modern geometryCUP Archive, 1963 - Geometry |
Contents
CHAPTER I | 1 |
Point at infinity | 7 |
CHAPTER III | 11 |
THEOREM | 12 |
A bc sin | 17 |
Definition of concurrence collinearity | 24 |
The medians of a triangle are concurrent | 30 |
THEOREM | 33 |
The sum of the squares on the radii of | 77 |
SECTION III | 80 |
49 | 87 |
Limiting points | 94 |
Definition of inverse points centre circle radius constant | 100 |
Provisional definition of pole and polar | 105 |
Two curves intersect at the same angles as their | 106 |
CHAPTER XII | 114 |
A circle whose centre is the midpoint of | 35 |
CHAPTER V | 46 |
If AB is divided harmonically at C D and if | 55 |
CHAPTER VII | 62 |
Circle of infinite radius | 69 |
Properties of the ellipse | 121 |
60 | 145 |
669 | 158 |
| 168 | |
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Common terms and phrases
ABCD altitudes base becomes bisected bisector called centre centroid CHAPTER chord circumcircle coincides collinear common concurrent Consider constant construction corresponding cross-ratio curves define Definition diagonals diameter difference distance divided draw drawn equal EXERCISES external figure Find fixed circle fixed point formed four given circle given points harmonic harmonic range infinite inscribed internal intersect inverse length limiting line joining locus mean medians meet mid-point middle point moves opposite sides orthocentre orthogonal pair parallel passes pencil perpendicular plane point at infinity points of contact polar position produced projection proof properties Prove quadrilateral radical axis radius ratio reader regard respect right angles sense Show sides sides BC similar Similarly squares straight line taken taking tangents THEOREM touch triangle ABC vertex vertices