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In his famous acceleration experiment, he showed that a uniform force -- this case, gravity -- produced a uniform acceleration. Here is how Galileo described his path-breaking method and conclusion in his two New Sciences:

A piece of wooden moulding… was taken: on the edge was cut a channel a little more than one finger in breadth. Having made this groove very straight, smooth and polished, and having lined it with parchment, also as smooth and polished as possible, we rolled along it a hard, smooth and very round bronze ball… Noting….the time required to make the descent… we now rolled the ball only one-quarter the length of the channel, and having measured the time of its descent, we found it precisely one-half of the former… In such experiment [over many distances], repeated a full hundred times, we always found that the space traveled were in each other as the squares of the times, and that this was true for all the inclinations of the plane.

With this and other experiments, Galileo also formulated the law of inertia. That is, rather than rest being the natural state of objects, an object continues in motion forever unless stopped by some external force. Aristotelian physics was in a shambles. ~ Page 576