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 DEF.-The 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 mẞ 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 313 - 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 181 - 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 279 - The locus of the middle points of a system of parallel chords in a parabola is called a diameter.
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 522 - ... the points of intersection of the three pairs of opposite sides, of a hexagon inscribed in a conic, lie in one straight line.
Page 160 - The coordinates of the vector in the ox'y' system are (x',y') and, furthermore, as may be verified, x' = x cos 6 + y sin 6 y
Page 212 - Prove that the area of the parallelogram formed by the tangents at the extremities of two conjugate diameters of an ellipse is constant, and is equal to 4 ab.
Page ii - A TREATISE ON THE ANALYTICAL GEOMETRY OF THE POINT, LINE, CIRCLE, & CONIC SECTIONS, Containing an Account of its most recent Extensions. With numerous Exercises.
Page 180 - 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.