An Elementary Treatise on Trilinear Co-ordinates: The Method of Reciprocal Polars, and the Theory Projections |
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Page viii
... Polar 52 • 53 23 . Equation of a Line joining Two given Points ib . 24 . Equation of the Tangent at a given Point . 54 25 . 26 . 27 . Pole of a given Straight Line Condition of Tangency . Condition for a Parabola Co - ordinates of the ...
... Polar 52 • 53 23 . Equation of a Line joining Two given Points ib . 24 . Equation of the Tangent at a given Point . 54 25 . 26 . 27 . Pole of a given Straight Line Condition of Tangency . Condition for a Parabola Co - ordinates of the ...
Page ix
... Polar of a given Point · ib . 9 . Co - ordinates of the Pole of a given Straight Line 79 10 . • Equation of the pair of Tangents drawn to the Conic from a given external Point 80 11 . Co - ordinates of the Centre . 82 • 12 . Equation of ...
... Polar of a given Point · ib . 9 . Co - ordinates of the Pole of a given Straight Line 79 10 . • Equation of the pair of Tangents drawn to the Conic from a given external Point 80 11 . Co - ordinates of the Centre . 82 • 12 . Equation of ...
Page x
... polar reciprocal of a conic is a conic 107 8 . Equation of the Polar Reciprocal of one Conic with regard to another ib . 10 . Instances of Transformation 109 • 12 . Brianchon's Theorem 112 13 . The anharmonic ratio of the Pencil ...
... polar reciprocal of a conic is a conic 107 8 . Equation of the Polar Reciprocal of one Conic with regard to another ib . 10 . Instances of Transformation 109 • 12 . Brianchon's Theorem 112 13 . The anharmonic ratio of the Pencil ...
Page xi
... polar reciprocal with respect to the other 116 Condition that two pairs of straight lines may form an har- monic pencil • ib . 20 . Reciprocation with respect to a Circle 118 23 . Reciprocation with respect to a Point 119 24 . The three ...
... polar reciprocal with respect to the other 116 Condition that two pairs of straight lines may form an har- monic pencil • ib . 20 . Reciprocation with respect to a Circle 118 23 . Reciprocation with respect to a Point 119 24 . The three ...
Page xii
... polar Co - ordinates 1-3 . 4-7 . 8 . EXAMPLES 141 142 144 145 CHAPTER VIII . ON THE INTERSECTION OF CONICS , AND ON PROJECTIONS . Any two conics intersect in four points , real or imaginary . Vertices of the quadrangle formed by these ...
... polar Co - ordinates 1-3 . 4-7 . 8 . EXAMPLES 141 142 144 145 CHAPTER VIII . ON THE INTERSECTION OF CONICS , AND ON PROJECTIONS . Any two conics intersect in four points , real or imaginary . Vertices of the quadrangle formed by these ...
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Common terms and phrases
aa+bB+cy angular points asymptotes auxiliary conic b₁ Brianchon's Theorem C₁ centre Chap chord co-ordinates coefficients common tangents conic passing conic section determinant directrix find the equation fixed point fixed straight line focus follows four points given conic given point given straight line Hence imaginary internal bisectors investigated Let the equation line at infinity locus meets the conic nine-point circle obtain opposite sides pair parabola Pascal's Theorem perpendicular point f point of intersection points at infinity points of contact polar reciprocal projection prove radical axis reciprocal curve reciprocated with respect rectangular hyperbola represented right angles second degree similar and similarly system of conics tangents drawn theorem three points three straight lines triangle of reference ua² uf+w'g+v'h Vb² vß² W'ab Wc² whence wy²