An Elementary Treatise on Trilinear Co-ordinates: The Method of Reciprocal Polars, and the Theory of Projections |
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Page viii
... Circle ib . • 7 . Equation of the Conic touching the Three Sides of the Triangle of Reference ib . 8 . Position of the Centre . Condition for a Parabola 40 9 . Condition of Tangency 42 IO . Equations of the Four Circles which touch the ...
... Circle ib . • 7 . Equation of the Conic touching the Three Sides of the Triangle of Reference ib . 8 . Position of the Centre . Condition for a Parabola 40 9 . Condition of Tangency 42 IO . Equations of the Four Circles which touch the ...
Page ix
... Circle 84 15 . All Circles pass through the same two points at infinity 86 16 . All Conics , similar and similarly situated to each other , intersect in the same two points in the line at infinity ib . ARTS . 17 . one another ...
... Circle 84 15 . All Circles pass through the same two points at infinity 86 16 . All Conics , similar and similarly situated to each other , intersect in the same two points in the line at infinity ib . ARTS . 17 . one another ...
Page x
... Circle The anharmonic ratio of the Pencil , formed by four intersect- ing straight lines , is the same as that of the range formed by their poles 106 109 18 . 19 . Polar reciprocal of one Circle with regard to another Reciprocation with ...
... Circle The anharmonic ratio of the Pencil , formed by four intersect- ing straight lines , is the same as that of the range formed by their poles 106 109 18 . 19 . Polar reciprocal of one Circle with regard to another Reciprocation with ...
Page xi
... Circle II - 13 . Tangential rectangular Co - ordinates 14. Tangential polar Co - ordinates EXAMPLES 128 • · · 129 130 132 ib . CHAPTER VIII . ON THE INTERSECTION OF CONICS , ON PROJECTIONS , AND ON THE DETERMINATION OF A CONIC FROM FIVE ...
... Circle II - 13 . Tangential rectangular Co - ordinates 14. Tangential polar Co - ordinates EXAMPLES 128 • · · 129 130 132 ib . CHAPTER VIII . ON THE INTERSECTION OF CONICS , ON PROJECTIONS , AND ON THE DETERMINATION OF A CONIC FROM FIVE ...
Page xii
... circles 141 19 . 20 . Projection of the foci and directrices of a Conic The anharmonic ratio of any pencil or range is unaltered by projection . ib . • 142 21 . Any two lines , which make an angle A with each other , form with the lines ...
... circles 141 19 . 20 . Projection of the foci and directrices of a Conic The anharmonic ratio of any pencil or range is unaltered by projection . ib . • 142 21 . Any two lines , which make an angle A with each other , form with the lines ...
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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