MATHEMATICAL TEXT-BOOKS BY GEORGE A. WENTWORTH Mental Arithmetic. Elementary Arithmetic. Practical Arithmetic. Primary Arithmetic. Grammar School Arithmetic High School Arithmetic. Advanced Arithmetic. First Steps in Algebra. New School Algebra. School Algebra. Elements of Algebra. Shorter Course in Algebra. Complete Algebra. Higher Algebra. College Algebra. Plane Geometry. Plane Geometry (Revised). Plane and Solid Geometry. Plane and Solid Geometry (Revised). Solid Geometry (Revised). Syllabus of Geometry. Geometrical Exercises. PLANE AND SOLID GEOMETRY BY G. A. WENTWORTH AUTHOR OF A SERIES OF TEXT-BOOKS IN MATHEMATICS REVISED EDITION BOSTON, U.S.A. GINN & COMPANY, PUBLISHERS The Athenæum Press Entered, according to Act of Congress, in the year 1888, by G. A. WENTWORTH in the Office of the Librarian of Congress, at Washington COPYRIGHT, 1899 BY G. A. WENTWORTH ALL RIGHTS RESERVED Most 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. Great care, therefore, has been taken to make the pages attractive. The figures have been carefully drawn and placed in the middle of the page, so that they fall directly under the eye in immediate connection with the text; and in no case is it necessary to turn the page in reading a demonstration. Full, long-dashed, and short-dashed lines of the figures indicate given, resulting, and auxiliary lines, respectively. Bold-faced, italic, and roman type has been skilfully used to distinguish the hypothesis, the conclusion to be proved, and the proof. As a further concession to the beginner, the reason for each statement in the early proofs is printed in small italics, immediately following the statement. This prevents the necessity of interrupting the logical train of thought by turning to a previous section, and compels the learner to become familiar with a large number of geometrical truths by constantly seeing and repeating them. This help is gradually discarded, and the pupil is left to depend upon the knowledge already acquired, or to find the reason for a step by turning to the given reference. It must not be inferred, because this is not a geometry of interrogation points, that the author has lost sight of the real object of the study. The training to be obtained from carefully following the logical steps of a complete proof has been provided for by the Propositions of the |