1630s, "words used in a ceremony or ritual" (earlier as a Latin word in English), from Latin formula "form, draft, contract, regulation;" in law, "a rule, method;" literally "small form," diminutive of forma "form" (see form (n.)). Modern sense is colored by Carlyle's use (1837) of the word in a sense of "rule slavishly followed without understanding" [OED]. From 1706 as "a prescription, a recipe;" mathematical use is from 1796; chemistry sense is from 1842. In motor racing, "class or specification of a car" (usually by engine size), 1927.
-ic
Middle English -ik, -ick, word-forming element making adjectives, "having to do with, having the nature of, being, made of, caused by, similar to," from French -ique and directly from Latin -icus or from cognate Greek -ikos "in the manner of; pertaining to." From PIE adjective suffix *-(i)ko, which also yielded Slavic -isku, adjectival suffix indicating origin, the source of the -sky (Russian -skii) in many surnames. In chemistry, indicating a higher valence than names in -ous (first in benzoic, 1791).
In Middle English and after often spelled -ick, -ike, -ique. Variant forms in -ick (critick, ethick) were common in early Modern English and survived in English dictionaries into early 19c. This spelling was supported by Johnson but opposed by Webster, who prevailed.