An Elementary Treatise on the Differential Calculus: Containing the Theory of Plane Curves, with Numerous Examples

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Longmans, Green, and Company, 1899 - Differential calculus - 472 pages
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Page 133 - A cos 6 = cos a cos c + sin a sin c cos B cos c = cos a cos 6 + sin a sin 6 cos C Law of Cosines for Angles cos A = — cos B...
Page 335 - This curve is the path described by a point on the circumference of a circle, which is supposed to roll upon a fixed right line.
Page 228 - O ; and if all the tangents to the curve be taken, the locus of their poles is a new curve. "We shall denote these curves by the letters A and B, respectively. Again, by elementary geometry, the point of intersection of any two lines is the pole of the line joining the poles of the lines...
Page 478 - A TREATISE ON THE ANALYTICAL GEOMETRY OF THE POINT, LINE, CIRCLE AND CONIC SECTIONS. Containing an Account of its most recent Extension.
Page 239 - Tcr' — a, where r and / are the distances of any point on the curve from two fixed points, and a, k are constants.
Page 326 - The curve is symmetrical with respect to the axis of x, and has two infinite branches ; the origin is a double cusp. The shape of the curve is exhibited in the figure annexed.
Page 207 - Find the locus of a point such that the sum of the squares of its distances from two fixed points shall be equivalent to the square of the distance between the fixed points.
Page 189 - A semicircle is described on the axis-major of an ellipse ; draw a line from one extremity of the axis so that the portion intercepted between the circle and the ellipse shall be a maximum.
Page 276 - A hyperbola. 3. Find the envelope of a right line when the sum of the squares of the perpendiculars on it from two given points is constant. 4. Find the envelope of a right line, when the rectangle under the perpendiculars from two given points is constant. An╗.
Page 216 - Let p be the length of the perpendicular from the origin on the tangent at any point on the curve...

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