OF PLANE AND SPHERICAL TRIGONOMETRY, WITH ITS APPLICATIONS TO THE PRINCIPLES OF NAVIGATION AND NAUTICAL ASTRONOMY; WITH THE LOGARITHMIC AND TRIGONOMETRICAL TABLES. BY J. R. YOUNG, PROFESSOR OF MATHEMATICS IN BELFAST COLLEGE, Tables;”“Computation of Logarithms ;" Integral Calculus;" and “Elements of Mechanics." TO WHICH ARE ADDED SOME ORIGINAL RESEARCHES IN SPHERICAL GEOMETRY; BY T. S. DAVIES, F.R.S. LOND. AND EDINB. LONDON: JOHN SOUTER, SCHOOL LIBRARY, 73, ST. PAUL'S CHURCH-YARD. 1833. PREFACE. It is the design of this treatise to establish the theory of Plane and Spherical Trigonometry analytically, and to present that theory, together with some of its most interesting and valuable applications, in a form fitted for elementary instruction. Of late years several analytical works on Trigonometry have been published in this country; but, as they are confined almost entirely to the theory of the subject, it may be questioned whether, to many young students, they prove much else than so many collections of mere algebraical exercises. Yet a book upon so practical a subject as Trigonometry ought undoubtedly to be something more than this, and ought not to be considered as complete when the various calculations which the science involves, and which its name implies, are wholly omitted. The symbolical expression of a practical rule, in algebraic language, will often, to the young student, but indistinctly point out the numerical operation. Those much occupied a |