Other editions of book The Teaching of Geometry

This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1911 edition. Excerpt: ...conversation that we cannot keep it to mean "congruent"; but our language will not permit it, and we are forced to use the newer word. Whenever it can be used without misunderstanding, however, it should be retained, as in the case of "equal straight lines," "equal angles," and "equal arcs of the same circle." The mathematical and educational world will never consent to use "congruent straight lines," or "congruent angles," for the reason that the terms are unnecessarily long, no misunderstanding being possible when "equal" is used. The word " equivalent" was introduced by Legendre at the close of the eighteenth century to indicate equality of length, or of area, or of volume. Euclid had said, "Parallelograms which are on the same base and in the same parallels are equal to one another," while Legendre and his followers would modify the wording somewhat and introduce "equivalent" for "equal." This usage has been retained. Congruent polygons are therefore necessarily equivalent, but equivalent polygons are not in general congruent. Congruent polygons have mutually equal sides and mutually equal angles, while equivalent polygons have no equality save that of area. In general, as already stated, these and other terms should be defined just before they are used instead of at the beginning of geometry. The reason for this, from the educational standpoint and considering the present position of geometry in the curriculum, is apparent. We shall now consider the definitions of Euclid's Book III, which is usually taken as Book II in America. 1. Equal Circles. Equal circles are those the diameters of which are equal, or the radii of which are...

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This scarce antiquarian book is a facsimile reprint of the original. Due to its age, it may contain imperfections such as marks, notations, marginalia and flawed pages. Because we believe this work is culturally important, we have made it available as part of our commitment for protecting, preserving, and promoting the world's literature in affordable, high quality, modern editions that are true to the original work.

Excerpt from The Teaching of GeometryIt is for this larger class, the great body of progressive teachers, that this book is written. It stands for Vitaliz ing 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 peru sal they will come to admire the subject more and more, and to teach it with greater interest. It offers no pana cea, 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 grad ual but definite improvement in the science and in the methods of its presentation.About the PublisherForgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.comThis book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.

Chapter I - Certain Questions now at Issue, Chapter II - Why Geometry is Studied, Chapter III - A Brief History of Geometry, Chapter IV - Development of The Teaching of Geometry, Chapter V - Euclid, Chapter VI - Efforts at Improving Euclid, Chapter VII - The Textbook in Geometry, Chapter VIII - The Relation of Algebra to Geometry, Chapter IX - The Introduction to Geometry, Chapter X - The Conduct of A Class in Geometry, Chapter XI - The Axioms and Postulates, Chapter XII - The Definitions of Geometry, Chapter XIII - How to Attack the Exercises, Chapter XIV - Book I and its Propositions, Chapter XV - The Leading Propositions of Book II, Chapter XVI - The Leading Propositions Of Book III, Chapter XVII - The Leading Propositions Of Book IV, Chapter XVIII - The Leading Propositions Of Book V, Chapter XIX - The Leading Propositions Of Book Vi, Chapter XX - The Leading Propositions Of Book Vii, Chapter XXI - The Leading Propositions Of Book Viii, L’envoi.

This work has been selected by scholars as being culturally important and is part of the knowledge base of civilization as we know it.This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. To ensure a quality reading experience, this work has been proofread and republished using a format that seamlessly blends the original graphical elements with text in an easy-to-read typeface.We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.

This work has been selected by scholars as being culturally important and is part of the knowledge base of civilization as we know it.This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. To ensure a quality reading experience, this work has been proofread and republished using a format that seamlessly blends the original graphical elements with text in an easy-to-read typeface.We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.

This work has been selected by scholars as being culturally important and is part of the knowledge base of civilization as we know it.This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. To ensure a quality reading experience, this work has been proofread and republished using a format that seamlessly blends the original graphical elements with text in an easy-to-read typeface.We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.