A of C_.

This may pass; but it is not a parallel argument that if _A is north of B and B west of C_, then _A is north-west of C_: for suppose that A is a mile to the north of B, and B a yard to the west of C, then A is practically north of C; at least, its westward position cannot be expressed in terms of the mariner's compass.

In such a case we require to know not only the directions but the distances of A and C from B; and then the exact direction of A from C is an affair of mathematical calculation.
Qualitative reasoning concerning position is only applicable to things in one dimension of space, or in time considered as having one dimension.

Under these conditions we may frame the following generalisation concerning all Mediate Inferences: Two terms definitely related to a third, and one of them positively, are related to one another as the other term is related to the third (that is, positively or negatively); provided that the relations given are of the same kind (that is, of Time, or Coinherence, or Likeness, or Equality).
Thus, to illustrate by relations of Time-- B is simultaneous with C; A is not simultaneous with B: .'.

A is not simultaneous with C.
Here the relations are of the same kind but of different logical quality, and (as in the syllogism) a negative copula in the premises leads to a negative conclusion.
An examination in detail of particular cases would show that the above generalisation concerning all Mediate Inferences is subject to too many qualifications to be called an Axiom; it stands to the real Axioms (the _Dictum_, etc.) as the notion of the Uniformity of Nature does to the definite principles of natural order (_cf._ chap.xiii.Sec.