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ABCD angular points antiparallel base bisect bisectors called centres of similitude chord co-axal circles coincident complete quadrangle complete quadrilateral concurrent conic conjugate points conjugates with respect considered continuous COR.—The corresponding corresponding points cross ratio curve DEFINITIONS described diagonal triangle diameter drawn elements equal equi-cross external extremities figure fixed points form a harmonic four points Geometry given circle harmonic conjugates harmonic pencil harmonic range imaginary points infinite distance infinity inscribed inter inverse involution length limiting points locus maximum meet middle points NOTE obtain opposite sides orthocentre Orthogonal pair parallel passes perimeter perpendicular plane points of intersection polar polygons projection radical axis radii range or pencil rays RECIPROCAL regard right angles segments straight lines joining symmedian taken tangents termed THEOREM touches transversal vertex vertices
Page 12 - D are said to be harmonic conjugates of each other with respect to the points A and B, and AB is said to be harmonically divided by the points C and D. If C and D are harmonic with respect to A and B, then A and B are harmonic with respect to C and D. Harmonic range The four points A, B, C, D are referred to as a harmonic range, denoted by (ABC D), \fC and D are harmonic conjugates with respect to A and B.
Page 19 - The locus of a point from which tangents drawn to two given circles are equal is a straight line*.
Page 20 - The locus of a point whose powers with respect to two given circles are equal is called the radical axis of the two given circles.
Page 6 - DEFINITION. Each of the three straight lines which join the angular points of a triangle to the middle points of the opposite sides is called a Median of the triangle. ON PROP. 37. 1. If, in the figure of Prop. 37, AC and BD intersect in K, shew that (i) the triangles AKB, DKC are equal in area, (ii) the quadrilaterals EBKA, FCKD are equal. 2. In the figure of I. 16, shew that the triangles ABC, FBC are equal in area. 3. On the...