An Elementary Treatise on Trilinear Co-ordinates: The Method of Reciprocal Polars, and the Theory of Projections |
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Page 4
... follows : Let P , Q be the two given points . Join PQ , and draw PM , QM ' perpen- Again , since - aa1 + bß1 + cy1 = 4 MODERN GEOMETRY . Identical relation between the Trilinear Co-ordinates of a Point Distance between two given Points.
... follows : Let P , Q be the two given points . Join PQ , and draw PM , QM ' perpen- Again , since - aa1 + bß1 + cy1 = 4 MODERN GEOMETRY . Identical relation between the Trilinear Co-ordinates of a Point Distance between two given Points.
Page 8
... angle A , we shall have , making the same construction as before , PG = PH . The straight line will be therefore represented by the equation ẞ = y . For the external bisector we proceed as follows . Let 8 MODERN GEOMETRY .
... angle A , we shall have , making the same construction as before , PG = PH . The straight line will be therefore represented by the equation ẞ = y . For the external bisector we proceed as follows . Let 8 MODERN GEOMETRY .
Page 9
... follows . Let Q be any point on the line , a , ß , y its co - ordinates . Draw QK perpendicular to AC , QL to AB . Then , as before , we have QK = QL . It will however be observed , that if Q and B lie on the same side of AC , Q and C ...
... follows . Let Q be any point on the line , a , ß , y its co - ordinates . Draw QK perpendicular to AC , QL to AB . Then , as before , we have QK = QL . It will however be observed , that if Q and B lie on the same side of AC , Q and C ...
Page 23
... follow one another . Thus , the an- harmonic ratio of the pencil OP , OR , OQ , OS , is different from that of the pencil OP , OQ , OR , OS , the former being equal to sin POQ . sin ROS sin POR . sin QOS sin POS . sin QOR ' the latter ...
... follow one another . Thus , the an- harmonic ratio of the pencil OP , OR , OQ , OS , is different from that of the pencil OP , OQ , OR , OS , the former being equal to sin POQ . sin ROS sin POR . sin QOS sin POS . sin QOR ' the latter ...
Page 27
... follows that the straight lines respectively represented by the equations B = 0 , B − ky = 0 , y = 0 , B + ky = 0 , form an harmonic pencil . 24. Hence we deduce a geometrical construction for the determination of the fourth harmonic ...
... follows that the straight lines respectively represented by the equations B = 0 , B − ky = 0 , y = 0 , B + ky = 0 , form an harmonic pencil . 24. Hence we deduce a geometrical construction for the determination of the fourth harmonic ...
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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