An Elementary Treatise on Trilinear Co-ordinates: The Method of Reciprocal Polars, and the Theory Projections |
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Page ix
... 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 . 16 . 17 . 18 CONTENTS . ix.
... 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 . 16 . 17 . 18 CONTENTS . ix.
Page 82
... These equations determine the centre . 12. To find the equation of the asymptotes . Writing 82 TRILINEAR CO - ORDINATES . Condition of Tangency Condition for a Parabola Co-ordinates of the Centre 55 11 Co-ordinates of the Centre.
... These equations determine the centre . 12. To find the equation of the asymptotes . Writing 82 TRILINEAR CO - ORDINATES . Condition of Tangency Condition for a Parabola Co-ordinates of the Centre 55 11 Co-ordinates of the Centre.
Page 83
... asymptotes . Writing a , B , y , for f , g , h , in the investigation of Art . 10 , and paying regard to equations ( A ) of Art . 11 , the asymptotes will be found to be represented by the equation or Þ ( α , B , y ) & ( α , B , y ) ...
... asymptotes . Writing a , B , y , for f , g , h , in the investigation of Art . 10 , and paying regard to equations ( A ) of Art . 11 , the asymptotes will be found to be represented by the equation or Þ ( α , B , y ) & ( α , B , y ) ...
Page 84
... asymptotes be la + mB + ny = 0 , = l'a + m'ß + n'y = 0 , the condition of their perpendicularity is ll ' + mm ' + nn ' — ( mn ' + m'n ) cos A- - - ( nl ' + n'l ) cos B - ( lm ' + l'm ) cos C = 0 . Writing , for shortness , Ua2 + Vb2 + ...
... asymptotes be la + mB + ny = 0 , = l'a + m'ß + n'y = 0 , the condition of their perpendicularity is ll ' + mm ' + nn ' — ( mn ' + m'n ) cos A- - - ( nl ' + n'l ) cos B - ( lm ' + l'm ) cos C = 0 . Writing , for shortness , Ua2 + Vb2 + ...
Page 103
... asymptotes is W + U ' + V ' · u , w ' , v ' , 1 2 ( x , y , z ) + u , w ' , v ' ( x + y + z ) 2 = 0 . w ' , v , u ' , 1 w ' , v , u ' v ' , u ' , w , 1 v ' , u ' , w 1 , 1 , 1 , 0 The radical axis of two circles ux2 + vy2 + wz2 + 2u'yz ...
... asymptotes is W + U ' + V ' · u , w ' , v ' , 1 2 ( x , y , z ) + u , w ' , v ' ( x + y + z ) 2 = 0 . w ' , v , u ' , 1 w ' , v , u ' v ' , u ' , w , 1 v ' , u ' , w 1 , 1 , 1 , 0 The radical axis of two circles ux2 + vy2 + wz2 + 2u'yz ...
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An Elementary Treatise on Trilinear Coordinates, the Method of Reciprocal ... Norman Macleod Ferrers No preview available - 2015 |
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