PREFACE. THE object of the present Treatise is to bring Spherical Trigonometry to the standard required for University Examinations, and demanded by the impulse given to mathematical subjects by modern text-books. Simplicity of treatment has been constantly kept in view. Part I. treats of the subject as far as the solution of Triangles, inclusive. In the text will be found all the propositions usually contained in treatises on the subject, besides such other theorems as appeared to us to be of special importance on account of their utility. The volume is replete with examples (in many cases worked out), the arrangement of which has been the subject of our special attention; our aim throughout being to place them in immediate connexion with the subject matter of which they are illustrative. At the end of each Chapter, Miscellaneous Examples bearing on all the preceding matter have been added. We have not hesitated to use Determinant Notation whenever elegance or simplicity could be gained thereby. This notation has now become so generally known as to render apology for its use early in the work quite unnecessary. The Numerical Solution of Triangles, treated of in Chapters IV. and V., has received much attention, each Case being treated of in detail. In connexion with these Numerical Examples, we must acknowledge our obligations to Mr. ROBERT BAILE, M. A., Athlone, who carefully worked and verified them all. They have also been independently verified and tested, and we therefore trust they will all be found correct to the nearest half second. Geometrical proofs of many Propositions have been added to those commonly given in text-books, e. g. the Analogies of Napier and Delambre. Most of the examples have been taken from University and Science and Art Examination Papers. Many, however, as far as we are aware, appear now for the first time. A series of Examples have been appended in the form of Examination Papers. Among published works on the subject, we are indebted chiefly to those of Todhunter, Snowball, and Luby. WM. J. M'CLELLAND, THOMAS PRESTON. May, 1885. PAGE CASE I. Having given two sides. Examples, CASE II. Having given two angles. Examples, CASE III.—Having given the hypotenuse and a side. CASE IV. Having given the hypotenuse and an angle. CASE V. Having given a side and the adjacent angle. Examples, 88 CASE VI.-Having given a side and the opposite angle. Examples, 89 |