Elementary Synthetic Geometry of the Point, Line and Circle in the Plane |
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Page 61
... range of Mathematics . Illustrations of its meaning and application in Geometry will occur frequently in the sequel , but the following are given by way of introduction . 1. A magnitude is continuous throughout its extent . Thus a line ...
... range of Mathematics . Illustrations of its meaning and application in Geometry will occur frequently in the sequel , but the following are given by way of introduction . 1. A magnitude is continuous throughout its extent . Thus a line ...
Page 63
... range of possibility . 105 ° . Let AB be a chord dividing the O into unequal arcs , and let P and Q be any points upon the major and minor arcs respectively . ( 102 ° , Def . ) Let O be the centre . I. The radii OA and OB form two ...
... range of possibility . 105 ° . Let AB be a chord dividing the O into unequal arcs , and let P and Q be any points upon the major and minor arcs respectively . ( 102 ° , Def . ) Let O be the centre . I. The radii OA and OB form two ...
Page 186
... the rotation in a + direction is equal to that in a - direction . RANGES AND PENCILS OF FOUR . 233 ° . Let A , B , C , P be a range of four , then AB.CP + BC . AP + CA . BP = 0 . Proof- AP - AC + CP , and BP = 186 SYNTHETIC GEOMETRY .
... the rotation in a + direction is equal to that in a - direction . RANGES AND PENCILS OF FOUR . 233 ° . Let A , B , C , P be a range of four , then AB.CP + BC . AP + CA . BP = 0 . Proof- AP - AC + CP , and BP = 186 SYNTHETIC GEOMETRY .
Page 189
Nathan Fellowes Dupuis. 237 ° . A , B , C being a range of three , and P any point not on the axis , AB . CP2 + BC . AP2 + CA.BP2 -- AB . BC . CA. Proof . Let PQ be 1 to AC . Then AQ = AC + CQ , BQ = BC + CQ , and the expression becomes ...
Nathan Fellowes Dupuis. 237 ° . A , B , C being a range of three , and P any point not on the axis , AB . CP2 + BC . AP2 + CA.BP2 -- AB . BC . CA. Proof . Let PQ be 1 to AC . Then AQ = AC + CQ , BQ = BC + CQ , and the expression becomes ...
Page 191
... range of points with a system of multiples we define the mean centre by the equation Σ ( a . AO ) = 0 , where Σ ( a . AO ) is a contraction for a . AO + b . BO + c . CO + ... , and the signs and magnitudes of the segments are both ...
... range of points with a system of multiples we define the mean centre by the equation Σ ( a . AO ) = 0 , where Σ ( a . AO ) is a contraction for a . AO + b . BO + c . CO + ... , and the signs and magnitudes of the segments are both ...
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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