Elementary Synthetic Geometry of the Point, Line and Circle in the Plane |
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... Similitude , PART V. SECTION I. — Anharmonic Division . SECTION II.— Harmonic Ratio . SECTION III . —Anharmonic Properties . SECTION IV . — Polar Reciprocals and Reciprocation . SECTION V. - Homography and Involution , PAGE 178 252 PART ...
... Similitude , PART V. SECTION I. — Anharmonic Division . SECTION II.— Harmonic Ratio . SECTION III . —Anharmonic Properties . SECTION IV . — Polar Reciprocals and Reciprocation . SECTION V. - Homography and Involution , PAGE 178 252 PART ...
Page 237
... - π Cor . 5. When 0 = 4 = 2 , Z cuts S and S ' orthogonally , and OL = 0 , and the centre of the cutting circle is on the radical axis of the two . SECTION VII . CENTRE AND AXES OF SIMILITUDE OR PERSPECTIVE OF THE RADICAL AXIS . 237.
... - π Cor . 5. When 0 = 4 = 2 , Z cuts S and S ' orthogonally , and OL = 0 , and the centre of the cutting circle is on the radical axis of the two . SECTION VII . CENTRE AND AXES OF SIMILITUDE OR PERSPECTIVE OF THE RADICAL AXIS . 237.
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... similitude . Cor . I. In the limiting form of the polygons , the line BC becomes a tangent at B , and the line bc ... similitude . 285 ° . Let S and S ' be two circles with centres C , C ' and radii r , respectively , and let O and O ...
... similitude . Cor . I. In the limiting form of the polygons , the line BC becomes a tangent at B , and the line bc ... similitude . 285 ° . Let S and S ' be two circles with centres C , C ' and radii r , respectively , and let O and O ...
Page 241
... similitude due to con- sidering the circles as being oppositely placed , Y S S ' Z ' 9 . and for this centre Z and Y ' as also U and U ' are ... similitude , and the transverse connector cuts it CENTRE OF SIMILITUDE OR PERSPECTIVE . 241.
... similitude due to con- sidering the circles as being oppositely placed , Y S S ' Z ' 9 . and for this centre Z and Y ' as also U and U ' are ... similitude , and the transverse connector cuts it CENTRE OF SIMILITUDE OR PERSPECTIVE . 241.
Page 242
Nathan Fellowes Dupuis. centre of similitude , and the transverse connector cuts it in the internal centre of similitude . 286 ° . Since OX : OX ' = OY : OY ' , if X and Y become coin- cident , X ' and Y ' become coincident also . .. a ...
Nathan Fellowes Dupuis. centre of similitude , and the transverse connector cuts it in the internal centre of similitude . 286 ° . Since OX : OX ' = OY : OY ' , if X and Y become coin- cident , X ' and Y ' become coincident also . .. a ...
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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