This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1826 Excerpt: ...the equation to the parabola, when referred to any diameter and the tangent at its extremity as axes, the origin being on the curve. The corresponding equation to the ellipse and hyperbola is (101).y2 = -;+4 CD a bn SP.PH, . r. a r Here -=--=-. (151)=-? (2a-r) = 2r.--7. a a a a a Now when the centre is infinitely ...
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This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1826 Excerpt: ...the equation to the parabola, when referred to any diameter and the tangent at its extremity as axes, the origin being on the curve. The corresponding equation to the ellipse and hyperbola is (101).y2 = -;+4 CD a bn SP.PH, . r. a r Here -=--=-. (151)=-? (2a-r) = 2r.--7. a a a a a Now when the centre is infinitely distant, a = a, because, in general, "The line 4 SP, which is the value of the parameter in the ellipse or hyperbola, when either passes into a parabola, is called the parameter of the diameter passing through P. Let Qp = 4SP. Then the equation to the parabola becomes y = Qpx, which is of the same form with that in (158). The axes to which the parabola is referred, are, by analogy, called conjugate axes. 165. Cor. 1. Let vQ he any ordinate to the diameter, passing through P. Then, we have, by the equation, 4SP. Pv = Qv 166. Cor. 2. Lines of the second order, when referred to any diameter, and the tangent at its extremity, may be defined by the equation, y = mx + -x, (m) being negative in the ellipse, positive in the hyperbola, and equal to nothing in the parabola. 167. Prop. 6. To find the equation to a tangent, at any point (x', y) of a parabola, when referred to any system of conjugate diameters. The equation to a secant passing through that point is y--y'=m (x--x) (1). Now, y2 = 2px, and yf = 2px'; therefore, subtracting, yy'2 = Qp (x--x'), or (y +y) (y-y') = Qp (x-x), and substituting for y-y, its value in (1). (y +y).m(x-x')=2p(x-x), 2p or m=. y+y Let now y =y, then the secant becomes a tangent; and m=-; therefore, the equation to the tangent is y-y' =?(--') (2), or, by reduction, 99'--P (+') (3) 168. Cor. 1. When the axes are rectangular, the equation to the tangent becomes 4 yy'=p (x-f-x'), p being = 2 AS; and therefore, ...
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Add this copy of The Principles of Analytical Geometry to cart. $39.12, new condition, Sold by Booksplease rated 4.0 out of 5 stars, ships from Southport, MERSEYSIDE, UNITED KINGDOM, published 2010 by Kessinger Publishing.
Add this copy of The Principles of Analytical Geometry to cart. $49.21, new condition, Sold by Booksplease rated 4.0 out of 5 stars, ships from Southport, MERSEYSIDE, UNITED KINGDOM, published 2007 by Kessinger Publishing.
Add this copy of The Principles of Analytical Geometry to cart. $53.70, good condition, Sold by Bonita rated 4.0 out of 5 stars, ships from Santa Clarita, CA, UNITED STATES, published 2010 by Kessinger Publishing.
Add this copy of The Principles of Analytical Geometry to cart. $65.41, good condition, Sold by Bonita rated 4.0 out of 5 stars, ships from Santa Clarita, CA, UNITED STATES, published 2007 by Kessinger Publishing.
Add this copy of The Principles of Analytical Geometry to cart. $70.74, good condition, Sold by Bonita rated 4.0 out of 5 stars, ships from Santa Clarita, CA, UNITED STATES, published 2015 by Palala Press.
