<P> Unlike Bacon, Descartes successfully applied his own ideas in practice . He made significant contributions to science, in particular in aberration - corrected optics . His work in analytic geometry was a necessary precedent to differential calculus and instrumental in bringing mathematical analysis to bear on scientific matters . </P> <P> During the period of religious conservatism brought about by the Reformation and Counter-Reformation, Galileo Galilei unveiled his new science of motion . Neither the contents of Galileo's science, nor the methods of study he selected were in keeping with Aristotelian teachings . Whereas Aristotle thought that a science should be demonstrated from first principles, Galileo had used experiments as a research tool . Galileo nevertheless presented his treatise in the form of mathematical demonstrations without reference to experimental results . It is important to understand that this in itself was a bold and innovative step in terms of scientific method . The usefulness of mathematics in obtaining scientific results was far from obvious . This is because mathematics did not lend itself to the primary pursuit of Aristotelian science: the discovery of causes . </P> <P> Whether it is because Galileo was realistic about the acceptability of presenting experimental results as evidence or because he himself had doubts about the epistemological status of experimental findings is not known . Nevertheless, it is not in his Latin treatise on motion that we find reference to experiments, but in his supplementary dialogues written in the Italian vernacular . In these dialogues experimental results are given, although Galileo may have found them inadequate for persuading his audience . Thought experiments showing logical contradictions in Aristotelian thinking, presented in the skilled rhetoric of Galileo's dialogue were further enticements for the reader . </P> <P> As an example, in the dramatic dialogue titled Third Day from his Two New Sciences, Galileo has the characters of the dialogue discuss an experiment involving two free falling objects of differing weight . An outline of the Aristotelian view is offered by the character Simplicio . For this experiment he expects that "a body which is ten times as heavy as another will move ten times as rapidly as the other". The character Salviati, representing Galileo's persona in the dialogue, replies by voicing his doubt that Aristotle ever attempted the experiment . Salviati then asks the two other characters of the dialogue to consider a thought experiment whereby two stones of differing weights are tied together before being released . Following Aristotle, Salviati reasons that "the more rapid one will be partly retarded by the slower, and the slower will be somewhat hastened by the swifter". But this leads to a contradiction, since the two stones together make a heavier object than either stone apart, the heavier object should in fact fall with a speed greater than that of either stone . From this contradiction, Salviati concludes that Aristotle must, in fact, be wrong and the objects will fall at the same speed regardless of their weight, a conclusion that is borne out by experiment . </P>

When did the scientific method start being used