An Elementary Treatise on Trilinear Co-ordinates: The Method of Reciprocal Polars, and the Theory of 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 . 24 . 25 . 26 . 27 . Equation of a Line joining Two given Points . Equation of the Tangent at a given Point Pole of a given ...
... meet the third Any Chord of a Conic is divided harmonically by the Conic , any Point , and its Polar • 52 53 23 . 24 . 25 . 26 . 27 . Equation of a Line joining Two given Points . Equation of the Tangent at a given Point Pole of a given ...
Page ix
... meets the Curve again Equation of the Tangent at a given Point 3 . 4 , 5 . Condition that a given Straight Line may touch the Conic 6 . Condition for a Parabola . 7 . Condition that the Conic may break up into Two Straight Lines . ib ...
... meets the Curve again Equation of the Tangent at a given Point 3 . 4 , 5 . Condition that a given Straight Line may touch the Conic 6 . Condition for a Parabola . 7 . Condition that the Conic may break up into Two Straight Lines . ib ...
Page 20
... meets AC , AB , respectively , we have shewn ( Art . 7 ) that 1 9 1/8 γ = 1 na b lbc ' ma 1 = - C lbc Now , let a denote the distance from ( f , g , h ) to ( l , m , n ) . Then ( qa + r2 — 2qr cos A ) * a ' + 99 + rh = L " ( af + bg + ...
... meets AC , AB , respectively , we have shewn ( Art . 7 ) that 1 9 1/8 γ = 1 na b lbc ' ma 1 = - C lbc Now , let a denote the distance from ( f , g , h ) to ( l , m , n ) . Then ( qa + r2 — 2qr cos A ) * a ' + 99 + rh = L " ( af + bg + ...
Page 22
... meet AP in D , D .; CR , AP meet BQ ' in E , E ; AP , BQ meet CR in F , F ; CD , BD , intersect in L ; AE , CE , in M ; BF , AF in N. Prove that AL , BM , CN intersect in a point . 2 12 ANHARMONIC RATIO . 19. We shall introduce , in ...
... meet AP in D , D .; CR , AP meet BQ ' in E , E ; AP , BQ meet CR in F , F ; CD , BD , intersect in L ; AE , CE , in M ; BF , AF in N. Prove that AL , BM , CN intersect in a point . 2 12 ANHARMONIC RATIO . 19. We shall introduce , in ...
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 -ly = 0 . Then that of ........ BC ' is λa ...
... 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 -ly = 0 . Then that of ........ BC ' is λa ...
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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