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Excerpt from A First Course in Projective Geometry
This work is intended for the use of students who have read the substance of Euclid, Books I.-XI., and who desire some introduction to the. Properties of the conic before proceeding to the study of the more advanced works on modern pure geometry. The subject of Geometrical Conics, through the medium of which such an introduction is usually acquired, often proves repulsive to the average student. In my Opinion this is due to two causes first, the demands which it makes upon the memory owing to its lack of coher ence as commonly treated; and, secondly, to the very slight extension of outlook as regards method which it affords. In the presentation here adopted, which, I venture to think, is in some respects original, I have endeavoured to overcome as far as possible these defects, while at the same time giving a slight sketch of the method of projection, and of the great principles of homography and duality upon which the further development of pure geometry so greatly depends. No systematic treatment of imaginary elements or of the theory of involution is attempted, as these subjects are, in my judgment, unsuitable for a first course.
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Paperback. Zustand: New. Print on Demand. This fascinating book introduces projective geometry, a fundamental branch of mathematics concerned with the study of geometric figures from a unique perspective. The author traces its historical roots back to the Greek mathematician Desargues, revealing the profound influence of his work on the development of this field. Through clear explanations and illustrative examples, this book explores the principles of geometric projection, duality, and perspective, providing readers with an accessible understanding of essential concepts. It examines the properties of conic sections, showing how these elegant curves can be characterized and constructed using projective techniques. The book emphasizes the importance of projective geometry in a wide range of disciplines, from architecture and engineering to computer graphics and design. It highlights the practical applications of these principles in areas such as perspective drawing, vanishing points, and the determination of hidden lines. By exploring the relationship between projective geometry and other branches of mathematics, the author demonstrates its deep connections to classical geometry, algebra, and calculus. This book is an excellent resource for students, researchers, and professionals seeking a comprehensive introduction to projective geometry and its enduring impact on various fields of study. 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 9781333554798_0
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