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
... Radical Axis .. SEC- TION VII . - Centres and Axes of Perspective or Similitude , PART V. SECTION I. - Anharmonic Division . SECTION II.— Harmonic Ratio . SECTION III . - Anharmonic Properties . SECTION IV . - Polar Reciprocals and ...
... Radical Axis .. SEC- TION VII . - Centres and Axes of Perspective or Similitude , PART V. SECTION I. - Anharmonic Division . SECTION II.— Harmonic Ratio . SECTION III . - Anharmonic Properties . SECTION IV . - Polar Reciprocals and ...
Page 137
... radical axis of the circles , and is a line of great importance in studying the relations of two or more circles . Cor . 1. The radical axis of two circles bisects their com- mon tangents . Cor . 2. When two circles intersect , their ...
... radical axis of the circles , and is a line of great importance in studying the relations of two or more circles . Cor . 1. The radical axis of two circles bisects their com- mon tangents . Cor . 2. When two circles intersect , their ...
Page 210
... radical axis . Cor . 4. A having its centre on the radical axis of two given Os , and cutting one of them orthogonally , cuts the other orthogonally also . 259 ° . Let P , Q be inverse points to circle S and D any S P'P B Q point on it ...
... radical axis . Cor . 4. A having its centre on the radical axis of two given Os , and cutting one of them orthogonally , cuts the other orthogonally also . 259 ° . Let P , Q be inverse points to circle S and D any S P'P B Q point on it ...
Page 213
... radical axis of the two circles . ( 178 ° , Def . ) Cor . 3. If a circle passes through the centre OF INVERSION AND INVERSE FIGURES . 213.
... radical axis of the two circles . ( 178 ° , Def . ) Cor . 3. If a circle passes through the centre OF INVERSION AND INVERSE FIGURES . 213.
Page 214
... radical axis . Let I be the circle of inver- sion , and let the circle S ' be the inverse of S. The tangents TT ' and VV ' meet at O ( 260 ° , Cor . 1 ) , and T , T ' are inverse points . D , the middle point of TT ' is on the radical ...
... radical axis . Let I be the circle of inver- sion , and let the circle S ' be the inverse of S. The tangents TT ' and VV ' meet at O ( 260 ° , Cor . 1 ) , and T , T ' are inverse points . D , the middle point of TT ' is on the radical ...
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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