On orders of Pope Paul V, Galileo is ordered not to hold or defend the Copernican theory. Later, in 1624, Galileo was allowed to write about the Copernican theory provided that he treated it as a mathematical hypothesis. When Galileo published Dialogue Concerning the Two Chief World Systems in1630, comparing the Ptolemaic and Copernican models, the Church stopped its distribution and condemned Galileo to house arrest for the rest of his life.
The final steps leading to the rejection of Aristotle and Ptolemy come from Johannes Kepler, Rene Descartes and Isaac Newton. Kepler's laws of planetary motion describe an elliptical form and operation of planetary orbits that contradict Aristotle's assertion that the orbits of the planets were round circles.
In 1637, Rene Descartes published Discourse of Method, a work setting forth the principles of deductive reasoning as used in the modern scientific method. In short, his method required (1) accepting as truth only clear, distinct ideas that could not be doubted, (2) breaking a problem down into parts, (3) deducing one conclusion from another, and (4) conducting a systematic synthesis of all things. Descartes based his entire philosophical approach to science on this deductive method of reasoning in contrast to Aristotelian philosophy based on simple observation through reason alone.
Last, but certainly not least, Isaac Newton published Philosophia Naturalis Principia Mathematica in 1687. This book lays out Newton's model of the universe according to the laws of motion and gravitation that serve as a basis for today's physics and astronomy. Aristotle had believed that there is only a velocity if there is a force, but Newton proved that an object with a certain velocity maintains that velocity unless a force acts on it to cause an acceleration. Aristotle has formed his believe through his observation that had failed to capture the role played by frictional forces.
In summary, this paper demonstrated why there was a Scientific Revolution in 16th and 17th centuries, not just simple evolution. Science as we know it did not really emerge until this period. Once underway it dispelled commonly held principles based on simple observation by predecessors such as Aristotle and Ptolemy. And, it did so despite greater efforts to cling to tradition and religious beliefs.