An Elementary Treatise on Trilinear Co-ordinates: The Method of Reciprocal Polars, and the Theory of Projections |
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Page 9
... observed , that if Q and B lie on the same side of AC , Q and C will lie on opposite sides of AB , and vice versa . Hence , if QK = B , QL = — y . We have therefore B + 7 = 0 as the equation of the line AQ , which externally bisects the ...
... observed , that if Q and B lie on the same side of AC , Q and C will lie on opposite sides of AB , and vice versa . Hence , if QK = B , QL = — y . We have therefore B + 7 = 0 as the equation of the line AQ , which externally bisects the ...
Page 15
... form which we shall occasionally use . It will be observed that this condition is the same in form as that which results from the elimination of a , ẞ , y be- tween the equations Ale $ 15- terr la + mß + ny = CONDITION OF PARALLELISM . 15.
... form which we shall occasionally use . It will be observed that this condition is the same in form as that which results from the elimination of a , ẞ , y be- tween the equations Ale $ 15- terr la + mß + ny = CONDITION OF PARALLELISM . 15.
Page 21
... observed , that the numerator of this expression . vanishes if the point ( f , g , h ) lie upon the line ( l , m , n ) , as manifestly ought to be the case . It will also be remarked , that the more nearly the ratios 1 : m : n approach ...
... observed , that the numerator of this expression . vanishes if the point ( f , g , h ) lie upon the line ( l , m , n ) , as manifestly ought to be the case . It will also be remarked , that the more nearly the ratios 1 : m : n approach ...
Page 37
... observed that the parabola satisfies the analytical condition of touching the straight line aa + bB + cy = 0. This is generally ex- pressed by saying that every parabola touches the line at infinity . 6. To investigate the equation of ...
... observed that the parabola satisfies the analytical condition of touching the straight line aa + bB + cy = 0. This is generally ex- pressed by saying that every parabola touches the line at infinity . 6. To investigate the equation of ...
Page 39
... observe , however , that if the conic touch all three of the sides of the triangle of reference , the three double signs in the above equations must be taken all negatively , or two positively and one negatively . For , if they be taken ...
... observe , however , that if the conic touch all three of the sides of the triangle of reference , the three double signs in the above equations must be taken all negatively , or two positively and one negatively . For , if they be taken ...
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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