. (London: Macmillan and Co., Ltd., 1906.) Price 1s. 6d.
(5) A New Shilling Arithmetic.
By C. Pendlebury, assisted by F. E. Robinson. Pp. xii + 176 + xxxiv. (London: George Bell and Sons, 1906.) Price, with answers, 1s. 4d.
(6) Junior Arithmetic Examples.
By W. G. Borchardt. Pp. viii + 171 + xl. (London: Rivingtons, 1906.) Price 1s. 6d.
(7) Clive's New Shil1ing Arithmetic.
Edited by Dr. W. Briggs. Pp. viii + 160. (London: W. B. Clive, University Tutorial Press, Ltd., 1906.) Price 1s.
(8) Junior Practical Mathematics.
By W. J. Stainer. Pp. x + 350. (London: George Bell and Sons, 1906.) Price 3s.
(9) A Rhythmic Approach to Mathematics.
By Edith L. Somervell, with a preface by Mary Everest Boole. Pp. 67. (London: George Philip and Son, Ltd., 1906.) Price 2s. 6d. net.
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(1) Trigonometry for Beginners (2) Trigonometry for Beginners (3) Geometry: an Elementary Treatise on the Theory and Practice of Euclid (4) Modern Commercial Arithmetic (5) A New Shilling Arithmetic (6) Junior Arithmetic Examples (7) Clive's New Shil1ing Arithmetic (8) Junior Practical Mathematics (9) A Rhythmic Approach to Mathematics . Nature 75, 409–410 (1907) doi:10.1038/075409a0