A Treatise on the Geometry of the Circle and Some Extensions to Conic Sections by the Method of Reciprocation: With Numerous Examples |
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Page xi
... POLES AND POLARS WITH RESPECT TO A CIRCLE . SECTION I. CONJUGATE POINTS . POLAR CIRCLE . 73. Definitions . Elementary Properties of Conjugate Points , 74. Theorem ,. Examples , 75 , 76. Theorems . Reciprocal Polar Triangles , 77. Self ...
... POLES AND POLARS WITH RESPECT TO A CIRCLE . SECTION I. CONJUGATE POINTS . POLAR CIRCLE . 73. Definitions . Elementary Properties of Conjugate Points , 74. Theorem ,. Examples , 75 , 76. Theorems . Reciprocal Polar Triangles , 77. Self ...
Page 81
... poles are L , M , N , pass through 01 . C Z M P L A B R * The point on the circum - circle from which perpendiculars or other isoclinals are let fall on the sides of an inscribed triangle is called the Pole of the Simson line.-V ...
... poles are L , M , N , pass through 01 . C Z M P L A B R * The point on the circum - circle from which perpendiculars or other isoclinals are let fall on the sides of an inscribed triangle is called the Pole of the Simson line.-V ...
Page 148
... whose pedal triangles with respect to ABC are equilateral . ] * Le cercle d'Apollonius du triangle ABC par rapport à AB . V. Educ . Times , Dec. , 1890 . CHAPTER VII . POLES AND POLARS WITH RESPECT TO A 148 INVERSE POINTS .
... whose pedal triangles with respect to ABC are equilateral . ] * Le cercle d'Apollonius du triangle ABC par rapport à AB . V. Educ . Times , Dec. , 1890 . CHAPTER VII . POLES AND POLARS WITH RESPECT TO A 148 INVERSE POINTS .
Page 149
With Numerous Examples William J. M'Clelland. CHAPTER VII . POLES AND POLARS WITH RESPECT TO A CIRCLE . SECTION I ... Pole and Polar with respect to the circle . Any point A or B on the polar is the Conjugate of C , hence the polar of ...
With Numerous Examples William J. M'Clelland. CHAPTER VII . POLES AND POLARS WITH RESPECT TO A CIRCLE . SECTION I ... Pole and Polar with respect to the circle . Any point A or B on the polar is the Conjugate of C , hence the polar of ...
Page 150
... at infinity in a direction perpendicular to AB . 4. The locus of a point which has a common conjugate with respect to three circles is their common orthogonal circle . 75. Theorem . - If A and B be any. 150 POLES AND POLARS .
... at infinity in a direction perpendicular to AB . 4. The locus of a point which has a common conjugate with respect to three circles is their common orthogonal circle . 75. Theorem . - If A and B be any. 150 POLES AND POLARS .
Contents
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Other editions - View all
A Treatise on the Geometry of the Circle: And Some Extensions to Conic ... William J. M'Clelland No preview available - 2017 |
A Treatise on the Geometry of the Circle and Some Extensions to Conic ... William J. M'Clelland No preview available - 2018 |
Common terms and phrases
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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