Over in merry old England 1800 would be the heart of the industrial revolution, and in the north, that means textiles. Since the spinning mule came about in 1779, I’d take one of these.
As well as a book illustrating how to use the thing. I’d be very wealthy very quickly.
I would take a Poloroid camera, if film counts as a “part” of which I have an endless supply. In New York City in the 1800s, I bet I could make a comfortable living taking Poloroid portraits.
Also, to mess with history, I would strictly caution all my customers that you must NEVER shake a Poloroid while it is developing, but rather hold it completely still. Take that, Outkast!
I’m also going to print out and bring a copy of this thread, so I can find all you Dopers with your machines in 1800. Perhaps the US Army could take out a single tank, but could they take out a tank and a Poloroid camera? Well, yes, probably. But you see my point. Nevermind dictatorship, I think oligarchy is the ticket for world domination in 1800.
In a Numerical Analysis class in grad school, I saw a video entitled, “What If Kepler Had a Computer”.
The video postulated that it would have hurt his work rather than helped: recall that planetary orbits were thought by many to be circular. Kepler eventually showed they were elliptical. But a computer would have allowed him to substitute number crunching for visualizing, essentially papering over the differences between the circular and elliptical models, and to falsely conclude that the orbits were circular.
I think a helicopter is much better than a tank if you want to take over the world. A tank will eventually get surrounded and led into a pit of some sort.
However, if you ally yourself with a preexisting military power, and are able to keep the helicopter secret from outsiders, and fly only at night, you should EASILY be able to conquer the world via occasional attacks deep behind enemy lines. And it will be made all the scarier by the fact that no one will have any idea what the heck is going on.