An Elementary Treatise on Trilinear Co-ordinates: The Method of Reciprocal Polars, and the Theory of Projections |
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Page 6
... values of l , m , n are independent of the positions of the points , the distance of which we wish to find , sup- pose these points to be B and C. Then 24 = - α1 = 0 , ẞ1 = = = b 2 Y1 = 0 , 2A = ; also ra . Hence Similarly 2A 2A a2 = -l ...
... values of l , m , n are independent of the positions of the points , the distance of which we wish to find , sup- pose these points to be B and C. Then 24 = - α1 = 0 , ẞ1 = = = b 2 Y1 = 0 , 2A = ; also ra . Hence Similarly 2A 2A a2 = -l ...
Page 12
... values of a , B , y , at the point of intersection . 10. To find the equation of the straight line , passing through two given points . Let f , g , h ; f ' , g ' , h ' , be the co - ordinates of the two given points , and suppose the ...
... values of a , B , y , at the point of intersection . 10. To find the equation of the straight line , passing through two given points . Let f , g , h ; f ' , g ' , h ' , be the co - ordinates of the two given points , and suppose the ...
Page 14
... values of a , B , y . This gives , eliminating a , B , y by cross - multipli- cation , - - = 1 ̧m ̧n ̧ − 1 ̧m ̧n + lm ̧n ̧− 1 ̧m ̧n ̧ + 1 ̧m ̧n — 1 ̧m ̧n ̧ — 0 , the required condition . The identity of form between the conditions ...
... values of a , B , y . This gives , eliminating a , B , y by cross - multipli- cation , - - = 1 ̧m ̧n ̧ − 1 ̧m ̧n + lm ̧n ̧− 1 ̧m ̧n ̧ + 1 ̧m ̧n — 1 ̧m ̧n ̧ — 0 , the required condition . The identity of form between the conditions ...
Page 16
... values of a , B , y , since , as we have already proved ( Art . 2 ) , aa + bß + cy = 2A . Hence the equa- tion ( 4 ) may be looked upon as an expression of the fact that the two equations la + mB + ny = 0 , l'a + m'B + n'y = 0 , cannot ...
... values of a , B , y , since , as we have already proved ( Art . 2 ) , aa + bß + cy = 2A . Hence the equa- tion ( 4 ) may be looked upon as an expression of the fact that the two equations la + mB + ny = 0 , l'a + m'B + n'y = 0 , cannot ...
Page 20
... ( - 1 ) + ( 1-1 ) x = bc α f + = The ( If + mg + nh ) . = lbc And from the values of q and r 1 cos A 9 r = 1 cos A b ( n a m cos A ) 1bc = a ( l cos B + m cos A – n ) lbc = 1 Similarly cos A = r 4 α l 20 TRILINEAR CO - ORDINATES .
... ( - 1 ) + ( 1-1 ) x = bc α f + = The ( If + mg + nh ) . = lbc And from the values of q and r 1 cos A 9 r = 1 cos A b ( n a m cos A ) 1bc = a ( l cos B + m cos A – n ) lbc = 1 Similarly cos A = r 4 α l 20 TRILINEAR CO - ORDINATES .
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angular points asymptotes ax+bB+cy b₁ b₂ C₁ Cambridge centre Chap co-ordinates coefficients College common tangents conic section Crown 8vo determinant directrix Edition equation Fcap find the equation fixed point follows four points given conic given point given straight line Hence imaginary investigated Let the equation line at infinity line joining locus meets the conic nine-point circle numerous Illustrations obtain opposite sides Owens College pair parabola Pascal's Theorem perpendicular point f points of intersection pole Professor prove radical axis ratios rectangular hyperbola represented respect right angles second degree shewn similar and similarly sin POS tangents tangents drawn term a,b,c theorem three straight lines tion touches the line triangle of reference Ua² ux² V'ca v'f+u'g+wh va² values Vb² vß² W. K. CLIFFORD W'ab whence wy² λα