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" Find its equation. Show that the radius of curvature at each point of the curve is inversely proportional to the length of the normal intercepted between the point on the curve and the ?/-axis. "
A Treatise on Infinitesimal Calculus: Differential calculus. 1857 - Page 315
by Bartholomew Price - 1857
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The Principles of the Differential Calculus: With Its Application to Curves ...

John Hind - Curves, Algebraic - 1831 - 552 pages
...the straight line joining this and the proposed point of the curve will be the tangent. 339. Con. 2. The length of the tangent intercepted between the point of contact and the plane of %y is equal to when o?' = 0, and is therefore expressed by V^ + o^+ar — = л л/! 4 (dJLV...
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An Elementary Treatise on the Differential Calculus Founded on the Method of ...

John Minot Rice, William Woolsey Johnson - Differential calculus - 1880 - 464 pages
..., _ a dsJ a ds = V(dx* + dy). . (0 (2) FIG. 33. 165. The distance PT (Fig. 34) on the tangent line intercepted between the point .of contact and the axis of x is sometimes called the tangent, and in like manner the intercept PN is called the normal. From the triangles...
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An Elementary Treatise on the Differential Calculus Founded on the Method of ...

John Minot Rice, William Woolsey Johnson - Differential calculus - 1880 - 490 pages
...as л and ds = \f(dS + dy1). . . (2) ° FIG зз 165. The distance PT (Fig. 34) on the tangent line intercepted between the point of contact and the axis of x is sometimes called the tangent, and in like manner the intercept PN is called the normal. From the triangles...
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An Elementary Treatise on the Differential and Integral Calculus

Edward Albert Bowser - 1884 - 424 pages
...tractriz or equitangential curve. If AB is a curve such that PT, the length of the intercepted tangent between the point of contact and the axis of x, is...then the locus of P is the equitangential curve. Let P and Q be two consecutive points on the curve; let (x, y) be the point P, and OA = PT = a. Then a...
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Elements of analytic geometry

Simon Newcomb - Geometry, Analytic - 1885 - 488 pages
...equation of the tangent. 136. The Subtangent. Def. The projection on the axis of X of that portion of the tangent intercepted between the point of contact and the axis of X is called the subtangent. To find where the tangent intersects the axis of X, we make y = 0 in the equation...
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An Elementary Treatise on the Differential Calculus: With Applications and ...

Joseph Edwards - Mathematics - 1892 - 550 pages
...foot of the ordinate on the tangent is of constant length. 11. In the tractory prove that the portion of the tangent intercepted between the point of contact and the axis of X is of constant length. 201. Polar Co-ordinates. If the equation of the curve be referred to polar co-ordinates,...
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Differential Calculus for Beginners

Joseph Edwards - Differential calculus - 1896 - 288 pages
...foot of the ordinate on the tangent is of constant length. 11. In the tractory prove that the portion of the tangent intercepted between the point of contact and the axis of x is of constant length. 91. Polar Co-ordinates. If the equation of the curve be referred to polar coordinates,...
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Golden Differential Calculus

Golden, N. P. Bali - Calculus - 2010 - 1104 pages
...90° - ¿NPT = Z.NTP = Ц> dy 1 dx tan \1> = j .'. cot \1> = — = — dx dy_ ay dx (i) The portion of tangent intercepted between the point of contact and the axis of x is called the lengtL of the tangent. л In the rt. La APTN, Length of tangent = PT = PN cosec у = PN...
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The Bombay University Calendar, Volume 2

University of Bombay - 1909 - 354 pages
...(o, a). Prove that the equation of the tangent at « is X + Y sinh u = ait, and hence shew tha- tho length of the tangent intercepted between the point of contact and the axis of x is constant. 6. Prove the formula for integration by parts. . 9 Integrate С M 7. Integrate ез> Integrate...
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How To Learn Calculus Of One Variable Vol. I, Volume 1

J. D. Ghosh - Mathematics - 2008 - 962 pages
...cos y \ y=i(*> y\~x\ dx)x~*\ y=y\ 1 + -,2 dx ) У=У\ J 2. Length of tangent: N SX *• X The portion of the tangent intercepted between the point of contact and the axis of x is called the length of the tangent. In A PTN . Length of tangent = PT = PN • cosec у -\¡] + = PN...
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