Other editions of book Mathematical Questions with Their Solutions, from the Educational Times

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 was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work.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.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.

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 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 was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work.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.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. 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 was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work.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.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.

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. 1884 Excerpt: ...to tho direction of its movement. Solution by the Proposer. Taking for axes of coordinates any pair of rectangular diameters of the plate in its original position, and denoting by r its radius, by I and m the components of its small movement of translation, by and T1 those of the resulting small displacement of any point xy of the lamina, and by « and v the potential and displacement functions respectively of the strain; then since, by hypothesis, = 0 and ij = 0 for all positions of xy at infinity, while for all points on the circumference of the plate in its original position, that is, for all points satisfying the equation x-+ y" = r', they arc connected with x and y hy the relation (x + £--l)2 + (y + 17--mf = r., or, neglecting small quantities of the second order, by the relation xg+yq = lx + my; we have accordingly, for the solution of the entire problem (including the above particulars) of the strain, first to find, if possible, a potential function u which shall satisfy, at once, the general equation 1 = 0 throughout the entire extent of the lamina, and the dx. dy aforesaid particular conditions at its outer and inner boundaries, and Ihen derive from it the corresponding displacement function v in tho usual manner. Both functions, in the present case, are found readily as follows. As the function Ix t my is homogeneous in x and y, and satisfies for all values of them the equation---+----= 0, therefore the function dx dy' k.----, where k is any constant, satisfies, for all values of k, the x +9" J.; 2 A general equation--+--= 0 throughout the entire extent of the lamina, dx: dyand the particular conditions = 0 and i)--0 at its outer boundary, and for the particular value k = r'-that for its inner boundary also. It follows therefore...

Excerpt from Mathematical Questions With Their Solutions, From the "Educational Times", Vol. 34: With Many Papers and Solutions Not Published in the "Educational Times"; From July to December, 1880Queen's College. Nord. Vxntr walter: Oll City. Pennsfilvania. Smru.c.. M.a. Sidney sussexco b. Srmwwooos. William. M.a.; Presi out Royal Societ Grosvenor Place, London.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.

Excerpt from Mathematical Questions With Their Solutions, From the "Educational Times", Vol. 34: With Many Papers and Solutions Not Published in the "Educational Times"; From July to December, 1880Cremona, luigi; Direttore della Scuola degli Ingegneri, S. Pietro in Vincoli, Rome.Croeton, M. W., b.a f.r.s. Professor of Ma thematics and Mechanics in the Royal Mili tary Academy), Woolwich.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 an EXACT reproduction of a book published before 1923. This IS NOT an OCR'd book with strange characters, introduced typographical errors, and jumbled words. 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 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 was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work. 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.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. 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 was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work.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.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.

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. 1872 Excerpt: ...all the parallels (modulus r) of curves traced on the ellipsoid (tubular surfaces). The singular solution represents the particular parallel (modulus r). But now impose the further condition that the ellipsoid and the surfaces have a common normal at corresponding points, so that and we have further the universal equality dz = pd.s + qdy (12). The elimination of p, q, r from (9), (10), (11), and (12) ought to give the previous result as the differential equation. To show this, we may compare (7) with (9). These equations become identical by the equalities z_ LP = iL, y-rJL _ JhL, Z+1=JL p e+a v e + b' v e+c But substituting the value of--, thence obtained in terms of 6, in (10) and (11), we get p--( + a), q _ =&±p/t K" b (» + »)' (9 + b) z' and by (12) regain the equation (8). II. Solution by Professor Twnsend. Since, from the equation of the ellipsoid, for any point (z, y, z) on the parallel, /rTA cos a'-/yF cos/92 /zTA cos-y.where ± k = the parameter of the parallel, and a, B, y the direction angles of its normal at x, y, z; therefore, substituting in this equation for cos a, cos 0, cos 7 their values--,,--, divided each by tho square root dx dy dz of the sum of their squares, and clearing the result of the radical invelved, we have at once the differential equation required; which, as the radical enters only as the divisor of k in the uncleared equation, is consequently the same for the two parallels equidistant in opposite directions by the intervals ±A from the original surface. By a similar process, substituting for x, y, z, in the equation of any surface, x±kcosa, y±k con $, z±£cos-y, changing cosa, &c., into the above values, and clearing the result of the radical invelved, we obtain the comm...

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 was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work.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.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.