An Elementary Treatise on Trilinear Co-ordinates: The Method of Reciprocal Polars, and the Theory of Projections |
From inside the book
Results 1-5 of 31
Page 5
... ( Y1 — Y1⁄2 ) cos A , ( B1 − B2 ) 2 + ( Y1 − Y2 ) 2 +2 ( ẞ1 − B2 ) ( Y1 − Y1⁄2 ) cos A sin2 A whence 2 a rational integral function of the second degree . - where l , m , n are certain functions of DISTANCE BETWEEN TWO POINTS . 5.
... ( Y1 — Y1⁄2 ) cos A , ( B1 − B2 ) 2 + ( Y1 − Y2 ) 2 +2 ( ẞ1 − B2 ) ( Y1 − Y1⁄2 ) cos A sin2 A whence 2 a rational integral function of the second degree . - where l , m , n are certain functions of DISTANCE BETWEEN TWO POINTS . 5.
Page 11
... whence Again , If + mg + nh = 0 , l ( a − f ) + m ( B − g ) + n ( y − h ) = 0 . ax + bB + cy = 2A , af + bg + ch = 2A ; :: a ( a − ƒ ) + b ( B − g ) + c ( y − h ) = 0 ; a - f B - g = .. bn - cm cl - an = y - h am - bl Hence , the ...
... whence Again , If + mg + nh = 0 , l ( a − f ) + m ( B − g ) + n ( y − h ) = 0 . ax + bB + cy = 2A , af + bg + ch = 2A ; :: a ( a − ƒ ) + b ( B − g ) + c ( y − h ) = 0 ; a - f B - g = .. bn - cm cl - an = y - h am - bl Hence , the ...
Page 12
... whence L Lf ' + Mg ' + Nh ' = 0 ; M N gh ' — g'h ̄ hƒ ' — h'ƒ ̄ ̄ ƒg ' — ƒ'g ' - - giving , as the equation of the required line , - - ( gh ' — g'h ) a + ( hf ' — h ' ƒ ) B + ( fg ' —ƒ'g ) y = 0 . 11. To find the general equation of a ...
... whence L Lf ' + Mg ' + Nh ' = 0 ; M N gh ' — g'h ̄ hƒ ' — h'ƒ ̄ ̄ ƒg ' — ƒ'g ' - - giving , as the equation of the required line , - - ( gh ' — g'h ) a + ( hf ' — h ' ƒ ) B + ( fg ' —ƒ'g ) y = 0 . 11. To find the general equation of a ...
Page 13
... λα , + μβ + v2 = 0 , λα , + μβ . + νγ = 0 , 3 whence , eliminating λ , μ , v , by cross multiplication , - the required condition . - = 13. To find the condition that three straight lines may THREE POINTS IN A STRAIGHT LINE . 13.
... λα , + μβ + v2 = 0 , λα , + μβ . + νγ = 0 , 3 whence , eliminating λ , μ , v , by cross multiplication , - the required condition . - = 13. To find the condition that three straight lines may THREE POINTS IN A STRAIGHT LINE . 13.
Page 16
... whence or gra bc b = 1 , qr с qr - q = m , b r = n ; bc m C bc α α . αν 012 = 1 - am bl Ъ - 9 = aq 1 = n τ ' an cl . It hence appears , that by making the ratios 7 : m : n suf- ficiently nearly equal to the ratios ab : c , the values of ...
... whence or gra bc b = 1 , qr с qr - q = m , b r = n ; bc m C bc α α . αν 012 = 1 - am bl Ъ - 9 = aq 1 = n τ ' an cl . It hence appears , that by making the ratios 7 : m : n suf- ficiently nearly equal to the ratios ab : c , the values of ...
Other editions - View all
Common terms and phrases
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