E. Cobham Brewer 18101897. Dictionary of Phrase and Fable. 1898.
means a stair (Greek), applied to the last of a gradation of arguments, each of which is stronger than the preceding. The last of a gradation of words of a similar character is also called a climax. The point of highest development.
In the very climax of his career he was stricken down.Chittenden: Recollections of Lincoln. chap. xlv. p. 454.