Actually, strictly speaking, Copernicus's system has more epicycles that Ptolemy's (or at least no fewer, depending on how you work out the details of it). Copernicus's big win is getting rid of the equant, easily the most mathematically ugly thing in the Ptolemaic system.
The equant has a planet moving in a circle around one point, but moving uniformly from the perspective of a different point--essentially a way to avoid the restriction to uniform circular motion. It's a cheap hack, and it's the flaw that drove Copernicus away from Ptolemy in the first place. Or anyway, it looks like a cheap hack, until Kepler comes along and realizes that it's hinting at, as you said, "equal areas in equal time".
So I guess what I mean to say is: yeah, Kepler's pretty awesome.
(Sorry, don't mind me. I just spent way too much time reading Ptolemy in college, and I have no reason to believe there will ever be another opportunity to apply that bit of my education.)
The equant has a planet moving in a circle around one point, but moving uniformly from the perspective of a different point--essentially a way to avoid the restriction to uniform circular motion. It's a cheap hack, and it's the flaw that drove Copernicus away from Ptolemy in the first place. Or anyway, it looks like a cheap hack, until Kepler comes along and realizes that it's hinting at, as you said, "equal areas in equal time".
So I guess what I mean to say is: yeah, Kepler's pretty awesome.
(Sorry, don't mind me. I just spent way too much time reading Ptolemy in college, and I have no reason to believe there will ever be another opportunity to apply that bit of my education.)