ABSTRACT
A moment’s reflection will show that many times quoted, or applied in thought, the axiom—Relations which are equal to the same relation are equal to each other, can never do anything else than establish the equality of some two relations by the intermediation of a series of relations severally equal to both: and there are few if any cases, save those furnished by algebraic and allied processes, in which the equality of two relations is the fact to be arrived at; or could be thus arrived at if it were. It will be deemed scarcely needful specifically to prove that each step in an algebraic argument is of the same nature. But though, by showing that the axiom—Relations which are equal to the same relation are equal to each other, twice involves an intuition, it may have been implied that the reasoning which proceeds upon that axiom, is built up of such intuitions.
