An Elementary Treatise On the Integral Calculus : Containing Applications to Plane Curves And Surfaces, With Numerous Examples

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J = i (a + i) ^ + f (ffl — i) sin cos ip.
26. Prove that the sides of a polygon of maximum perimeter inscribed in a conic are tangents to a confocal conic. — Chasles, Comptes liendus, 1 845.
27. To two arcs of an equilateral hyperbola, whose difference is rectifiable, correspond equal arcs of the lenmiscate which is the pedal of the hyperbola.
Jbid: Examples. 249 28. The tangents at the extremities of two arcs of a oonio, whose difference is reotifiaUe, form a quadrilateral, whose sides are tan
...gents to the same circle. — Ibid.
29. In an equilateral hyperbola prove that rds = Ja'rf(tau2e), and hence show that jrds taken between any two points on the curve is equal to the rectangle under the chord joining the points and the line connecting the middle point of the chord with the centre of the hyperbola. Mr. AV". S. M'Cay.
30. If he any point on a curve, show that the arc is the integral of «V/^^^. (M.Serret What curve do the equations represent ?
3 1 . Through any point in a plane two conies of a conf ocal system can be drawn.


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