  Thus, what Newton has taken the trouble to do in Section 10 is to show that Huygens's theory of pendulums under uniform parallel gravity is a limit-case of Newton's theory of pendulums under universal gravity. At the end of Section 2 he points out in passing that this limit strategy also captures Galileo's theory of projectile motion. In other words, Newton took the trouble to show that the Galilean-Huygensian theory of local motion under their uniform gravity is a particular limit-case of his theory of universal gravity, just as Einstein took the trouble to show that Newtonian gravity is a limit-case of the theory of gravity of general relativity. Newton's main reason for doing this appears to have been the need to validate a measurement pivotal to the evidential reasoning for universal gravity in Book 3. From a philosophic standpoint, however, what is striking is not merely his recognizing this need, but more so the trouble he went to to fulfill it. Section 10 may thus illustrate best of all that Newton had a clear reason for including everything he chose to include in the Principia.