An Elementary Treatise on Trilinear Co-ordinates: The Method of Reciprocal Polars, and the Theory 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 84 86 ARTS . PAGE 15 ...
... 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 84 86 ARTS . PAGE 15 ...
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 . 20 . Reciprocation with respect to a Circle 118 23 . Reciprocation with respect to a ...
... 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 . 20 . Reciprocation with respect to a Circle 118 23 . Reciprocation with respect to a ...
Page xii
... pair only is real Invariants of two Conics . 146 147 150 ON PROJECTIONS . 9 . 10 . Definition of Projections Projection to infinity 152 ib . 13 . Any quadrilateral may be projected , in an infinite number of ways , into a parallelogram ...
... pair only is real Invariants of two Conics . 146 147 150 ON PROJECTIONS . 9 . 10 . Definition of Projections Projection to infinity 152 ib . 13 . Any quadrilateral may be projected , in an infinite number of ways , into a parallelogram ...
Page 22
... pairs of points are taken , B1 , C1 ; C2 , A2 ; A ̧ , B ; such that the points of intersection of BC with BC2 , of CA with С1 , and of AB with AB , lie in a straight line ; BC2 , CB , intersect in L ; CA ,, AC , in M ; AB1 , BA , in N ...
... pairs of points are taken , B1 , C1 ; C2 , A2 ; A ̧ , B ; such that the points of intersection of BC with BC2 , of CA with С1 , and of AB with AB , lie in a straight line ; BC2 , CB , intersect in L ; CA ,, AC , in M ; AB1 , BA , in N ...
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 , a 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 , a the distance of the centre from the same point . Then , by ...
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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