Sentence Examples

  • If we solve the equations connecting the original and transformed unbrae we find (A �) (- a 2) =A i( - A 2) + �'1A1, (A �) a1 = A2(- A2)+�2A1, and we find that, except for the factor (A /), -a 2 and +ai are trans formed to -A 2 and +A i by the same substitutions as x i and x 2 are transformed to i and E2.
  • In the extensive calculus of the nth category, we have, first of all, n independent " units," el, e2, ...
  • We can eliminate the quantities S l, E2, ��� In and obtain n relations AbXi = (2B 11 - Ab)'�k1 +2B21x2+2B31x3+���, AbX2 = 2B12x1+ (2B22 - Ab) x2 +2B32x3+..., and from these another equivalent set Abx1 = (2B11 - X1 +2B12X2+2B13X3+���, Abx2 = 2B21X1+(2B22 - Ab)X2+2B23X3+���, and now writing 2Bii - Ab 2Bik - aii, Ob = aik, Ob we have a transformation which is orthogonal, because EX 2 = Ex2 and the elements aii, a ik are functions of the 2n(n- I) independent quantities b.
  • By assuming the truth of the associative law of multiplication, and taking account of the reducing formulae for binary products, - 'el ' 'e2 ' 'e3 we may construct derived units of the third, fourth ...
  • Siace E2 + if + ~1, or ef, is necessarily an absolute invariant for all transformations of the (rectangular) co-ordinate axes, we infer that XE + un + v~ is also an absolute invariant.

Words near E-2 in the dictionary