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Synopsis
In this book, which is planned for an introductory course, the first eight chapters include the subjects usually treated in rectangular coordinates. They presuppose as much knowledge of algebra, geometry, and trigonometry as is contained in the major requirement of the College Entrance Examination Board, and as much plane analytic geometry as is contained in the better elementary textbooks. In this portion, proofs of theorems from more advanced subjects in algebra are supplied as needed. A mong the features of this part are the development of linear systems of planes, plane coordinates, the concept of infinity, the treatment of imaginaries, and the distinction between centers and vertices of quadric surfaces. The study of this portion can be regarded as a first course, not demanding more than thirty or forty lessons. In Chapter IX tetrahedral coordinates are introduced by means of linear transformations, under which various invariant properties are established. These coordinates are used throughout the next three chapters. The notation is so chosen that no ambiguity can arise between tetrahedral and rectangular systems. The selection of subject matter is such as to be of greatest service for further study of algebraic geometry. In Chapter XIII a more advanced knowledge of plane analytic geometry is presupposed, but the part involving Pliicker snumbers may be omitted without disturbing the continuity of the subject. In the last chapter extensive use is made of the calculus, including the use of partial differentiation and of the element of arc. The second part will require about fifty lessons.
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Analytic Geometry of Space (Classic Reprint)
Print on DemandSeller: Forgotten Books, London, United Kingdom
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Paperback. Condition: New. Print on Demand. This book offers a comprehensive exploration of the geometry of three-dimensional space, a field that has fascinated mathematicians for centuries. Building upon the foundations of plane analytic geometry, the author guides readers through a detailed examination of planes, lines, and quadric surfaces. The book employs various coordinate systems ââ â including rectangular, polar, cylindrical, and spherical ââ â to provide a multifaceted understanding of spatial relationships. The text delves into the complex relationship between equations and geometric figures, offering readers a powerful tool for visualizing and analyzing three-dimensional objects. Through the exploration of diverse forms of quadric surfaces, including ellipsoids, hyperboloids, paraboloids, and cones, the author reveals the underlying patterns and principles that govern spatial geometry. The bookââ â¢s exploration of linear transformations and invariant properties offers a deeper understanding of the fundamental nature of geometric objects. The use of tetrahedral coordinates, introduced through linear transformations, provides a unique and elegant framework for studying quadric surfaces and their properties. Ultimately, this book serves as a valuable resource for those seeking to unravel the complexities of spatial geometry. 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. Seller Inventory # 9781440091773_0
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Analytic Geometry of Space Classic Reprint
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PAP. Condition: New. New Book. Shipped from UK. Established seller since 2000. Seller Inventory # LW-9781440091773
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Analytic Geometry of Space Classic Reprint
Seller: PBShop.store UK, Fairford, GLOS, United Kingdom
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PAP. Condition: New. New Book. Shipped from UK. Established seller since 2000. Seller Inventory # LW-9781440091773
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Analytic Geometry of Space (Classic Reprint)
Print on DemandSeller: Revaluation Books, Exeter, United Kingdom
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Paperback. Condition: Brand New. 306 pages. 9.00x6.00x0.69 inches. This item is printed on demand. Seller Inventory # zk1440091773
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