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

After Pythagoras, Anaxagoras the Clazomenian succeeded, who undertook many things pertaining to geometry. And Oenopides the Chian, was somewhat junior to Anaxagoras, and whom Plato mentions in his Rivals, as one who obtained mathematical glory. To these succeeded Hippocrates, the Chian, who invented the quadrature of the lunula, and Theodorus the Cyrenean, both of them eminent in geometrical knowledge. For the first of these, Hippocrates composed geometrical elements: but Plato, who was posterior to these, caused as well geometry itself, as the other mathematical disciplines, to receive a remarkable addition, on account of the great study he bestowed in their investigation. This he himself manifests, and his books, replete with mathematical discourses, evince: to which we may add, that he every where excites whatever in them is wonderful, and extends to philosophy. But in his time also lived Leodamas the Thasian, Architas the Tarentine, and Theætetus the Athenian; by whom theorems were increased, and advanced to a more skilful constitution. But Neoclides was junior to Leodamas, and his disciple was Leon; who added many things to those thought of by former geometricians. So that Leon also constructed elements more accurate, both on account of their multitude, and on account of the use which they exhibit: and besides this, he discovered a method of determining when a problem, whose investigation is sought for, is possible, and when it is impossible.

Not much younger than these (sc. Hermotimus of Colophon and Philippus of Mende) is Euclid, who put together the Elements, collecting many of Eudoxus' theorems, perfecting many of Theaetetus', and also bringing to irrefragable demonstration the things which were only somewhat loosely proved by his predecessors. This man lived in the time of the first Ptolemy. For Archimedes, who came immediately after the first (Ptolemy), makes mention of Euclid: and, further, they say that Ptolemy once asked him if there was in geometry any shorter way than that of the elements, and he answered that there was no royal road to geometry. He is then younger than pupils of Plato but older than Eratosthenes and Archimedes; for the latter were contemporary with one another, as Eratosthenes somewhere says.

The person who has found him is unable to tell this to others as he has seen it, for the discovery is not made by the soul who makes a statement, but by the soul who is initiated in and lies outstretched towards the divine light, not moving with its own movement, but keeping its own silence as it were. For if it is by nature not able to grasp the essential nature of other realities either by name or by a defining proposition or by scientific knowledge, but by intuitive thought (noêsis) alone, as he himself says in the Letters, how could it discover the essential nature of the Demiurge in any other way than intuitively (noerôs)? How could the soul, having found him in this way, be able to report what it had seen by means of nouns and verbs and convey this to others? After all, because discursive thought proceeds through combination, it is unable to express the nature that is unified and simple. ... If discovery takes place by the soul who keeps silent, how could the flow of language through the mouth be sufficient to bring to light the essential nature of what has been discovered?