The few historical references to Euclid were written centuries after he lived, by Proclus and Pappus of Alexandria.

The only reference that historians rely on of Euclid having written the Elements was from Proclus, who briefly in his Commentary on the Elements ascribes Euclid as its author.

Proclus ( 410-485 ), author of Commentary on the First Book of Euclid, was one of the last important players in Hellenistic geometry.

* Proclus ' Commentary on Euclid, Book I. PDF scans of Friedlein's Greek edition, now in the public domain ( Classical Greek )

Proclus, a Greek mathematician who lived several centuries after Euclid, wrote in his commentary of the Elements: " 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 ".

Proclus ( the commentator on Euclid ) and Hero of Alexandria ( the last of the engineers of antiquity ) also mention him.

Euclid is said to have replied to King Ptolemy's request for an easier way of learning mathematics that " there is no Royal Road to geometry ," following Proclus.

The only evidence comes from traditions recorded in works such as Proclus ’ commentary on Euclid written centuries later.

Pythagoras is widely credited with recognizing the mathematical basis of musical harmony and, according to Proclus ' commentary on Euclid, he discovered the theory of proportionals and constructed regular solids.

The curve was alluded to by Proclus in his commentary on Euclid and attributed to Diocles by Geminus as early as the beginning of the 1st century.

According to Proclus, philosophy is the activity which can liberate the soul from a subjection to bodily passions, remind it of its origin in Soul, Intellect, and the One, and prepare it not only to ascend to the higher levels while still in this life, but to avoid falling immediately back into a new body after death.

It had great authority because of its supposed Aristotelian origin, and it was only when Proclus ' Elements were translated into Latin that Thomas Aquinas realised its true origin.

( Ref Opus cit Butler ) A certain Proclus ( or Proculus ), who had confessed the faith before the prosecutors and underwent torments in defence of it, subsequently was seduced into heresy by Asclepiodotus and Theodotus the banker, both disciples of Theodotus the Tanner, whom Victor, Zephyrinus's predecessor in the Chair of Peter, had excommunicated for reviving the heresy of Ebion that affirmed that Christ was only a mere man, though a prophet.

Proclus, who summarized the lost epic, the Aethiopis of Arctinos of Miletus, of which only five lines survive in a quotation, gave the events of Penthesilea's life.

In his view not only Plotinus, but also Syrianus, Proclus, and Ammonius, are great philosophers, who have penetrated into the depths of the wisdom of Plato.

It may be only an accidental coincidence that about the end of the 2nd century " Archon " was one of the names given by the Platonist Harpocration to the " Second God " of Numenius ( Proclus in Tim.

The works of Proclus, 5 more published by Cardinal Mai, of which 3 are preserved only in a Syriac version, the Greek being lost ; 7 letters, along with several addressed to him by other persons ; and a few fragments of other letters and sermons.

If we had no other information, we should only know that he was later than Ptolemy ( died c. 168 AD ), whom he quotes, and earlier than Proclus ( born c. 411 AD ), who quotes him.

Aside from the Odyssey and the Iliad, the cyclic epics only survive in fragments, the most important of which is a detailed summary written by someone named Proclus ( not the same person as the philosopher Proclus Diadochus ).

In the metaphysics of Proclus, the Nous is only one level of hypostasis, with higher ones like Life, Being, and Unity above it.

The central poem of Book III is a summary of Proclus ' Commentary on the Timaeus, and Book V contains the important principle of Proclus that things are known not according to their own nature, but according to the character of the knowing subject.

See also Van den Berg, Proclus ' Commentary, p. 49, with reference to Plutarch, On the E at Delphi .</ ref > Neoplatonists sometimes interpreted the Eleusinian Mysteries as a fabula of celestial phenomena:

The first recorded use of the Greek word translated trapezoid ( τραπέζοειδη, trapézoeide, " table-like ") was by Marinus Proclus ( 412 to 485 AD ) in his Commentary on the first book of Euclid's Elements.

* Proclus, in his Commentary on Plato's Timaeus ( II, 38, I )

He was a pupil of Proclus in Athens, and taught at Alexandria for most of his life, writing commentaries on Plato, Aristotle, and other philosophers.

His work, a commentary on Plato's Timaeus, is lost, but Proclus, a Neoplatonist of the fifth century AD, reports on it.

Another passage from Proclus ' commentary on the Timaeus gives a description of the geography of Atlantis: That an island of such nature and size once existed is evident from what is said by certain authors who investigated the things around the outer sea.

* Proclus, A commentary on the First Book of Euclid's Elements, translated by Glenn Raymond Morrow, Princeton University Press, 1992.

Later ancient commentators such as Proclus ( 410 – 485 CE ) treated many questions about infinity as issues demanding proof and, e. g., Proclus claimed to prove the infinite divisibility of a line, based on a proof by contradiction in which he considered the cases of even and odd numbers of points constituting it.

The majority of Proclus ' works are commentaries on dialogues of Plato ( Alcibiades, Cratylus, Parmenides, Republic, Timaeus ).

Proclus also wrote an influential commentary on the first book of Euclid's Elements of Geometry.

In his commentary on Plato's Timaeus Proclus explains the role the Soul as a principle has in mediating the Forms in Intellect to the body of the material world as a whole.

Another important source for the influence of Proclus on the Middle Ages is Boethius ' Consolation of Philosophy, which has a number of Proclus principles and motifs.

Modern scholarship on Proclus essentially begins with E. R.

The following epigram is engraved on the tomb which houses Proclus and his master Syrianus:

The crater Proclus on the Moon is named after him.

The study was eidetic, approaching the philosophical objectives sought by considering it from each aspect of the quadrivium within the general structure demonstrated by Proclus, namely arithmetic and music on the one hand, and geometry and cosmology on the other.

Averroes rejected Avicenna's Neoplatonism which was partly based on the works of neo-Platonic philosophers, Plotinus and Proclus, that were mistakenly attributed to Aristotle.

A summary of Proclus ' Elements of Theology circulated under the name Liber de Causis ( the Book of Causes ).

The Liber de Causis ( Book of Causes ) is not a work by Proclus, but a summary of his work the Elements of Theology, likely written by an Arabic interpreter.

Especially important was his translation of the Theological Elements of Proclus ( made in 1268 ), because the Theological Elements is one of the fundamental sources of the revived Neo-Platonic philosophical currents of the 13th century.

Take the historical development of geometry as an example ; the first steps in the abstraction of geometry were made by the ancient Greeks, with Euclid's Elements being the earliest extant documentation of the axioms of plane geometry — though Proclus tells of an earlier axiomatisation by Hippocrates of Chios.

Pappus also wrote commentaries on Euclid's Elements ( of which fragments are preserved in Proclus and the Scholia, while that on the tenth Book has been found in an Arabic manuscript ), and on Ptolemy's Ἁρμονικά ( Harmonika ).

* Proclus ( c. 440 AD ) on Plato's Parmenides and Timaeus and Euclid's Elements

Barozzi translated many works of the ancients, including Proclus ’ s edition of Euclid's Elements ( published in Venice in 1560 ), as well as mathematical works by Hero, Pappus of Alexandria, and Archimedes.