That is freakin' unbelievable. My cousin is in High School and he can barely do fractions.
It’s not really a mathematical leap. It’s a conceptual leap. Same with Tycho. In Ptolemy you have a system which tries to explain what things look like with the assumptions of earth at the center and “regular [constant velocity] circular motion.” Appearances differ so much that epicycles and equants (centers which are not the earth but around which the planets maintain regular angular velocity.) Then if you look at the resulting account, you see that a lot could be simplified if you stopped assuming the earth at the center.
Copernicus still assumed regular circular motion. The world had to wait for Kepler for ellipses and a system which realy “saved the appearances.”
The REAL problem, and the reason Tycho was attractive, was parallax. If the earth moved, the “fixed stars” should have apparent motion. And they do, but the instruments at the time (I’m told) weren’t precise enough to detect it. And it didn’t seem to occur to folks that the fixed stars were far enough away to make the motion so small, so the absence of apparent motion was considered, as it should have been, a powerful refutation of the moving earth theory.
(We did Ptolemy, that is the general system and then the details of one “inner planet” - between us and the sun, and one “outer planet” at my college.)