A Syllabus of Modern Plane Geometry |
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Page 12
... form a HARMONIC RANGE ; and C and D are HARMONIC CONJUGATES with respect to A and B ; AC , AB , AD are said to be in HARMONIC PROGRESSION ; and AB is said to be the HARMONIC MEAN between AC and AD . [ These latter definitions agree with ...
... form a HARMONIC RANGE ; and C and D are HARMONIC CONJUGATES with respect to A and B ; AC , AB , AD are said to be in HARMONIC PROGRESSION ; and AB is said to be the HARMONIC MEAN between AC and AD . [ These latter definitions agree with ...
Page 13
... Harmonic Conjugate of C with respect to A and B is at an infinite distance . 4 If S be a point without the straight ... form with its internal and external bisectors a harmonic pencil . 7 If in a harmonic pencil one ray bisect the angle ...
... Harmonic Conjugate of C with respect to A and B is at an infinite distance . 4 If S be a point without the straight ... form with its internal and external bisectors a harmonic pencil . 7 If in a harmonic pencil one ray bisect the angle ...
Page 18
... harmonic range form a harmonic pencil ; and , conversely , the poles of the four rays of a harmonic pencil form a harmonic range . VI . - PROPERTIES OF TWO OR MORE CIRCLES . 18 A SYLLABUS OF.
... harmonic range form a harmonic pencil ; and , conversely , the poles of the four rays of a harmonic pencil form a harmonic range . VI . - PROPERTIES OF TWO OR MORE CIRCLES . 18 A SYLLABUS OF.
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...