GIFT OF Dr. Horace I'vic RAY'S SERIES, 67529 T3 EMBRACING A Thorough and Progressive Course in Arithmetic, Algebra, and the Higher Mathematics. Educ. + Higher Arithmetic. Test Examples in Arithmetic. Plane and Solid Geometry. BY ELI T. TAPPAN, A.M., Pres't Kenyon College. 12mo, cloth, 276 pp. Geometry and Trigonometry. By ELI T. TAPPAN, A.M. Pres't Kenyon College. 8vo, sheep, 420 pp. Analytic Geometry. By GEO. H. HowISON, A.M., Prof. in Mass. Institute of Technology. Treatise on Analytic Geometry, especially as applied to the Properties of Conics: including the Modern Methods of Abridged Notation. Elements of Astronomy. By S. H. PEABODY, A.M., Prof. of Physics and Civil Engineering, Amherst College. Handsomely and profusely illustrated. 8vo, sheep, 336 pp. 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. The books most freely used are, "Cours de géométrie élémentaire, par A. J. H. Vincent et M. Bourdon;" "Géométrie théorique et pratique, etc., par H. Sonnet;" "Die (iii) |