WENTWORTH'S SERIES OF MATHEMATICS. First Steps in Number. Mental Arithmetic. Primary Arithmetic. Elementary Arithmetic. Grammar School Arithmetic. High School Arithmetic. Exercises in Arithmetic. First Steps in Algebra. School Algebra. Complete Algebra. College Algebra. Higher Algebra. Exercises in Algebra. New Plane Geometry. New Plane and Solid Geometry. New Solid Geometry. Exercises in Geometry. Analytic Geometry. New Pl. and Sol. Geometry and Pl. Trigonometry. Plane and Spherical Trigonometry and Tables. A TEXT-BOOK OF GEOMETRY. REVISED EDITION. BY G. A. WENTWORTH, A.M., AUTHOR OF A SERIES OF TEXT-BOOKS IN MATHEMATICS. BOSTON, U.S.A.: GINN & COMPANY, PUBLISHERS. 1895. Entered, according to Act of Congress, in the year 1888, by in the Office of the Librarian of Congress, at Washington ALL RIGHTS RESERVED TYPOGRAPHY BY J. S. CUSHING & Co., BOSTON, U.S A PRESSWORK BY GINN & Co.. BosTON, US A. PREFACE. M° OST persons do not possess, and do not easily acquire, the power of abstraction requisite for apprehending geometrical conceptions, and for keeping in mind the successive steps of a continuous argument. Hence, with a very large proportion of beginners in Geometry, it depends mainly upon the form in which the subject is presented whether they pursue the study with indifference, not to say aversion, or with increasing interest and pleasure. In compiling the present treatise, the author has kept this fact con stantly in view. All unnecessary discussions and scholia have been avoided; and such methods have been adopted as experience and attentive observation, combined with repeated trials, have shown to be most readily comprehended. No attempt has been made to render more intelligible the simple notions of position, magnitude, and direction, which every child derives from observation; but it is believed that these notions have been limited and defined with mathematical precision. A few symbols, which stand for words and not for operations, have been used, but these are of so great utility in giving style and perspicuity to the demonstrations that no apology seems necessary for their introduction. Great pains have been taken to make the page attractive. The figures are large and distinct, and are placed in the middle of the page, so that they fall directly under the eye in immediate connection with the corresponding text. The given lines of the figures are full lines, the lines employed as aids in the demonstrations are shortdotted, and the resulting lines are long-dotted. |