I must be missing something very fundamental here, so bear with me. On the first gearbox he showcases, the one that multiples by 5/19's, I don't understand how you can combine a set of gears that multiples by 5, with another set that multiples by 3/5 to get 19/5s.
19 appears to be prime, so I don't see how any combination of multiplying/dividing 5's and 3's could results in any number divisible by 19. Does the differential itself have a ratio of teeth of 19/15 (53/519/15 = 19/5?) or is there another key piece I'm missing?
Otherwise, very impressive. I love it.