Modern science is the practice of skepticism. Skepticism is defined as acritical attitude which systematically questions the notion that absolute knowledge and certainty are possible...in particular ... Earth truly moved. These assumptions were, of course, based on the works of Aristotle. Galileo wrote to him to correct his errors by using simple geometry (Machamer 29). It is suspected that it was at this point that Galileo began to contemplate the possibilty of heliocentric universe. He admitted in 1597 ( ... discipline which have not to this day been shut. Modern scientists still depend on ...

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... plane curves (polynomials of degree three in two variables), made substantial contributions to the theory of finite differences, and was the first to use fractional indices and to employ coordinate geometry to derive solutions to Diophantine equations. He approximated partial sums of the harmonic series by logarithms (a precursor to Euler's summation formula) and was the first to use power series ... development of mathematical analysis. In addition to analysis, Leibniz made a number of important discoveries in other fields of mathematics: combinatorics, algebra (the principles of the the...

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• Grade Level: Undergraduate