An Elementary Treatise on Trilinear Co-ordinates: The Method of Reciprocal Polars, and the Theory of Projections |
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Page ix
... Terms of a Determinant 8 . 9 . 10 . 11 . Multiplication of a Determinant by a given Quantity Minors of a Determinant PAGE 59 · 60 • 65 · 66 • . 67 • 588 68 • ib . 69 71 Condition that a Quadratic Function may be resolvable into Two ...
... Terms of a Determinant 8 . 9 . 10 . 11 . Multiplication of a Determinant by a given Quantity Minors of a Determinant PAGE 59 · 60 • 65 · 66 • . 67 • 588 68 • ib . 69 71 Condition that a Quadratic Function may be resolvable into Two ...
Page 3
... ordinates , B and y for example , and this may be made homo- az + bB + cy geneous in a , B , y by multiplying each term by 2A " raised to a suitable power . Thus , the equation 1-2 AREA OF THE TRIANGLE OF REFERENCE . 3.
... ordinates , B and y for example , and this may be made homo- az + bB + cy geneous in a , B , y by multiplying each term by 2A " raised to a suitable power . Thus , the equation 1-2 AREA OF THE TRIANGLE OF REFERENCE . 3.
Page 4
... terms of their trilinear co - ordinates . 19 Let a ,, B1 , Y1 ; a ,, B , Y , be the co - ordinates of two given points , r the distance between them . Then , r2 will be a rational integral function of α- ɑ „ B1- B2 Y1 - Y2 , of the ...
... terms of their trilinear co - ordinates . 19 Let a ,, B1 , Y1 ; a ,, B , Y , be the co - ordinates of two given points , r the distance between them . Then , r2 will be a rational integral function of α- ɑ „ B1- B2 Y1 - Y2 , of the ...
Page 17
... terms , — and can only be admitted as a limiting form to which possi- ble equations may continually tend . 15. To find the equation of a straight line , drawn through a given point , parallel to a given straight line . Let ( 1 , m , n ) ...
... terms , — and can only be admitted as a limiting form to which possi- ble equations may continually tend . 15. To find the equation of a straight line , drawn through a given point , parallel to a given straight line . Let ( 1 , m , n ) ...
Page 25
... term harmonic is employed on account of the cir- cumstance , that if the points P , Q , R , S form what is above defined as an harmonic range , PR will be an harmonic mean between PQ and PS . For PQ . RSPS.QR ; -- .. PQ ( PS – PR ) = PS ...
... term harmonic is employed on account of the cir- cumstance , that if the points P , Q , R , S form what is above defined as an harmonic range , PR will be an harmonic mean between PQ and PS . For PQ . RSPS.QR ; -- .. PQ ( PS – PR ) = PS ...
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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