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Descartes reasoning was based on deriving principles that were then the premise of deductive reasoning. Bacon, on the other hand, used empirical observations that were then used for inductive reasoning.
Rene Descartes and Francis Bacon are known for their philosophical contributions in the scientific revolution. Descartes contributions are in the areas of science and mathematics. He came up with the reasoning to the issues in these areas which are truth based and incontrovertible. While Francis Baconâ??s Scientific Method stressed on to replace the deductive reasoning by inductive reasoning.
René Descartes believed that every human us a "noble savage" when in the state of nature.
Short answer: Descartes' doubt was like WWI - the doubt to end all doubt. Only by doubting everything could Descartes hope to find anything that was certain (even if the only certainty is that nothing else is certain!).
Descartes did not invent polynomials.