Front matter
Reading edition
GINN AND COMPANY
BOSTON · NEW YORK · CHICAGO · LONDON
COPYRIGHT, 1911, BY DAVID EUGENE SMITH ALL RIGHTS RESERVED 911.6
The Athenæum Press
GINN AND COMPANY · PROPRIETORS BOSTON · U.S.A.
PREFACE
A book upon the teaching of geometry may be planned in divers ways. It may be written to exploit a new theory of geometry, or a new method of presenting the science as we already have it. On the other hand, it may be ultraconservative, making a plea for the ancient teaching and the ancient geometry. It may be prepared for the purpose of setting forth the work as it now is, or with the tempting but dangerous idea of prophecy. It may appeal to the iconoclast by its spirit of destruction, or to the disciples of laissez faire by its spirit of conserving what the past has bequeathed. It may be written for the few who always lead, or think they lead, or for the many who are ranked by the few as followers. And in view of these varied pathways into the joint domain of geometry and education, a writer may well afford to pause before he sets his pen to paper, and to decide with care the route that he will take.
At present in America we have a fairly well-defined body of matter in geometry, and this occupies a fairly well-defined place in the curriculum. There are not wanting many earnest teachers who would change both the matter and the place in a very radical fashion. There are not wanting others, also many in number, who are content with things as they find them. But by far the largest part of the teaching body is of a mind to welcome the natural and gradual evolution of geometry toward better things, contributing to this evolution as much as it can, glad to know the best that others have to offer, receptive of ideas that make for better teaching, but out of sympathy with either the extreme of revolution or the extreme of stagnation.
It is for this larger class, the great body of progressive teachers, that this book is written. It stands for vitalizing geometry in every legitimate way; for improving the subject matter in such manner as not to destroy the pupil's interest; for so teaching geometry as to make it appeal to pupils as strongly as any other subject in the curriculum; but for the recognition of geometry for geometry's sake and not for the sake of a fancied utility that hardly exists. Expressing full appreciation of the desirability of establishing a motive for all studies, so as to have the work proceed with interest and vigor, it does not hesitate to express doubt as to certain motives that have been exploited, nor to stand for such a genuine, thought-compelling development of the science as is in harmony with the mental powers of the pupils in the American high school.
For this class of teachers the author hopes that the book will prove of service, and that through its perusal they will come to admire the subject more and more, and to teach it with greater interest. It offers no panacea, it champions no single method, but it seeks to set forth plainly the reasons for teaching a geometry of the kind that we have inherited, and for hoping for a gradual but definite improvement in the science and in the methods of its presentation.
DAVID EUGENE SMITH
CONTENTS
CHAPTERPAGE
I.Certain Questions now at Issue1
II.Why Geometry is Studied7
III.A Brief History of Geometry26
IV.Development of the Teaching of Geometry40
V.Euclid47
VI.Efforts at Improving Euclid57
VII.The Textbook in Geometry70
VIII.The Relation of Algebra to Geometry84
IX.The Introduction to Geometry93
X.The Conduct of a Class in Geometry108
XI.The Axioms and Postulates116
XII.The Definitions of Geometry132
XIII.How to attack the Exercises160
XIV.Book I and its Propositions165
XV.The Leading Propositions of Book II201
XVI.The Leading Propositions of Book III227
XVII.The Leading Propositions of Book IV252
XVIII.The Leading Propositions of Book V269
XIX.The Leading Propositions of Book VI289
XX.The Leading Propositions of Book VII303
XXI.The Leading Propositions of Book VIII321
INDEX335