In Proclus we find this conception of an emanation of the world out of the Deity, or the absolute, made more exact, the process being regarded as threefold-0) persistence of cause in effect, (2) the departure of effect from cause, and (3) the tendency of effect to revert to its cause.
In later times Orphic theology engaged the attention of Greek philosophersEudemus the Peripatetic, Chrysippus the Stoic, and Proclus the Neoplatonist, but it was an especially favourite study of the grammarians of Alexandria, where it became so intermixed with Egyptian elements that Orpheus came to be looked upon as the founder of mysticism.
The fragment of a polemical treatise against the Neoplatonist Proclus is now assigned to Nicolaus, archbishop of Methone in Peloponnesus (fl.
He wrote An Astronomical Description of the late Comet (1619); Canicularia (1648); and translated Proclus' De Sphaera, and Ptolemy's De Planetarum Hypothesibus (1620).
The quadratrix of Dinostratus was well known to the ancient Greek geometers, and is mentioned by Proclus, who ascribes the invention of the curve to a contemporary of Socrates, probably Hippias of Elis.
The objections of the Alogi were restated and maintained by the Roman presbyter Caius in his controversy with the Montanist Proclus (Eus.
Finally this pagan theosophy was driven from Alexandria back to Athens under Plutarch and Proclus, and occupied itself largely in purely historical work based mainly on the attempt to re-organize ancient philosophy in conformity with the system of Plotinus.
According to Proclus, a man named Hippias, probably Hippias of Elis (c. 460 B.C.), trisected an angle with a mechanical curve, named the quadratrix.
In the 5th century we may place Hesychius of Alexandria, the compiler of the most extensive of our ancient Greek lexicons, and Proclus, the author of a chrestomathy, to the extracts from which (as preserved by Photius) we owe almost all our knowledge of the contents of the lost epics of early Greece.
The most distinguished teachers at Athens were Plutarch (q.v.), his disciple Syrianus (who did important work as a commentator on Plato and Aristotle, and further deserves mention for his vigorous defence of the freedom of the will), but above all Proclus (411-485).
Proclus is the great schoolman of Neoplatonism.
" It was reserved for Proclus," says Zeller, " to bring the Neoplatonic philosophy to its formal conclusion by the rigorous consistency of his dialectic, and, keeping in view all the modifications which it had undergone in the course of two centuries, to give it that form in which it was transferred to Christianity and Mahommedanism in the middle ages."
The works of Proclus, as the last testament of Hellenism to the church and the middle ages, exerted an incalculable influence on the next thousand years.
The disciples of Proclus are not eminent (Marinus, Asclepiodotus, Ammonius, Zenodotus, Isidorus, Hegias, Damascius).
The works of the pseudoDionysius contain a gnosis in which, by means of the teaching of Iamblichus and Proclus, the church's theology is turned into a scholastic mysticism with directions on matters of practice and ritual.
Thus in the history of science Neoplatonism has played a part and rendered services of which Plotinus or Iamblichus or Proclus never dreamt.
8), exclaiming in his dialogues, according to Proclus, that he could not sympathize with the dogma even if it should be thought that he was opposing, it out of contentiousness; while Plutarch says that his attacks on the forms by means of his exoteric dialogues were thought by some.
He 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 MS.), and on Ptolemy's `Ap/20vcKfi.
According to Proclus an angle must be either a quality or a quantity, or a relationship. The first concept was utilized by Eudemus, who regarded an angle as a deviation from a straight line; the second by Carpus of Antioch, who regarded it as the interval or space between the intersecting lines; Euclid adopted the third concept, although his definitions of right, acute, and obtuse angles are certainly quantitative.
Held by St Sahak and 1Iesrop on receipt of letters from Proclus and Cyril after the council of Ephesus, when the "Glory in the Highest" was adopted.
Proclus, too, in his summary of the history of geometry before Euclid, which he probably derived from Eudemus of Rhodes, says that Thales, having visited Egypt, first brought the knowledge of geometry into Greece, Assyrian Discoveries, p. 409.
Lair.; Proclus, In primum Euclidis Elementorum Librum Commentarii, ed.
This difficulty has, however, been lessened since the translation and publication of the papyrus Rhind by Eisenlohr; 1 and it is now generally admitted that, in the distinction made in the last passage quoted above from Proclus, reference is made to the two forms of his work - aL a - Tr Epov pointing to what he derived from Egypt or arrived at in an Egyptian manner, while indicates the discoveries which he made in accordance with the Greek spirit.
No doubt we are informed by Proclus, on the authority of Eudemus, that the theorem Euclid i.
During his pontificate the dispute was settled between Cyril of Alexandria and John of Antioch, who had been at variance since the council of Ephesus, but he himself had some difficulties with Proclus of Constantinople with regard to the vicariate of Thessalonica.
Homestead And Exemption Laws 639 Cyclus oder die homerischen Dichter (Bonn, 1835-1849); on Proclus and the Cycle reference may also be made to Wilamowitz-M011endorf p. 328 seq.; E.
He wrote also an attack on Proclus (De aeternitate mundi).
He is important as the teacher of Proclus, and, like Plutarch and Proclus, as a commentator on Plato and Aristotle.
His views were identical with those of Proclus, who regarded him with great affection and left orders that he should be buried in the same tomb.
During the seven years of enforced abandonment of teaching he produced, besides the Fragmens, the edition of the works of Proclus (6 vols., 1820-1827), and the works of Descartes (ii vols., 1826).
We learn from Plato (Parmenides, 127 D) that "the first hypothesis of the first argument" of Zeno's book above mentioned ran as follows: "If existences are many, they must be both like and unlike [unlike, inasmuch as they are not one and the same, and like, inasmuch as they agree in not being one and the same, Proclus, On the Parmenides, ii.
V = 3rA = 2 1 4 / 3 n F tan -II cot e a = 2 I 1 3 n F cot e a cos a/ (sin' a -cos t 13) 2 R =1-/ tan IT tan 0=1/ sin 13/(sin e a-cost r =Zl tan 21 cot a= Il cot a cos 13/(sin" a -cos' (3)L 1 In the language of Proclus, the commentator: " The equilateral triangle is the proximate cause of the three elements, ` fire,' ` air ' and ` water '; but the square is annexed to the ` earth.'
On the authority of the two great commentators Pappus and Proclus, Euclid wrote four books on conics, but the originals are now lost, and all we have is chiefly to be found in the works of Apollonius of Perga.
In the oldest existing version of the legend - that of Arctinus of Miletus, which has so far been preserved in the excerpts of Proclus - the calamity is lessened by the fact that only one of the two sons is killed; and this, as has been pointed out (Arch.
As an ardent upholder of the old pagan religion Proclus incurred the hatred of the Christians, and was obliged to take refuge in Asia Minor.
Although possessed of ample means, Proclus led a most temperate, even ascetic life, and employed his wealth in generous relief of the poor.
The Ztol X ELwoLs BEoXoyu i 7 (Institutio theologica) contains a compendious account of the principles of Neoplatonism and the modifications introduced in it by Proclus himself.
Other philosophical works by Proclus are /roL X ELwoLS 4VO K 7 ti 7 HEpi KLV 7) Uews (Institutio physica sive De motu, a compendium of the last five books of Aristotle's IIEpt qu6LK?7s aKpoaaEWS, De physica auscultatione), and De providentia et fato, Decem dubitationes circa providentiann, De malorum subsistentia, known only by the Latin translation of William of Moerbeke (archbishop of Corinth, 1277-1281), who also translated the JTOtX€LW cs 9EoaoyLK17 into Latin.
In addition to the epitaph already mentioned, Proclus was the author of hymns, seven of which have been preserved (to Helios, Aphrodite, the Muses, the Gods, the Lycian Aphrodite, Hecate and Janus, and Athena), and of an epigram in the Greek Anthology (Anthol.
The Xprt6ToyaOia ypaµµartld by a Proclus, who is identified by Suidas with the Neoplatonist, is probably the work of a grammarian of the 2nd or 3rd century, though WilamowitzMollendorff (Philolog.
On Proclus generally and his works see article in Suidas; Marinus, Vita Procli; J.
13, where Proclus is styled the "Hegel of Neoplatonism"; on his philosophy, T.