'On' is cousin to 'anatomy,' 'analysis,' and 'anarchy' — all from Greek 'ana' (up, upon), from PIE *h2eno-.
Physically in contact with and supported by a surface; indicating continuation of an action or state.
From Old English 'on' (on, upon, in, into, at, to), from Proto-Germanic *ana (on, upon), from PIE *h₂en- or *h₂eno- (on, upon). Related to but distinct from the 'in' preposition (*h₁en). Greek 'aná' (up, upon, throughout) and Gothic 'ana' (on, upon) are direct cognates. The word has been remarkably stable in form for thousands of years, though its range of meaning in Old English was considerably broader than in Modern English. Key
English 'on' and Greek 'aná' (up, upon) are cognates from PIE *h₂eno-. Greek 'aná' gave English 'anatomy' (cutting up), 'analysis' (loosening up, breaking apart), 'anabaptist' (baptizing again — upon a second time), and 'anarchy' (without a ruler on top). The humble preposition 'on' is cousin to the Greek prefix that dissects, dissolves, and overthrows.