symmetry (n.)

1560s, "relation of parts, proportion," a sense now obsolete, from French symmétrie (16c.) and directly from Latin symmetria, from Greek symmetria "agreement in dimensions, due proportion, arrangement," from symmetros "having a common measure, even, proportionate." This is from assimilated form of syn- "together" (see syn-) + metron "measure" (from PIE root *me- (2) "to measure").

The meaning "a due, just, or harmonic arrangement of parts" is attested by 1590s, especially in reference to the proper proportion and commensurability of the parts of the human body, according to a canon, hence "beauty of form."

The scientific sense of "metrical correspondence and mirror image of parts in reference to a median plane" is by 1823 in botany, zoology, etc.