A Treatise on the Geometry of the Circle and Some Extensions to Conic Sections by the Method of Reciprocation: With Numerous ExamplesMacmillan, 1891 - 299 σελίδες |
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Σελίδα x
... : 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 .
Σελίδα 20
... the particular case when a = b = c , the equation for d reduces to hence ( d - 2a ) ( d + a ) 2 = 0 ; d = 2a , thus showing that the quadrilateral is half the regular inscribed hexagon . B C d D E Now , ABDE is a 20 MAXIMUM AND MINIMUM .
... the particular case when a = b = c , the equation for d reduces to hence ( d - 2a ) ( d + a ) 2 = 0 ; d = 2a , thus showing that the quadrilateral is half the regular inscribed hexagon . B C d D E Now , ABDE is a 20 MAXIMUM AND MINIMUM .
Σελίδα 39
... ) NOTE . - If a = = 0 the quadrilateral is found to be one half of the inscribed hexagon . If a 90 the maximum quadrilateral is the inscribed square . SECTION III . THE POINT O THEOREM . 19. Theorem. MAXIMUM AND MINIMUM . 39 Cosine Circle,
... ) NOTE . - If a = = 0 the quadrilateral is found to be one half of the inscribed hexagon . If a 90 the maximum quadrilateral is the inscribed square . SECTION III . THE POINT O THEOREM . 19. Theorem. MAXIMUM AND MINIMUM . 39 Cosine Circle,
Σελίδα 70
... A'B'C'A " B " C " is a cyclic hexagon since each pair of points AA ' and BB ′ form a cyclic quadrilateral . ( " Nine Points " Circle . ) and BOA we have therefore AC AC - AB " 70 RECENT GEOMETRY . Theorems, Examples,
... A'B'C'A " B " C " is a cyclic hexagon since each pair of points AA ' and BB ′ form a cyclic quadrilateral . ( " Nine Points " Circle . ) and BOA we have therefore AC AC - AB " 70 RECENT GEOMETRY . Theorems, Examples,
Σελίδα 124
... hexagon are in perspective ; or , the opposite sides of a cyclic hexagon meet in three collinear points . The centre and axis of perspective of any two triangles in perspective are called the Pascal Point and Line of the hexagon XX'YY ...
... hexagon are in perspective ; or , the opposite sides of a cyclic hexagon meet in three collinear points . The centre and axis of perspective of any two triangles in perspective are called the Pascal Point and Line of the hexagon XX'YY ...
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Άλλες εκδόσεις - Προβολή όλων
A Treatise on the Geometry of the Circle: And Some Extensions to Conic ... William J. M'Clelland Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2017 |
A Treatise on the Geometry of the Circle and Some Extensions to Conic ... William J. M'Clelland Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2018 |
Συχνά εμφανιζόμενοι όροι και φράσεις
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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