1. In Book I of "Principia", Newton opened with definitions the three laws of motion now known as Newton's laws (laws of inertia, action and reaction, and acceleration proportional to force). Book II presented Newton's new scientific philosophy which came to replace Cartesianism. Finally, Book III consisted of applications of his dynamics, including an explanation for tides and a theory of lunar motion.
2. To test his hypothesis of universal gravitation, Newton wrote Flamsteed to ask if Saturn had been observed to slow down upon passing Jupiter. The surprised Flamsteed replied that an effect had indeed been observed, and it was closely predicted by the calculations Newton had provided. Newton's equations were further confirmed by observing the shape of the Earth to be oblate spheroidal as Newton claimed it should be, rather than prolate spheroidal as claimed by the Cartesians. Newton's equations also described the motion of Moon by successive approximations; and correctly predicted the return of Halley1 s Comet.
3. Newton also correctly formulated and solved the first ever problem in the calculus of variations which involved finding the surface of revolution which would give minimum resistance to flow assuring a specific drag law).