An Elementary Treatise on Trilinear Co-ordinates: The Method of Reciprocal Polars, and the Theory of 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 ax + 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 ax + 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 { O. 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 PS ...
... called the anharmonic ratio of the pencil OP , OQ , OR , OS , and is expressed by the notation { O. 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 PS ...
Page 25
... called an harmonic pencil . A range , of which the anharmonic ratio is unity , is called an barmonic 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 barmonic 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
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