There are a lot of prepositions and prepositional phrases, so I’m only going over the ones that I don’t think I’ll go over in another post. And there’s still a lot to go over, so this is going to be a two parter. Now let’s go!
A…the article and the preposition, not the letter, showed up in the mid twelfth century, coming from the Old English an. And yes, that’s where an comes from, although it used to have a long vowel sound, making it more like ain, I guess. Anyway, an actually meant one in Old English (also, where we got one from, although that’s a story for another day) and it can be traced to the Proto Germanic ainaz and Proto Indo European oi-no, one. As for why people dropped the N before consonants…who knows why they do anything?
At comes from the Old English æt, which, of course, comes from the Proto Germanic at. Sometimes, language, I don’t know why you even bother. Anyway, before that it’s from the Proto Indo European ad, which is where we get the prefix ad- from. Except by way of classical Latin, not Proto Germanic, because of course.
By comes from the Old English be/bi, roughly meaning what we know it as. Before that, it was the Proto Germanic bi, around or about, and even further back, the Proto Indo European umbi, which just happens to be where the prefix ambi- comes from, although again, by way of Latin. I guess we get our prepositions from Germanic and our prefixes from Latin.
Often confused word than comes from the Old English Þan—Þ is thorn, a forgotten letter. It’s pronounced like the th in math, making this word just than. Apparently the reason it looks so much like then is because it Þan comes from Þanne, which is then in Old English. Þanne can be traced further back to the Proto Germanic thana, a descendant of the Proto Indo European to.
Tony Jebson’s page on the Origins of Old English