Other editions of book An Introduction to the Ancient and Modern Geometry of Conics, Being a Geometrical Treatise on the Conic Sections With a Collection of Problems and Historical Notes and Prolegomena

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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. 1881 Excerpt: ...is a parabola or a hyperbola touching the two sides from which the extremes are measured at the extremities of the third side. 431. On a straight line drawn through a fixed point C to intersect two given straight lines a length CD is estimated a mean proportional to the intercepts between the fixed point and the two points of section; prove that the locus of D is a hyperbola whose asymptotes are the parallels through C to the fixed lines. 432. A diameter of a parabola and the tangent at its extremity being taken as the asymptotes of a hyperbola, what are the magnitudes to which the ordinate and abscissa of their point of concourse with respect to that diameter are a pair of mean proportionals? Conversely shew how to find a pair of mean proportionals to two given magnitudes. 433. The intercept on any parallel to an asymptote of a hyperbola (or to the axis of a parabola) between any point upon it and the polar of that point is bisected by the curve. 434. The intercept made upon any straight line through either vertex of a hyperbola by parallels drawn to the asymptotes through the other vertex is bisected at the point in which the straight line meets the curve again; the locus of the middle point of the intercept made upon any straight line through a fixed point by two given straight lines is a hyperbola to whose asymptotes they are parallel; and further, if the latter intercept be cut in any other constant ratio, the locus of the point of section will still be a hyperbola. In what case will the eccentricity of the locus be independent of the ratio in which this intercept is divided? 435. If Q be a point on a hyperbola and N a point on the nearer asymptote, and if QE be drawn parallel to that See the Arithmttka Univennlu, prob. 25. asymptote to meet the diamet...

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.

Lang: - English, Pages 483. Reprinted in 2019 with the help of original edition published long back [1881]. This book is Printed in black & white, Hardcover, sewing binding for longer life with Matt laminated multi-Colour Dust Cover, Printed on high quality Paper, re-sized as per Current standards, professionally processed without changing its contents. As these are old books, we processed each page manually and make them readable but in some cases some pages which are blur or missing or black spots. If it is multi volume set, then it is only single volume, if you wish to order a specific or all the volumes you may contact us. We expect that you will understand our compulsion in these books. We found this book important for the readers who want to know more about our old treasure so we brought it back to the shelves. (Any type of Customisation is possible with extra charges). Hope you will like it and give your comments and suggestions.