Old English fang "prey, spoils, plunder, booty; a seizing or taking," from gefangen, strong past participle of fon "seize, take, capture," from Proto-Germanic *fāhanan (source also of Old Frisian fangia, Middle Dutch and Dutch vangen, Old Norse fanga, German fangen, Gothic fahan), from nasalized form of PIE root *pag- "to fasten" (source also of Latin pax "peace").
The sense of "canine tooth" (1550s) was not in Middle English and probably developed from Old English fengtoð, literally "catching- or grasping-tooth." Compare German Fangzahn. Transferred to the venom tooth of a serpent, etc., by 1800.
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