Books with title 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. 1902 edition. Excerpt: ...be indefinitely increased. The proof is exactly the same as that of Prop. XXXII, if we substitute cone for cylinder and pyramids for prisms. 721. Cor. The volume of a frustum of a cone is the limit of the volumes of the frustums of the inscribed and circumscribed pyramids, if the number of lateral faces is indefinitely increased, and the lateral area of the frustum of a cone is the limit of the lateral areas of the frustums of the inscribed and circumscribed pyramids. Proposition XXXIX. Theorem. 722. The lateral area of a cone of revolution is equal to half the product of the slant height by the circumference of the base. Let S denote the lateral area, C the circumference of the base, and L the slant height, of the given cone. To prove that S = iC X L. Proof. Circumscribe about the cone a regular pyramid. Denote the perimeter of its base by P, and its lateral area by 8. Then 8 = J P X L. §643 If the number of the lateral faces of the circumscribed pyramid is indefinitely increased, S' approaches S as a limit, and P approaches C as a limit..-. P X L approaches £ C X L as a limit. But 8 = iP X L, always..-.S = iCxL. Proposition XL. Theorem. 724. The volume of a circular cone is equal to one third the product of its base by its altitude. Let V denote the volume, B the base, and H the altitude of the given cone. To prove that V = i-B X H. Proof. Inscribe in the cone a pyramid with a regular polygon for its base. Denote its volume by V, and its base by £'. Then V' = iB'xH. §652 If the number of the lateral faces of the inscribed pyramid is indefinitely increased, V approaches V as a limit, § 720 and B' approaches B as a limit. § 454.-. B' X H approaches i B X H as a limit. § 279 But V = iB' X H, always. § 652.-....

This is a pre-1923 historical reproduction that was curated for quality. Quality assurance was conducted on each of these books in an attempt to remove books with imperfections introduced by the digitization process. Though we have made best efforts - the books may have occasional errors that do not impede the reading experience. We believe this work is culturally important and have elected to bring the book back into print as part of our continuing commitment to the preservation of printed works worldwide.

This is a pre-1923 historical reproduction that was curated for quality. Quality assurance was conducted on each of these books in an attempt to remove books with imperfections introduced by the digitization process. Though we have made best efforts - the books may have occasional errors that do not impede the reading experience. We believe this work is culturally important and have elected to bring the book back into print as part of our continuing commitment to the preservation of printed works worldwide. This text refers to the Bibliobazaar edition.

This is a reproduction of a book published before 1923. This book may have occasional imperfections such as missing or blurred pages, poor pictures, errant marks, etc. that were either part of the original artifact, or were introduced by the scanning process. We believe this work is culturally important, and despite the imperfections, have elected to bring it back into print as part of our continuing commitment to the preservation of printed works worldwide. We appreciate your understanding of the imperfections in the preservation process, and hope you enjoy this valuable book.

This is a pre-1923 historical reproduction that was curated for quality. Quality assurance was conducted on each of these books in an attempt to remove books with imperfections introduced by the digitization process. Though we have made best efforts - the books may have occasional errors that do not impede the reading experience. We believe this work is culturally important and have elected to bring the book back into print as part of our continuing commitment to the preservation of printed works worldwide. This text refers to the Bibliobazaar edition.

This is a reproduction of a book published before 1923. This book may have occasional imperfections such as missing or blurred pages, poor pictures, errant marks, etc. that were either part of the original artifact, or were introduced by the scanning process. We believe this work is culturally important, and despite the imperfections, have elected to bring it back into print as part of our continuing commitment to the preservation of printed works worldwide. We appreciate your understanding of the imperfections in the preservation process, and hope you enjoy this valuable book.

Excerpt from Plane Geometry Although the study of geometry is important from an informational point of view, it is generally recognized that a genuine mastery of the subject means real achievement in the solution of original exercises. The chief aim of the authors in preparing this text has been to give such assistance to students as will stimulate insight and develop power to solve exercises of gradually increasing difficulty. The content and organization of the first book of geometry are determining factors in the student's progress in the sub ject. The first ten or twenty theorems determine whether a student will grasp quickly the general trend of the subject or remain bewildered for an indefinite period. The simplicity and directness of the early theorems and the order in which they are presented are elements of the highest importance in an effective introduction. These elements were given the most careful consideration in the preparation of this text. If the first theorem is used in proving the second and the sec ond in proving the third, and so on, the student will soon see a reason for mastering the content of each theorem. But if the initial theorem is used for the first time in the fifteenth theorem, and the second is used next in the eighth, the first month's work will give the impression: that geometry deals with unrelated facts which lead nowhere. Such an arrange ment of the theorems of geometry will hamper even the strongest students, and will make progress almost impossible for the less capable. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This 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.