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 65 8 . Sign changed by interchange of Two Consecutive Lines or Co- lumns 9 . Multiplication of a Determinant by a given Quantity • 10 . 11 . Minors of a Determinant Condition that a Quadratic Function may be ...
... Terms of a Determinant 65 8 . Sign changed by interchange of Two Consecutive Lines or Co- lumns 9 . Multiplication of a Determinant by a given Quantity • 10 . 11 . Minors of a Determinant Condition that a Quadratic Function may be ...
Page 3
... ordinates , B and y for example , and this may be made homo- ax + 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- ax + 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 a1 , B1 , Y1 ; α , B2 Y2 , be the co - ordinates of two given points , r the distance between them . Then , will be a rational integral function of a , -a , B1 - B2 Y12 , of the second ...
... terms of their trilinear co - ordinates . 19 Let a1 , B1 , Y1 ; α , B2 Y2 , be the co - ordinates of two given points , r the distance between them . Then , will be a rational integral function of a , -a , B1 - B2 Y12 , of the second ...
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 ( l , 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 ( l , 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.RS PS.QR ; - = - .. PQ ( PS – PR ) ...
... 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.RS PS.QR ; - = - .. PQ ( PS – PR ) ...
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Common terms and phrases
angular points anharmonic ratio asymptotes auxiliary conic b₁ b₂ C₁ centre Chap chord co-ordinates coefficients common tangents conic section determinant directrix find the equation fixed point fixed straight line follows four points given conic given point given straight line given triangle Hence investigated Let the equation line at infinity line joining locus meets the conic nine-point circle obtain opposite sides parabola Pascal's Theorem perpendicular point f points at infinity points of contact points of intersection PQRS prove radical axis reciprocal curve reciprocated with respect rectangular hyperbola represented right angles second degree shewn similar and similarly sin POS tangents drawn term a,b,c theorem three points three straight lines triangle of reference ua² uf+w'g+v'h ux² V'ca va² Vb² vß² W'ab whence wy² λα