per

"per" takes the ACCUSATIVE. Physically it is motion through something ("per silvam", through the wood); extended to time it means right through a stretch of it ("per totam noctem", all night long); extended to means it gives the instrument or intermediary, "by" or "by means of".

Keep that last sense apart from the "by" of a passive verb. The person who performs a passive action is "a" or "ab" plus the ablative, so a letter written by Caesar is "a Caesare", while a message sent by letter is "per litteras". "per" is also the source of the English prefix in "perfect" and "perform", where it intensifies rather than points anywhere.