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Excerpt from On the Geometry of Surfaces
The Theory of Surfaces is an extensive one, and a thoroughly comprehensive treatise would necessarily be voluminous. I have therefore decided to limit this work to the more elementary portions of the subject, and have abstained from introducing investigations which require a knowledge of the Theory of Functions and of the higher branches of Modern Algebra. The ordinary methods of Analytical Geometry are quite sufficient to enable the properties of cubic and quartic surfaces and twisted curves, and also the point and plane singularities of surfaces, to be discussed with tolerable completeness, and to demonstrate a number of interesting and important theorems connected with them; but for the purpose of confining this treatise within a moderate compass, I have abstained from any general discussion of surfaces of higher degree than the fourth.
The properties of a point singularity may usually be examined by means of a surface of low degree just as well as by one of the nth degree; but if the degree is less than a certain limit, which depends on the character of the singularity, the latter appears in an incomplete form on the surface. Thus the properties of a triple line cannot be fully investigated without employing a surface of the seventh degree, and this fact has rendered it necessary to partially discuss surfaces of higher degree than a quartic.
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Paperback. Zustand: New. Print on Demand. This book is an extensive and easily comprehensible, triple-threat treatise on the theory of surfaces that is also groundbreaking. It covers surface geometry in great depth. It reveals the complex points of contact and common ground between curves and surfaces and between plane and twisted curves. This book is of foundational importance to budding mathematicians, opening up all the main areas of surface investigation and offering a balanced and engaging overview of a complex and beautiful branch of mathematics. It introduces new methods of exploring surfaces and reinforces more established ones, re-examining old theorems and presenting a host of new ones. Breaking new ground, the author resolves a number of multiple points into their constituent conic nodes and binodes. 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 9781330387009_0
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