 A treatise in the Aristotelian corpus probably not by Aristotle himself (On Indivisible Lines) addresses and refutes a number of arguments offered for the existence of indivisible lines, without naming their author. Plato’s student Xenocrates (396–314 BCE), third head of the Academy, is reported to believe in indivisible lines, and he may well be the target of the Aristotelian treatise. One of the arguments attacked addresses a Zenonian problem about traversing or touching in succession an infinite series of parts. The idea that there are indivisible lines offers an alternative to the view that any extended magnitude must be divisible to infinity. A distinct argument claims that, if the physical elements composing a body are regarded as the ultimate parts, they cannot be further divisible. Although this does not argue for indivisible lines per se, it is used to suggest that the objects of sense as well as those of thought must include things without parts.