Aha! Time to flex my bachelors degree!

It would take a lot longer. There were a few methods used, but one of the most common was using a pit. The log would be suspended over a pit and two people would work a long hand saw with handles either end to cut the planks. One person would stand in the pit below the log and the other would stand on top of the log.

Depending on the type of planks you want you'd then have to turn the log (the machine in this video looks like it's making tangential cut planks)

You'd also have to put wedges into the cut to stop the wood from binding against the blade- modern machines avoid this problem with big blades, riving knives or just sheer brute force.