Investigate

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early 16th century: from Latin investigat- ‘traced out’, from the verb investigare, from in- ‘into’ + vestigare ‘track, trace out’.

wiktionary

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Recorded since circa 1510, a Back-formation from investigation., from Latin investīgātiō(“a searching into”), from investīgātus, the past participle of investigare, equivalent to in- +‎ vestigate.

etymonline

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investigate (v.)

c. 1500, back-formation from investigation or else from Latin investigatus, past participle of investigare "to trace out, search after," figuratively "search into, investigate," from in- "in, into" (from PIE root *en "in") + vestigare "to track, trace," from vestigium "footprint, track" (see vestige). Related: Investigated; investigating.