Today's "antipyretic" derives, ultimately from Greek "pur" or fire. (This, on authority the Wordsmith email). I wondered if "pure" also derived from "pur." A Sherlock (Mac) search yields the result, from Dictionary.com, that it *may*:

\Pure\, a. [Compar. Purer; superl. Purest.] [OE. pur, F. pur, fr. L. purus; akin to putus pure, clear, putare to clean, trim, prune, set in order, settle, reckon, consider, think, Skr. p? to clean, and perh. E. fire. Cf. Putative.] 1. Separate from all heterogeneous or extraneous matter; free from mixture or combination; clean; mere; simple; unmixed; as, pure water; pure clay; pure air; pure compassion.

I wonder if this is from an obsolete concept of combustion.

I also wondered if "putus," nearer the top of this definition, is related to the Spanish "puta" and, if so, why.