How did Galileo remove the mistakes in Aristotle’s theory of Motion?

For example, stripped to its essentials, Aristotle believed that a stone fell to the ground because the stone and the ground were similar in substance (in terms of the 4 basic elements, they were mostly "earth"). Likewise, smoke rose away from the Earth because in terms of the 4 basic elements it was primarily air (and some fire), and therefore the smoke wished to be closer to air and further away from earth and water. By the same token, Aristotle held that the more perfect substance (the _____ ________ ___ _____ ____ ________ _____.
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