An Elementary Treatise on Trilinear Co-ordinates: The Method of Reciprocal Polars, and the Theory of Projections |
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Page viii
... 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 . Position of ...
... 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 . Position of ...
Page ix
... 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 Pole of a given Straight Line 10 . · Equation of the pair of Tangents ...
... 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 Pole of a given Straight Line 10 . · Equation of the pair of Tangents ...
Page x
... Parabola . 21 . Locus of the intersection of two Tangents at right angles to one another . To find the magnitudes of the axes of the Conic 315 93 94 22 . To find the area of the Conic . Criterion to distinguish be- tween an Ellipse and ...
... Parabola . 21 . Locus of the intersection of two Tangents at right angles to one another . To find the magnitudes of the axes of the Conic 315 93 94 22 . To find the area of the Conic . Criterion to distinguish be- tween an Ellipse and ...
Page xi
... line , and of the centre . Condition for a Parabola 139 10 . Circular points at infinity ib . Conditions for a Circle 140 • 11 . Self - conjugate Conic 141 ARTS . EXAMPLES 12. Tangential rectangular Co - ordinates 15. CONTENTS . xi.
... line , and of the centre . Condition for a Parabola 139 10 . Circular points at infinity ib . Conditions for a Circle 140 • 11 . Self - conjugate Conic 141 ARTS . EXAMPLES 12. Tangential rectangular Co - ordinates 15. CONTENTS . xi.
Page 36
... parabola is at an infinite distance , its co - ordinates will satisfy the equation ax + bB + cy = 0 . We hence obtain the following equation : λ3a2 + μ2b2 + v3c2 - 2μvbc - 2vλca - 2xμab = 0 , which is equivalent to ± ( λa ) * ± 36 ...
... parabola is at an infinite distance , its co - ordinates will satisfy the equation ax + bB + cy = 0 . We hence obtain the following equation : λ3a2 + μ2b2 + v3c2 - 2μvbc - 2vλca - 2xμab = 0 , which is equivalent to ± ( λa ) * ± 36 ...
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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