[Book Reviews]

Abstract

IN the 500 pages of which this volume consists, the author has placed before students of trigonometry an elementary text-book which only wants reading carefully to be thoroughly understood. One cannot do more than state in clear and plain language the various methods of expressing trigonometrical ratios, the applications of algebraic signs, ratios of multiple and sub-multiple angles, &c.; and this the author has done, interpolating neatly printed figures and concise explanations wherever they seem necessary for a clearer exposition. A great number of excellent examples is also given, the answers being collected at the end. No very marked deviations from the usual sequence of the subject-matter adopted in such text-books have been made, but it is noticeable that here and there are given at some length many pieces of book-work which are passed over in a few words in some books. The second of the two parts into which the book is divided deals more with the analytical side of trigonometry, that is, with exponential and logarithmic series, expansions of trigonometrical quantities, summations of series, &c. In this part the treatment of complex quantities has been so handled as to lead the student up to the methods of the more advanced treatises. The concluding two chapters deal briefly with errors of observations, some miscellaneous propositions, solution of a cubic equation, maximum and minimum values, &c. A very useful list of all the principal formulas which the student should commit to memory is separately printed, and precedes the first chapter. Beginners will find it better on their first reading to omit the articles specially marked for this end, and also to make selections from the examples. It would be hard to find a better introduction to plane trigonometry book.

Plane Trigonometry.

By S. L. Loney. (Cambridge: University Press, 1893.)