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Algebra Analytical Geometry applied arbitrary function axis becomes binomial binomial theorem Calculus centre circle conic section corresponding cos2 cosines cubic equation curvature curve deduced determine Differential Calculus differential coefficients differential equations direction displacement distance dx dx eliminate ellipse ellipsoid equal equilibrium expanded expression factor finite force formula fraction Geometry gives Hence hyperbola independent infinite integer integral logarithms method multiply negative obtain origin parabola parallel partial differential partial differential equations perpendicular plane of xy plane wave points of intersection positive integer problem quantities radius represent Residual Calculus residue respectively result right angles roots sides solution spherical straight line Substituting these values subtracting suppose surface symbols of operation tangent plane Taylor's theorem theorem theory tion triangle vanish variables velocity vibration wave whence
Page 221 - To find the locus of a point, the sum of whose distances from two given points is constant. Let S, H be the two fixed points
Page 230 - where a is one-fourth of the parameter, and m the trigonometrical tangent of the angle which the tangent makes with the axis of y. Hence, if x
Page 10 - is the tangent of the angle which the tangent to the curve makes with the axis of x.
Page 104 - particles attracting each other according to the law of the inverse square of the distance, and
Page 11 - To find the locus of the intersection of two tangents to an ellipse, which are at right angles to
Page 51 - of the instrument, and at last reduce it to rest. If this happen before the top fall, it must then be spinning in such a position that the point can remain stationary ; but this cannot be if it be inclined. Hence it must have a tendency to erect itself into a vertical position.
Page 186 - the vertical line through the centres of gravity of the body and of the fluid displaced
Page 74 - which being independent of a, is the same for all sections for which r is the same ; that is, for all those which are made by planes touching the sphere. From this it appears, that the latus rectum is equal to the diameter of the sphere multiplied by the tangent of half the vertical angle of the cone,