Both Uses of

acknowledge
in
All's Well That Ends Well, by Shakespeare

Nay, 'tis strange, 'tis very strange; that is the brief and the tedious of it; and he's of a most facinerious spirit that will not acknowledge it to be the,— LAFEU.†
Scene 2.3 *

acknowledge = recognize

The great prerogative and right of love, Which, as your due, time claims, he does acknowledge; But puts it off to a compell'd restraint; Whose want, and whose delay, is strew'd with sweets; Which they distil now in the curbed time, To make the coming hour o'erflow with joy And pleasure drown the brim.†
Scene 2.4

Definitions:

(1) (acknowledge as in: acknowledge her or the truth)
express recognition or appreciation of someone or something; or admit something
(2) (meaning too rare to warrant focus)
meaning too rare to warrant focus:

Specialized senses include sending an "acknowledgement" (letter or other message) to indicate that something was received and the "acknowledgements" section at the beginning of a book where an author recognizes and thanks other people who helped in creating the book or ideas contained in it.