If one is already firmly convinced, moreover, like Galileo thanks to the Renaissance's return to ancient philosophy of the possibility of philosophy as episteme achieving an objective science of the world, and if it had just been revealed that pure mathematics, applied to nature, consummately fulfills the postulate of episteme in its sphere of shapes: did not this also have to suggest to Galileo the idea of a nature which is constructively determinable in the same manner in all its other aspects?