For this reason the umbrae -a 2, a l are said to be cogredient to 5 1 and x 2.
We frequently meet with cogredient and contragedient quantities, and we have in general the following definitions:-(i) " If two equally numerous sets of quantities x, y, z,...
By the same scheme of linear substitution the two sets are said to be cogredient quantities."
(I.) Introduce now new umbrae dl, d 2 and recall that +d 2 -d 1 are cogredient with x, and x 2.
We may in any relation substitute for any pair of quantities any other cogredient pair so that writing -}-d 2, -d l for x 1 and x 2, and noting that gx then becomes (gd), the above-written identity bceomes (ad)(bc)+(bd)(ca)+(cd)(ab) = 0.