Description
Excerpt from Conic Sections: Treated Geometrically
IF a straight line and a point be given in position in a plane, and if a point move in a plane in such a manner that its distance from the given point always bears the same ratio to its distance from the given line, the curve traced out by the moving point is called a Conic Section.
The fixed point is called the Focus, and the fixed line the Directrix of the conic section.
When the ratio is one of equality, the curve is called a Parabola.
When the ratio is one of less inequality, the curve is called an Ellipse.
When the ratio is one of greater inequality, the curve is called an Hyperbola.
These curves are called Conic Sections, because they can all be obtained from the intersections of a Cone by planes in different directions, a fact which will he proved hereafter.
It may be mentioned that a circle is a particular case of an ellipse, that two straight lines constitute a particular case of an hyperbola, and that a parabola may be looked upon as the limiting form of an ellipse or an hyperbola, under certain conditions of variation in the lines and magnitudes upon which those curves depend for their form.
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This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
IF a straight line and a point be given in position in a plane, and if a point move in a plane in such a manner that its distance from the given point always bears the same ratio to its distance from the given line, the curve traced out by the moving point is called a Conic Section.
The fixed point is called the Focus, and the fixed line the Directrix of the conic section.
When the ratio is one of equality, the curve is called a Parabola.
When the ratio is one of less inequality, the curve is called an Ellipse.
When the ratio is one of greater inequality, the curve is called an Hyperbola.
These curves are called Conic Sections, because they can all be obtained from the intersections of a Cone by planes in different directions, a fact which will he proved hereafter.
It may be mentioned that a circle is a particular case of an ellipse, that two straight lines constitute a particular case of an hyperbola, and that a parabola may be looked upon as the limiting form of an ellipse or an hyperbola, under certain conditions of variation in the lines and magnitudes upon which those curves depend for their form.
About the Publisher
Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com
This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
Details
Publisher - Forgotten Books
Language - English
Hardback
Contributors
Author
W. H. Besant
Published Date -
ISBN - 9780331277524
Dimensions - 22.9 x 15.2 x 1.9 cm
Page Count - 351
Paperback
Contributors
Author
W. H. Besant
Published Date -
ISBN - 9781332770021
Dimensions - 22.9 x 15.2 x 1.9 cm
Page Count - 353
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