An Elementary Treatise on Trilinear Co-ordinates: The Method of Reciprocal Polars, and the Theory Projections |
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Page viii
... meet the third Any Chord of a conic is divided harmonically by the Conic , any Point , and its Polar 52 • 53 23 . Equation of a Line joining Two given Points ib . 24 . Equation of the Tangent at a given Point . 54 25 . 26 . 27 . Pole of ...
... meet the third Any Chord of a conic is divided harmonically by the Conic , any Point , and its Polar 52 • 53 23 . Equation of a Line joining Two given Points ib . 24 . Equation of the Tangent at a given Point . 54 25 . 26 . 27 . Pole of ...
Page ix
... meets the conic again Equation of the Tangent at a given Point . 74 75 4 , 5 . 6 . Condition that a given Straight Line may touch the Conic Condition for a Parabola . 76 78 · 7 . Condition that the Conic may break up into Two Straight ...
... meets the conic again Equation of the Tangent at a given Point . 74 75 4 , 5 . 6 . Condition that a given Straight Line may touch the Conic Condition for a Parabola . 76 78 · 7 . Condition that the Conic may break up into Two Straight ...
Page 20
... meets AC , AB , respectively , we have shewn ( Art . 7 ) that 1 q 1 = = - 1 na b lbc ' 1 ma lbc r Now , let a ' denote the distance from ( f , g , h ) to ( l , m , n ) . Then ( q2 + r2 - 2gr cos A ) * a ' + qg + rh = qr be ( af + bg + ...
... meets AC , AB , respectively , we have shewn ( Art . 7 ) that 1 q 1 = = - 1 na b lbc ' 1 ma lbc r Now , let a ' denote the distance from ( f , g , h ) to ( l , m , n ) . Then ( q2 + r2 - 2gr cos A ) * a ' + qg + rh = qr be ( af + bg + ...
Page 22
... meet AP ' in D1 , D .; CR , AP meet BQ ' in E1 , E2 ; AP , BQ meet CR ' in F1 , F2 ; CD1 , BD , intersect in L ; AE ,, CE , in M ; BF1 , AF in N. Prove that AL , BM , CN intersect in a point . ANHARMONIC RATIO . 19. We shall introduce ...
... meet AP ' in D1 , D .; CR , AP meet BQ ' in E1 , E2 ; AP , BQ meet CR ' in F1 , F2 ; CD1 , BD , intersect in L ; AE ,, CE , in M ; BF1 , AF in N. Prove that AL , BM , CN intersect in a point . ANHARMONIC RATIO . 19. We shall introduce ...
Page 28
... meet in E. Join AE , then AE shall be the fourth harmonic required . For , let ABC be the triangle of reference , and let the equation of AD be B - ky - 0 . Let the equation of B'C ' be λα + β - ky = 0 . Then that of BC ' is λa - kry ...
... meet in E. Join AE , then AE shall be the fourth harmonic required . For , let ABC be the triangle of reference , and let the equation of AD be B - ky - 0 . Let the equation of B'C ' be λα + β - ky = 0 . Then that of BC ' is λa - kry ...
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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