A Syllabus of Modern Plane Geometry |
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Page 10
... chord parallel to BC , then BR will meet the circle again in a point 2 such that the angle NBC = QCA ΩΑΒ . Each of these angles is called the Brocard angle of the triangle and is denoted by w . The Brocard angle of a triangle depends ...
... chord parallel to BC , then BR will meet the circle again in a point 2 such that the angle NBC = QCA ΩΑΒ . Each of these angles is called the Brocard angle of the triangle and is denoted by w . The Brocard angle of a triangle depends ...
Page 18
... chords through the point . COR . — The polar of a point external to the circle is the chord of contact of tangents drawn from that point , and the polar of a point on the circumference is the tangent at the point . DEF . A triangle of ...
... chords through the point . COR . — The polar of a point external to the circle is the chord of contact of tangents drawn from that point , and the polar of a point on the circumference is the tangent at the point . DEF . A triangle of ...
Page 19
... chord of intersection are complementary . 5 The locus of the points of intersection of the straight lines . joining two fixed points on a circle to the extremities of a variable diameter is the circle through the fixed points ortho ...
... chord of intersection are complementary . 5 The locus of the points of intersection of the straight lines . joining two fixed points on a circle to the extremities of a variable diameter is the circle through the fixed points ortho ...
Page 21
... chords RS , rs ; R'S , r's ' ; RS ' , rs ' ; R'S , r's , are parallel ; and the pairs RS , r's ' ; R'S ' , rs ; RS ' , r's ; R'S , rs ' , intersect on the radical axis of the circles . : 18 The centres of similitude of three circles are ...
... chords RS , rs ; R'S , r's ' ; RS ' , rs ' ; R'S , r's , are parallel ; and the pairs RS , r's ' ; R'S ' , rs ; RS ' , r's ; R'S , rs ' , intersect on the radical axis of the circles . : 18 The centres of similitude of three circles are ...
Page 27
... SE , SE ' respectively ) ; to the points E , E ' , the asymptotes ; to the chord EE ' , the centre ; to the line FF ' bisecting SE , SE ' , the other focus S ' . IX . - PROJECTION . DEFINITIONS . If two figures MODERN PLANE GEOMETRY . 27.
... SE , SE ' respectively ) ; to the points E , E ' , the asymptotes ; to the chord EE ' , the centre ; to the line FF ' bisecting SE , SE ' , the other focus S ' . IX . - PROJECTION . DEFINITIONS . If two figures MODERN PLANE GEOMETRY . 27.
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...