From PIE *h2embhi (around) — cousin of Latin 'ambi-' and Greek 'amphi-,' all about surrounding and encirclement.
Indicating proximity, the agent of an action, the means of achieving something, or a deadline.
From Old English 'bī, bīg' (by, near, beside, about, around), from Proto-Germanic *bi (around, about, near), from PIE *h₂embʰi (around, on both sides). The same root produced Latin 'ambi-' (around, on both sides), Greek 'amphí' (around, on both sides), and the English prefix 'be-.' The original sense was 'around,' which narrowed to 'near, beside,' and
'By,' 'be-' (as in become, believe, below), Latin 'ambi-' (as in ambidextrous, ambiguous, ambient), and Greek 'amphi-' (as in amphitheater, amphibian) all come from PIE *h₂embʰi (around, on both sides). An amphitheater is a 'theater on both sides' — a theater with seating all around — and it shares a root with the humble English preposition 'by.'