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Democritus: Greek Atomists
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The early Greeks, most notably Democritus, argued that matter is composed of fundamental particles called atoms. The views of the atomists... lacked the authority that comes from experiment, and evidence of the existence of atoms was not forthcoming for two millennia until the emergence of quantitative, empirical science in the 18th century.
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Democritus' predecessor, the atomist Leucippus, indicated a way out. Atomists can keep the doctrine of the atoms, together with the testimony of the senses regarding the existence of change and plurality, provided that they are willing to admit some role for not-being.
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Archimedes, the most brilliant mathematician of antiquity, gave Democritus credit for the discovery that the volume of a cone is one-third that of a cylinder having the same base and altitude. Archimedes added... that this theorem was enunciated by Democritus "without proof." In Democritus's time Greek geometry had not yet reached the stage at which it demanded rigorous proofs of its theorems. Democritus stated: "If a cone is cut by a plane parallel to its base, shall we regard the surfaces forming the sections as equal or unequal? If unequal, they make the cone uneven, having numerous indentations and protrusions, like a flight of stairs. But if the surfaces are equal, the sections will be equal and the cone comes to look like a cylinder, consisting of equal circles."
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Greek Atomists