"small, tailed, salamander-like amphibian," early 15c., neute, newte, a misdivision of an ewte (see N for other examples), a variation of Middle English evete (see eft). "Eft, though now only provincial, is strictly the correct form" [Century Dictionary]. OED notes that "the change of v to w is unusual."
1650s, "advancement" (a sense now obsolete); 1868 in the philological sense "carrying of the final letter of a word into the next one" (as in newt), from Late Latin provectionem (nominative provectio) "advancement," noun of action from past-participle stem provehere "to carry forward," from pro "toward, ahead" (see pro-) + vehere "to carry" (from PIE root *wegh- "to go, move, transport in a vehicle"). Middle English had a verb provecten "to advance (someone), exalt" (mid-15c.), from Latin provectus, past participle of provehere.
mid-14c., salamandre, "legendary lizard-like creature supposed to live in fire," from Old French salamandre "legendary fiery beast," also "cricket" (12c.), from Latin salamandra, from Greek salamandra, a kind of lizard supposed to be an extinguisher of fire, a word probably of eastern origin or, as per Beekes, of Pre-Greek origin.
The application in zoology to a tailed amphibian (known commonly as an eft or newt, but these words are sometimes applied only to the water-salamanders), is recorded by 1610s. Aristotle, and especially Pliny, are responsible for the fiction of an animal that thrives in and extinguishes fires. The eft lives in damp logs and secretes a milky substance when threatened, but there is no obvious natural explanation for the myth. The word also was given as a name to a type of imaginary elemental of fire (1680s).
With some technical extensions to things used in connection with the fire or used when very hot (1660s). Also used 18c. for "a woman who lives chastely in the midst of temptations" (after Addison), and "a soldier who exposes himself to fire in battle." A salamander-stove (1842) was a small portable stove used to heat a room. To rub someone a salamander was a 19c. form of German student drinking toast (einem einen salamander reiben).
Related adjectives: Salamandrous (1711); salamandrine (1712); salamandroid (1854); salamandry (c. 1600).