The work develops a mathematical framework for natural motion by presenting precise definitions and axioms, deriving laws of motion from geometrical reasoning, and applying centripetal force principles to predict planetary and terrestrial phenomena. It demonstrates how inverse-square attraction explains orbital shapes and motions, analyzes motion in different media, and treats perturbations, tides, and precession through geometric proofs and limiting ratios. Organized into systematic books, it combines rigorous demonstration with physical interpretation, moving from fundamental principles and methods to applications that connect celestial mechanics with observable phenomena. The emphasis is on geometrical synthesis, the use of limiting ratios, and the deduction of physical laws from mathematical principles.