An Elementary Treatise on Modern Pure Geometry |
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Common terms and phrases
ABCD axis of perspective bisect Brocard Brocard circle Brocard points Brocard triangle centre of perspective centre of similitude circle of inversion circle which cuts circle whose centre circle with respect circle X circles cut circles X1 circumcentre circumcircle coaxal system collinear points common tangents concurrent conjugate points corresponding lines corresponding points cut orthogonally cut the circle cut the sides denote diameter directly similar figure F fixed circle fixed point harmonic conjugate harmonic range Hence homothetic centre inscribed circle inverse circles inverse points isogonal conjugate limiting points line at infinity line joining locus middle points nine-point circle opposite connectors orthocentre pairs of opposite pencil in involution perpendicular point of intersection points with respect polar radical axis range in involution reciprocal straight line symmedian point tetragram tetrastigm theorem three given circles triangle ABC triangle formed variable circle
Popular passages
Page 180 - Hyperbola is the locus of a point which moves so that its distance from a fixed point, called the focus, bears a constant ratio, which is greater than unity, to its distance from a fixed straight line, called the directrix.
Page 4 - CONTINUITY (Lat. continuitas, from continuus, uninterrupted, from continere, to hold VOL. V.— 23. together, from com-, together + tenere, to hold). In geometry, a vital principle which asserts that if from the nature of a particular problem we would expect a certain number of solutions, then there will be the same number of solutions in every case, although some may be imaginary. Eg a straight line and a circle in the same plane intersect in two points real, coincident or imaginary. The sum of...
Page 67 - The circle which passes through the middle points of the sides of a triangle touches the four circles which touch the three sides.
Page 181 - The parabola is the locus of a point which moves so that its distance from a fixed point is equal to its distance from a fixed line.
Page 22 - Find the locus of a point, P, which moves so that the sum of its distances from two fixed points, A and B, is constant, 1870.
Page 67 - ... given circle is equidistant from two given straight lines : describe another circle which shall touch these two straight lines and shall cut off from the given circle a segment containing an angle equal to a given angle. 319.
Page 104 - CA' and C'A in B 19 AB' and A'B in C 19 then the triangle A 1 B 1 C 1 will be in perspective with each of the given triangles, and the three triangles will have a common axis of perspective. » 5. When three triangles are in perspective two by two and have the same axis of perspective, their three centres of perspective are collinear. 6. The points Q and...
Page 52 - We may here notice that the perpendiculars from the vertices of a triangle to the opposite sides are concurrent ; their meet is called the orthocentre, and the triangle obtained by joining the feet of the perpendiculars is called the pedal triangle.