Elementary Synthetic Geometry of the Point, Line and Circle in the Plane |
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... Perspective or 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 ...
... Perspective or 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 205
... perspective at O , which is called their centre of perspective . The term perspective is introduced from Optics , because an eye placed at O would see A ' coinciding with A and B ' with B , and the segment A'B ' coinciding with AB . By ...
... perspective at O , which is called their centre of perspective . The term perspective is introduced from Optics , because an eye placed at O would see A ' coinciding with A and B ' with B , and the segment A'B ' coinciding with AB . By ...
Page 206
... perspective when the joins of their vertices , in pairs , are concurrent . Cor . 2. When two triangles are in perspective , their ver- tices connect concurrently , and their corresponding sides intersect collinearly . ( 253 ° ) In ...
... perspective when the joins of their vertices , in pairs , are concurrent . Cor . 2. When two triangles are in perspective , their ver- tices connect concurrently , and their corresponding sides intersect collinearly . ( 253 ° ) In ...
Page 207
... perspective with it . 2. The three chords of contact of the excircles of any tri- angle form a triangle in perspective with the original . 3. The tangents to the circumcircle of a triangle at the three vertices form a triangle in ...
... perspective with it . 2. The three chords of contact of the excircles of any tri- angle form a triangle in perspective with the original . 3. The tangents to the circumcircle of a triangle at the three vertices form a triangle in ...
Page 225
... perspective . Let ABC and A'B'C ' be polar recipro- cals . Let AP , AP ' be perpendiculars on A'B ' and A'C ' , BQ and BQ ' be perpen- diculars on B'C ' and B'A ' , etc. Then ( 271 ° ) But = = AP'_AO BQ'_BO BQ BO ' CR CO ' AP ' . BQ ...
... perspective . Let ABC and A'B'C ' be polar recipro- cals . Let AP , AP ' be perpendiculars on A'B ' and A'C ' , BQ and BQ ' be perpen- diculars on B'C ' and B'A ' , etc. Then ( 271 ° ) But = = AP'_AO BQ'_BO BQ BO ' CR CO ' AP ' . BQ ...
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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