Trilinear Coordinates and Other Methods of Modern Analytical Geometry of Two Dimensions: An Elementary Treatise |
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Common terms and phrases
a₁ aa+bB+cy angular points anharmonic ratio asymptotes B₁ chord of contact circle circular points coefficients coincident points collinear common tangents condition conic section conjugate conjugate point cubic curve cusp d'f d'f dB dy denote determinant df df df diameter direction sines ellipse equa equation Art expression find the equation fixed point foci given point given straight line harmonic homogeneous function hyperbola imaginary points inscribed la² last article line at infinity line whose equation lines of reference locus meet middle points P₁ parabola parallel perpendicular distances point of intersection points at infinity points of contact points of inflexion points of reference polar quadratic quadrilateral radical axis respect self-conjugate shew straight line joining tangents triangle ABC triangle of reference triangular coordinates trilinear coordinates Y₁
Popular passages
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 i - WHITWORTH (WA) Trilinear Co-ordinates, and other methods of Modern Analytical Geometry of Two Dimensions. An Elementary Treatise. By W. Allen Whitworth, MA, Professor of Mathematics in Queen's College, Liverpool, and late Scholar of St. John's College, Cambridge. 8vo.
Page 251 - A point moves so that the sum of the squares of its distances from the points (0, 0), (1, 0) is constant.
Page 456 - If upon the sides of a triangle as diagonals, parallelograms be described, having their sides parallel to two given lines, the other diagonals of the parallelograms will meet in a point. 45. If from a fixed point 0 a straight line be drawn OABCD... meeting in A, B, C, D,... any given fixed straight lines in one plane, and if 1111 OX~ OA^ OB^ OC^'" X being a point in OA, the locus of X is a straight line.
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 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 252 - Find the equation to the locus of a point which moves so as to be always equi-distant from the lines — — a=0.
Page 316 - ... and the two exterior diagonals coincide (EF). II. If a quadrilateral be inscribed in a conic, the points of intersection of opposite sides and the points of intersection of tangents at opposite angles lie all in one straight line.
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.