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When we first encounter Theaetetus and his friend young Socrates in the Theaetetus,
they are applying oil to themselves as part of their cleanup after a
workout. They most likely carried their oil to the gym in an aryballos, a small flask, though probably a less elaborate one than this aryballos from about 2 centuries before Theaetetus' time. This image comes to us again from the fabulous collection at Perseus, and ultimately from the J. Paul Getty Museum.