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Author: Clement Vavasor Durell Publisher: Forgotten Books ISBN: 9780260327413 Category : Mathematics Languages : en Pages : 378
Book Description
Excerpt from A Course of Plane Geometry for Advanced Students, Vol. 2 The author ))olds very strongly that the educational value of higher geometry lies in that novelty of idea and generality of con ception which is more characteristic of this subject than of any other branch of elementary mathematics. A course of geometrical conics, based on the focus-directrix definition and developed by Euclidean methods, provides excellent practice in rider-work but although the student may gain from it a systematic knowledge of the metrical properties of the conic, yet he will assimilate few, if any, really new ideas. On the other hand a projective treatment introduces the student to a region of geometrical thought, unlike anything he has seen in the past - a transition as abrupt and fertile as the crossing from algebra to the calculus. There are constant surprises, apparent contradictions, features of absorbing interest, and principles which, by the generality of their application and the variety of their expression, cannot fail to fascinate the reader and incite him to investigate their developments for himself. Experience proves incontestably that analytical methods frequently elucidate difficult geometrical conceptions. The theory of ideal elements in pure geometry, the notion of one-to - one correspondence and its application to homography and involution, the principles of conical projection are undoubtedly illuminated by a joint use of geometry and analysis. 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.
Author: Clement Vavasor Durell Publisher: Forgotten Books ISBN: 9780260327413 Category : Mathematics Languages : en Pages : 378
Book Description
Excerpt from A Course of Plane Geometry for Advanced Students, Vol. 2 The author ))olds very strongly that the educational value of higher geometry lies in that novelty of idea and generality of con ception which is more characteristic of this subject than of any other branch of elementary mathematics. A course of geometrical conics, based on the focus-directrix definition and developed by Euclidean methods, provides excellent practice in rider-work but although the student may gain from it a systematic knowledge of the metrical properties of the conic, yet he will assimilate few, if any, really new ideas. On the other hand a projective treatment introduces the student to a region of geometrical thought, unlike anything he has seen in the past - a transition as abrupt and fertile as the crossing from algebra to the calculus. There are constant surprises, apparent contradictions, features of absorbing interest, and principles which, by the generality of their application and the variety of their expression, cannot fail to fascinate the reader and incite him to investigate their developments for himself. Experience proves incontestably that analytical methods frequently elucidate difficult geometrical conceptions. The theory of ideal elements in pure geometry, the notion of one-to - one correspondence and its application to homography and involution, the principles of conical projection are undoubtedly illuminated by a joint use of geometry and analysis. 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.
Author: Clement Vavasor Durell Publisher: Nabu Press ISBN: 9781295540105 Category : Languages : en Pages : 388
Book Description
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.
Author: Clement Vavasor Durell Publisher: Theclassics.Us ISBN: 9781230447575 Category : Languages : en Pages : 94
Book Description
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. 1910 edition. Excerpt: ... is the envelope of x. Now the pole of x lies on b;.'. the pole of b lies on x;.'. x envelopes the pole of b;.'. the reciprocal of a, viz. A, is the pole of b. q.e.d. THEOREM 101. (1) If P, Q are conjugate points w.r.t. Sv then p, q are conjugate lines w.r.t. S2; and conversely. (2) If PQR is a self-conjugate triangle w.r.t. Sx, then pqr is a self-conjugate triangle w.r.t. S2. The proof is left to the reader. THEOREM 102. (1) If O is the centre of the base-conic S, the centre of Sx reciprocates into the polar of O w.r.t. S2, and the polar of O w.r.t. Sx reciprocates into the centre of SQ. (2) The reciprocal of O is the line at infinity; and conversely. (3) The asymptotes of Sj reciprocate into the meets of S2 with the polar of O w.r.t. S2. (4) is an ellipse, parabola, or hyperbola, according as O lies inside, on, or outside Sx. The proof is left to the reader. 1. Prove Theorem 95. 2. Prove Theorem 96. 3. Prove Theorem 99. 4. Prove Theorem 101. 5. Prove Theorem 102. 6. If two conics touch each other, prove that their reciprocals touch each other. 7. What is the reciprocal of a common chord of two conics? 8. What is the reciprocal of a common tangent of two conics? 9. Two conics cut at P; what is the reciprocal of the tangents at P to the conics? 10. What is the reciprocal of two parallel tangents to a conic? 11. What is the reciprocal of a pair of conjugate diameters of a conic? 12. What is the reciprocal of two parallel chords of a conic? 13. P, Q are two points on a tangent // to a conic 5i; the other tangents from P, Q to Sx meet at R; construct the reciprocal figure. 14. PQR is a triangle, self-conjugate to a conic Su and circumscribing a conic S; what is the reciprocal figure? Attention has already been directed to the fact that all...
Author: Clement V Durell Publisher: Alpha Edition ISBN: 9789353893712 Category : History Languages : en Pages : 376
Book Description
This book has been considered by academicians and scholars of great significance and value to literature. This forms a part of the knowledge base for future generations. So that the book is never forgotten we have represented this book in a print format as the same form as it was originally first published. Hence any marks or annotations seen are left intentionally to preserve its true nature.
Author: Clement Vavasor Durell Publisher: Wentworth Press ISBN: 9780526200283 Category : Mathematics Languages : en Pages : 370
Book Description
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.
Author: Clement Vavasor Durell Publisher: Andesite Press ISBN: 9781375766012 Category : Juvenile Nonfiction Languages : en Pages : 382
Book Description
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.
Author: Clement Vavasor Durell Publisher: ISBN: 9781296285081 Category : Languages : en Pages : 372
Book Description
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.
Author: Edith Long Publisher: Forgotten Books ISBN: 9781333710231 Category : Mathematics Languages : en Pages : 286
Book Description
Excerpt from Plane Geometry IN this text, as in the Algebra, the authors have at tempted to present the subject-matter in a way more suitable to beginners than is the case in most of the modern books. Brief and concise methods of exposition are therefore largely avoided, especially at the start, and much space is given to the explanation and analysis of theorems and problems, in order to bring out clearly the plan of attack and the method Of proof. In the presentation of theorems, where complete proofs are given, the following plan has been adopted. 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.
Author: Clement Vavasor Durell
Author: Clement Vavasor Durell
Author: Clement Vavasor Durell
Author: Clement Vavasor Durell
Author: Clement V Durell
Author: Clement Vavasor Durell
Author: Clement Vavasor Durell
Author: Clement Vavasor Durell
Author: Clement Vavasor Durell
Author: Clement Vavasor Durell
Author: Edith Long