PREFACE. THE aim of the author in this treatise has been to present to the student in as concise a form as is consistent with clearness that portion of the subject of Trigonometry which is generally given in a college course. The first part of the subject is presented in much detail, each point being emphasized as far as possible by means of numerous examples and illustrations. Farther on the student is thrown more upon his own resources, with the object of developing in him the power of making intelligent use of the materials furnished by the previous part of the course. If a shorter course is desired, it may be had, without impairing the continuity of the text, by omitting §§ 8, 38, 42, 47-49, 51, 52, 57–59, 73, 74, 76–84, 95, 96, 106, 111, 114, 116, 118, 120, 125, and 126. Any who prefer to take up the solution of right triangles before the derivation of the general formulæ may insert §§ 53–56 immediately after § 24. In the chapter upon the solution of spherical oblique triangles it will be seen that two methods of solution are given for each of the first four cases, one by Napier's analogies and the other by means of a perpendicular. Either the first or |