"There is a well-known sophism of the ancients"

 This paradox was invented by Zeno of Elea (c.490-430 BC). Zeno was one of the earliest Greek philosophers, active before the time of Socrates. He is mainly known to the world through Plato's depiction of him in the Parmenides. See below for a funny re-telling of the paradox of Achilles and the tortoise.