The verb exhaust first started showing up in English in the mid-sixteenth century, with pretty much the same definition as today. It's borrowed from Latin exhaustus, which is the past principle of the verb exhaurire, meaning "to draw off" or "to use up". That's composed of the prefix ex-, meaning "out", and the root haurire, meaning "to draw up" (as in water) or "take out". More figuratively, it could mean "remove", and that's how we got the sense of exhaust being something that's pushed away rather than pulled toward, despite the Romans maybe having a different conceptualization of the word. Finally, haurire comes, through Proto-Italic auzjo, from the Proto-Indo-European reconstruction hews, meaning "east" or "dawn", with the connection being the notion of the sun being drawn upwards.
Hello! I'm Adam Aleksic. This year, I graduated from Harvard University with a degree in Government and Linguistics. There, I co-founded the Harvard Undergraduate Linguistics Society and wrote a thesis on Serbo-Croatian language policy, magna cum laude. In addition to etymology, I also really enjoy philosophy, trivia, vexillology, geography, board games, conlanging, art history, and law.