An Elementary Treatise on Trilinear Co-ordinates: The Method of Reciprocal Polars, and the Theory Projections |
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Page ix
... Terms of a Determinant 65 8 . Sign changed by interchange of Two Consecutive Lines or Columns 9 . Multiplication of a Determinant by a given Quantity 10 . Minors of a Determinant 83865 66 67 11 . Condition that a Quadratic Function may ...
... Terms of a Determinant 65 8 . Sign changed by interchange of Two Consecutive Lines or Columns 9 . Multiplication of a Determinant by a given Quantity 10 . Minors of a Determinant 83865 66 67 11 . Condition that a Quadratic Function may ...
Page 3
... ordinates , B and y for example , and this may be made homo- aa + bB + cy geneous in a , ẞ , y by multiplying each term by 24 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- aa + bB + cy geneous in a , ẞ , y by multiplying each term by 24 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 2 ' Let a ,, B1 , Y1 ; α , B , Y , be the co - ordinates of two given points , r the distance between them . -- Then , 2 will be a rational integral function of ɑ , — ɑ¿ B1 — B2 Y1 - Y2 , of ...
... terms of their trilinear co - ordinates . 19 2 ' Let a ,, B1 , Y1 ; α , B , Y , be the co - ordinates of two given points , r the distance between them . -- Then , 2 will be a rational integral function of ɑ , — ɑ¿ B1 — B2 Y1 - Y2 , of ...
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 . 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
aa+bB+cy angular points asymptotes auxiliary conic b₁ Brianchon's Theorem C₁ centre Chap chord co-ordinates coefficients common tangents conic passing conic section determinant directrix find the equation fixed point fixed straight line focus follows four points given conic given point given straight line Hence imaginary internal bisectors investigated Let the equation line at infinity locus meets the conic nine-point circle obtain opposite sides pair parabola Pascal's Theorem perpendicular point f point of intersection points at infinity points of contact polar reciprocal projection prove radical axis reciprocal curve reciprocated with respect rectangular hyperbola represented right angles second degree similar and similarly system of conics tangents drawn theorem three points three straight lines triangle of reference ua² uf+w'g+v'h Vb² vß² W'ab Wc² whence wy²