History and Origin of The Name of The Archimedean Property
The concept is named after the ancient Greek geometer and physicist Archimedes of Syracuse.
The Archimedean property appears in Book V of Euclid's Elements as Definition 4:
Magnitudes are said to have a ratio to one another which can, when multiplied, exceed one another.Because Archimedes credited it to Eudoxus of Cnidus it is also known as the "Theorem of Eudoxus" or the Eudoxus axiom.
Archimedes used infinitesimals in heuristic arguments, although he denied that those were finished mathematical proofs.
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