TREATISE ON GEOMETRY AND TRIGONOMETRY: FOR COLLEGES, SCHOOLS, AND PRIVATE WRITTEN FOR THE MATHEMATICAL COURSE OF JOSEPH RAY, M.D., BY ELI T. TAPPAN, M. A., PROFESSOR OF MATHEMATICS, OHIO UNIVERSITY. VAN ANTWERP, BRAGG & CO., 137 WALNUT STREET, CINCINNATI. 28 BOND STREET, NEW YORK. Educ T 148.79.822 KARYAAD COLLEGE LIBRARY BY EXCHANGE FROM NEW YORK STATE LIBRARY RAY'S SERIES, EMBRACING A Thorough and Progressive Course in Arithmetic, Algebra, and the Higher Mathematics. Primary Arithmetic. Intellectual Arithmetic. Practical Arithmetic. Higher Arithmetic. Test Examples in Arithmetic. Plane and Solid Geometry. BY ELI T. TAPPAN, A.M., Pres't Geometry and Trigonometry. By ELI T. TAPPAN, A.M. Analytic Geometry. By GEO. H. HOWISON, A.M., Prof. in Mass. Elements of Astronomy. By S. H. PEABODY, A.M., Prof. of KEYS. Ray's Arithmetical Key (To Intellectual and Practical); Key to Ray's Higher Arithmetic; Key to Ray's New Elementary and Higher Algebras. The Publishers furnish Descriptive Circulars of the above Mathematical Text-Books, with Prices and other information concerning them. Entered according to Act of Congress, in the year 1868, by SARGENT, WILSON & PREFACE. THE science of Elementary Geometry, after remaining nearly stationary for two thousand years, has, for a century past, been making decided progress. This is owing, mainly, to two causes: discoveries in the higher mathematics have thrown new light upon the elements of the science; and the demands of schools, in all enlightened nations, have called out many works by able mathematicians and skillful teachers. Professor Hayward, of Harvard University, as early as 1825, defined parallel lines as lines having the same direction. Euclid's definitions of a straight line, of an angle, and of a plane, were based on the idea of direction, which is, indeed, the essence of form. This thought, employed in all these leading definitions, adds clearness to the science and simplicity to the study. In the present work, it is sought to combine these ideas with the best methods and latest discoveries in the science. By careful arrangement of topics, the theory of each class of figures is given in uninterrupted connection. No attempt. is made to exclude any method of demonstration, but rather to present examples of all. "Cours de géométrie The books most freely used are, élémentaire, par A. J. H. Vincent et M. Bourdon;" "Géométrie théorique et pratique, etc., par H. Sonnet; " "Die |