insane adj.

word-forming element meaning "not, opposite of, without" (also im-, il-, ir- by assimilation of -n- with following consonant, a tendency which began in later Latin), from Latin in- "not," cognate with Greek an-, Old English un-, all from PIE root *ne- "not."

In Old French and Middle English often en-, but most of these forms have not survived in Modern English, and the few that do (enemy, for instance) no longer are felt as negative. The rule of thumb in English has been to use in- with obviously Latin elements, un- with native or nativized ones.

"of sound mind, mentally sound," 1721, a back-formation from insane or sanity or else from Latin sanus "sound, healthy," in its figurative or transferred use, "of sound mind, rational, sane," also, of style, "correct;" a word of uncertain origin.

It is perhaps from PIE *seh-no- from *seh- "to tie." That reconstruction "is purely mechanical," according to de Vaan, the meaning might be "which is in place, in order." Or it could be from a different root meaning "to satisfy" as in Latin satis "enough."

Used earlier, of the body, with a sense of "healthy" (1620s), but this has been rare in English. OED writes, "The almost entire restriction in English to a sense 'mentally sound' is due to the use in antithesis with insane, which (like the Latin insanus, its source) always referred to mental condition." Related: Sanely; saneness.