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 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.

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 was cited by Cotton Mather in his work entitled Psalterium Americanum ( a commentary on the Book of Psalms ) for his view on the book of Psalms.

His translation of Proclus ' commentary on Plato's Parmenides which included Plato's dialogue up to 142b in Stephanus pagination made this text available in Latin for the first time.

Important examples include those of Proclus and of Damascius, and an anonymous 3rd or 4th commentary possibly due to Porphyry.

The 13th century translation of Proclus ' commentary by Dominican friar William of Moerbeke stirred subsequent medieval interest ( Klibansky, 1941 ).

In the 15th century, Proclus ' commentary influenced the philosophy of Nicolas of Cusa, and Neoplatonists Giovanni Pico della Mirandola and Marsilio Ficino penned a major commentaries.

), Proclus ' commentary on Plato's Parmenides.

We learn from the commentary of Proclus on the Timaeus of Plato that Syrianus also wrote a commentary on the same book.

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.

A separate edition of the Parmenides ( 1839 ), with the commentary of Proclus, deserves mention.

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.

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.

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

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

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.

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.

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.

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

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.

Neither did he have any share, as was wrongly ascribed to him, in the First Council of Ephesus of 431, though, in consequence of disputes which arose in Armenia between the followers of Nestorius and the disciples of Acathius of Melitene and Rabbula, Isaac and his church did appeal to Constantinople and through Saint Proclus obtained the desired explanations.

Successful recreations have been performed by Anthemius of Tralles ( 6th century AD ), Proclus ( 6th century ) ( who by this means purportedly destroyed the fleet of Vitellus besieging Constantinople ), Ibn Sahl in his On Burning Mirrors and Lenses ( 10th century ), Alhazen in his Book of Optics ( 1021 ), Roger Bacon ( 13th century ), Giambattista della Porta and his friends ( 16th century ), Athanasius Kircher and Gaspar Schott ( 17th century ), the Comte du Buffon in 1740 in Paris, Ioannis Sakas in the 1970s in Greece, and others.

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.

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 ).

Euclid's commentator Proclus gave a proof of this postulate using the previous postulates, but it may be argued that this proof makes use of some hidden assumptions.

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.

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.

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

: Chasles's contribution to our comprehension of the Porisms tends to be obscured by the inherent unreasonableness of his claim to have restored substantially the contents of Euclid's book on the basis of the meagre data of Pappus and Proclus ... one still turns to Chasles for the first appreciation of the interest in the Porisms from the point of view of modern geometry.

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.