Excerpt from Elements of Plane and Spherical Trigonometry: With Their Applications to Heights and Distances, Projections of the Sphere, Dialling, Astronomy, the Solution of Equations, and Geodesic Operations
Plane Trigonometry geometrically, and haveshown the application of that theory to the logarithmic solutions Of the usual cases into which this portion of the subject is conveniently distributed. I have endeavoured to conduct these introductory inquiries with the utmost perspicuity; that the student, by obtaining a thorough comprehension of the principal topics of research, and by seeing a little of their utility, may enter with the greater relish upon the subsequent investigations; and by tracing the correspondence of these results with such as will afterwards appear in the analytical theory of Plane Trigonometry, may be prepared to lean with full confidence upon the analytical formula that are in other places to be laid before him. The deductions from theory in the succeeding chapters are usually Obtained by analytical processes; and their utility is shown in the logarithmic and trigonometric solution of a great number of problems, classified under the particular heads of the several applications, as specified in the ta ble of contents. The whole, except what relates to the minute variations of the sides and angle of triangles, and'the differential analogies which apply to them, may, I am persuaded, be readily comprehended by any per son who is tolerably conversant with the elements of Geometry and Algebra.
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