Where can I learn about the geometry and dimensions of bicycles?

I agree with Bob A. That is the best and quickest way to get the right size bike. They will give you the measurements if you do not buy a bike from them. You might have to pay for the time invested.

You want to be able to comfortable stand over the top tube of the frame with both feet planted flat.
Your seat should be ~6 inches higher than the tube for a race bike, ~5 higher for distance touring (which is probably you for triathlon). Sitting on it your knee should be just slightly bent when the pedal is at the bottom. with the crank arms horizontal, pedal at 3 o'clock, your knee should be just forward of in line with the pedal. grasping the handlebars at the brake hoods with your arms straight, your body should be about 45 degrees angle from horizontal and your leg extended should form about a 90-100 degree angle with your upper body.

You'll have best results at a local shop talking to the mechanics, they know alot and can fit you well. Don't expect any help at big stores like Dick's. Buy local.