sane

Sane is the adverb of sanus, "sound, healthy", so its oldest meaning is "soundly, sensibly" and everything else grows out of that. In practice it does three things: it affirms a statement, "certainly, to be sure"; it intensifies an adjective or an adverb, where the best English is often just "very"; and in dialogue it stands alone as agreement, "quite so", frequently as sane quidem.

Two details. With a negative it usually weakens rather than reverses, so non sane is "not really, hardly" rather than "certainly not". And it heads concessions - sane sit ita, "granted that it is so" - where the speaker gives ground before taking it back. English sane, sanity and sanitary come from the adjective, not the adverb.