Yours, Etc.: Origins and Uses of 8 Sign-Offs
mid-14c., "lying face-down" (in submission, worship, etc.), from Latin prostratus, past participle of prosternere "strew in front, throw down," from pro- "forth" (see pro-) + sternere "to spread out," from PIE root *stere- "to spread, extend, stretch out" (see structure (n.)). Figurative use from 1590s. General sense of "laid out, knocked flat" is from 1670s.
early 15c., prostraten, "prostrate oneself," from prostrate (adj.). Related: Prostrated; prostrating.