An Elementary Treatise on Trilinear Co-ordinates: The Method of Reciprocal Polars, and the Theory of Projections |
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Page 43
... chap . I. 10. To find the equations of the four circles which touch the three sides of the triangle of reference . These may be obtained most readily by the employment of the equations for the determination of the centre , obtained in ...
... chap . I. 10. To find the equations of the four circles which touch the three sides of the triangle of reference . These may be obtained most readily by the employment of the equations for the determination of the centre , obtained in ...
Page 70
... , then AF , BD , CE become the tangents at A , B , C , respectively , and we obtain the theorem enunciated in Ex . 1 , Chap . II . Again , by supposing D to coincide with B , and E with C , we 70 TRILINEAR CO - ORDINATES .
... , then AF , BD , CE become the tangents at A , B , C , respectively , and we obtain the theorem enunciated in Ex . 1 , Chap . II . Again , by supposing D to coincide with B , and E with C , we 70 TRILINEAR CO - ORDINATES .
Page 74
... Chap . II . ) , represents a conic section . 2. To find the point in which a straight line , drawn in a given direction through a given point of the conic , meets the conic again . Let f , g , h be the co - ordinates of the given point ...
... Chap . II . ) , represents a conic section . 2. To find the point in which a straight line , drawn in a given direction through a given point of the conic , meets the conic again . Let f , g , h be the co - ordinates of the given point ...
Page 78
... Chap . III . to be u , w ' , v ' w ' , v , v ' , u ' , w = 0 or uvw + 2u'v'w ' GMG - · uu " 2 — vv22 — ww'2 : = 0 . 8. To find the equation of the polar of a given point . If through a given point any straight line be drawn cutting a ...
... Chap . III . to be u , w ' , v ' w ' , v , v ' , u ' , w = 0 or uvw + 2u'v'w ' GMG - · uu " 2 — vv22 — ww'2 : = 0 . 8. To find the equation of the polar of a given point . If through a given point any straight line be drawn cutting a ...
Page 79
... Chap . I. ) . Again , the equations of the tangents at ( f1 , 91 , h1 ) , f , g , h ) respectively , are ƒ1 ( ua + w'ß + v'y ) +9 , ( w'a + vß + u'y ) + h ̧ ( v ́a + u'ß + wy ) = 0 , ƒ2 ( ux + w'ß + v'g ) + 92 ( w'a + vß + u'y ) + h2 ...
... Chap . I. ) . Again , the equations of the tangents at ( f1 , 91 , h1 ) , f , g , h ) respectively , are ƒ1 ( ua + w'ß + v'y ) +9 , ( w'a + vß + u'y ) + h ̧ ( v ́a + u'ß + wy ) = 0 , ƒ2 ( ux + w'ß + v'g ) + 92 ( w'a + vß + u'y ) + h2 ...
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Common terms and phrases
angular points asymptotes ax+bB+cy b₁ b₂ C₁ Cambridge centre Chap co-ordinates coefficients College common tangents conic section Crown 8vo determinant directrix Edition equation Fcap find the equation fixed point follows four points given conic given point given straight line Hence imaginary investigated Let the equation line at infinity line joining locus meets the conic nine-point circle numerous Illustrations obtain opposite sides Owens College pair parabola Pascal's Theorem perpendicular point f points of intersection pole Professor prove radical axis ratios rectangular hyperbola represented respect right angles second degree shewn similar and similarly sin POS tangents tangents drawn term a,b,c theorem three straight lines tion touches the line triangle of reference Ua² ux² V'ca v'f+u'g+wh va² values Vb² vß² W. K. CLIFFORD W'ab whence wy² λα