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 Points may lie in the same Straight Line Condition that Three Straight Lines may intersect in a Point 14 Condition that Two Straight Lines may be parallel to one another . Line at Infinity Equation of a Straight ...
... Condition that Three Points may lie in the same Straight Line Condition that Three Straight Lines may intersect in a Point 14 Condition that Two Straight Lines may be parallel to one another . Line at Infinity Equation of a Straight ...
Page viii
... Condition for a Parabola 35 5 . Condition of Tangency . Every Parabola touches the Line at Infinity 37 6 . Equation of the Circumscribing Circle ib . 7 . Equation of the Conic touching the Three Sides of the Tri- angle of Reference 39 8 ...
... Condition for a Parabola 35 5 . Condition of Tangency . Every Parabola touches the Line at Infinity 37 6 . Equation of the Circumscribing Circle ib . 7 . Equation of the Conic touching the Three Sides of the Tri- angle of Reference 39 8 ...
Page ix
... Condition that a given Straight Line may touch the Conic Condition for a Parabola 76 • 78 7 . Condition that the Conie may break up into Two Straight Lines ib . 8 . Equation of the Polar of a given Point ib . 9 . Co - ordinates of the ...
... Condition that a given Straight Line may touch the Conic Condition for a Parabola 76 • 78 7 . Condition that the Conie may break up into Two Straight Lines ib . 8 . Equation of the Polar of a given Point ib . 9 . Co - ordinates of the ...
Page xi
... Condition that two pairs of straight lines may form an har- . monic pencil ib . 118 • 119 24 , Foci of a ... Condition for a Parabola 139 10 . Circular points at infinity ib . Conditions for a Circle 140 • 11 . Self - conjugate Conic 141 ...
... Condition that two pairs of straight lines may form an har- . monic pencil ib . 118 • 119 24 , Foci of a ... Condition for a Parabola 139 10 . Circular points at infinity ib . Conditions for a Circle 140 • 11 . Self - conjugate Conic 141 ...
Page xiii
... conditions to these 9. Conjugate triad ib . ib . 165 ON THE LOCUS OF THE CENTRE OF A SYSTEM OF CONICS WHICH SATISFY FOUR CONDITIONS . 11 . Four points given 12. Three points and a tangent 13 . 14 . 15 . Two points and two tangents . One ...
... conditions to these 9. Conjugate triad ib . ib . 165 ON THE LOCUS OF THE CENTRE OF A SYSTEM OF CONICS WHICH SATISFY FOUR CONDITIONS . 11 . Four points given 12. Three points and a tangent 13 . 14 . 15 . Two points and two tangents . One ...
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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