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.

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.

The few historical references to Euclid were written centuries after he lived, by Proclus and Pappus of Alexandria.

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.

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.

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.

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 ).

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.

His work inspired the New England Transcendentalists, including Ralph Waldo Emerson, who declared in 1843 that, in reading Proclus, " I am filled with hilarity & spring, my heart dances, my sight is quickened, I behold shining relations between all beings, and am impelled to write and almost to sing.

:" I am Proclus,

To Proclus the matter appeared so serious that towards the close of 437 he wrote to John I of Antioch, as the leading prelate of the East, though really having no canonical jurisdiction over Osrhoene, begging him to persuade Ibas, if innocent, to remove the scandal by condemning publicly certain propositions chiefly drawn from Theodore's writings against the errors of Nestorius.

Churches were built in their honor by Archbishop Proclus and by Emperor Justinian I ( 527 – 565 ), who sumptuously restored the city of Cyrus and dedicated it to the twins, but brought their relics to Constantinople ; there, following his cure, ascribed to the intercession of Cosmas and Damian, Justinian, in gratitude also built and adorned their church at Constantinople, and it became a celebrated place of pilgrimage.

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

She therefore ( as mentioned at the Kypria according to Proclus as part of a plan hatched by Zeus and Themis ) tossed into the party the Apple of Discord, a golden apple inscribed Kallisti – " For the most beautiful one ", or " To the Fairest One " – provoking the goddesses to begin quarreling about the appropriate recipient.

Saint Proclus, Patriarch of Constantinople ( 434-446 ), hoping to bring about the reconciliation of these Johannites, preached a homily praising his predecessor in the Church of Hagia Sophia.

As Platonism developed in the phases commonly called ' middle Platonism ' and neoplatonism, such writers as Plutarch, Porphyry, Proclus, Olympiodorus and Damascius wrote explicitly about the symbolic interpretation of traditional and Orphic myths.

He shows familiarity with Proclus, which indicates he wrote no earlier than the 5th century, as well as influence from Saint Clement of Alexandria, the Cappadocian Fathers, Origen of Alexandria, and others.

During the 19th century modernist Catholics too came generally to accept that the author must have lived after the time of Proclus.

The compilers of the Stanford Encyclopedia of Philosophy find pseudo-Dionysius to be most probably " a pupil of Proclus, perhaps of Syrian origin, who knew enough of Platonism and the Christian tradition to transform them both.

Since Proclus died in 485, and since the first clear citation of Dionysius ' works is by Severus of Antioch between 518 and 528, then we can place Dionysius ' authorship between 485 and 518-28.

" Ronald Hathaway provides a table listing most of the major identifications of Dionysius: e. g., Ammonius Saccas, Dionysius the Great, Peter the Fuller, Dionysius the Scholastic, Severus of Antioch, Sergius of Reshaina, unnamed Christian followers of everyone from Origen of Alexandria to Basil of Caesarea, Eutyches to Proclus.