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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 probably carried their oil to the gym in an aryballos, a small flask, though most likely not an aryballos
as fancy as this one from about 2 centuries before their time. This
excellent image comes to us once again from the fabulous collection at Perseus.