Trilinear Coordinates and Other Methods of Modern Analytical Geometry of Two Dimensions: An Elementary Treatise
Deighton, 1866 - Coordinates, Trilinear - 506 pages
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angles angular points asymptotes axes becomes called centre CHAPTER circle circumscribing coefficients coincident common condition conic conic section conjugate constant cubic curve denote described determinant df df df diameter direction distance double drawn equal equation expression find the equation fixed point focus follows four give given given point harmonic Hence identical imaginary inscribed line at infinity locus meet method middle points observed obtained parabola parallel passing perpendicular point of intersection points of contact polar pole prove quadrilateral ratio reciprocation relation represent respect result satisfy shew sides Similarly straight line substituting suppose tangents third tion touch triangle of reference triangular coordinates trilinear coordinates values written
Page 475 - An ellipse is described so as to touch the three sides of a triangle ; prove that if one of its foci move along the circumference of a circle passing through two of the angular points of the triangle, the other will move along the circumference of another circle, passing through the same two angular points. Prove also that if one of these circles pass through the centre of the circle inscribed in the triangle, the two circles will coincide.
Page 386 - ... equal to the sum of the latera-recta of the other three. 3. On a fixed tangent to a conic are taken a fixed point A, and two moveable points P, Q, such that AP, AQ, subtend equal angles at a fixed point 0. From P, Q are drawn two other tangents to the conic, prove that the locus of their point of intersection is a straight line. 4. Two variable tangents are drawn to a conic section so that the portion of a fixed tangent, intercepted between them, subtends a right angle at a fixed point. Prove...
Page 253 - A point moves so that the sum of the squares of its distances from the points (0, 0), (1, 0) is constant.
Page i - Trilinear Co-ordinates, and other methods of Modern Analytical Geometry of Two Dimensions. By the Rev. W. ALLEN WHITWORTH, MA, Professor of Mathematics in Queen's College, Liverpool, and late Scholar of St John's College, Cambridge. 8vo. 16*.
Page 43 - О and ß be the given vector. Solution. Let P be any point on the line AP, which is parallel to the vector ß.
Page 477 - If the lines which bisect the angles between pairs of tangents to an ellipse be parallel to a fixed straight line, prove that the locus of the points of intersection of the tangents will be a rectangular hyperbola.
Page 254 - Find the equation to the locus of a point which moves so as to be always equi-distant from the lines — — a=0.
Page 19 - To find the co-ordinates of the point which divides in a given ratio the straight line joining two given points.
Page 471 - ... the intersection of the perpendiculars from the angles on the opposite sides, and the other at the centre of the circle circumscribing the triangle.
Page 475 - FIND a point the distances of which from three given points, not in the same straight line, are proportional to p, q and r respectively, the four points being in the same plane. 2. If TP, TQ be two tangents drawn from any point T to touch a conic in P and Q, and if S and H be the foci, then SI