Heath notes in the introduction to some of the mathematics referred to by Aristotle in his works:-
... Aristotle was aware of the important discoveries of Eudoxus which affected profoundly the exposition of the Elements by Euclid. One allusion clearly shows that Aristotle knew of Eudoxus's great Theory of Proportion which was expounded by Euclid in his Book V, and recognised the importance of it. Another passage recalls the fundamental assumption on which Eudoxus based his ' method of exhaustion' for measuring areas and volumes; and, of course, Aristotle was familiar with the system of concentric spheres by which Eudoxus and Callippus accounted theoretically for the independent motions of the sun, moon, and planets. ...
The incommensurable is mentioned over and over again, but the case mentioned is that of the diagonal of a square in relation to its side; there is no allusion to the extension of the theory to other cases by Theodorus and Theaetetus...
Heath also mentions the mathematics which Aristotle, perhaps surprising, does not refer to. There is:-
... no allusion to conic sections, to the doubling of the cube, or to the trisection of an angle. The problem of squaring the circle is mentioned in connection with the attempts of Antiphon, Bryson, and Hippocrates to solve it; but there is nothing about the curve of Hippias ...
While Heath discusses the many mathematical references in Aristotle, the book attempts to construct (or reconstruct) a work on Aristotle's view of the philosophy of mathematics. As Apostle writes in:-
... numerous passages on mathematics are distributed throughout the works we possess and indicate a definite philosophy of mathematics, so that an attempt to construct or reconstruct that philosophy with a fairly high degree of accuracy is possible.
We end our discussion with an illustration of Aristotle's ideas of 'continuous' and 'infinite' in mathematics. Heath explains Aristotle's idea that 'continuous':-
... could not be made up of indivisible parts; the continuous is that in which the boundary or limit between two consecutive parts, where they touch, is one and the same...
As to the infinite Aristotle believed that it did not actually exist but only potentially exists. Aristotle writes in Physics (see for example ):-
But my argument does not anyhow rob mathematicians of their study, although it denies the existence of the infinite in the sense of actual existence as something increased to such an extent that it cannot be gone through; for, as it is, they do not need the infinite or use it, but only require that the finite straight line shall be as long as they please. ... Hence it will make no difference to them for the purpose of proofs.
J J O'Connor and E F Robertson