An Elementary Treatise On Conic Sections And Algebraic Geometry, With Numerous Examples And Hints for Their Solutions, Especially Designed for the Use of Beginners
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In our eReader you can find the full English version of the book. Read An Elementary Treatise On Conic Sections And Algebraic Geometry, With Numerous Examples And Hints for Their Solutions, Especially Designed for the Use of Beginners Online - link to read the book on full screen. Our eReader also allows you to upload and read Pdf, Txt, ePub and fb2 books. In the Mini eReder on the page below you can quickly view all pages of the book - Read Book An Elementary Treatise On Conic Sections And Algebraic Geometry, With Numerous Examples And Hints for Their Solutions, Especially Designed for the Use of Beginners
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Putting x = aein the equation to the curve, we have or y = + - ; hence the latus rectum = — = 2a (1 — e") in the ellipse, and = 2a (e* — 1) in the hyperbola.
*201. In the ellipse the normal bisects the interior angle between the focal distances, and in the hyperbola the exterior angle; and the focal radii make equal angles with the tangent.
The equation to HP, since it passes through {x'y), (ae, 0) is -^=^y- (1), x — ae X —ae ^ ' and similarly, the equation to 8P\b ^JL^ = ^Jl— (2).
X ■{■ ae X ■...{■ ae Hence, forming the equation to the bisector PG of the angle between (1) and (2), we have, by the rules of Art. 59; — {fC — ae) y + y'x — aey _ (a;' + ae) y — y'x — aey' .„.
{y'-+{x--aey]k ~ {y^+(a,' + ae)'}i --W.
which we might shew by reduction to be the equation to the normal at {x'y"). This may however be proved briefly as fol- lows. The denominators of (3) are evidently HP and SP, and therefore reduce, for the ellipse, to a — ea;' and a + ea;', as in Art.
What to read after An Elementary Treatise On Conic Sections And Algebraic Geometry, With Numerous Examples And Hints for Their Solutions, Especially Designed for the Use of Beginners?
You can find similar books in the "Read Also" column, or choose other free books by G Hale George Hale Puckle to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
Putting x = aein the equation to the curve, we have or y = + - ; hence the latus rectum = — = 2a (1 — e") in the ellipse, and = 2a (e* — 1) in the hyperbola.
*201. In the ellipse the normal bisects the interior angle between the focal distances, and in the hyperbola the exterior angle; and the focal radii make equal angles with the tangent.
The equation to HP, since it passes through {x'y), (ae, 0) is -^=^y- (1), x — ae X —ae ^ ' and similarly, the equation to 8P\b ^JL^ = ^Jl— (2).
X ■{■ ae X ■...{■ ae Hence, forming the equation to the bisector PG of the angle between (1) and (2), we have, by the rules of Art. 59; — {fC — ae) y + y'x — aey _ (a;' + ae) y — y'x — aey' .„.
{y'-+{x--aey]k ~ {y^+(a,' + ae)'}i --W.
which we might shew by reduction to be the equation to the normal at {x'y"). This may however be proved briefly as fol- lows. The denominators of (3) are evidently HP and SP, and therefore reduce, for the ellipse, to a — ea;' and a + ea;', as in Art.
What to read after An Elementary Treatise On Conic Sections And Algebraic Geometry, With Numerous Examples And Hints for Their Solutions, Especially Designed for the Use of Beginners?
You can find similar books in the "Read Also" column, or choose other free books by G Hale George Hale Puckle to read onlineMoreLess
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