THE CENTRAL STAIR HALL OF THE LIBRARY OF CONGRESS The Library of Congress stands as the acme of America's architectural achievement. Its conception, design, and execution are the product solely of American talent, art, and workmanship. Copyright, 1927, by THE JOHN C. WINSTON COMPANY COPYRIGHT IN GREAT BRITAIN AND THE BRITISH DOMINIONS AND POSSESSIONS All rights reserved PRINTED IN THE U. S. A. Geometry P-4-27 =79 PREFACE This book aims to provide an interesting and thorough course in plane geometry in accord with the more recent advancements in methods of teaching the subject. It is believed that the treatment as a whole will commend itself to teachers because of its simplicity, its clearness, and its thoroughness. The Introduction is so designed that at the beginning the pupil may easily obtain by himself an idea of the fundamental concepts and terminology of geometry; then he is led gradually into the formal proof by the use of simple one-step exercises which involve principally the use of angles. Oral exercises always follow a group of related definitions to clinch their meaning and to illustrate their use. The propositions have been appropriately lettered (C, c, N, and n) to indicate the requirements of the College Entrance Examination Board and the recommendations of the National Committee. The requirements of other leading syllabi have also been followed. (For Key to the Lettering of Propositions, cf. § 57.) The statements of many theorems have been simplified and condensed by placing the subject (or hypothesis) first and the predicate (or conclusion) last. This arrangement is simple, logical, and emphatic. (cf. §§ 65, 120, 211, 301, 305, etc.) Simplicity of proof The proofs are simple and rigorous. has been secured in three ways: first, by choosing a sequence which has eliminated a number of indirect proofs and any necessity for the commensurable and incommensurable proofs of certain theorems; second, by a new order of M305026 |