Let the determinant of the b's be Ab and B rs, the minor corresponding to b rs .
We write;L 22 = a 1 a 2 .b 1 n-2 b2s 3 n - 3 3 n-3 3 n-3 3 a 3 = a 1 a 2 .b 1 b 2 .c 1 c2, and so on whenever we require to represent a product of real coefficients symbolically; we then have a one-to-one correspondence between the products of real coefficients and their symbolic forms. If we have a function of degree s in the coefficients, we may select any s sets of umbrae for use, and having made a selection we may when only one quantic is under consideration at any time permute the sets of umbrae in any manner without altering the real significance of the symbolism.
The words introducing this form (6Tav bE TO '&TL Tptrov irpoo-KaTnyopijTac, chap. so, s 9 b s 9), which are the origin of the phrase tertii adjacentis, disengage the verb of being (g un) partially but not entirely, because they still treat it as an extra part of the predicate, and not as a distinct copula.
Suppose B not to be fixed, but to be capable of moving against some third body C (which might, e.g., contain cylindrical bearings, if B were a drum with its shaft), itself fixed, - and further, suppose the frictional resistance between B and C to be the only resistance to B's motion.
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