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 |
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Página 13
... described to touch them ; the group of four is touched by a circle . [ Let the triangle formed by the circles be ABC , and let a < b < c . Then s - as - b > s - c . If the in- and ex - circles are numbered * This proof is an application ...
... described to touch them ; the group of four is touched by a circle . [ Let the triangle formed by the circles be ABC , and let a < b < c . Then s - as - b > s - c . If the in- and ex - circles are numbered * This proof is an application ...
Página 15
... described on the base , containing an angle equal to the vertical angle . ( Euc . III . 21. ) Let a number of tri- angles be constructed satisfying the given conditions , and it will be observed that as the vertex recedes from either ...
... described on the base , containing an angle equal to the vertical angle . ( Euc . III . 21. ) Let a number of tri- angles be constructed satisfying the given conditions , and it will be observed that as the vertex recedes from either ...
Página 19
... locus of C is therefore a circle ( Euc . vi . 3 ) ; this locus intersects the circle described with D as centre and c as radius at the point C ; therefore , etc. A'B'C D ' , the area of the circle ABCD. MAXIMUM AND MINIMUM . 19.
... locus of C is therefore a circle ( Euc . vi . 3 ) ; this locus intersects the circle described with D as centre and c as radius at the point C ; therefore , etc. A'B'C D ' , the area of the circle ABCD. MAXIMUM AND MINIMUM . 19.
Página 42
... described are similar , the ratio OP : OQ is termed their Ratio of Similitude and the point O the Centre of Similitude . Thus since O is a point invariably connected with a variable inscribed triangle PQR of given species , the ortho ...
... described are similar , the ratio OP : OQ is termed their Ratio of Similitude and the point O the Centre of Similitude . Thus since O is a point invariably connected with a variable inscribed triangle PQR of given species , the ortho ...
Página 52
... described on the sides . C B D If the points B and D coincide , O coincides with them , and the circle ADO meeting CD in coincident points D and O therefore touches CD . In the same case the circle BCO touches AB . COR . The centres of ...
... described on the sides . C B D If the points B and D coincide , O coincides with them , and the circle ADO meeting CD in coincident points D and O therefore touches CD . In the same case the circle BCO touches AB . COR . The centres of ...
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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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