A Syllabus of Modern Plane Geometry |
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Page 9
... antiparallel to the sides of the original triangle , and are respectively perpendicular to the corresponding radii of the circumcircle . B BROCARD POINTS . If a circle be described touching AB MODERN PLANE GEOMETRY . 9.
... antiparallel to the sides of the original triangle , and are respectively perpendicular to the corresponding radii of the circumcircle . B BROCARD POINTS . If a circle be described touching AB MODERN PLANE GEOMETRY . 9.
Page 13
... of the straight lines which connect corre- sponding points meet in a point , then the fourth connector passes through the same point . COR . If two corresponding points coincide in the inter- MODERN PLANE GEOMETRY . 13.
... of the straight lines which connect corre- sponding points meet in a point , then the fourth connector passes through the same point . COR . If two corresponding points coincide in the inter- MODERN PLANE GEOMETRY . 13.
Page 14
... corresponding points are concurrent . 10 If two harmonic pencils are such that the three points of intersection of three pairs of corresponding rays are in a straight line , then the point of intersection of the fourth pair of rays is ...
... corresponding points are concurrent . 10 If two harmonic pencils are such that the three points of intersection of three pairs of corresponding rays are in a straight line , then the point of intersection of the fourth pair of rays is ...
Page 16
... corresponding or correlative theorem by means of the above and similar changes . Thus corresponding to " concurrent lines " we have " collinear points , " to " line joining two points " we have " point of inter- section of two lines ...
... corresponding or correlative theorem by means of the above and similar changes . Thus corresponding to " concurrent lines " we have " collinear points , " to " line joining two points " we have " point of inter- section of two lines ...
Page 27
... corresponds the point of intersection of two lines of the other ( Chap . V. , Theor . 7 ) ; to a number of collinear points , a number of concurrent lines ; to parallel lines , points collinear with S ; to the angle between two lines ...
... corresponds the point of intersection of two lines of the other ( Chap . V. , Theor . 7 ) ; to a number of collinear points , a number of concurrent lines ; to parallel lines , points collinear with S ; to the angle between two lines ...
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...