It took no fewer than sixteen turns after the Mongols built Newton's for Greece and Egypt to finally get ToG, but the waiting did pay off as I then bought Magnetism @5th and resold it for ToG and Mil Trad in a three-fer, then pulled a two-fer between Steam Power and Democracy. I revolted, as the worker speed would be quite important to building as many rails as I could on one coal and iron purchase.
Naturally, we don't have any coal. And nobody has any available for sale. That is of course because there are spots like this, where nobody has the coal hooked up:
So I started a crazy plan, sending out a boat with an MDI or two to clear barbarians, and some workers to try to colonize that tile and build roads from it to somebody's harbor. That harbor would have to be Egypt to the south, since the cities adjacent to the coal in the other direction didn't have harbors.
There was one problem with that plan, though...
Excuse me, could you move that boat out of the way, please? No? Oh well, forget I asked.
Some time later, that boat did finally move and I got some workers over to the coal area. But the plan still didn't work out as Egypt was at war with somebody, and kept moving spearmen all over the mountains there so I could never get my workers in the right places to build a road to connect it.
Of course, there WAS another coal nearby, in an Iron Works-on-a-silver-platter location, no less, but there's nothing we can do with that. Oh well, that's what I get for trying silly things like an OCC. :)
I wanted to move workers in to hook up that coal so Carthage could trade it to me, but then the Mongols went to war with them and captured the only city on that island with a harbor. Fine. The Mongols moved up to Hadrumetum and were ready to capture it as in the picture above... but then MADE PEACE! Aargh!
Well, okay, I can go hook up that coal for Carthage anyway, and build the road for it to trade through the Mongol harbor, and buy the coal from Hannibal. But just as I'm about to do THAT, Mongolia and Carthage go back to war! DOUBLE Aargh!
But in 1570 AD, Mongolia suddenly has an extra coal to sell. Oddly, I can find only one in their territory - but I take it of course! It only costs me 120 gold. They also have Iron available for sale for the low low price of 300 gold. (Low, but it's still a quarter of a technology...)
I'd traded Steam Power to Egypt for Free Artistry just to have Shakespeare's available to prebuild a factory. Then I also traded FA to Carthage for three workers.
The entire world was at war by this time - everybody in at least two conflicts except little ol' me. 
Finally (1665 AD) I snagged Medicine and Industrialization in a two-fer, also reselling Medicine to Egypt and Carthage for some cash.
I could still go for Shakespeare's at this point. It'd be due in 4 turns, and it will save roughly 8 gpt in lux tax and imports once a hospital gets built. But that would require delaying the Factory and everything after it by 16 turns, all but sacrificing Theory of Evolution. Finally, the clincher is that this is my last turn of imported iron, so building Shake's would cost an extra 300 gold to import more. No deal, so we crash-complete a factory instead and also get in a coal plant just before the coal import runs out.
I got Sanitation via minimun science (although didn't get a monopoly), and grabbed Corporation and Electricity in a two-fer and traded all three techs to Greece for Nationalism. I didn't get a sniff of Scientific Method before the Mongols built ToE, though.
In 1802 AD, the hospital completes, and in 1804 AD workers pile in to take the city to size 21.
In 1824 AD, I pulled a five-for-one brokerage deal, buying Refining to resell for Steel and Scientific Method and reselling those two for Espionage and Communism. My entire 20-turn future income is just about keeping pace with the increasing tech costs. So if I can pull a brokerage every 20 turns, that's a tech every 10 turns, plus a one-beaker run every now and then, which believe it or not is enough to keep up in tech with only the one city. I wouldn't try this on anything larger than a small map, though. Maybe a standard map with the Colossus in hand and better terrain than this, but nothing larger.
Combustion-for-Replaceable Parts follows 20 turns after that. And - WE HAVE A RESOURCE! Rubber.
And now we have another resource. 
Sometimes it's better to be lucky, of course. 
Although, maybe it was the Gods of Coal taking pity on me for my earlier efforts to procure the fossil fuel. 
Although it really doesn't do me any good just now - I've got my rails built, and the only AI lacking coal is Greece and they don't have anything to trade me for it.
My next bit of financial wizardry was this. One-beaker research on Atomic Theory finished, and I'm ready to broker Electronics for Mass Production. Only one problem, though - even after lowering lux tax to 0%, I can't afford it!
Ah, but there's still a way. I had to swap my city to Wealth for the extra income, giving up about 150 shields worth towards my Commercial Dock prebuild, but it was worth it.
I brokered that to Greece for Mass Production and to Carthage for about 400 gold.
