BY C. A. HART - INSTRUCTOR OF MATHEMATICS, WADLEIGH HIGH SCHOOL, NEW YORK CITY AND DANIEL D. FELDMAN HEAD OF DEPARTMENT OF MATHEMATICS, ERASMUS HALL HIGH SCHOOL, BROOKLYN WITH THE EDITORIAL COÖPERATION OF J. H. TANNER AND VIRGIL SNYDER PROFESSORS OF MATHEMATICS IN CORNELL UNIVERSITY AC NEW YORK .:. CINCINNATI: CHICAGO BOOK COMPANY بدل 623177 COPYRIGHT, 1911, BY AMERICAN BOOK COMPANY. ENTERED AT STATIONERS' HALL, LONDON. H.-F. PLANE GEOMETRY. W. P. I PREFACE THIS book is the outgrowth of an experience of many years in the teaching of mathematics in secondary schools. The text has been used by many different teachers, in classes of all stages of development, and under varying conditions of secondary school teaching. The proofs have had the benefit of the criticisms of hundreds of experienced teachers of mathematics throughout the country. The book in its present form is therefore the combined product of experience, classroom test, and severe criticism. The following are some of the leading features of the book: The student is rapidly initiated into the subject. Definitions are given only as needed. The selection and arrangement of theorems is such as to meet the general demand of teachers, as expressed through the Mathematical Associations of the country. Most of the proofs have been given in full. Proofs of some of the easier theorems and constructions are left as exercises for the student, or are given in an incomplete form; but in every case in which the proof is not complete, the incompleteness is specifically stated. The authors believe that the proofs of most of the propositions should be complete, first, in order to serve as models for the handling of exercises; second, to prevent the serious error of making the student feel contented with loose and slipshod reasoning which defeats the main purpose of instruction in geometry; and third, as an excellent means of reviewing the previous theorems on which they depend. The indirect method of proof is consistently applied. The usual method of proving such propositions as Arts. 189 and |