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 3
... pairs of angles are formed by taking any pair of rays with the remaining or Conjugate pair . Thus BOC and AOD may be conveniently denoted by a and a ' , COA and BOD by ẞ and B ' , and AOB and COD by y and y ' . With this notation ( 3 ) ...
... pairs of angles are formed by taking any pair of rays with the remaining or Conjugate pair . Thus BOC and AOD may be conveniently denoted by a and a ' , COA and BOD by ẞ and B ' , and AOB and COD by y and y ' . With this notation ( 3 ) ...
Page 12
... pairs of circles whose contacts are alternate . Thus in the figure , O1 , r1 and Оg , r have alternate contacts with the given circle , therefore the term 31.24 is negative , and taking the absolute values only the equation is 23.14 + ...
... pairs of circles whose contacts are alternate . Thus in the figure , O1 , r1 and Оg , r have alternate contacts with the given circle , therefore the term 31.24 is negative , and taking the absolute values only the equation is 23.14 + ...
Page 20
... pair of opposite sides BC and AD , its area is a maximum when BC is parallel to AD . [ Take any position of the quadrilateral and through C draw CE parallel and equal to 8. Join BE and AE . The triangles BDE and BCD are equal ( Euc . I ...
... pair of opposite sides BC and AD , its area is a maximum when BC is parallel to AD . [ Take any position of the quadrilateral and through C draw CE parallel and equal to 8. Join BE and AE . The triangles BDE and BCD are equal ( Euc . I ...
Page 48
... pairs of opposite connectors of four points be denoted by a , c ; b , d ; & , & ' to prove the relation 828'2 = a2c2 + b2d2-2abcd cos ( 0 + 0 ' ) , where 0+ is the sum of a pair of opposite angles of the quadrilateral . [ Let A , B , C ...
... pairs of opposite connectors of four points be denoted by a , c ; b , d ; & , & ' to prove the relation 828'2 = a2c2 + b2d2-2abcd cos ( 0 + 0 ' ) , where 0+ is the sum of a pair of opposite angles of the quadrilateral . [ Let A , B , C ...
Page 52
... pairs of non - corresponding extremities and the inter- section O of the given lines . Or it may be regarded as the common vertex of two similar triangles described on the sides . C B D If the points B and D coincide , O coincides with ...
... pairs of non - corresponding extremities and the inter- section O of the given lines . Or it may be regarded as the common vertex of two similar triangles described on the sides . C B D If the points B and D coincide , O coincides with ...
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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