It is told that those who first brought out the irrationals from concealment into the open perished in shipwreck, to a man. For the unutterable and t… - Proclus

A transition, therefore, is not undeservedly made from sense to consideration, and from this to the nobler energies of intellect. Hence, as the certain knowledge of numbers received its origin among the Phœnicians, on account of merchandise and commerce, so geometry was found out among the Egyptians from the distribution of land. When Thales, therefore, first went into Egypt, he transferred this knowledge from thence into Greece: and he invented many things himself, and communicated to his successors the principles of many. Some of which were, indeed, more universal, but others extended to sensibles.

To a given right line to apply a parallelogram equal to a given triangle in an angle which is equal to a given right lined angle.
According to the Familiars of Eudemus, the inventions respecting the application, excess, and defect of spaces, is ancient and belongs to the Pythagoric muse. But junior mathematicians receiving names from these, transferred them to the lines which are called conic, because one of these they denominate a parabola, but the other an hyperbola, and the third an ellipsis; since, indeed these ancient and divine men, in the plane description of spaces on a terminated right line, regarded the things indicated by these appellations. For when a right line being proposed, you adapt a given space to the whole right line, then that space is said to be applied, but when you make the longitude of the space greater than that of the right line, then the space is said to exceed; but when less, so that some part of the right line is external to the described space, then the space is said to be deficient. And after this manner, Euclid, in the sixth book, mentions both excess and defect. But in the present problem he requires application...

This, therefore, is mathematics: she reminds you of the invisible form of the soul; she gives life to her own discoveries; she awakens the mind and purifies the intellect; she brings light to our intrinsic ideas; she abolishes oblivion and ignorance which are ours by birth.