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 chord of contact circumcentre circumcircle coaxal coefficients collinear concurrent concyclic confocal cos² curve DEF.-The 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 Hence the proposition homologous infinity inscribed isogonal conjugates join latus rectum line at infinity meet middle points mẞ nine-points circle normal orthocentre osculating osculating circle pair 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 similitude 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 309 - 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 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 iii - CASEY.— A TREATISE ON THE ANALYTICAL GEOMETRY OF THE POINT, LINE, CIRCLE, AND CONIC SECTIONS.
Page 34 - A line which divides two sides of a triangle proportionally is parallel to the third side.
Page 326 - If the three pairs of opposite sides of a hexagon inscribed in a conic section be produced to meet, the three points of...
Page 188 - The locus of the intersection of tangents to a circle, at the extremities of a chord which passes through a given point, is , B . . __E_ the polar of the point.
Page 251 - To find the locus of the centre of a circle which passes through a given point and touches a given straight line.