BOWSER'S MATHEMATICS. ACADEMIC ALGEBRA. With numerous Examples. AN ELEMENTARY TREATISE ON ANALYTIC GEOMETRY, embracing Plane Geometry, and an Introduction to Geometry of Three Dimensions. AN ELEMENTARY TREATISE ON THE DIFFERENTIAL AND INTEGRAL CALCULUS. With numerous Examples. AN ELEMENTARY TREATISE ON ANALYTIC MECHANICS. With numerous Examples. AN ELEMENTARY TREATISE ON HYDROMECHANICS. With numerous Examples. EDWARD A. BOWSER, LL.D., PROFESSOR OF MATHEMATICS AND ENGINEERING IN RUTGERS COLLEGE. SECOND EDITION. BOSTON, U.S.A.: D. C. HEATH & CO., PUBLISHERS. 1891. PREFACE. IN N the present work on Elementary Geometry, or what is commonly known as the Euclidian Geometry, it is aimed to combine the excellencies of Euclid with those of the best modern writers, especially of Legendre, and Rouché and Comberousse. Many of the demonstrations are those of Euclid, with minor changes frequently introduced, and the syllogistic form is retained throughout; but the arrangement is quite different. Many objections have been made against Euclid. His definitions are not all of them the best, nor are they in their proper places. His treatment of angles is deficient. His arrangement of the propositions is often poor, mixing straight lines, angles, triangles, etc., without any regular classification; and his demonstrations are sometimes cumbersome and prolix. Nevertheless, although numerous attempts have been made to improve upon Euclid, it still remains the great model, the unrivalled original, on which is founded the whole system of elementary Geometry. Perhaps a more finished specimen of exact logic has never been produced than that of the old Greek Geometer. In the present treatise it is desired to effect two objects: (1) to teach geometric truths; (2) to discipline and invigorate the mind, to train it to habits of clear and consecutive reasoning. Accordingly, more numerous propositions have been given, and the demonstrations made more complete, than either object alone would seem to demand. In each proposition is a distinct statement, of what is given, of what is required, and of the proof. Each assertion in the proof begins a new line, and is accompanied by a reference to the preceding principle on which the assertion depends. These references are quoted two or three times in small type, and afterwards referred to only by number. The student should always be ready, if required, to quote the proper reference, and to show its application. The text is so arranged that the enunciation, figure, and proof of each proposition iii |