• Journal for History of Mathematics
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• v.22 no.1
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• pp.1-24
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• 2009

In this paper we have inferred the influence of Zeno on the construction of the potential infinite of Aristotle based on arguments of Zeno's paradoxes. When we examine the potential infinite of Aristotle as the basis of the ancient Greek mathematics, we can see that they did not permit the concept of the actual infinite necessary for calculus. The reason Why they recognized the potential infinite, denying the actual infinite as seen in Aristotle's physics could be found in their attempt to escape the illogicality shown in Zeno's arguments. Accordingly, this paper could provided one of reasons why the ancient Greeks had used uneasy exhaustion's method instead of developing the quadrature involving the limit concept.