DEVELOPED BY THE SYLLABUS METHOD BY EUGENE RANDOLPH SMITH, A.M. HEAD OF THE DEPARTMENT OF MATHEMATICS, POLYTECHNIC PREPARATORY (FORMERLY HEAD OF THE DEPARTMENT OF MATHEMATICS, NEW YORK .:. CINCINNATI .:. CHICAGO COPYRIGHT, 1909, BY EUGENE RANDOLPH SMITH. ENTERED AT STATIONERS' HALL, LONDON. SMITH SYL. GEOM. W. P. I 4 558 PREFACE THE belief that the proofs of Geometry should be, as far as possible, worked out by the pupils, either in class discussions or individually, is becoming more widespread every year. The day of memorizing proofs will soon be past, and the most efficient method for mental training along logical lines will be the one generally adopted. This syllabus is written with the hope of encouraging teachers to undertake Geometry by the "no text" method. The author believes very decidedly that this method gives a maximum of mental training with a minimum waste of energy. The list of theorems is based on the latest reports of the Mathematical Associations, and, while much shorter than that in many of the text-books, it will be found sufficient to prepare the pupils for any of the colleges. It contains all the theorems of the "New England List" with a few additions that simplify proofs. The order is the development of ten years' class use, and will be found different from that of any text. Whenever a theorem has seemed to be simplified, either in. content or in proof, by making a change in its place in the order of theorems, that change has been tried in class, and has been made permanent if it proved of advantage. Any teacher using this book should feel equally free to make changes in the order if he is convinced that there is a decided advantage in the change. M306177 |