An Elementary Treatise on Trilinear Co-ordinates: The Method of Reciprocal Polars, and the Theory Projections |
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Page 1
... called the triangle of reference , its sides , lines of reference , and the distances of a point from its three sides will be called the trilinear co - ordinates of that point . We shall usually denote the angular points of the triangle ...
... called the triangle of reference , its sides , lines of reference , and the distances of a point from its three sides will be called the trilinear co - ordinates of that point . We shall usually denote the angular points of the triangle ...
Page 17
... called to the fact , that the equation aa + bB + cy = 0 is , in itself , impossible , —in fact , a contradiction in terms , - and can only be admitted as a limiting form to which possi- ble equations may continually tend . 15 . To find ...
... called to the fact , that the equation aa + bB + cy = 0 is , in itself , impossible , —in fact , a contradiction in terms , - and can only be admitted as a limiting form to which possi- ble equations may continually tend . 15 . To find ...
Page 23
... called the anharmonic ratio of the pencil OP , OQ , OR , OS , and is expressed by the notation { 0. PQRS } * . DEF . 2. If P , Q , R , S be four points in a straight line , PQ . RS is called the anharmonic ratio of the range the ratio ...
... called the anharmonic ratio of the pencil OP , OQ , OR , OS , and is expressed by the notation { 0. PQRS } * . DEF . 2. If P , Q , R , S be four points in a straight line , PQ . RS is called the anharmonic ratio of the range the ratio ...
Page 25
... called an harmonic pencil . A range , of which the anharmonic ratio is unity , is called an harmonic range , and the straight line , on which the range lies , is said to be divided harmonically . From what has been said above , it will ...
... called an harmonic pencil . A range , of which the anharmonic ratio is unity , is called an harmonic range , and the straight line , on which the range lies , is said to be divided harmonically . From what has been said above , it will ...
Page 30
... called harmonics of one another with respect to the triangle ABC . By combining the proposition last proved with that proved in Art . ( 22 ) , we shall obtain a demonstration of the statements made in Art . 6 ; that the points in which ...
... called harmonics of one another with respect to the triangle ABC . By combining the proposition last proved with that proved in Art . ( 22 ) , we shall obtain a demonstration of the statements made in Art . 6 ; that the points in which ...
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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