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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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An Elementary Course in Synthetic Projective Geometry (Classic Reprint)
Print-on-DemandAnbieter: Forgotten Books, London, Vereinigtes Königreich
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Paperback. Zustand: 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. Bestandsnummer des Verkäufers 9781330376997_0
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An Elementary Course in Synthetic Projective Geometry Classic Reprint
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PAP. Zustand: New. New Book. Shipped from UK. Established seller since 2000. Bestandsnummer des Verkäufers LW-9781330376997
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An Elementary Course in Synthetic Projective Geometry Classic Reprint
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PAP. Zustand: New. New Book. Shipped from UK. Established seller since 2000. Bestandsnummer des Verkäufers LW-9781330376997
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An Elementary Course in Synthetic Projective Geometry (Classic Reprint)
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Paperback. Zustand: Brand New. 142 pages. 9.00x6.00x0.32 inches. This item is printed on demand. Bestandsnummer des Verkäufers zk1330376994
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