An Elementary Treatise on Trilinear Co-ordinates: The Method of Reciprocal Polars, and the Theory of Projections |
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Page vii
... drawn through a given Point , parallel to a given Straight Line 14 16 · · • 17 16 . Inclination of a Straight Line to a side of the Triangle of Reference 18 17 . Condition of Perpendicularity 19 18 . Distance from a Point to a Straight ...
... drawn through a given Point , parallel to a given Straight Line 14 16 · · • 17 16 . Inclination of a Straight Line to a side of the Triangle of Reference 18 17 . Condition of Perpendicularity 19 18 . Distance from a Point to a Straight ...
Page ix
... drawn in a given direction through a given Point of the Conic , 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 ...
... drawn in a given direction through a given Point of the Conic , 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 ...
Page xii
... drawn · 148 32 . If one point and four tangents be given , two conics can be drawn • ib . 33 . 34 . If five tangents be given , one conic only can be drawn Reduction of certain other conditions to these . . ib . · ib . · 35 . Conjugate ...
... drawn · 148 32 . If one point and four tangents be given , two conics can be drawn • ib . 33 . 34 . If five tangents be given , one conic only can be drawn Reduction of certain other conditions to these . . ib . · ib . · 35 . Conjugate ...
Page 2
... draw PD perpendicular to BC . Then PD - a , and aa = twice the area of the triangle PBC . Fig . 1 . B D Similarly 68 = twice the area of PCA , cy twice the area of PAB , = Adding these equations , we get aa + bB + cy = 2A . Next ...
... draw PD perpendicular to BC . Then PD - a , and aa = twice the area of the triangle PBC . Fig . 1 . B D Similarly 68 = twice the area of PCA , cy twice the area of PAB , = Adding these equations , we get aa + bB + cy = 2A . Next ...
Page 4
... : 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.
... : 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.
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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