PROFESSOR OF MATHEMATICS IN KING'S COLLEGE, LONDON, THE FOURTH EDITION. LONDON: B. FELLOWES, LUDGATE STREET. PREFACE. BEFORE a student can successfully attempt the perusal of works on Physical Science, he will find it expedient to have some acquaintance with the principles of Trigonometry. For a student deficient in this knowledge, the following Treatise was written; and its object is to teach so much of Trigonometry as may be necessary for his purpose, and no more. Keeping this object in view, no fantastic combinations of chords, or secants, or versed sines, have been allowed to perplex the reader, or to withdraw him from the study of propositions which are all-important. No theorem has been introduced which is not either of itself eminently useful, or upon which important reasonings may not be founded. The very copious Table of Contents exhibits a plan of the work; and it may be profitably used as a general Syllabus of Trigonometry. The Introduction, and the first four Chapters, contain the principles of Plane Trigonometry; and every theorem in them must be carefully impressed upon the memory of the student, before he directs his attention to higher subjects. The propositions in the fifth Chapter are curious, and deserving of attention, particularly that in which the area of the circle is identified with that of a polygon of an infinite number of sides. The theorems demonstrated in the sixth Chapter are so important in the applications of Analysis to Physics, that a Treatise upon Trigonometry would be considered incomplete without them. But no theorem has been introduced, the proof of which demands more than a tolerably good acquaintance with the first part of Algebra, and the Binomial Theorem; and it is confidently hoped that what has been written will be easily understood by the careful reader. In the Treatise on Spherical Trigonometry, the early Chapters which contain the formulas for the solution of right and oblique-angled spherical triangles, are the most important; and when the reader is familiarized with them, he may without difficulty understand the calculations of Practical Astronomy, a science to which the latter part of this work is almost wholly subservient. The work is concluded by two Chapters containing formulas for finding the area of the spherical triangle, and various propositions of Solid Geometry, respecting the regular polyhedrons, and the parallelopipedon, without which a Treatise on Spherical Trigonometry would be considered incomplete. KING'S COLLEGE, LONDON, September, 1848. T. G. HALL. IV. Rules for converting French degrees into English, and} V. Examples CHAPTER I. I. Definitions of complement and supplement II. Definitions of sine, cosine, tangent, secant, versed sine, cotangent, cosecant III. Sine of an angle cosine of the complement . Cosine of an angle sine of the complement - sin. A; cos. (— A) = cos. A . Sine (-4) = PAGE 1 2 3 4 6 7 9 11 |