Elementary Synthetic Geometry of the Point, Line and Circle in the Plane |
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Page 55
... Join AB and BC , and let L and M be the A right bisectors of AB and BC respectively . 1. Then , because AB and BC intersect at B , L and M intersect at some point O , O M D B ( 79 ° , Cor . ) and .. the O is equidistant from A , B THE ...
... Join AB and BC , and let L and M be the A right bisectors of AB and BC respectively . 1. Then , because AB and BC intersect at B , L and M intersect at some point O , O M D B ( 79 ° , Cor . ) and .. the O is equidistant from A , B THE ...
Page 65
... Join P and C. B Then LAPC is supplementary to LABC , ( 106 ° , Cor . 2 ) LADC is supplementary to LABC , and which is not true . LAPC = LADC , .. the cannot cut AD in any point other than D , Hence A , B , C , and D are concyclic ...
... Join P and C. B Then LAPC is supplementary to LABC , ( 106 ° , Cor . 2 ) LADC is supplementary to LABC , and which is not true . LAPC = LADC , .. the cannot cut AD in any point other than D , Hence A , B , C , and D are concyclic ...
Page 78
... join D and P. Then DP is to L. .. the construction draws a to L at a given point in L. ( Compare 119 ° , Cor . 2 ) Cor . 2. Let L be a given line and C a given point . To draw through C a line parallel to L. With C as the centre of a ...
... join D and P. Then DP is to L. .. the construction draws a to L at a given point in L. ( Compare 119 ° , Cor . 2 ) Cor . 2. Let L be a given line and C a given point . To draw through C a line parallel to L. With C as the centre of a ...
Page 82
... Join P and Q upon opposite sides of the and draw QG || to BC . Draw SX I to PQ to meet BC in E , and draw EF to CD . Then △ QPG = AFSE , square , C D and OR SE = PQ . Hence the construction : - Join any two points PQ , and through a ...
... Join P and Q upon opposite sides of the and draw QG || to BC . Draw SX I to PQ to meet BC in E , and draw EF to CD . Then △ QPG = AFSE , square , C D and OR SE = PQ . Hence the construction : - Join any two points PQ , and through a ...
Page 83
Nathan Fellowes Dupuis. SX to PQ . On SX take SE = PQ and join E with the fourth point R. ER is a side of the square in position and direction , and the points first joined , P and Q , are on oppo- site sides of the required square ...
Nathan Fellowes Dupuis. SX to PQ . On SX take SE = PQ and join E with the fourth point R. ER is a side of the square in position and direction , and the points first joined , P and Q , are on oppo- site sides of the required square ...
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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