Elementary Synthetic Geometry of the Point, Line and Circle in the PlaneElementary Synthetic Geometry of the Point, Line and Circle in the Plane by Nathan Fellowes Dupuis, first published in 1889, is a rare manuscript, the original residing in one of the great libraries of the world. This book is a reproduction of that original, which has been scanned and cleaned by state-of-the-art publishing tools for better readability and enhanced appreciation. Restoration Editors' mission is to bring long out of print manuscripts back to life. Some smudges, annotations or unclear text may still exist, due to permanent damage to the original work. We believe the literary significance of the text justifies offering this reproduction, allowing a new generation to appreciate it. |
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Page x
... 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 algebraic altitude apothem bisects c.p.-circles centre of similitude centre-line chord of contact circles touch circumcircle co-axal coincide collinear concurrent concurrent lines concyclic congruent corresponding cut the circle denote diagonals diameter divided 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