An Elementary Treatise on Trilinear Co-ordinates: The Method of Reciprocal Polars, and the Theory of Projections |
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Page viii
... Angle form , with the Lines containing it , an Harmonic Pencil · Anharmonic Ratio of a given Pencil Fourth Harmonic to Three given Straight Lines Harmonic Relation of Points and Lines ON INVOLUTION . Definitions Anharmonic Properties of ...
... Angle form , with the Lines containing it , an Harmonic Pencil · Anharmonic Ratio of a given Pencil Fourth Harmonic to Three given Straight Lines Harmonic Relation of Points and Lines ON INVOLUTION . Definitions Anharmonic Properties of ...
Page x
... angles to PAGE 87 18 . To find the magnitudes of the axes of the Conic 89 19 . To find the area of the Conic . Criterion to ... angle in the Reciprocal Curve 113 22 . Co - ordinates of the foci of a Conic · 115 EXAMPLES 116 23 . Double ...
... angles to PAGE 87 18 . To find the magnitudes of the axes of the Conic 89 19 . To find the area of the Conic . Criterion to ... angle in the Reciprocal Curve 113 22 . Co - ordinates of the foci of a Conic · 115 EXAMPLES 116 23 . Double ...
Page xi
... which the angles are of any magnitude Projection of Tangents , of Poles , and Polars 13 . 138 139 14 . Any two conics may be projected into concentric curves 140 ARTS . PAGE 15 . Also into similar and similarly CONTENTS . xi.
... which the angles are of any magnitude Projection of Tangents , of Poles , and Polars 13 . 138 139 14 . Any two conics may be projected into concentric curves 140 ARTS . PAGE 15 . Also into similar and similarly CONTENTS . xi.
Page xii
... angle A with each other , form with the lines joining the circular 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 ...
... angle A with each other , form with the lines joining the circular 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 ...
Page 8
... angles to BC . COR . It may hence be shewn that the three straight lines drawn through the angular points of a triangle ... angle A , we shall have , making the same construction as before , PG = PH . The straight line will be therefore ...
... angles to BC . COR . It may hence be shewn that the three straight lines drawn through the angular points of a triangle ... angle A , we shall have , making the same construction as before , PG = PH . The straight line will be therefore ...
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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