late 14c., "pertaining to form or arrangement;" also, in philosophy and theology, "pertaining to the form or essence of a thing," from Old French formal, formel "formal, constituent" (13c.) and directly from Latin formalis, from forma "a form, figure, shape" (see form (n.)). From early 15c. as "in due or proper form, according to recognized form," As a noun, c. 1600 (plural) "things that are formal;" as a short way to say formal dance, recorded by 1906 among U.S. college students.
Japanese art of formal flower arrangement, 1901, from Japanese, from ikeru "to keep alive, arrange" + hana "flower."
formal term of address to a lady, 1590s, see madam, which is an earlier borrowing of the same French phrase. Originally a title of respect for a woman of rank, now given to any married woman. It is more formal or affected than madam. OED recommends madam as an English title, madame in reference to foreign women.
early 14c., "a quarrel, dispute, disagreement" (now archaic), from Old French debat, from debatre(see debate (v.)). Sense of "contention by argument" is from late 14c., that of "a formal dispute, a debating contest, interchange of arguments in a somewhat formal manner" is perhaps from early 15c.