Books with title Mathematical Questions with Their Solutions, from the "Educational Times", Vol. XXVII. From June to December 1877

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. ++++ The below data was compiled from various identification fields in the bibliographic record of this title. This data is provided as an additional tool in helping to ensure edition identification: ++++ <title> Mathematical Questions With Their Solutions, From The "Educational Times"...; Volume 15 Of Mathematical Questions With Their Solutions, From The "Educational Times"; D. Biddle; Volume 15 Of Mathematical Questions And Solutions, From The "Educational Times": With Many Papers And Solutions In Addition To Those Published In The "Educational Times"; W. J. C. Miller<editors> W. J. C. Miller, D. Biddle<publisher> Hodgson, 1871<subjects> History; General; History / General; Mathematics; Mathematics / General

About the Book Mathematics is the study of such problems as quantity, structure, space, and change. Mathematicians seek out and implement patterns to formulate new theories; they resolve the veracity of theories by applying mathematical proofs. When mathematical frameworks provide good replications of actual events, then mathematics can improve our predictions about natural phenomena. Using theoretical abstraction and logic, over thousands of years mathematics has developed from simple calculation and measurement, to the systematic study of the shapes and dynamics of physical objects. About us Leopold Classic Library has the goal of making available to readers the classic books that have been out of print for decades. While these books may have occasional imperfections, we consider that only hand checking of every page ensures readable content without poor picture quality, blurred or missing text etc. That's why we: republish only hand checked books; that are high quality; enabling readers to see classic books in original formats; that are unlikely to have missing or blurred pages. You can search "Leopold Classic Library" in categories of your interest to find other books in our extensive collection. Happy reading!

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 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 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.

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.

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.

This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1901 edition. Excerpt: ...A, 0 This determinant is, when worked out, (/+ g cos C) (g + h cos A) (A +/cos B) + (A + g cos A) (/+ h cos B) (g +/cos C), which breaks up identically into the product of sin A + g sin B + h sin C into gh sin A + A/sin B + _/j sin C; this result determining the locus of (/, g. A), according to what we all know, to be the circle circumscribing the original triangle. The geographical statement of this theorem homographically transformed, runs thus: Consider two fixed points joined by a line intersecting the three sides of a triangle; to each point of intersection successively let there be taken the harmonic conjugate with the fixed points as a pair of conjugates: join each point so determined with any point on the conic passing through the fixed points and the vertices of the triangle; the intersections of these connectors each with the "corresponding" side of the original triangle, lie in a straight line. And, analytically stated, the proposition is as follows; Let (a,/8, 7), (a', /8', 7') be the two fixed points, and (/, g, h) the arbitrary point on the conic circumscribing the triangle of reference. The coordinates of the "harmonic conjugates" spoken of above are as follows; viz., x: y: z = y'a. + 7o': /$ + yff: 277' for that corresponding to the point of intersection on the side x, and similar expressions for the other two. The coordinates of the point where the line joining this conjugate with the point (f, g, h) intersects the side 2, are x: y: z = h (7'a + 7o')--2/77': h (y'0 + y0')--2gyy': 0, with similar expressions for the other two points of intersection; and the condition that these three should lie in a straight line is 0, f(a'0 + a$')-2gaa', f (a'y + ay')-2haa' 1 0 03a' + iS'o)-ye/', 0, g (#7 + 0Y)-2 W-0....