An Elementary Treatise on Trilinear Co-ordinates: The Method of Reciprocal Polars, and the Theory of Projections |
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Page ix
... pair of Tangents drawn to the Conic from a given external Point 80 11 . Co - ordinates of the Centre 82 12 . Equation of the Asymptotes 83 13. Condition for a Rectangular Hyperbola 14. Conditions for a Circle : 22 8888 79 84 86 ARTS ...
... pair of Tangents drawn to the Conic from a given external Point 80 11 . Co - ordinates of the Centre 82 12 . Equation of the Asymptotes 83 13. Condition for a Rectangular Hyperbola 14. Conditions for a Circle : 22 8888 79 84 86 ARTS ...
Page xi
... pair will be its own polar reciprocal with respect to the other 116 Condition that two pairs of straight lines may form an har- . monic pencil ib . 118 • 119 24 , Foci of a quadrilateral 25 . 28 . 29 . 30 . The three circles described ...
... pair will be its own polar reciprocal with respect to the other 116 Condition that two pairs of straight lines may form an har- . monic pencil ib . 118 • 119 24 , Foci of a quadrilateral 25 . 28 . 29 . 30 . The three circles described ...
Page xii
... pair only is real Invariants of two Conics • 146 • 147 150 • ON PROJECTIONS . 9 . Definition of Projections 10 . 13 . 152 ib . • Projection to infinity Any quadrilateral may be projected , in an infinite number of ways , into a ...
... pair only is real Invariants of two Conics • 146 • 147 150 • ON PROJECTIONS . 9 . Definition of Projections 10 . 13 . 152 ib . • Projection to infinity Any quadrilateral may be projected , in an infinite number of ways , into a ...
Page 22
... pairs of points are taken , B , C1 ; С2 , A ̧ ; A ̧ , B .; such that the points of intersection of BC with B , C ,, of CA with C , 4 ,, and of AB with AB , lie in a straight line ; BC ,, CB , intersect in L ; CA , AC , in M ; AB1 , BA ...
... pairs of points are taken , B , C1 ; С2 , A ̧ ; A ̧ , B .; such that the points of intersection of BC with B , C ,, of CA with C , 4 ,, and of AB with AB , lie in a straight line ; BC ,, CB , intersect in L ; CA , AC , in M ; AB1 , BA ...
Page 31
... pair of conjugate points be given ; as may be seen as follows . Let p , p , q , q ' be the respective distances of the four points from any arbitrary point on the line , x the distance of the centre from the same point . Then , by ...
... pair of conjugate points be given ; as may be seen as follows . Let p , p , q , q ' be the respective distances of the four points from any arbitrary point on the line , x the distance of the centre from the same point . Then , by ...
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Common terms and phrases
angular points asymptotes ax+bB+cy b₁ b₂ C₁ Cambridge centre Chap co-ordinates coefficients College common tangents conic section Crown 8vo determinant directrix Edition equation Fcap find the equation fixed point follows four points given conic given point given straight line Hence imaginary investigated Let the equation line at infinity line joining locus meets the conic nine-point circle numerous Illustrations obtain opposite sides Owens College pair parabola Pascal's Theorem perpendicular point f points of intersection pole Professor prove radical axis ratios rectangular hyperbola represented respect right angles second degree shewn similar and similarly sin POS tangents tangents drawn term a,b,c theorem three straight lines tion touches the line triangle of reference Ua² ux² V'ca v'f+u'g+wh va² values Vb² vß² W. K. CLIFFORD W'ab whence wy² λα