A Syllabus of Modern Plane Geometry |
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Page 3
... points on a straight line , AP + PB AB . ( 2 ) Two fixed points ( A and B ) being taken on a straight line , the position of any other point P ( on the same straight line ) is given when the ratio of the segments AP : PB is given . 4 A ...
... points on a straight line , AP + PB AB . ( 2 ) Two fixed points ( A and B ) being taken on a straight line , the position of any other point P ( on the same straight line ) is given when the ratio of the segments AP : PB is given . 4 A ...
Page 9
... points B , c , b , C are concyclic . The antiparallel bc is fixed as regards direction , being always parallel to the tangent to the circumcircle at A. Let PQR be the triangle formed by the tangents to the circum- circle at A , B , C so ...
... points B , c , b , C are concyclic . The antiparallel bc is fixed as regards direction , being always parallel to the tangent to the circumcircle at A. Let PQR be the triangle formed by the tangents to the circum- circle at A , B , C so ...
Page 16
... points as elements in the description of the figures , and each Theorem can be obtained from the other by ... fixed points , and P be a point such that the ratio PC : PD is constant , then the locus of P is a circle except when the ...
... points as elements in the description of the figures , and each Theorem can be obtained from the other by ... fixed points , and P be a point such that the ratio PC : PD is constant , then the locus of P is a circle except when the ...
Page 19
... 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- gonal to the given circle . RADICAL Axis . 6 The locus of a point ...
... 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- gonal to the given circle . RADICAL Axis . 6 The locus of a point ...
Page 20
... POINTS of the system , and may be considered as circles of the system whose radii are inde- finitely diminished . NOTE . — In a system of intersecting co - axal circles there are no limiting ... fixed point with regard to 20 A SYLLABUS OF.
... POINTS of the system , and may be considered as circles of the system whose radii are inde- finitely diminished . NOTE . — In a system of intersecting co - axal circles there are no limiting ... fixed point with regard to 20 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...