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.

Excerpt from The Cambridge and Dublin Mathematical Journal, 1846, Vol. 1: Being Vol. V. Of the Cambridge Mathematical Journal Notes and other passages enclosed in brackets are insertions made by the Editor. The date of actual publication of any article, or portion Of an article. 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.

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.

Excerpt from The Cambridge and Dublin Mathematical Journal, 1854, Vol. 9 One of the theorems r'especting the internal pressures at any point within a body at rest, to which Mr. Rankine alluded in this Journal (no. Xxv. P. Is so elegant that it seems to deserve a place in our University mathematics. 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.

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 usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1848 edition. Excerpt: ...thus. Let T, U, V, TV, be four solutions which are of the form $ (a, x), $ (Jb, z), &c. Let b, c, e be a + 0, a + 20, a + 30, and throw AT + BV4 CV+ EW into the form AT + B&T + C"Aar+ E'A'T, AT being U-T, &c; and this again into the form whence the usual result is easily obtained. ON THE RELATION BETWEEN DIFFERENT CURVES AND CONES CONNECTED WITH A SERIES OF CONFOCAL ELLIPSOIDS. By John Y. Rtttledqe, B.A., Trinity College, Dublin. Thb object of the present paper is to shew the natural connexion that exists between several systems of curves traced upon the surface of an ellipsoid, which hitherto have been viewed as isolated objects of curiosity, but which, from the fact of their resulting from one and the same source, may be regarded in a still more interesting and instructive point of view. It is well known that all questions relating to conjugate diameters in central surfaces of the second order may be discussed as questions relating to rectangular axes, by the transformation where x, y, z, x1, y, ', x," y," z," are the coordinates of the extremities of the conjugate semidiameters, and a, 3 y a, /3', y', &c. are the angles made by the new rectangular axes of reference with the original axes of x, y, z. Suppose that we have a number of confocal ellipsoids: x2 y2, X y2 z2, . z y2 z2, . o c tr o c a o c In the first let us take three conjugate semidiameters, the respective coordinates of the extremities of which are x, y, z, x," y', z, and x," y," z." Let us take the corresponding points on the remaining ellipsoids, i.e. points such that? = =-&c a a a Then, if we connect the origin of coordinates with these points on the respective ellipsoids, it is easy to see...