An Elementary Treatise on Trilinear Co-ordinates: The Method of Reciprocal Polars, and the Theory of Projections |
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Page 6
... expression for . It may also be proved in a similar manner that p2 = = abc 442 { a cos △ ( α , − a ) 2 + b cos B ( ß ̧ — ß2 ) ? - - + ccos C ' ( y , -Y , ) ' } . 4. We next proceed to investigate the equation of a straight line ; and ...
... expression for . It may also be proved in a similar manner that p2 = = abc 442 { a cos △ ( α , − a ) 2 + b cos B ( ß ̧ — ß2 ) ? - - + ccos C ' ( y , -Y , ) ' } . 4. We next proceed to investigate the equation of a straight line ; and ...
Page 16
... expression of the fact that the two equations la + mB + ny = 0 , l'a + m'B + n'y = 0 , cannot be simultaneously satisfied by any values of a , B , y , or , in other words , that the two straight lines represented by them do not ...
... expression of the fact that the two equations la + mB + ny = 0 , l'a + m'B + n'y = 0 , cannot be simultaneously satisfied by any values of a , B , y , or , in other words , that the two straight lines represented by them do not ...
Page 17
... expressed by saying that the equation ax + bB + cy = 0 , or the equivalent equation a sin A + ẞ sin B + y sin C = 0 , represents the straight line at infinity . This phraseology is very convenient , and free from objec- tion , if the ...
... expressed by saying that the equation ax + bB + cy = 0 , or the equivalent equation a sin A + ẞ sin B + y sin C = 0 , represents the straight line at infinity . This phraseology is very convenient , and free from objec- tion , if the ...
Page 21
... expression . - It will be observed , that the numerator of this expression . vanishes if the point ( f , g , h ) lie upon the line ( l , m , n ) , as manifestly ought to be the case . It will also be remarked , that the more nearly the ...
... expression . - It will be observed , that the numerator of this expression . vanishes if the point ( f , g , h ) lie upon the line ( l , m , n ) , as manifestly ought to be the case . It will also be remarked , that the more nearly the ...
Page 23
... expressed by the notation { O. PQRS } * . DEF . 2. If P , Q , R , S be four points in a straight line , PQ.RS is called the anharmonic ratio of the range the ratio PS . QR P , Q , R , S , and may be expressed thus [ PQRS ] . n using ...
... expressed by the notation { O. PQRS } * . DEF . 2. If P , Q , R , S be four points in a straight line , PQ.RS is called the anharmonic ratio of the range the ratio PS . QR P , Q , R , S , and may be expressed thus [ PQRS ] . n using ...
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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