Sinopsis
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.
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Reseña del editor
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 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.
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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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An Elementary Course in Synthetic Projective Geometry (Classic Reprint)
Impresión bajo demandaLibrería: Forgotten Books, London, Reino Unido
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Paperback. Condición: New. Print on Demand. This book offers a clear and accessible introduction to the essentials of synthetic projective geometry. While following the traditional approach established by the great masters of the subject, the author presents the theory in a more streamlined way, particularly in the chapter on involution. The author emphasizes the importance of a purely projective understanding of involution, advocating for a treatment free from reliance on metrical foundations. The book explores the relationships between fundamental geometric forms like point-rows, pencils of rays, and axial pencils, using the concept of one-to-one correspondence to highlight their shared characteristics and demonstrate how they can be transformed into one another. It delves into the crucial theorem of Desargues, examining its significance for understanding complete quadrangles and the concept of harmonic points. The author also introduces the concept of projective invariance, demonstrating how certain geometric relationships remain constant even when the forms are projected onto different configurations. This leads to a deeper understanding of the connections between projective and metrical geometry, as well as the role of the infinitely distant point in bridging the gap between the two. Ultimately, the book provides a foundation for understanding the rich and intricate world of synthetic projective geometry, showcasing its power to illuminate the relationships between fundamental geometric forms and offer a fresh perspective on the nature of space itself. 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. Nº de ref. del artículo: 9781330376997_0
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An Elementary Course in Synthetic Projective Geometry Classic Reprint
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An Elementary Course in Synthetic Projective Geometry Classic Reprint
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PAP. Condición: New. New Book. Shipped from UK. Established seller since 2000. Nº de ref. del artículo: LW-9781330376997
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An Elementary Course in Synthetic Projective Geometry (Classic Reprint)
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Paperback. Condición: Brand New. 142 pages. 9.00x6.00x0.32 inches. This item is printed on demand. Nº de ref. del artículo: zk1330376994
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