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In the 5th century BC Zeno of Elea propounded four arguments about motion leading to paradoxical propositions: that a finite distance cannot be traversed by a moving object, that a faster runner cannot overtake a slower one. that an arrow flight is at rest, that half a given time is equal to the whole. These paradoxes were intended as support for the doctrine of Parmenides that all apparent motion is illusory, and of the attempts that have been made to show wherein they are fallacious none has met with universal acceptance. In this work solutions are suggested for the first three paradoxes. There is an exposition of the atomic theory of space and time which has been thought to underlie the fourth, and attempts which some commentators have made to explain the fourth on that basis are examined.