A Syllabus of Modern Plane Geometry |
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Page 10
... angle NBC = QCA ΩΑΒ . Each of these angles is called the Brocard angle of the triangle and is denoted by w . The ... right extremity of the base . TRIPLICATE RATIO CIRCLE . If through the symmedian point K parallels F'KE , D'KF , E'FD be ...
... angle NBC = QCA ΩΑΒ . Each of these angles is called the Brocard angle of the triangle and is denoted by w . The ... right extremity of the base . TRIPLICATE RATIO CIRCLE . If through the symmedian point K parallels F'KE , D'KF , E'FD be ...
Page 13
... angle between the two rays not conjugate to it , then it is perpendicular to its conjugate . 8 If in a harmonic pencil one pair of conjugate rays be at right angles , then these are the internal and external bisectors of the angle ...
... angle between the two rays not conjugate to it , then it is perpendicular to its conjugate . 8 If in a harmonic pencil one pair of conjugate rays be at right angles , then these are the internal and external bisectors of the angle ...
Page 19
... right angles are said to be ORTHOGONAL . THEOREM I If two circles are orthogonal , the tangent to either at a point of section passes through the centre of the other . 2 If two points C , D are harmonic conjugates with respect to two ...
... right angles are said to be ORTHOGONAL . THEOREM I If two circles are orthogonal , the tangent to either at a point of section passes through the centre of the other . 2 If two points C , D are harmonic conjugates with respect to two ...
Page 20
... right angles to the fixed diameter . COR . - No pair of such a system of circles intersect each other . DEFS . — If a system of circles be such that every pair has the same radical axis , then the circles are said to be CO - AXAL . With ...
... right angles to the fixed diameter . COR . - No pair of such a system of circles intersect each other . DEFS . — If a system of circles be such that every pair has the same radical axis , then the circles are said to be CO - AXAL . With ...
Common terms and phrases
ABCD angular points antiparallel axis of projection bisect Brocard circle Brocard point centre of projection centres of similitude circumcircle co-axal circles coincident collinear points complete quadrangle complete quadrilateral concurrent lines conic conjugate points conjugates with respect COR.-The corresponding points cross ratio DEFINITIONS diagonal triangle equi-cross external bisectors figure focoids form a harmonic four points four straight lines given circle harmonic conjugates harmonic pencil harmonic range imaginary points infinite distance inscribed isogonal conjugates joining the centres limiting points line at infinity line be drawn locus meet middle points nine-point circle opposite sides opposite vertices orthocentre pair of conjugate perpendicular points lie points of intersection points or rays POLE AND POLAR polygons radical axis radii range or pencil right angles segments semiperimeter sides BC sponding straight line joining symmedian point system of co-axal tangents drawn Theor THEOREM three circles transversal vanishing line vertex
Popular passages
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 7 - The bisectors of the angles of a triangle meet the opposite sides in three points on a straight line.
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...