Elementary Synthetic Geometry of the Point, Line and Circle in the Plane |
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Page 1
... proved , or it may be deduced from some previous course of reasoning . In the former case it is called a Proposition , that is , some- thing proposed , and consists of ( a ) the statement or enuncia- tion of the theorem , and ( b ) the ...
... proved , or it may be deduced from some previous course of reasoning . In the former case it is called a Proposition , that is , some- thing proposed , and consists of ( a ) the statement or enuncia- tion of the theorem , and ( b ) the ...
Page 3
Nathan Fellowes Dupuis. positive , and vice versa , and hence if either is proved the other is proved also . 6 ° . Two theorems are converse to one another when the hypothesis and conclusion of the one are respectively the conclusion and ...
Nathan Fellowes Dupuis. positive , and vice versa , and hence if either is proved the other is proved also . 6 ° . Two theorems are converse to one another when the hypothesis and conclusion of the one are respectively the conclusion and ...
Page 27
... prove the conclusion of the theorem to be true by showing that the acceptance of any other conclusion leads us to some relation which is absurd or untrue . 55 ° . Def . - The line - segment from a vertex of a triangle to the middle of ...
... prove the conclusion of the theorem to be true by showing that the acceptance of any other conclusion leads us to some relation which is absurd or untrue . 55 ° . Def . - The line - segment from a vertex of a triangle to the middle of ...
Page 32
... proved that PD = PB . Therefore two equal segments can be drawn from any point P to the line BC ; and these lie upon opposite sides of PA . No other segment can be drawn equal to PD or PB . For it must lie upon the same side of the ...
... proved that PD = PB . Therefore two equal segments can be drawn from any point P to the line BC ; and these lie upon opposite sides of PA . No other segment can be drawn equal to PD or PB . For it must lie upon the same side of the ...
Page 39
... Prove 58 ° from the axiom " a straight line is the shortest distance between two given points . " 9. Show from 60 ° that a triangle cannot have two of its angles right angles . 10. If a triangle has a right angle , the side opposite ...
... Prove 58 ° from the axiom " a straight line is the shortest distance between two given points . " 9. Show from 60 ° that a triangle cannot have two of its angles right angles . 10. If a triangle has a right angle , the side opposite ...
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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