Sentence Examples

  • It may be written in the form n n-1 2 ax 1 +bx1 x2 +cx 1 x 2 + ...; or in the form n n n=1 n n-2 2 +(1)bx x2+ ?
  • May be a simultaneous invariant of a number of different forms az', bx 2, cx 3, ..., where n1, n 2, n3, ...
  • (III.) Again in (I.) transposing a x (bc) to the other side and squaring, we obtain 2(ac) (bc)axbx = (bc) 2 a'+(ac) 2 bx- (ab) 2 c1.
  • (ab)(ac)bxcx = - (ab)(bc)axcx = 2(ab)c x {(ac)bx-(bc)axi = 1(ab)2ci; so that the covariant of the quadratic on the left is half the product of the quadratic itself and its only invariant.
  • - We have seen that (ab) is a simultaneous invariant of the two different linear forms a x, bx, and we observe that (ab) is equivalent to where f =a x, 4)=b.

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