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In a sense, Einstein's theory is simpler than Newton's, and there is a corresponding sense in which Copernicus' theory is simpler than Ptolemy's.

But ' simplicity ' here refers to systematic simplicity.

The number of primitive ideas in systematically-simple theories is reduced to a minimum.

The Axioms required to make the theoretical machinery operate are set out tersely and powerfully, so that all permissible operations within the theory can be traced rigorously back to these axioms, rules, and primitive notions.

This characterizes Euclid's formulation of geometry, but not Ptolemy's astronomy.

There are in The Almagest no rules for determining in advance whether a new epicycle will be required for dealing with abberations in lunar, solar, or planetary behavior.

The strongest appeal of the Copernican formulation consisted in just this: ideally, the justification for dealing with special problems in particular ways is completely set out in the basic ' rules ' of the theory.

The lower-level hypotheses are never ' ad hoc ', never introduced ex post facto just to sweep up within the theory some recalcitrant datum.

Copernicus, to an extent unachieved by Ptolemy, approximated to Euclid's vision.

De Revolutionibus is not just a collection of facts and techniques.

It is an organized system of these things.

Solving astronomical problems requires, for Copernicus, not a random search of unrelated tables, but a regular employment of the rules defining the entire discipline.