early 15c., in pathology, "excessive redness or swelling in a body part," from Old French inflammation (14c.) and directly from Latin inflammationem (nominative inflammatio) "a kindling, a setting on fire," noun of action from past participle stem of inflammare "to set on fire" (see inflame). Literal sense "act of setting on fire" in English is from 1560s.
1726, in on the qui vive "on the alert," from French être sur le qui vive "be on the alert," from the phrase qui voulez-vous qui vive? sentinel's challenge, "whom do you wish to live?" In other words "(long) live who?" meaning "whose side are you on?" (The answer might be Vive la France, Vive le roi, etc.). From qui (from Latin qui "who") + vive, third person singular present subjunctive of vivre, from Latin vivere "to live" (see viva).
"account, bill, check," 1888, American English colloquial, probably a shortened form of tabulation or of tablet in the sense "a sheet for writing on." Figurative phrase keep a tab on is recorded from 1890.
1610s, "one who rigs ships," agent noun from rig (v.). Extended to one who works on aircraft by 1912; sense of "one who works on an oil rig" is by 1949.
1640s, from Medieval Latin *infinitudo, from Latin infinitus (see infinite) on model of multitudo, magnitudo. Or the English word is perhaps from or modeled on French infinitude (1610s).