The Elements of Curves: Comprising, I, the Geometrical Principles of the Conic Sections; II. An Introduction to the Algebraic Theory of Curves (Classic Reprint) - Hardcover

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9780265606902: The Elements of Curves: Comprising, I, the Geometrical Principles of the Conic Sections; II. An Introduction to the Algebraic Theory of Curves (Classic Reprint)

Hardcover

ISBN 10: 026560690X ISBN 13: 9780265606902

Publisher: Forgotten Books, 2018

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This book explores the geometrical principles underlying conic sections - the curves formed when a plane intersects a cone. Beginning with the parabola, the author deduces the primary properties in Plano from the cone and provides a series of demonstrations that establish these properties - without any deduction from the cone, except the simple cases where the axis and its vertical tangents are concerned. These can be substituted for the others by those readers who prefer such a method. The text proceeds to the ellipse and hyperbola, investigating properties referring to the axis, any diameter, and various other characteristics. There are several propositions on tangents, which highlight properties such as the square of the tangent segment being equal to the rectangle contained under the segments of the secant. The author also includes investigations into asymptotes, the variation of radius vector, and a general problem concerning three lines converging to a given point. By approaching the subject from a purely geometrical perspective, this book provides a comprehensive and rigorous examination of conic sections. Whether seeking a deeper understanding of their properties or seeking a grounding in the subject, readers will find this book an invaluable resource.

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