How Archimedes used infinitesimals

The ancient Greek mathematician, physicist, and engineer Archimedes of Syracuse was the first mathematician to make explicit use of infinitesimals. His work with infinitesimals is found in the celebrated Archimedes Palimpsest. The palimpsest embodies Archimedes' account of his "mechanical method", so called because it relies on the concepts of torque exerted on a lever and of center of gravity. Both of those concepts were first introduced by Archimedes.

Related Topics:
Archimedes - Syracuse - Infinitesimal - Archimedes Palimpsest - Torque - Center of gravity

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Ironically, Archimedes disbelieved in the existence of infinitesimals, and therefore said explicitly that his arguments fall short of being finished mathematical proofs.

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The proof of the first proposition in the palimpsest appears below.

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