Babbage Was a True Genius (2006)
tomforsyth1000.github.io
tomforsyth1000.github.io
The article says that his engine "would have done it far better than the existing mechanisms (a room full of people adding stuff manually)." I seem to recall, though, that a bunch of people adding stuff up wasn't the only approach. I think a lot of mechanical (i.e. analogue) devices were used to perform computation (e.g. tide prediction machine https://www.youtube.com/watch?v=uFhjGlriDYE). Like a lot of tech, there was a cross-over period in which machines were quite competitive with digital devices, until the new tech eventually held sway.
Here's on on a differential analyser: https://www.youtube.com/watch?v=LqTL2JBETzE. You can basically solve differential equations using a series of pulleys and gears.
But it's actually decent content. It's an overview of how Babbage's Analytical Engine was intended to function. The implementation problem was that what Babbage wanted was way way way over-designed. E.g. 50 decimal digit arithmetic.
You know who are true geniuses in my book? The guys who wrote this: https://en.wikipedia.org/wiki/Altair_BASIC
They started a trillion dollar company because they were smart enough to write a program that actually worked, that turned 1970s hardware into something that was useful to a lot of people.