The preposition 'by' is a versatile and high-frequency word in English, expressing proximity ('stand by me'), agency ('painted by Rembrandt'), means ('travel by train'), and deadline ('finished by Friday'). This semantic range descends from a single ancient concept: 'around, on both sides.'
The word comes from Old English 'bī' or 'bīg' (by, near, beside, about, around), from Proto-Germanic *bi (around, about, near), from PIE *h₂embʰi (around, on both sides). The loss of the initial vowel and the medial *-mbʰ- cluster in the Germanic branch is regular: PIE *h₂embʰi simplified to *bi through a series of well-attested sound changes.
The PIE root *h₂embʰi produced striking cognates in the classical languages. Latin 'ambi-' (around, on both sides) gave English 'ambidextrous' (using both hands — literally 'right-handed on both sides'), 'ambiguous' (driving on both sides — going two ways), 'ambient' (going around), 'ambition' (a going around — originally canvassing for votes in Rome), and 'ambulance' (a walking-around — originally a mobile field hospital). Greek 'amphí' (ἀμφί, around, on both sides) gave 'amphitheater' (a theater with seating on both sides, all around), 'amphibian' (living on both sides — land and water), 'amphora' (a vessel with handles on both sides), and 'amphibology' (an ambiguity — a meaning that goes both ways).
Within English, the prefix 'be-' is the unstressed form of 'by,' and it appears in dozens of common words. 'Become' is 'by-come' (to come around to a state). 'Before' is 'by-fore' (in front, around the front). 'Behind' is 'by-hind' (at the back). 'Below' is 'by-low.' 'Between' is 'by-twain' (by the two, in the space around two things). 'Believe' descends from Old
The compound 'bylaw' preserves a different etymology: the 'by-' in 'bylaw' is from Old Norse 'bȳr' (settlement, town), not from the preposition 'by.' A bylaw is a town-law, a local regulation. However, compounds like 'bystander' (one standing by), 'bypass' (a way going by), 'bygone' (gone by, past), and 'by-product' (a product produced alongside the main one) all use the preposition 'by' in its proximity sense.
German 'bei' (by, at, near) and Dutch 'bij' (at, near, by) are the direct cognates, preserving the spatial proximity sense. The agentive use of 'by' in passive constructions ('the book was written by her') developed in Middle English and represents an extension of the proximity sense: the agent is conceptualized as standing 'beside' the action.