An Elementary Treatise on Trilinear Co-ordinates: The Method of Reciprocal Polars, and the Theory of Projections |
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Page viii
... Points and Lines ON INVOLUTION . Definitions Anharmonic Properties of Points ... Four Circles which touch the Three Sides of the Triangle of Reference 43 II ... points where they meet the third Any Chord of a Conic is divided harmonically ...
... Points and Lines ON INVOLUTION . Definitions Anharmonic Properties of Points ... Four Circles which touch the Three Sides of the Triangle of Reference 43 II ... points where they meet the third Any Chord of a Conic is divided harmonically ...
Page x
... Point 2 . Formulæ relating to Straight Lines 94 3 . Formulæ relating to Conics ... four intersect- ing straight lines , is the same as that of the range formed ... Points and Lines . The angle between the radius vector and tangent in any ...
... Point 2 . Formulæ relating to Straight Lines 94 3 . Formulæ relating to Conics ... four intersect- ing straight lines , is the same as that of the range formed ... Points and Lines . The angle between the radius vector and tangent in any ...
Page xi
... points General Equation of a Point · PAGE . 119 ib . Identical relation between the co - ordinates of any straight ... four points , real or imaginary . Vertices of the quadrangle formed by these points 4-7 . If the four points of ...
... points General Equation of a Point · PAGE . 119 ib . Identical relation between the co - ordinates of any straight ... four points , real or imaginary . Vertices of the quadrangle formed by these points 4-7 . If the four points of ...
Page xii
... points at infinity to their point of intersection a pencil of which the anharmonic ratio is ( π - 24 ) √ = 1 143 22 . The anharmonic ratio of any four points on , or any four tan- gents to , a conic , is constant 144 23 , 24. Any system of ...
... points at infinity to their point of intersection a pencil of which the anharmonic ratio is ( π - 24 ) √ = 1 143 22 . The anharmonic ratio of any four points on , or any four tan- gents to , a conic , is constant 144 23 , 24. Any system of ...
Page 23
... four straight lines in- tersecting in a point , the ratio sin POQ . sin ROS sin POS . sin QOR is 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 straight lines in- tersecting in a point , the ratio sin POQ . sin ROS sin POS . sin QOR is 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 ...
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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