An Elementary Course in Synthetic Projective Geometry (Classic Reprint) - Couverture souple

Derrick Norman Lehmer

Couverture souple

ISBN 10 : 1330376994 ISBN 13 : 9781330376997

Editeur : Forgotten Books, 2018

Synopsis

An Elementary Course in Synthetic Projective Geometry presents a clear path into the ideas of projective geometry, showing how points and lines relate through duality and polarity. The text emphasizes a balance between analytic and synthetic methods, revealing how each approach strengthens the other.

Across concise chapters, readers explore fundamental concepts such as poles and polars, projective correspondences, and the metrical properties of conic sections. The book connects classic theorems—such as Brianchon and Pascal—with modern viewpoints, illustrating how geometric ideas evolve when seen through a projective lens. It also discusses how infinity and harmonic divisions play into a unified framework that unites shapes, transformations, and invariants.

• Learn the pole–polar relationship and how it creates a one-to-one correspondence between points and lines


• See how projective pencils, point-rows, and duality interrelate to reveal deeper structure


• Study metrical properties of conics, including diameters, centers, and asymptotes


• Encounter classical theorems and their dual forms in a cohesive, beginner-friendly way

Ideal for readers of introductory geometry who want a solid foundation in projective methods and their surprising connections to analytic thinking.

A propos du livre

Présentation de l'éditeur

Engineering OJ statical WS ci( nces Library -471 PREFACE The following course is intended to give, in as simple a way as possible, the essentials of synthetic projective geometry. While, in the main, the theory is developed along the well-beaten track laid out by the great masters of the subject, it is believed that there has been a slight smoothing of the road in some places. Especially will this be observed in the chapter on I nvolution. The author has never felt satisfied with the usual treatment of that subject by means of circles and anharmonic ratios. A purely projective notion ought not to be based on metrical foundations. Metrical developments should be made there, as elsewhere in the theory, by the introduction of infinitely distant elements. The author has departed from the century-old custom of writing in parallel columns each theorem and its dual. He has not found that it conduces to sharpness of vision to try to focus his eyes on two things at once. Those who prefer the usual method of procedure can, of course, develop the two sets of theorems side by side ;the author has not found this the better plan in actual teaching. As regards nomenclature, the author has followed the lead of the earlier writers in English, and has called the system of lines in a plane which all pass through a point a pencil of rays instead of a bundle of rays, as later writers seem inclined to do.
(Typographical errors above are due to OCR software and don't occur in the book.)

About the Publisher

Forgotten Books is a publisher of historical writings, such as: Philosophy, Classics, Science, Religion, History, Folklore and Mythology.

Forgotten Books' Classic Reprint Series utilizes the latest technology to regenerate facsimiles of historically important writings. Careful attention has been made to accurately preserve the original format of each page whilst digitally enhancing the aged text.

Présentation de l'éditeur

Excerpt from An Elementary Course in Synthetic Projective Geometry

The following course is intended to give, in as simple a way as possible, the essentials of synthetic projective geometry. While, in the main, the theory is developed along the well-beaten track laid out by the great masters of the subject, it is believed that there has been a slight smoothing of the road in some places. Especially will this be observed in the chapter on Involution. The author has never felt satisfied with the usual treatment of that subject by means of circles and anharmonie ratios. A purely projective notion ought not to be based on metrical foundations. Metrical developments should be made there, as elsewhere in the theory, by the introduction of infinitely distant elements.

The author has departed from the century-old custom of writing in parallel columns each theorem and its dual. He has not found that it conduces to sharpness of vision to try to focus his eyes 011 two things at once. Those who prefer the usual method of procedure can, of course, develop the two sets of theorems side by side; the author has not found this the better plan in actual teaching.

As regards nomenclature, the author has followed the lead of the earlier writers in English, and has called the system of lines in a plane which all pass through a point a pencil of rays instead of a bundle of rays, as later writers seem inclined to do.

About the Publisher

Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com

Détails de l'édition

• Éditeur: Forgotten Books
• Date d'édition: 2018
• Langue: anglais
• ISBN 10: 1330376994
• ISBN 13: 9781330376997
• Reliure: Broché
• Nombre de pages: 141
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