A Treatise on the Analytical Geometry of the Point, Line, Circle, and Conic Sections: Containing an Account of Its Most Recent Extensions, with Numerous Examples |
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Common terms and phrases
2hxy A₁ anharmonic ratio asymptotes ax² axes barycentric co-ordinates bisects Brocard by² C₁ centre of perspective chord of contact circumcentre circumcircle circumscribed coaxal coefficients collinear common tangents concyclic confocal cos² curve Dem.-Let denote diameter directrix double contact double point drawn ellipse envelope equal equilateral hyperbola Find the equation fixed point foci focus given point harmonic harmonic conjugates homologous incentre infinity inscribed isogonal conjugates join latus rectum line at infinity meet middle points nine-points circle normal orthocentre osculating osculating circle parabola parallel pedal triangle pencil perpendicular point of intersection point x'y points of contact polar pole polygon quadrilateral radical axis reciprocal respect S₁ S₂ sides sin² summits symmedian point tangential equation tangents theorem touch triangle ABC triangle formed triangle of reference variable vertex
Popular passages
Page 179 - The locus of the middle points of a system of parallel chords in a parabola is called a diameter.
Page 311 - We learn that the locus of a point, such that the tangent from it to a fixed circle is in a constant ratio to its distance from a fixed line...
Page 179 - The area of the triangle formed by three tangents to a parabola is equal to half the area of the triangle formed by joining the points of contact. 86. PQ is any chord of a parabola cutting the axis in L; R, R' are the two points in the parabola at which this chord subtend a right angle. If RR be joined, meeting the axis in L', then LL...
Page 91 - Find the locus of a point the sum of whose distances from two given straight lines is equal to a given constant le.
Page 520 - ... the points of intersection of the three pairs of opposite sides, of a hexagon inscribed in a conic, lie in one straight line.
Page 178 - Catalan, depends on the fact that the circle circumscribing the triangle formed by three tangents to a parabola passes through the focus.
Page 34 - A line which divides two sides of a triangle proportionally is parallel to the third side.
Page 132 - The angles of the triangle formed by joining the points of contact of the inscribed circle of a triangle with the sides are equal to the halves of the supplements of the corresponding angles of the original triangle. 4. If ABC, A'B'C...
Page 328 - If the three pairs of opposite sides of a hexagon inscribed in a conic section be produced to meet, the three points of...