An Elementary Treatise on Trilinear Co-ordinates: The Method of Reciprocal Polars, and the Theory of Projections |
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Page 1
... point in a plane is determined by means of its distances from two given ... points of the triangle of reference by the letters A , B , C , the lengths of the sides ... F. 1 the triangle of reference ( fig . 1 ) . 831 CHAPTER TRILINEAR CO ...
... point in a plane is determined by means of its distances from two given ... points of the triangle of reference by the letters A , B , C , the lengths of the sides ... F. 1 the triangle of reference ( fig . 1 ) . 831 CHAPTER TRILINEAR CO ...
Page 11
... f , g , h be the co - ordinates of any fixed point D on the locus of the equation , a , ẞ , y those of any point P. Draw DE , PM perpendicular to AC , DF , PN perpendi- cular to AB . Also draw Dm , Dn , perpendicular respectively . to ...
... f , g , h be the co - ordinates of any fixed point D on the locus of the equation , a , ẞ , y those of any point P. Draw DE , PM perpendicular to AC , DF , PN perpendi- cular to AB . Also draw Dm , Dn , perpendicular respectively . to ...
Page 12
... point on the locus P may represent . This can only be true when that locus is a straight line . 9. To find the co ... f , g , h ; f ' , g ' , h ' , be the co - ordinates of the two given points , and suppose the equation of the required ...
... point on the locus P may represent . This can only be true when that locus is a straight line . 9. To find the co ... f , g , h ; f ' , g ' , h ' , be the co - ordinates of the two given points , and suppose the equation of the required ...
Page 14
... point . Let the equations of the straight lines be 112a + m1ß + n1y = 0 , l2a + m2ß + n2y = 0 , l ̧x + m ̧ß + n ̧y ... ( f , g , h ) ( a , B , y ) be the co - ordinates of any two points in ( 1 ) , ( f ' , g ' , h ' ) ( a ' , B ' , y ...
... point . Let the equations of the straight lines be 112a + m1ß + n1y = 0 , l2a + m2ß + n2y = 0 , l ̧x + m ̧ß + n ̧y ... ( f , g , h ) ( a , B , y ) be the co - ordinates of any two points in ( 1 ) , ( f ' , g ' , h ' ) ( a ' , B ' , y ...
Page 17
... point , parallel to a given straight line . Let ( l , m , n ) be the given straight line , ( f , g , h ) the given point , then the equation of the required straight line will be la + mB + ny If + mg + nh aa + bB + cy af + bg + ch • For ...
... point , parallel to a given straight line . Let ( l , m , n ) be the given straight line , ( f , g , h ) the given point , then the equation of the required straight line will be la + mB + ny If + mg + nh aa + bB + cy af + bg + ch • For ...
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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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