A Treatise on the Geometry of the Circle and Some Extensions to Conic Sections by the Method of Reciprocation: With Numerous ExamplesMacmillan, 1891 - 299 páginas |
Dentro del libro
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... Its Diagonal Triangle , 132 Problem , 133 • Examples . Maximum Polygon of any Order escribed to a Circle , 134 · · Note on Pascal and Brianchon Hexagons , 136 ARTICLE CHAPTER VI . INVERSE POINTS WITH RESPECT TO A X CONTENTS .
... Its Diagonal Triangle , 132 Problem , 133 • Examples . Maximum Polygon of any Order escribed to a Circle , 134 · · Note on Pascal and Brianchon Hexagons , 136 ARTICLE CHAPTER VI . INVERSE POINTS WITH RESPECT TO A X CONTENTS .
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... RESPECT TO A CIRCLE . 69. Particular Cases , 70 , 71. Theorems , . Examples , 72. Theorem . Corollaries , Examples . Radical Centre and Product , Conjugate Lines of a Quadrilateral , Circle of Apollonius , . PAGE 139 • 139 140 140 143 ...
... RESPECT TO A CIRCLE . 69. Particular Cases , 70 , 71. Theorems , . Examples , 72. Theorem . Corollaries , Examples . Radical Centre and Product , Conjugate Lines of a Quadrilateral , Circle of Apollonius , . PAGE 139 • 139 140 140 143 ...
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... respect to A'B ' is a line passing through 0 ; and 1 + 1 = 2 PA PB PQ .. ( By Ex . 6. ) Note . By Euc . VI . 2 if the variable PQ is bisected at Q ' the locus of Q ' is a parallel to OQ and 1 " 1 + = PAT PB 1 PQ Hence for any three ...
... respect to A'B ' is a line passing through 0 ; and 1 + 1 = 2 PA PB PQ .. ( By Ex . 6. ) Note . By Euc . VI . 2 if the variable PQ is bisected at Q ' the locus of Q ' is a parallel to OQ and 1 " 1 + = PAT PB 1 PQ Hence for any three ...
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... a perpendicular BL and make B'L - BL . Join AB and let C be its intersection with L. Take any other point P on the line and join AP and B'P . The triangles BCL and B'CL are equal in every respect. MAXIMUM AND MINIMUM . 21.
... a perpendicular BL and make B'L - BL . Join AB and let C be its intersection with L. Take any other point P on the line and join AP and B'P . The triangles BCL and B'CL are equal in every respect. MAXIMUM AND MINIMUM . 21.
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... respect ( Euc . I. 4 ) ; hence BC = B'C . Similarly BP = B'P . Hence since ( Euc . I. 20 ) AP + B'P > AB ' it follows that AP + BP > AC + BC . COR . 1. If the line L cuts the base internally the difference of the sides ( AC - BC ) is a ...
... respect ( Euc . I. 4 ) ; hence BC = B'C . Similarly BP = B'P . Hence since ( Euc . I. 20 ) AP + B'P > AB ' it follows that AP + BP > AC + BC . COR . 1. If the line L cuts the base internally the difference of the sides ( AC - BC ) is a ...
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Otras ediciones - Ver todas
A Treatise on the Geometry of the Circle: And Some Extensions to Conic ... William J. M'Clelland Sin vista previa disponible - 2017 |
A Treatise on the Geometry of the Circle and Some Extensions to Conic ... William J. M'Clelland Sin vista previa disponible - 2018 |
Términos y frases comunes
ABCD bisected bisector Brocard points centre of similitude centres of perspective circum-centre circum-circle coaxal system coincide common tangents concurrent concurrent lines conic constant corresponding cyclic polygon cyclic quadrilateral denote diagonals diameter distances equal equation equianharmonic ex-circles fixed point given circles hence hexagon in-circle infinity inscribed inverse points Isogonal Conjugates isosceles limiting points line at infinity lines joining locus maximum mean centre median median triangle meet middle point minimum multiples opposite sides orthocentre orthogonally pair of inverse parallel pedal triangle perpendiculars point of intersection points of contact polar polygon prove r₁ radical axis radius reciprocal rectangle right angles segments sides of ABC similar triangles Similarly Simson lines species squares subtend symmedian point system of points tangents Theorem transversal triangle ABC triangle PQR vertex vertical angle
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