An Elementary Treatise on Trilinear Co-ordinates: The Method of Reciprocal Polars, and the Theory Projections |
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Page vii
... Condition that Three Straight Lines may intersect in a Point Condition that Two Straight Lines may be parallel to one another . Line at Infinity ib . 14 ib . 15 . Equation of a Straight Line , drawn through a given Point , parallel to a ...
... Condition that Three Straight Lines may intersect in a Point Condition that Two Straight Lines may be parallel to one another . Line at Infinity ib . 14 ib . 15 . Equation of a Straight Line , drawn through a given Point , parallel to a ...
Page viii
... Condition for a Parabola 40 9 . Condition of Tangency 42 10 . Equations of the Four Circles which touch the Three Sides of the Triangle of Reference 11-15 . Equation involving the Squares only of the Variables 16. Condition of Tangency ...
... Condition for a Parabola 40 9 . Condition of Tangency 42 10 . Equations of the Four Circles which touch the Three Sides of the Triangle of Reference 11-15 . Equation involving the Squares only of the Variables 16. Condition of Tangency ...
Page ix
... Condition that a given Straight Line may touch the Conic Condition for a Parabola . 76 78 · 7 . Condition that the Conic may break up into Two Straight Lines ib . 8 . Equation of the Polar of a given Point · ib . 9 . Co - ordinates of ...
... Condition that a given Straight Line may touch the Conic Condition for a Parabola . 76 78 · 7 . Condition that the Conic may break up into Two Straight Lines ib . 8 . Equation of the Polar of a given Point · ib . 9 . Co - ordinates of ...
Page xi
... Condition that two pairs of straight lines may form an har- monic pencil • ib . 20 . Reciprocation with respect to a ... Condition for a Parabola 139 10 . Circular points at infinity ib . Conditions for a Circle 140 11 . Self - conjugate ...
... Condition that two pairs of straight lines may form an har- monic pencil • ib . 20 . Reciprocation with respect to a ... Condition for a Parabola 139 10 . Circular points at infinity ib . Conditions for a Circle 140 11 . Self - conjugate ...
Page xiii
... conditions to these ib . • ib . · 9 . Conjugate triad 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 . Two points and two tangents 14 . One ...
... conditions to these ib . • ib . · 9 . Conjugate triad 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 . Two points and two tangents 14 . One ...
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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