Books with author George Albert Wentworth

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.

Excerpt from Solid GeometryWhile rigorous proofs have claimed first attention, still every effort has been made to bring the proofs within the comprehension of students who read the subject for the first time. Woodcuts are employed to illustrate the definitions, and are placed by the side of the ordinary figures used in demonstrations. It is expected that these woodcuts will be of great value in helping the student to gain clear conceptions of the figures and to cultivate a correct geometrical imagination.Book IX, Conic Sections, has been carefully revised, and new figures have been substituted for the old ones.The excellent cuts of the Solid Geometry are largely due to Miss M. Gertrude Cross, of Boston, Mass.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.

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.-....

Most persons do not possess, and do not easily acquire, the power of abstraction requisite for apprehending the 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. In compiling the present treatise, this fact has been kept constantly in view. All unnecessary discussions and scholia have been avoided; and such methods have been adopted as experience and attentive observation, confined with repeated trials, have shown to be most readily comprehended. No attempt has been made to render more intelligible the simple notions of position, magnitude, and direction, which every child derives from observation; but it is believed that these notions have been limited and defined with mathematical precision. A few symbols, -which stand for words and not for operations, have been used, but these are of so great utility in giving style and perspicuity to the demonstrations that no apology seems necessary for their introduction. Great pains have been taken to make the page attractive. The figures are large and distinct, and are placed in the middle of the page, so that they fall directly under the eye in immediate connection with the corresponding text.(Typographical errors above are due to OCR software and don't occur in the book.)About the Publisher Forgotten Books is a publisher of historical writings, such as: Philosophy, Classics, Science, Religion, History, Folklore and Mythology.Forgotten Books' Classic Reprint Series utilizes the latest technology to regenerate facsimiles of historically important writings. Careful attention has been made to accurately preserve the original format of each page whilst digital

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.

Most persons do not possess, and do not easily acquire, the power of abstraction requisite for apprehending the 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. In compiling the present treatise, this fieust has been kept constantly in view. All unnecessary discussions and scholia have been avoided; and such methods have been adopted as experience and attentive observation, combined with repeated trials, have shown, to be most readily comprehended. No attempt has been made to render more intelligible the simple notions of position, magnitude, and direction, which every child derives from observation; but it is believed that these notions have been limited and defined with mathematical precision. A few symbols, which stand for words and not for operations, have been used, but these are of so great utility in giving styU and perspicuity to the demonstrations that no apology seems necessary for their introduction. Great pains have been taken to make the page attractive. The figures are large and distinct, and are placed in the middle of the page, so that they fall directly under the eye in immediate connection with the corresponding text.(Typographical errors above are due to OCR software and don't occur in the book.)About the Publisher Forgotten Books is a publisher of historical writings, such as: Philosophy, Classics, Science, Religion, History, Folklore and Mythology.Forgotten Books' Classic Reprint Series utilizes the latest technology to regenerate facsimiles of historically important writings. Careful attention has been made to accurately preserve the original format of each page whilst digita

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 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.