PREFACE THE present volume consists of the first five books of the authors' "Elements of Geometry," or that portion which relates to Plane Geometry. While the book speaks for itself, we would call attention to some of its most important features. The Introduction presents in the shortest possible compass the general outlines of the science to be studied, and leads at once to the actual study itself. The definitions are distributed through the book as they are needed, instead of being grouped in long lists many pages in advance of the propositions to which they apply. An alphabetical index is added for easy reference. The constructions are also distributed, so that the student is taught how to make a figure at the same time that he is required to use it in demonstration. Extensive use has been made of natural and symmetrical methods of demonstration. Such methods are used for deducing the formula for the sum of the angles of a triangle, for the sum of the exterior and interior angles of a polygon, for parallel lines, for the theorems on regular polygons, and for similar figures. The theory of limits is treated with rigor, and not passed over as self-evident. Attention is also called to the theorems of proportion and the use of corollaries as exercises to supply the need of "inventional geometry." We would here express our grateful acknowledgments to all who have aided in the preparation of this book; to Miss Elizabeth H. Richards, whose successful experience in fitting students for college in Plane Geometry has rendered her criticisms and suggestions most valuable; and to our colleagues, Messrs. W. M. Strong and Joseph Bowden, Jr. Mr. Strong has selected, for the most part, the exercises at the end of the book, and Mr. Bowden has examined critically the references and proof-sheets of the book. ANDREW W. PHILLIPS, YALE UNIVERSITY. |