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.
Source: Dictionary of Phrase and Fable, E. Cobham Brewer, 1894