Articles liés à Plane Geometry
Synopsis
Il s'agit d'une reproduction exacte d'un livre publié avant 1923. Il ne s'agit pas d'un livre OCR avec des personnages étranges, des erreurs typographiques introduites et des mots mélangés. Ce livre peut présenter des imperfections occasionnelles telles que des pages manquantes ou floues, des images médiocres, des marques errantes, etc. qui faisaient partie de l'artefact original, ou ont été introduites par le processus de numérisation. Nous pensons que ce travail est culturellement important, et malgré les imperfections, nous avons choisi de le ramener à l'impression dans le cadre de notre engagement continu à la préservation des œuvres imprimées dans le monde entier. Nous apprécions votre compréhension des imperfections dans le processus de conservation et espérons que vous apprécierez ce livre précieux.
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Présentation de l'éditeur
It is intended to have the first sixteen pages of this book simply read in the class, with such running comment and discussion as may be useful to help the beginner catch the spirit of the subject-matter, and not leave him to the mere letter of dry definitions. In like manner, the definitions at the beginning of each Book should be read and discussed in the recitation room. There is a decided advantage in having the de_nitions for each Book in a single group so that they can be included in one survey and discussion. For a similar reason the theorems of limits are considered together. The subject of limits is exceedingly interesting in itself, and it was thought best to include in the theory of limits in the second Book every principle required for Plane and Solid Geometry. Most persons do not possess, and do not easily acquire, the power of abstraction requisite for apprehending geometrical conceptions, and for keeping in mind the successive steps of a continuous argument. Hence, with a very large proportion of beginners in Geometry, it depends mainly upon the form in which the subject is presented whether they pursue the study with indifference, not to say aversion, or with increasing interest and pleasure. Great care, therefore, has been taken to make the pages attractive. The figures have been carefully drawn and placed in the middle of the page, so that they fall directly under the eye in immediate connection with the text; and in no case is it necessary to turn the page in reading a demonstration. Full, long-dashed, and short-dashed lines of the _gures indicate given, resulting, and auxiliary lines, respectively. Bold-faced, italic, and roman type has been skilfully used to distinguish the hypothesis, the conclusion to be proved, and the proof. As a further concession to the beginner, the reason for each statement in the early proofs is printed in small italics, immediately following the statement. This prevents the necessity of interrupting the logical train of thought by turning to a previous section, and compels the learner to become familiar with a large number of geometrical truths by constantly seeing and repeating them. This help is gradually discarded, and the pupil is left to depend upon the knowledge already acquired, or to _nd the reason for a step by turning to the given reference. It must not be inferred, because this is not a geometry of interrogation points, that the author has lost sight of the real object of the study. The training to be obtained from carefully following the logical steps of a complete proof has been provided for by the Propositions of the Geometry, and the development of the power to grasp and prove new truths has been provided for by original exercises. The chief value of any Geometry consists in the happy combination of these two kinds of training. The exercises have been arranged according to the test of experience, and are so abundant that it is not expected that any one class will work them all out. The methods of attacking and proving original theorems are fully explained in the first Book, and illustrated by su_cient examples; and the methods of attacking and solving original problems are explained in the second Book, and illustrated by examples worked out in full. None but the very simplest exercises are inserted until the student has become familiar with geometrical methods, and is furnished with elementary but much needed instruction in the art of handling original propositions; and he is assisted by diagrams and hints as long as these helps are necessary to develop his mental powers su_ciently to enable him to carry on the work by himself. The law of converse theorems, the distinction between positive and negative quantities, and the principles of reciprocity and continuity have been briey explained; but the application of these principles is left mainly to the discretion of teachers.
Présentation de l'éditeur
Leopold is delighted to publish this classic book as part of our extensive Classic Library collection. Many of the books in our collection have been out of print for decades, and therefore have not been accessible to the general public. The aim of our publishing program is to facilitate rapid access to this vast reservoir of literature, and our view is that this is a significant literary work, which deserves to be brought back into print after many decades. The contents of the vast majority of titles in the Classic Library have been scanned from the original works. To ensure a high quality product, each title has been meticulously hand curated by our staff. This means that we have checked every single page in every title, making it highly unlikely that any material imperfections – such as poor picture quality, blurred or missing text - remain. When our staff observed such imperfections in the original work, these have either been repaired, or the title has been excluded from the Leopold Classic Library catalogue. As part of our on-going commitment to delivering value to the reader, within the book we have also provided you with a link to a website, where you may download a digital version of this work for free. Our philosophy has been guided by a desire to provide the reader with a book that is as close as possible to ownership of the original work. We hope that you will enjoy this wonderful classic work, and that for you it becomes an enriching experience. If you would like to learn more about the Leopold Classic Library collection please visit our website at www.leopoldclassiclibrary.com
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