Elementary Synthetic Geometry of the Point, Line and Circle in the Plane |
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Page 3
... four legs . Converse . If an animal has four legs it is a horse . As is readily seen from the foregoing example , the truth of a theorem does not necessarily establish the truth of its con- verse , and hence a theorem and its converse ...
... four legs . Converse . If an animal has four legs it is a horse . As is readily seen from the foregoing example , the truth of a theorem does not necessarily establish the truth of its con- verse , and hence a theorem and its converse ...
Page 17
... four angles is a circumangle ( 37 ° ) , therefore the sum of each pair is a straight angle ( 36 ° ) . q.e.d. Cor . 1. The angle between the opposite directions of a line is a straight angle . B Cor . 2. If a radius vector be rotated ...
... four angles is a circumangle ( 37 ° ) , therefore the sum of each pair is a straight angle ( 36 ° ) . q.e.d. Cor . 1. The angle between the opposite directions of a line is a straight angle . B Cor . 2. If a radius vector be rotated ...
Page 18
... four angles are formed about the point of intersection , any one of which may be taken to be the angle between the lines . These four angles consist of two pairs of opposite or vertical angles , viz . , A , A ' , and B , B ' , A being ...
... four angles are formed about the point of intersection , any one of which may be taken to be the angle between the lines . These four angles consist of two pairs of opposite or vertical angles , viz . , A , A ' , and B , B ' , A being ...
Page 19
... four angles equal in opposite pairs . But if any one of these is a right angle , all four are right angles . Perpendicularity is the most important directional relation in the applications of Geometry . Def . 4. - An acute angle is less ...
... four angles equal in opposite pairs . But if any one of these is a right angle , all four are right angles . Perpendicularity is the most important directional relation in the applications of Geometry . Def . 4. - An acute angle is less ...
Page 22
... lines taken two and two . But if L , M , N be the lines the groups are LM , MN , and NL . Therefore three lines determine by their intersections at most three points . 47 ° . Theorem . - Four points determine at 22 SYNTHETIC GEOMETRY .
... lines taken two and two . But if L , M , N be the lines the groups are LM , MN , and NL . Therefore three lines determine by their intersections at most three points . 47 ° . Theorem . - Four points determine at 22 SYNTHETIC GEOMETRY .
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Common terms and phrases
ABCD Algebra altitude becomes bisects c.p.-circles centre of similitude chord of contact circles touch circumcircle co-axal coincide collinear concurrent concurrent lines concyclic congruent cut the circle denote diagonals diameter divided double points end-points equal angles equianharmonic equilateral triangle excircles external bisector fixed point geometric given circles given line given point harmonic range Hence hexagram homographic homologous hypothenuse incircle internal angles inverse points isosceles joins LAOB line-segment locus median middle point nine-points circle opposite sides orthogonally pair parallel parallelogram passes pencil perpendicular perspective plane point of contact point of intersection polar reciprocal Proof quadrangle radical axis radical centre radii radius rectangle rectilinear figure regular polygon rhombus right angle right bisector rotation secant similar Similarly square straight angle symbol tangent tensor theorem Theorem.-The three circles transversal vertex vertices