It’s worth noting that Kepler had the intuition that the motions of the planets ought to be produced by distinct lines of force adding up to regular curves—much as Galileo points out that constant acceleration is enough to cause mundane objects to fall in parabolic curves. But he didn’t quite have enough math to formalize this persuasively—that had to wait until Newton.
Likewise, ellipses are more difficult to work with than circles, until something like Cartesian analytic geometry lets you formalize them simply without any direct reference to conic sections.
It’s worth noting that Kepler had the intuition that the motions of the planets ought to be produced by distinct lines of force adding up to regular curves—much as Galileo points out that constant acceleration is enough to cause mundane objects to fall in parabolic curves. But he didn’t quite have enough math to formalize this persuasively—that had to wait until Newton.
Likewise, ellipses are more difficult to work with than circles, until something like Cartesian analytic geometry lets you formalize them simply without any direct reference to conic sections.