An Elementary Treatise on Trilinear Co-ordinates: The Method of Reciprocal Polars, and the Theory of Projections |
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Page vii
... Condition that Three Straight Lines may intersect in a Point Condition that Two Straight Lines may be parallel to one another . Line at Infinity Equation of a Straight Line , drawn through a given Point , parallel to a given Straight ...
... Condition that Three Straight Lines may intersect in a Point Condition that Two Straight Lines may be parallel to one another . Line at Infinity Equation of a Straight Line , drawn through a given Point , parallel to a given Straight ...
Page viii
... Condition for a Parabola 40 9 . Condition of Tangency 42 IO . Equations of the Four Circles which touch the Three Sides of the Triangle of Reference 43 II - 15 . Equation involving the Squares only of the Variables 45 16 . Condition of ...
... Condition for a Parabola 40 9 . Condition of Tangency 42 IO . Equations of the Four Circles which touch the Three Sides of the Triangle of Reference 43 II - 15 . Equation involving the Squares only of the Variables 45 16 . Condition of ...
Page ix
... 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 . 8 . Equation of the Polar of a given Point 9 . Co - ordinates of the Pole ...
... 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 . 8 . Equation of the Polar of a given Point 9 . Co - ordinates of the Pole ...
Page xi
... Condition for a Parabola 127 9 . Circular points at infinity ib . IO . EXAMPLES Conditions for a Circle II - 13 . Tangential rectangular Co - ordinates 14. Tangential polar Co - ordinates EXAMPLES 128 • · · 129 130 132 ib . CHAPTER VIII ...
... Condition for a Parabola 127 9 . Circular points at infinity ib . IO . EXAMPLES Conditions for a Circle II - 13 . Tangential rectangular Co - ordinates 14. Tangential polar Co - ordinates EXAMPLES 128 • · · 129 130 132 ib . CHAPTER VIII ...
Page xii
... CONDITIONS . 28 . If five points be given , one conic only can be drawn • 146 29 . · If four points and one tangent be given , two conics can be drawn 147 30 . • If three points and two tangents be given , four conics can be drawn ib ...
... CONDITIONS . 28 . If five points be given , one conic only can be drawn • 146 29 . · If four points and one tangent be given , two conics can be drawn 147 30 . • If three points and two tangents be given , four conics can be drawn ib ...
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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