An Elementary Treatise on Trilinear Co-ordinates: The Method of Reciprocal Polars, and the Theory Projections |
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Results 1-5 of 18
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 + y = 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 + y = 0 as the equation of the line AQ , which externally bisects the ...
Page 15
... 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 between the equations la + mB + ny = 0 , l'a + CONDITION OF PARALLELISM . 15.
... 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 between the equations la + mB + 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 . It will also be remarked , that the more nearly the ratios 1 m n approach to the ...
... 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 to the ...
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
aa+bB+cy angular points asymptotes auxiliary conic b₁ Brianchon's Theorem C₁ centre Chap chord co-ordinates coefficients common tangents conic passing conic section determinant directrix find the equation fixed point fixed straight line focus follows four points given conic given point given straight line Hence imaginary internal bisectors investigated Let the equation line at infinity locus meets the conic nine-point circle obtain opposite sides pair parabola Pascal's Theorem perpendicular point f point of intersection points at infinity points of contact polar reciprocal projection prove radical axis reciprocal curve reciprocated with respect rectangular hyperbola represented right angles second degree similar and similarly system of conics tangents drawn theorem three points three straight lines triangle of reference ua² uf+w'g+v'h Vb² vß² W'ab Wc² whence wy²