An Elementary Treatise on Trilinear Co-ordinates: The Method of Reciprocal Polars, and the Theory of Projections |
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Page xi
... common radical axis · Foci of a quadrilateral ་ ་ ib . ib . . 25 . 28 . 29 . 30 . 31 . Orthocentre of a triangle The director circles of all conics which touch four given straight lines have a common radical axis • Polar reciprocal of a ...
... common radical axis · Foci of a quadrilateral ་ ་ ib . ib . . 25 . 28 . 29 . 30 . 31 . Orthocentre of a triangle The director circles of all conics which touch four given straight lines have a common radical axis • Polar reciprocal of a ...
Page xii
... common chords are real ; if not , one pair only is real • PAGE 140 141 143 ib . 145 · 146 148 • 149 150 8 . Invariants of two Conics ON PROJECTIONS . 9 . Definition of Projections IO . 13 . Projection to infinity Any quadrilateral may ...
... common chords are real ; if not , one pair only is real • PAGE 140 141 143 ib . 145 · 146 148 • 149 150 8 . Invariants of two Conics ON PROJECTIONS . 9 . Definition of Projections IO . 13 . Projection to infinity Any quadrilateral may ...
Page 57
... common point meet the sides of the triangle which intersect their respective conics in three points lying in a straight line ; and that the other common tangents to each pair of conics intersect the sides of the triangle which touch the ...
... common point meet the sides of the triangle which intersect their respective conics in three points lying in a straight line ; and that the other common tangents to each pair of conics intersect the sides of the triangle which touch the ...
Page 92
... common radical axis with them . 20. We have investigated , in Art . 10 , the equation of the pair of tangents drawn to the conic from a given point ( f , g , h ) . If these two tangents be at right angles to one another , they may be ...
... common radical axis with them . 20. We have investigated , in Art . 10 , the equation of the pair of tangents drawn to the conic from a given point ( f , g , h ) . If these two tangents be at right angles to one another , they may be ...
Page 97
... common radical axis . 4. If A , B , C , A ' , B , C ' be six points , such that the straight lines B'C ' , C'A ' , A'B ' are the several polars of the points A , B , C , with respect to a given conic , prove that The three straight ...
... common radical axis . 4. If A , B , C , A ' , B , C ' be six points , such that the straight lines B'C ' , C'A ' , A'B ' are the several polars of the points A , B , C , with respect to a given conic , prove that The three straight ...
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Common terms and phrases
aa+bB+cy angular points anharmonic ratio asymptotes b₁ b₂ centre Chap chord coefficients common tangents condition of tangency conic section Crown 8vo curve determine directrix distance escribed circles Fcap find the equation fixed point foci focus four points given conic given point given straight line harmonic pencil Hence imaginary internal bisectors investigated Let the equation line at infinity line joining locus meets the conic nine-point circle obtain opposite sides pair parabola parallel Pascal's Theorem perpendicular point f point of intersection points at infinity points of contact pole prove radical axis reciprocated with respect rectangular hyperbola represented right angles second degree sin POS tangents tangents drawn theorem three points three straight lines touches the line triangle of reference ua² V'ca values vß² W'ab whence wy² λα
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