ad infinitum

Restoration satirist Jonathan Swift, who lived in an age fascinated by the discoveries of the microscope, is to thank for a favorite example of the phrase. In On Poetry: A Rhapsody, he writes:

So, naturalists observe, a flea
Has smaller fleas that on him prey;
And these have smaller still to bite 'em;
And so proceed ad infinitum.

Ad in`fi*ni"tum (#). [L., to infinity.]

Without limit; endlessly.

© Webster 1913.