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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.
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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.
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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.
Reseña del editor
Excerpt from A Course of Plane Geometry for Advanced Students, Vol. 2
The first part of this treatise, published a year ago, dealt with the geometry of the straight line and circle; the present volume contains a moderately comprehensive treatment of the geometry of the conic.
The author holds very strongly that the educational value of higher geometry lies in that novelty of idea and generality of conception 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 transidon 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 inconteslably 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.
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A Course of Plane Geometry for Advanced Students, Vol. 2 (Classic Reprint)
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Paperback. Zustand: New. Print on Demand. This book on advanced plane geometry marks a paradigm shift in higher geometrical education. It bridges the gap between Euclidean methods and the more generalized ideas of modern projective geometry. The author's approach is unique in introducing students to the latest theoretical ideas at an early stage. Conic sectionsâ"the main subject of the bookâ"are treated as the projections of circles, enabling the author to explore their properties from new and exciting angles. The author, whose deep respect for the history of mathematics shines through, provides an accessible introduction to the remarkable work of notable thinkers, such as Chasles, Cremona, Pascal, and Brianchon. The book's significance lies in its innovative fusion of analytical and geometrical perspectives. The author demonstrates how a judicious use of analytical methods, far from diminishing geometrical intuition, can open up a whole new dimension of understanding. Students will come away with a profound appreciation of conic sections that goes far beyond memorizing theorems. This book is a reproduction of an important historical work, digitally reconstructed using state-of-the-art technology to preserve the original format. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in the book. print-on-demand item. Bestandsnummer des Verkäufers 9781330115084_0
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A Course of Plane Geometry for Advanced Students, Vol 2 Classic Reprint
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A Course of Plane Geometry for Advanced Students, Vol 2 Classic Reprint
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PAP. Zustand: New. New Book. Shipped from UK. Established seller since 2000. Bestandsnummer des Verkäufers LW-9781330115084
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A Course of Plane Geometry for Advanced Students, Vol. 2 (Classic Reprint)
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Paperback. Zustand: Brand New. 380 pages. 8.98x5.98x0.94 inches. This item is printed on demand. Bestandsnummer des Verkäufers zk1330115082
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