mid-14c., coitidian, "daily, occurring or returning daily," from Old French cotidiien (Modern French quotidien), from Latin cottidianus, quotidianus "daily," from Latin quotus "how many? which in order or number?" (from PIE root *kwo-, stem of relative and interrogative pronouns) + dies "day" (from PIE root *dyeu- "to shine").
The qu- spelling in English dates from 16c. Meaning "ordinary, commonplace, trivial" is from mid-15c. Quotidian fever "intermittent fever" is from late 14c. The noun meaning "something that returns or is expected every day" is from c. 1400, originally of fevers.
Old English pyffan, *puffian "to blow with the mouth," of imitative origin. Compare pouf, from French. Especially "to blow with quick, intermittent blasts" (early 14c.). Meaning "pant, breathe hard and fast" is from late 14c.
The meaning "to fill, inflate, or expand with breath or air" is by 1530s. The intransitive sense, in reference to small swellings and round protuberances, is by 1725. The transitive figurative sense of "exalt" is from 1530s; shading by early 18c. into the meaning "praise with self-interest, give undue or servile praise to." Related: Puffed; puffing.
c. 1300, "coldness of an object to the touch, relative absence of heat," from cold (adj.). Meaning "sensation produced by loss of heat from the body or some part of it" is from c. 1200.
Sense of "indisposition involving catarrhal inflammation of the mucous membranes of the nose or throat" is from 1530s, so called because the symptoms resemble those of exposure to cold; compare cold (n.) in earlier senses "indisposition or disease caused by excessive exposure to cold" (early 14c.), "chills of intermittent fever" (late 14c.). To be left out in the cold in the figurative sense is from 1861.
1740, "unwholesome air, air contaminated with the poison producing intermittent and remittent fever," from Italian mal'aria, from mala aria, literally "bad air," from mala "bad" (fem. of malo, from Latin malus; see mal-) + aria "air" (see air (n.1)). Probably first used by Italian physician Francisco Torti (1658-1741). By 1866 it had come to be used of the disease itself (earlier malaria fever, by 1814). The disease, now known to be mosquito-borne, once was thought to be caused by foul air in marshy districts. Replaced native ague.
"having to do with the fourth," especially of attacks of an intermittent fever, etc., "occurring every fourth day" (by inclusive reckoning; now we would say every third day), early 14c., (feuer) quartain, from Old French (fievre) quartaine or cartaine and directly from Latin (febris) quartana, "quartan (fever)," fem. of quartanus "of or belonging to the fourth; of or occurring on the fourth day," from quartus "the fourth, fourth part" (related to quattuor "four," from PIE root *kwetwer- "four").
Also as a noun, "an ague or fever which recurs on the fourth (third) day," late 14c. Under inclusive reckoning, both days of consecutive occurrence are counted (if you have it on Wednesday and again on Saturday, the ancients would count that as "every four days").