Sentence Examples

  • It will be observed that in the first process the value of the modulus is in fact calculated from the formula.
  • For the substitution rr xl =A 11 +1 2 12, 52=A21+�2E2, of modulus A1 �i = (Al�.2-A2�1) = (AM), A 2 �2 the quadratic form a k xi -1-2a 1 x i x 2 +a 2 4 = x =f (x), becomes A41 +2A1E16 =At = OW, where Ao = aoA i +2a1AiA2 +a2Az, _ _ A 1 = ao A l�l +ai(A1/.22+A2�1) +7,2X2/22, A2 = ao�l +2a1�1/�2 +a 2�2 � We pass to the symbolic forms a:= (aixi+a2x2) 2, A 2 = (A 151+ A 26) 2/ by writing for ao, al, a2 the symbols ai, a 1 a 2, a?
  • = (A11+A22)n by the substitutions 51 = A l, E1+�1 2, 52 = A2E1+�2E2, the umbrae Al, A2 are expressed in terms of the umbrae al, a 2 by the formulae A l = Alai +A2a2, A2 = �la1 +�2a2� We gather that A1, A2 are transformed to a l, a 2 in such wise that the determinant of transformation reads by rows as the original determinant reads by columns, and that the modulus of the transformation is, as before, (A / .c).
  • If u, a quantic in x, y, z, ..., be expressed in terms of new variables X, Y, Z ...; and if, n,, ..., be quantities contragredient to x, y, z, ...; there are found to exist functions of, n, ?, ..., and of the coefficients in u, which need, at most, be multiplied by powers of the modulus to be made equal to the same functions of E, H, Z, ...
  • The transformation to the normal form, by the solution of a cubic and a quadratic, therefore, supplies a solution of the quartic. If (X�) is the modulus of the transformation by which a2 is reduced to 3 the normal form, i becomes (X /2) 4 i, and j, (Ap) 3 j; hence?

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