Excerpt from Plane and Spherical Trigonometry
Of late years, in the writing of textbooks of trigonometry, a tendency to amplification has shown itself, doubtless with the idea that amplification means simplification. Unfortunately the amplification has spent itself upon details rather than upon principles, which latter have too often been inadequately treated. The result has been textbooks which overlook the comparative maturity of the boys and girls who study trigonometry and which cling almost with affection to the practices of the most elementary mathematics.
The present test aims to present the trigonometry in such a way as to make it interesting to students approaching some maturity, and so as to connect the subject, not only with the mathematics which the student has already had, but also with the mathematics which, in many cases at least, is to follow. A subject may be so burdened with detailed explanations as to become monotonous and lifeless, or, on the other hand, presented in so concise and difficult a manner as to be repellent. The present work endeavors to avoid both extremes. Full explanations are given of important principles, but many simple details are left to the work of the student.
The following points in the text may be noted:
1. Positive and negative angles of any magnitude and the trigonometric functions of such angles, defined by means of a system of rectangular coordinates, are taken up in the beginning of the book; acute angles, with their functions, being mentioned as a special ease.
2. Thus the basic trigonometric identities are got at once for all angles.
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