A major intellectual shift between Copernicus and the mid-17th century was the rejection of Aristotelian assertions concerning the relationship of mathematics to physical nature. Aristotle asserted that “The minute accuracy of mathematics is not to be demanded in all cases, but only in the case of things which have no matter. Therefore its method is not that of natural science; for presumably all nature has matter.” Thus, he pulled out the rug from under the feet of the aspiration to a (...) mathematically based natural sciences, asserting that: “And at the same time not even this is true, that mensuration deals with perceptible and perishable magnitudes; for then it would have perished, when they perished. And astronomy also cannot be dealing with perceptible magnitudes nor with this heaven above us. For neither are perceptible lines such lines as the geometer speaks of, nor are the movement and complex orbits in the heaven like those which astronomy treats, nor have geometrical points the same nature as the actual stars.”. (shrink)