countenanceyoudaoicibaDictYouDict[countenance 词源字典]
countenance: [13] A person’s countenance has nothing to do with computation. Etymologically, it is how they ‘contain’ themselves, or conduct themselves, and the word itself is a parallel construction with continence. It was borrowed from Old French contenance (a derivative of the verb contenir ‘contain’), which meant ‘behaviour’, ‘demeanour’, or ‘calmness’ as well as ‘contents’, and originally had this somewhat abstract sense in English.

It was not until the 14th century that the meaning began to develop through ‘facial expression’ to the now familiar ‘face’ (traces of the original sense survive in such expressions as ‘put someone out of countenance’, meaning to make them lose their cool).
=> contain, continence[countenance etymology, countenance origin, 英语词源]
countenance (v.)youdaoicibaDictYouDict
late 15c., "to behave or act," from countenance (n.). Sense of "to favor, patronize" is from 1560s, from notion of "to look upon with sanction or smiles." Related: Countenanced; countenancing.
countenance (n.)youdaoicibaDictYouDict
mid-13c., from Old French contenance "demeanor, bearing, conduct," from Latin continentia "restraint, abstemiousness, moderation," literally "way one contains oneself," from continentem, present participle of continere (see contain). Meaning evolving Middle English from "appearance" to "facial expression betraying a state of mind," to "face" itself (late 14c.).