Apart from historical Platonism originating from thinkers such as Plato himself, Numenius, Plotinus, Augustine and Proclus, we may wish to consider the theory of abstract objects in the modern sense.

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.

Proclus introduces Euclid only briefly in his fifth-century Commentary on the Elements, as the author of Elements, that he was mentioned by Archimedes, and that when King Ptolemy asked if there was a shorter path to learning geometry than Euclid's Elements, " Euclid replied there is no royal road to geometry.

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 Lycaeus (; 8 February 412 – 17 April 485 AD ), called the Successor ( Greek, Próklos ho Diádokhos ), was a Greek Neoplatonist philosopher, one of the last major Classical philosophers ( see Damascius ).

Proclus was born February 8, 412 AD ( his birth date is deduced from a horoscope cast by a disciple, Marinus ) in Constantinople to a family of high social status in Lycia ( his father Patricius was a high legal official, very important in the Byzantine Empire's court system ) and raised in Xanthus.

Proclus died aged ~ 73, and was buried near Mount Lycabettus in a tomb.

Proclus was however a close reader of Plato, and quite often makes very astute points about his Platonic sources.

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.

Before the contemporary period, the most significant scholar of Proclus in the English speaking world was Thomas Taylor, who produced English translations of most of his works, with commentaries.

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.

He was called Menelaus of Alexandria by both Pappus of Alexandria and Proclus, and a conversation of his with Lucius, held in Rome, is recorded by Plutarch.

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.

( 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.

Some very early Greek sources in the Epic Cycle affirmed that Artemis rescued Iphigenia from the human sacrifice her father was about to perform, for instance in the lost epic Cypria, which survives in a summary by Proclus: " Artemis, however, snatched her away and transported her to the Tauroi, making her immortal, and put a stag in place of the girl upon the altar.

Probably also the property of the Platonist school, which in the time of Proclus was valued at more than 1000 gold pieces, was confiscated ; at least, Justinian deprived the physicians and teachers of the liberal arts of the provision-money which had been assigned to them by previous emperors, and confiscated funds which the citizens had provided for spectacles and other civic purposes.

As a student of Pseudo-Dionysius, Maximus was one of many Christian theologians who preserved and interpreted the earlier Neo-Platonic philosophy, including the thought of such figures as Plotinus and Proclus.

He also translated for the use of Prince Arthur an astronomical treatise of Proclus, De sphaera, which was printed at Venice by Aldus in 1499.

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.

" Greek philosophers, Aristotle, Critolaus and Proclus held that the world was eternal.

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.

* Catalogue of the Prometheus Trust " Thomas Taylor Series " which includes translations of many of the works of Proclus.

According to Proclus the term was used to describe a theorem that is all-pervading and helps furnishing proofs of many other theorems.

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 ".

After first working as a clerk in Lubbock's Bank, he was appointed Assistant Secretary to the Society for the Encouragement of Art ( precursor to the Royal Society of Arts ), in which capacity he made many influential friends, who furnished the means for publishing his various translations, which besides Plato and Aristotle, include Proclus, Porphyry, Apuleius, Ocellus Lucanus and other Neoplatonists and Pythagoreans.

Although this work has not survived, many extracts are preserved by Proclus, Eutocius, and others.

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.

When they reached adulthood, Aedesia accompanied her sons to Athens where they studied under Proclus.

In naval warfare, the fleet of the Byzantine Emperor Anastasius I ( r. 491 – 518 ) is recorded by the chronicler John Malalas as having utilized a sulphur-based mixture to defeat the revolt of Vitalian in AD 515, following the advice of a philosopher from Athens called Proclus.

However, following Iamblichus, Plutarch of Athens, and his master Syrianus, Proclus presents a much more elaborate universe than Plotinus, subdividing the elements of Plotinus ' system into their logically distinct parts, and positing these parts as individual things.

* Greek Neoplatonist philosopher Proclus begins studying at the Academy in Athens.

He came to Athens at a time when, with the exception of Proclus, there was a great dearth of eminent men in the Neoplatonist school.

He became head of the school in Athens in succession to Marinus, who followed Proclus.

In Athens, he studied under Proclus, and learned the doctrine of Aristotle from Marinus.

He was in Athens when Proclus died ( in 485 ), and later when Marinus took over as head ( scholarch ) of the Neoplatonist school.

Plato's Phaedo had a significant readership throughout antiquity, and has been commented on by a number of ancient philosophers, such as Harpocration of Argos, Porphyry, Iamblichus, Paterius, Plutarch of Athens, Syrianus and Proclus.

The origins of Neoplatonist teaching in Athens are uncertain, but when Proclus arrived in Athens in the early 430's, he found Plutarch of Athens and his colleague Syrianus teaching in an Academy there.

The heads of the Neoplatonic Academy were Plutarch of Athens, Syrianus, Proclus, Marinus, Isidore, and finally Damascius.

Finally this pagan theosophy was driven from Alexandria back to Athens under Plutarch of Athens and Proclus, and occupied itself largely in commentaries based mainly on the attempt to re-organize ancient philosophy in conformity with the system of Plotinus.

He was a pupil and sometime amanuensis to the Neoplatonic philosopher Ammonius Hermiae, who had studied at Athens under Proclus.