An Elementary Treatise on Trilinear Co-ordinates: The Method of Reciprocal Polars, and the Theory of Projections |
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Page 50
... Combining therewith aa + bB + cy = 2A , we get for the co - ordinates of the centre α b L2 M2 2A 2A 2A α 2 b2 29 c2 b2 2 + + L2 TM M2 TM M2 + I3 M2 N2 + + + I M2 N2 Each of these becomes infinite when the conic is a 50 MODERN GEOMETRY .
... Combining therewith aa + bB + cy = 2A , we get for the co - ordinates of the centre α b L2 M2 2A 2A 2A α 2 b2 29 c2 b2 2 + + L2 TM M2 TM M2 + I3 M2 N2 + + + I M2 N2 Each of these becomes infinite when the conic is a 50 MODERN GEOMETRY .
Page 51
... becomes infinite when the conic is a para- bola , as manifestly ought to be the case . 19. To find the equation of the circle with respect to which the triangle of reference is self - conjugate . It is a distinguishing property of the ...
... becomes infinite when the conic is a para- bola , as manifestly ought to be the case . 19. To find the equation of the circle with respect to which the triangle of reference is self - conjugate . It is a distinguishing property of the ...
Page 56
... become infinite when 4k bca " , as mani- festly ought to be the case , since , as has been shewn in Art . 24 , the conic is then a parabola . EXAMPLES . 1. A triangle is inscribed in a conic ; prove that the points , in which each side ...
... become infinite when 4k bca " , as mani- festly ought to be the case , since , as has been shewn in Art . 24 , the conic is then a parabola . EXAMPLES . 1. A triangle is inscribed in a conic ; prove that the points , in which each side ...
Page 70
... become the tangents at A , B , C respectively , and we obtain the theorem enunciated in Ex . 1. Chap . II . Again ... becomes the tangent at A , we see that , if AE , DB be produced to meet in G , AB , EC in H , and GH in- tersect CD in ...
... become the tangents at A , B , C respectively , and we obtain the theorem enunciated in Ex . 1. Chap . II . Again ... becomes the tangent at A , we see that , if AE , DB be produced to meet in G , AB , EC in H , and GH in- tersect CD in ...
Page 77
... become identical . line . 9. To find the co - ordinates of the pole of a given straight Let the equation of the given straight line be la + mB + ny = 0 . If ( f , g , h ) be the POLE AND POLAR . 77 Co-ordinates of the Pole of a given ...
... become identical . line . 9. To find the co - ordinates of the pole of a given straight Let the equation of the given straight line be la + mB + ny = 0 . If ( f , g , h ) be the POLE AND POLAR . 77 Co-ordinates of the Pole of a given ...
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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