The "creation" of mathematics spoken of by Ficino, Cardano and others signified a mental production entirely free from material presuppositions, and for that reason not less true but true in a higher sense. It is almost the same sense as that found in Descartes and his followers. Locke asserts the reality of mathematical truths, though he admits that there are in nature no figures corresponding to the archetypes existing in the mind of the geometrician;[44] and Leibniz, commenting on this passage, says that "the ideas of justice and temperance are no more our own invention than those of the circle and the square."[45] Tommaso Cornelio, whom we have quoted on the contrast between physical science and mathematics, also believed that mathematics rested on "certain notions and understandings which nature has put into the minds of men as foundations of science."[46] Another kind of "creation," and one which seems to have more connexion with Vico's _"fingere"_ is discussed in a passage of Aristotle's _Metaphysics_ which has had a good deal of influence. "We find also," Aristotle says, "geometrical figures by actualising them (ἐνεργεία), because they are found by being divided: if they _were_ divided, they would be obvious, but in reality they exist potentially. Why has the triangle two right angles? Because the angles round one point are equal to two right angles. If then we construct the angle along one side, it would become plain to any one looking at it. Why is the angle in the semicircle equal to a right angle? Because if there are three equal lines, two in the base and one drawn perpendicular to it, it is plain to any one who sees it and knows that. Whence it is evident that we discover things that exist potentially by reducing them to actuality. This is because the actuality is understanding, and the potentiality proceeds from the actuality; so we know by making (καὶ διὰ τοῡτο ποιοῡντες γιγνώσκουσιν)."[47] But these observations belong to the explanations given by Aristotle in this passage of the conceptions of potentiality and actuality; they are not at all opposed to his theory of mathematics as studying the intelligible matter which subsists in sensible matter, and they only explain the difference between potential and actual truth. In the same way we sometimes find in later philosophers the assertion that mathematical truths are demonstrated and problems resolved "by making them." Thus Sarpi writes in the passage mentioned above: "in mathematics, he who constructs knows because he makes, and he who analyses learns because he seeks how the thing is made. The mode of composition then belongs to the inventive faculty and that of analysis to the discursive: the former is that of problems, the latter of theorems; the latter are demonstrated by analysis, the former by composition."[48]