Elements of Plane and Spherical Trigonometry With the First Principles of Analytic Geometry (Classic Reprint)

Excerpt from Elements of Plane and Spherical Trigonometry: With the First Principles of Analytic Geometry
The first edition of this work was intended chiefly as a Text-Book for the use of the students in the Belfast Institution, when the Author was Professor of Mathematics in that establishment; and it was therefore written, not as a regular and complete treatise on Trigonometry, but as an outline to be filled up, and illustrated orally in the Lectures. It was received, however, by other readers in a more favourable manner than the Author could have anticipated omits nature and form; and, in consequence of this, he has been induced, in the subsequent editions, to make various alterations, and, it is hoped, improvements. The investigations, though still concise, are given at such length as to be easily understood by readers of ordinary talents and attainments; and various interesting additions are introduced, some from the best recent works on the subject, and others that have occurred to the Author himself. Of the latter kind are the improvements in the numerical resolution of triangles, established in Nos. 57, 58, 73, and 74, and exemplified in Nos. 62, 63, and 110; which, with the modes of operation previously known, seem to render the subject as simple and easy as can be desired. In the present edition, also, a scholium of considerable interest will be found at the end of the third section: and the last four pages of the ninth section contain some curious propositions in Spherical Geometry, most of which the Author believes to be new.
It has been everywhere the aim of the Author, to comprise in a small compass much useful and interesting matter; and, whatever may be the imperfections of the work, he trusts that the person who shall make himself well acquainted with what it contains, will find it easy to acquire a knowledge of all that is yet known in Trigonometry, and to apply it in Astronomy, and other branches of science.
In the present edition, the sines, tangents, c.are defined as mere numbers or ratios. This mode of representing them has been in use for some time in the University of Cambridge; and it is attended with considerable advantage, particularly in the application of Trigonometry in Natural Philosophy. Should any persons prefer the common mode, they may have recourse to the Note at the end of the volume.
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