I wonder why he cut gear teeth with a triangular file. As long as he was using a lathe and drill press, I mean. Is it just that gear cutting requires nonstandard machine tools?
He's trying to do at least one example of each type of required task with tools that would have been available at the time. Most of the gears were actually cut with a gear cutter (consisting of an electronic indexer on the headstock of a mini lathe and some Sherline lathe parts mounted on the mini lathe's cross slide, using a homemade 60° D-bit). That has included making (and using) a pump drill with various flywheels he's made from bronze he alloyed and cast himself, making drill bits and files from iron, which were then case-hardened (because steel, as such, wasn't a thing back then), along with various other plausible tools. The only place he hasn't gone is making a lathe, for which there is ample documentary evidence (by the standards of "ample" in documents from antiquity).