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 = -7 . 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 = -7 . 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 , B , y be- tween the equations la + mß + ny = 0 , l'a + 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 , B , y be- tween the equations la + mß + ny = 0 , l'a + 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 . : mn 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 . : mn 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 + b + 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 + b + 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
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