Three Generations: From Tartaglia to Galileo

Abstract

To follow the evolution of the concepts that finally led to the correct formulation of the laws of motion would require several thick volumes. We have, therefore, chosen to report a few last episodes in this long chain of events. In the 16th century Nicolo Tartaglia studied the motion of cannonballs. Because Aristotelian physics forbad mixing natural and enforced motions, the accepted theory was that a cannonball moves first along a straight line and, when its impetus is exhausted, falls directly down towards the Earth’s center. Tartaglia, after some hesitation, came to the conclusion that the trajectory of a “projectile” is curved along all its length. The Aristotelian doctrine had been refuted, although the precise shape of the trajectory remained unknown. According to Aristotle, the velocity of a falling body depends on its weight. Gianbattista Benedetti, a disciple of Tartaglia, considered this problem. Benedetti argued that only bodies “of the same nature” fall with the same velocity regardless of their weights. The correct answer had to wait until Galileo Galilei, the disciple of Benedetti, came on the scene. Although Galileo never used the term “principle of inertia,” the fact that he applied this principle to his theory of uniform motions makes him its discoverer. The theory of free-fall is also of the greatest importance because it provides a “clinical case” of a uniformly accelerated motion that can be isolated from the “rest of the universe” and studied independently. These two issues are the cornerstones of Galilean mechanics.