An Elementary Treatise on Trilinear Co-ordinates: The Method of Reciprocal Polars, and the Theory of Projections |
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Page 35
... determine the position of the centre of the conic . Through the angular points A , B , C of the triangle of re- ference draw the tangents EAF , FBD , DCE . Bisect Fig . 14 . + . B T E H Q D AC , AB respectively in H , I , join EH , FI ...
... determine the position of the centre of the conic . Through the angular points A , B , C of the triangle of re- ference draw the tangents EAF , FBD , DCE . Bisect Fig . 14 . + . B T E H Q D AC , AB respectively in H , I , join EH , FI ...
Page 36
... determine the position of the centre . COR . We may hence deduce the relation which must hold between λ , u , v , in order that the conic may be a para- bola . For , since the centre of a parabola is at an infinite distance , its co ...
... determine the position of the centre . COR . We may hence deduce the relation which must hold between λ , u , v , in order that the conic may be a para- bola . For , since the centre of a parabola is at an infinite distance , its co ...
Page 37
... determine the condition that a given straight line may touch the conic . If the conic be touched by the straight ... determines these is − xlBy + ( μy + vß ) ( mß + ny ) = 0 , - and the condition that the two values of By be equal , is ...
... determine the condition that a given straight line may touch the conic . If the conic be touched by the straight ... determines these is − xlBy + ( μy + vß ) ( mß + ny ) = 0 , - and the condition that the two values of By be equal , is ...
Page 40
... of the conic ( see p . 32 ) . We have then to find the equations of BH , CI , which , by their in- tersection , determine 0 . B H Fig . 16 . Let f , g , h , be the co 40 MODERN GEOMETRY . 8 Position of the Centre Condition for a Parabola ...
... of the conic ( see p . 32 ) . We have then to find the equations of BH , CI , which , by their in- tersection , determine 0 . B H Fig . 16 . Let f , g , h , be the co 40 MODERN GEOMETRY . 8 Position of the Centre Condition for a Parabola ...
Page 42
... determine the co - ordinates of the centre . COR . Hence may be obtained the condition that the conic may be a parabola . For the centre of a parabola is in- finitely distant , its co - ordinates must therefore satisfy the alge- braical ...
... determine the co - ordinates of the centre . COR . Hence may be obtained the condition that the conic may be a parabola . For the centre of a parabola is in- finitely distant , its co - ordinates must therefore satisfy the alge- braical ...
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Common terms and phrases
a₁ aa+bB+cy Algebra angular points anharmonic ratio Arithmetic asymptotes auxiliary conic b₁ c₁ CAMBRIDGE CLASS BOOKS centre Chap chord cloth co-ordinates coefficients College common tangents condition conic passing conic section conics intersect Crown 8vo curve determine directrix ellipse find the equation fixed point focus four points given conic given point given straight line Hence hyperbola imaginary investigated line at infinity line joining locus meets the conic obtain pair parabola Pascal's Theorem perpendicular point f point of intersection points at infinity points of contact PQRS projection prove reciprocal polars represented respect right angles second degree Second Edition Similarly sin POS system of conics tangents tangents drawn theorem three points three straight lines touches the line Treatise triangle of reference U'bc ua² V'ca Vb² vß² W'ab wy² λα