An Elementary Treatise on Trilinear Co-ordinates: The Method of Reciprocal Polars, and the Theory Projections |
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Page viii
... touching the Three Sides of the Tri- angle of Reference . 39 · 8 . Position of the Centre . 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 ...
... touching the Three Sides of the Tri- angle of Reference . 39 · 8 . Position of the Centre . 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 ...
Page ix
... 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 the Pole of a given Straight Line 79 10 ...
... 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 the Pole of a given Straight Line 79 10 ...
Page xi
... touch four given straight lines have a common radical axis . 121 29 . 30 . Polar reciprocal of a circle with regard ... touching the three sides of the triangle of reference . ib . 8 . Equation of circumscribed Conic 138 · 9 .. Equation ...
... touch four given straight lines have a common radical axis . 121 29 . 30 . Polar reciprocal of a circle with regard ... touching the three sides of the triangle of reference . ib . 8 . Equation of circumscribed Conic 138 · 9 .. Equation ...
Page 22
... touching BC externally and AB , AC produced . 6. On the sides BC , CA , AB of the triangle ABC , respectively , pairs of points are taken , B1 , C1 ; C2 , A2 ; A ̧ , B ; such that the points of intersection of BC with BC2 , of CA with ...
... touching BC externally and AB , AC produced . 6. On the sides BC , CA , AB of the triangle ABC , respectively , pairs of points are taken , B1 , C1 ; C2 , A2 ; A ̧ , B ; such that the points of intersection of BC with BC2 , of CA with ...
Page 34
... 0 . Hence the straight line and the conic meet one another in coincident points , that is , they touch one another at the point A. Similarly , the equations of the tangents at B and 34 TRILINEAR CO - ORDINATES . ence.
... 0 . Hence the straight line and the conic meet one another in coincident points , that is , they touch one another at the point A. Similarly , the equations of the tangents at B and 34 TRILINEAR CO - ORDINATES . ence.
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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