The men before Galileo
In the first half of the 1300s, a handful of scholars at Oxford University, most of whom were at Merton College, applied observation and careful thought to what had been proposed by Aristotle and other Classical philosophers.
Their first innovation was to distinguish between kinematics (motion of bodies regardless of the forces acting upon them) and dynamics (the study of the forces that initiate or affect motion). Their use of observation, experimentation, and mathematics led them to understand that Aristotle was wrong when he said the motion/speed of a falling body was determined by its weight (which, to Aristotle, was affected by the proportions in the object of the four elements; water and earth tended to make it fall faster, while a greater amount of fire or air made it fall more slowly). They understood that two bodies of different weights accelerated similarly; they were able to prove this with math. This knowledge spread to universities on the continent. Nicholas Oresme, a bishop in France, and Giovanni di Casali, a Franciscan in Italy, were each inspired to produce graphs and diagrams to explain this motion.
Despite this dissemination of information, it is assumed that these works were not likely to have been known by Galileo (1564-1642), who gets the credit in physics texts for developing the theory of falling bodies.