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 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 PS ...
... 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 PS ...
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
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