"inner membrane of a calf's fourth stomach," c. 1400, probably from an unrecorded Old English *rynet, related to gerennan "cause to run together," because it makes milk run or curdle; from Proto-Germanic *rannijanan, causative of *renwanan "to run" (from PIE root *rei- "to run, flow"). Compare German rinnen "to run," gerinnen "to curdle."
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