Any Corollary (as I shall use the term) would be a proposition deduced directly from propositions already established without the use of any other construction than one necessarily suggested in apprehending the enunciation of the proposition; and any such proposition would be a Corollary.

A corollary, as I shall use the word, is an inference drawn in general terms without the use of any construction.

I shall term the step of so introducing into a demonstration a new idea not explicitly or directly contained in the premisses of the reasoning or in the condition of the proposition which gets proved by the aid of this introduction, a theoric step. [—] Now to propositions which can only be proved by the aid of theoric steps (or which, at any rate, could hardly otherwise be proved), I propose to restrict the application of the hitherto vague word “theorem,” calling all others, which are deducible from their premisses by the general principles of logic, by the name of corollaries.