Books with author George Wentworth

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Excerpt from Wentworth's Plane GeometryD. Is an abbreviation that has long been used in geometry for the Latin words quod erat demonstrandum which was to be proved.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 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.-....