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axes bicircular quartic centres of similitude circumscribed circumscribing circle coefficient collinear common chord concurrent lines conic pass conies conjugate contact of tangents coordinates cos2 cubic cubic curve curvature diameter distance Dominical Letters ellipse envelope equally inclined equation fixed point foci focus four points given conic given points harmonic harmonic conjugates hence hyperbola inscribed integral involution J. J. Walker James Dale line joining locus major axis maximum middle points osculate the conic osculating circle pairs parabola parallel perpendicular point of intersection points of contact polar circle Proposed by J. J. Proposed by Professor prove quadric quadrilateral radical axis radii radius respectively right angles roots semicubical parabola sin2 Solution by J. J. Solution by James square Stephen Watson straight line tangents drawn theorem touches triangle Tucker values vertices W. K. Clifford whence Wolstenholme
Page xiii - D, in which the circumscribing circle cuts the ellipse, is equal to 3 fj(a2+42) -t-?'2}, r being the semi-diameter drawn to the point ; and (3) the sum of the squares of the diameters of the ellipse passing through the points A, B, C, is equal to the sum of the squares of three conjugate diameters ................ 69 2917. If a conic pass through two given points and touch a given conic at a given point, the chord of intersection with the given conic will pass through a fixed point on the given straight...
Page 90 - ... 2446. (Proposed by WK CLIFFORD, BA) — PQ is a chord of a conic, equally inclined to the axis with the tangent at P. Any circle through PQ, cuts the conic in RS. Show that the harmonic conjugate of RS relative to P lies on the straight line joining Q. to the other extremity of the diameter through P. Hence show by inversion that if chords be drawn to a circular cubic through the point where the asymptote cuts the curve, the locus of their middle points is a circle through the double point. Solution...
Page 99 - AQ . [Ар sm2Py (Here al means the distance between the points a, I, and BP means the angle between the lines B, P.) 3.
Page 67 - ... the percussive action is the same as if the whole mass of the body were concentrated at that point, is called the center of percussion. This point is located at the same point as the center of oscillation. CENTER REAMERS. A " center reamer " is a reamer the teeth of which meet in a point.
Page 92 - ... curves. It is hardly necessary to add that instead of a zone we may take a patch of matter bounded by a contour of any form within the circle C, and then, finding the inverse of this contour so as to obtain a corresponding external patch, the two together, by the combined attractions of their particles according to the inverse fifth power of the distance, will serve to make a body describe the circle...
Page 116 - ARITHMETIC; being a Text-Book for Class Teaching; and comprising a Course of Fractional and Proportional Arithmetic, an Introduction to Logarithms, and Selections from the Civil Service, College of Preceptors, and Oxford Exam. Papers.
Page 55 - TUCKEB remarks that the theorem is a particular case of the theorem, " Given four points on a conic, its chord of intersection with a fixed conic passing through two of these points will pass through a fixed point," which is readily seen to lie on the fixed line.
Page xiv - PQ (Here al means the distance between the points a, I, and BP means the angle between the lines B, P.) 3. Find analogous propositions for a curve of any order on a plane or on a sphere ................ 99 No.
Page 116 - Thirteenth Edition, 12mo, cloth, price Is., EXAMPLES IN ALGEBRA FOR JUNIOR CLASSES. Adapted to all Text-Books ; and arranged to assist both the Tutor and the Pupil. Third Edition, cloth, lettered. 12mo, price 3s., EXAMPLES IN ALGEBRA FOR SENIOR CLASSES.
Page 50 - Denoting by M and N any pair of lines dividing harmonically the three diagonals of the quadrilateral ; by A and A', B and B', C and C' the three pairs of concurrent lines passing through their six extremities ; and by T and T' the pair of concurrent tangents to any conic inserted in the quadrilateral ; then, since, by a well-known property, the four pairs of concurrent lines A and A', B and B', C and C...