A Syllabus of Modern Plane Geometry |
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Page 9
... parallel to QR meeting CA , AB in ß , y respectively Py PB PC = PB . Hence every antiparallel to BC is bisected by ... parallels to those sides are bisected by the " medians " AA ' , BB ′ , CC ' concurring at G the centroid . Analogously ...
... parallel to QR meeting CA , AB in ß , y respectively Py PB PC = PB . Hence every antiparallel to BC is bisected by ... parallels to those sides are bisected by the " medians " AA ' , BB ′ , CC ' concurring at G the centroid . Analogously ...
Page 10
... parallel to BC , then BR will meet the circle again in a point 2 such that the angle NBC = QCA ΩΑΒ . Each of these ... parallels F'KE , D'KF , E'FD be drawn to the sides , ( 1 ) The six points D , D ' , E , E , F , F ' all lie on a ...
... parallel to BC , then BR will meet the circle again in a point 2 such that the angle NBC = QCA ΩΑΒ . Each of these ... parallels F'KE , D'KF , E'FD be drawn to the sides , ( 1 ) The six points D , D ' , E , E , F , F ' all lie on a ...
Page 13
... parallel to SD meeting SA , SB at G , H respectively , then GC ** CH . 5 If in the figure of the last proposition any other transversal be drawn meeting SA , SB , SC , SD in A ' , B ′ , C ' , D ′ respectively , then A'C'B'D ' is a ...
... parallel to SD meeting SA , SB at G , H respectively , then GC ** CH . 5 If in the figure of the last proposition any other transversal be drawn meeting SA , SB , SC , SD in A ' , B ′ , C ' , D ′ respectively , then A'C'B'D ' is a ...
Page 17
... parallel to the tangent at A or B , then DE is called the POLAR of C , and C the POLE of DE with respect to the circle . HARMONIC PROPERTY OF POLE AND POLAR . 6 Any straight line through the pole is cut harmonically by the circle , pole ...
... parallel to the tangent at A or B , then DE is called the POLAR of C , and C the POLE of DE with respect to the circle . HARMONIC PROPERTY OF POLE AND POLAR . 6 Any straight line through the pole is cut harmonically by the circle , pole ...
Page 21
... parallel radii ; and the portion of the line between either pair of parallel radii is divided by the centre of similitude into segments which have the same ratio as the radii . 17 If through a centre of similitude of two circles , two ...
... parallel radii ; and the portion of the line between either pair of parallel radii is divided by the centre of similitude into segments which have the same ratio as the radii . 17 If through a centre of similitude of two circles , two ...
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...