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accordingly angle asymptotes axis Cartesian centre of curvature circle of inflexions co-ordinates conic constant corresponding cusp cycloid degree denote derived functions determined differential coefficients differential equation double point du du dV dV dx dx dx dy dx dxdy dy dz easily seen Eliminate ellipse envelope epicycloid epitrochoid Examples expansion expression finite fixed circle fixed point foci fraction geometrical Hence homogeneous function hyperbola hypocycloid hypotrochoid independent variable infinitely small inverse Jacobian Limaçon limit locus maxima and minima maximum method minimum values negative normal origin osculating circle oval parabola pedal perpendicular plane point of contact point of inflexion positive preceding prove quadratic radii radius of curvature represented respect result right line rolling circle roots solid harmonic spherical spherical harmonic substituting suppose tangent Taylor's Theorem theorem tion transformation triangle zero уг
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 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».