THE ELEMENTS OF GEOMETRY BY HENRY W. KEIGWIN Teacher in the Norwich Free Academy NEW YORK HENRY HOLT AND COMPANY 1897 PREFACE. IN this book I have attempted to follow a middle course between the treatise which fully proves the propositions of elementary geometry and the syllabus which contains no proofs whatever. The early propositions are proved at length in order to make clear the form of geometrical demonstration and the details of proof are gradually removed in order to throw the pupil on his own resources. It hardly needs argument to show the wisdom of retaining and intensifying the pupil's interest in the study, and many teachers are convinced that this is best done by expecting easy original work very early and by making the exercises an integral part of the course. How far I have succeeded in giving just the right amount of assistance of course depends on the character of the class. The teacher should be ready to supplement and expand the hints to meet the need of students. This requires judgment, as all teaching does. I shall be especially grateful for criticism and suggestion on this feature of the book. The order of propositions in Plane Geometry is nearly. the conventional order of American text-books, but I have placed in Book I the elementary relations of rectilinear figures and of the circle; in Book II proportional line segments including similar and regular figures; in Book III the relations of areas, and measurement. The constructions are established before they are used in demonstration. This is believed to be pedagogically sound, whatever may be said of the logic of hypothetical constructions; and this arrange ment also emphasizes drawing, which is a valuable means of discipline in geometry. In Solid Geometry success is made to depend on the faithfulness with which the student makes models of his figures as explained in Notes at the end. Experience has shown that most of the puzzling features of Solid Geometry are removed when open models, which can be marked on and rebuilt, are used. A part of the class work should consist in making plane drawings of the models. My thanks are due to two of my associate teachers, Mr. M. E. Jensen and Miss Charlotte C. Gulliver, for assistance, and I am under special obligation to Miss Elizabeth Keith Price of the Springfield (Mass.) High School for encouragement and valuable suggestions. NORWICH, CONN., Sept. 1897. H. W. K. |