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In 1589 he was appointed professor of mathematics in the University of Pisa, and within a year or two established through experiment the foundations of the science of dynamics. As early as 1590 he put on record, in a Latin treatise _Concerning Motion_ (_De Motu_), his dissent from the theories of Aristotle in reference to moving bodies, confuting the Philosopher both by reason and ocular demonstration. Aristotle had held that two moving bodies of the same sort and in the same medium have velocities in proportion to their weights. If a moving body, whose weight is represented by _b_, be carried through the line _c--e_ which is divided in the point _d_, if, also, the moving body is divided according to the same proportion as line _c--e_ is in the point _d_, it is manifest that in the time taken to carry the whole body through _c--e_, the part will be moved through _c--d_. Galileo said that it is as clear as daylight that this view is ridiculous, for who would believe that when two lead spheres are dropped from a great height, the one being a hundred times heavier than the other, if the larger took an hour to reach the earth, the smaller would take a hundred hours? Or, that if from a high tower two stones, one twice the weight of the other, should be pushed out at the same moment, the larger would strike the ground while the smaller was still midway? His biography tells that Galileo in the presence of professors and students dropped bodies of different weights from the height of the Leaning Tower of Pisa to demonstrate the truth of his views. If allowance be made for the friction of the air, all bodies fall from the same height in equal times: the final velocities are proportional to the times; the spaces passed through are proportional to the squares of the times. The experimental basis of the last two statements was furnished by means of an inclined plane, down a smooth groove in which a bronze ball was allowed to pass, the time being ascertained by means of an improvised water-clock.
Galileo's mature views on dynamics received expression in a work published in 1638, _Mathematical Discourses and Demonstrations concerning Two New Sciences relating to Mechanics and Local Movements_. It treats of cohesion and resistance to fracture (strength of materials), and uniform, accelerated, and projectile motion (dynamics). The discussion is in conversation form. The opening sentence shows Galileo's tendency to base theory on the empirical. It might be freely translated thus: "Large scope for intellectual speculation, I should think, would be afforded, gentlemen, by frequent visits to your famous Venetian Dockyard (_arsenale_), especially that part where mechanics are in demand; seeing that there every sort of instrument and machine is put to use by numbers of workmen, among whom, taught both by tradition and their own observation, there must be some very skillful and also able to talk." The view of the shipbuilders, that a large galley before being set afloat is in greater danger of breaking under its own weight than a small galley, is the starting-point of this most important of Galileo's contributions to science.