Seventeenth century atomism envisioned Nature as a set of mechanical systems to be treated mathemati-cally. But the basic discontinuity of atomic theory of matter appeared inconsistent with the essential con-tinuous character of geometrical magnitudes. In his old age Galileo devised a way to unify mathematics and physics via composing matter and continuous magnitudes out of an infinity of indivisible (atomic) units. Even though he forwarded the analysis of infinite sets, he couldn't establish a calculus to compute and compare different accelerated motions. In physics he never solved the basic problem of condensation and rarefaction of substances. But the side results were interesting and even fascinating. Keywords: atomism, mathematics, continuum, condensation and rarefaction, Seventeenth-century science, Galileo.
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