Proclus

Proclus Lycius (/ˈprɒkləs laɪˈsiːəs/; 8 February 412 – 17 April 485 AD), called Proclus the Successor (Greek Πρόκλος ὁ Διάδοχος, Próklos ho Diádokhos), was a Greek Neoplatonist philosopher, one of the last major classical philosophers. He set forth one of the most elaborate and fully developed systems of Neoplatonism. He stands near the end of the classical development of philosophy and influenced Western medieval philosophy (Greek and Latin).[1]

Biography

Proclus was born on 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 Eastern Roman Empire's court system) and raised in Xanthus. He studied rhetoric, philosophy and mathematics in Alexandria, with the intent of pursuing a judicial position like his father. Before completing his studies, he returned to Constantinople when his rector, his principal instructor (one Leonas), had business there.

Proclus became a successful practicing lawyer. However, the experience of the practice of law made Proclus realize that he truly preferred philosophy. He returned to Alexandria, and began determinedly studying the works of Aristotle under Olympiodorus the Elder. He also began studying mathematics during this period as well with a teacher named Heron (no relation to Hero of Alexandria, who was also known as Heron). As a gifted student, he eventually became dissatisfied with the level of philosophical instruction available in Alexandria, and went to Athens, the pre-eminent philosophical center of the day, in 431 to study at the Neoplatonic successor of the famous Academy founded 800 years earlier (in 387 BC) by Plato; there he was taught by Plutarch of Athens (not to be confused with Plutarch of Chaeronea), Syrianus, and Asclepigenia; he succeeded Syrianus as head of the Academy, and would in turn be succeeded on his death by Marinus of Neapolis.

He lived in Athens as a vegetarian bachelor, prosperous and generous to his friends, until the end of his life, except for a voluntary one-year exile, which was designed to lessen the pressure put on him by his political-philosophical activity, little appreciated by the Christian rulers; he spent the exile traveling and being initiated into various mystery cults. He was also instructed in the "theurgic" Neoplatonism, as derived from the Orphic and Chaldean Oracles. His house has been discovered recently in Athens, under the pavement of Dionysiou Areopagitou Street, south of Acropolis, opposite the theater of Dionysus. He had a great devotion to the goddess Athena, who he believed guided him at key moments in his life. Marinus reports that when Christians removed the statue of the goddess from the Parthenon, a beautiful woman appeared to Proclus in a dream and announced that the "Athenian Lady" wished to stay at his home.[2] Proclus died aged 73, and was buried near Mount Lycabettus in a tomb. It is reported that he was writing 700 lines each day.
Works

The majority of Proclus's works are commentaries on dialogues of Plato (Alcibiades, Cratylus, Parmenides, Republic, Timaeus). In these commentaries he presents his own philosophical system as a faithful interpretation of Plato, and in this he did not differ from other Neoplatonists, as he considered that "nothing in Plato’s corpus is unintended or there by chance", that "that Plato’s writings were divinely inspired" (ὁ θεῖος Πλάτων ho theios Platon—the divine Plato, inspired by the gods), that "the formal structure and the content of Platonic texts imitated those of the universe",[3] and therefore that they spoke often of things under a veil, hiding the truth from the philosophically uninitiate. Proclus was however a close reader of Plato, and quite often makes very astute points about his Platonic sources. A number of his Platonic commentaries are lost.

Proclus, the scholiast to Euclid, knew Eudemus of Rhodes' History of Geometry well, and gave a short sketch of the early history of geometry, which appeared to be founded on the older, lost book of Eudemus. The passage has been referred to as "the Eudemian summary," and determines some approximate dates, which otherwise might have remained unknown.[4] The influential commentary on the first book of Euclid's Elements of Geometry is one of the most valuable sources we have for the history of ancient mathematics,[5] and its Platonic account of the status of mathematical objects was influential. In this work, Proclus also listed the first mathematicians associated with Plato: a mature set of mathematicians (Leodamas of Thasos, Archytas of Taras, and Theaetetus), a second set of younger mathematicians (Neoclides, Eudoxus of Cnidus), and a third yet younger set (Amyntas, Menaechmus and his brother Dinostratus, Theudius of Magnesia, Hermotimus of Colophon and Philip of Opus). Some of these mathematicians were influential in arranging the Elements that Euclid later published.

In addition to his commentaries, Proclus wrote two major systematic works. The Elements of Theology (Στοιχείωσις θεολογική) consists of 211 propositions, each followed by a proof, beginning from the existence of the One (divine Unity) and ending with the descent of individual souls into the material world. The Platonic Theology (Περὶ τῆς κατὰ Πλάτωνα θεολογίας) is a systematisation of material from Platonic dialogues, showing from them the characteristics of the divine orders, the part of the universe which is closest to the One.

We also have three essays, extant only in Latin translation: Ten doubts concerning providence (De decem dubitationibus circa providentiam); On providence and fate (De providentia et fato); On the existence of evils (De malorum subsistentia).

He also wrote a number of minor works, which are listed in the bibliography below.
System

This section needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed. (January 2016) (Learn how and when to remove this template message)

Proclus's system, like that of the other Neoplatonists, is a combination of Platonic, Aristotelian, and Stoic elements. In its broad outlines, Proclus's system agrees with that of Plotinus with a notable difference: unlike Plotinus, Proclus did not hold that matter was evil, an idea that caused contradictions in the system of Plotinus. However, following Iamblichus, Plutarch of Athens, and his master Syrianus, Proclus presents a much more elaborate universe than Plotinus, subdividing the elements of Plotinus's system into their logically distinct parts, and positing these parts as individual things. This multiplication of entities is balanced by the monism which is common to all Neoplatonists. What this means is that, on the one hand the universe is composed of hierarchically distinct things, but on the other all things are part of a single continuous emanation of power from the One. From this latter perspective, the many distinctions to be found in the universe are a result of the divided perspective of the human soul, which needs to make distinctions in its own thought in order to understand unified realities. The idealist tendency is taken further in John Scotus Eriugena.

There is a double motivation found in Neoplatonic systems. The first is a need to account for the origin and character of all things in the universe. The second is a need to account for how we can know this origin and character of things. These two aims are related: they begin from the assumption that we can know reality, and then ask the question of what reality must be like, in its origin and unfolding, so that we can know it. An important element in the Neoplatonic answer to these questions is its reaction to Scepticism. In response to the sceptical position that we only know the appearances presented by our senses, and not the world as it is, Plotinus placed the object of knowledge inside the soul itself, and accounted for this interior truth through the soul's kinship with its own productive principles.
The One

The first principle in Neoplatonism is the One (Greek: to Hen). Being proceeds from the One. The One cannot itself be a being. If it were a being, it would have a particular nature, and so could not be universally productive. Because it is beyond being (epekeina tes ousias, a phrase from Plato's Republic 509b), it is also beyond thought, because thinking requires the determinations which belong to being: the division between subject and object, and the distinction of one thing from another. For this reason, even the name The One is not a positive name, but rather the most non-multiple name possible, a name derived from our own inadequate conception of the simplicity of the first principle. The One causes all things by conferring unity, in the form of individuality, on them, and in Neoplatonism existence, unity, and form tend to become equivalent. The One causes things to exist by donating unity, and the particular manner in which a thing is one is its form (a dog and a house are individual in different manners, for example). Because the One makes things exist by giving them the individuality which makes them what they are as distinct and separate beings, the Neoplatonists thought of it also as the source of the good of everything. So the other name for the One is the Good. Despite appearances, the first principle is not double; all things have a double relation to it, as coming from them (One) and then being oriented back towards them to receive their perfection or completion (Good).

The particular characteristic of Proclus's system is his elaboration of a level of individual ones, called henads, between the One which is before being and intelligible divinity. The henads exist "superabundantly", also beyond being, but they stand at the head of chains of causation (seirai) and in some manner give to these chains their particular character. He identifies them with the Greek gods, so one henad might be Apollo and be the cause of all things apollonian, while another might be Helios and be the cause of all sunny things. Each henad participates in every other henad, according to its character. What appears to be multiplicity is not multiplicity at all, because any henad may rightly be considered the center of the polycentric system.
Intellect

The principle which is produced below the level of the One and the Henads is the divine Intellect (Nous). The One cannot have a determinate nature if it is to be the source of all determinate natures, so what it produces is the totality of all determinate natures, or Being. By determination is meant existence within boundaries, a being this and not that. The most important determinate natures are the Greatest Kinds from Plato's Sophist (Being, Same, Other, Rest, Motion) and Aristotle's ten categories (Quantity, Quality, etc.). In other words, the One produces what Plato called the Forms, and the Forms are understood to be the first determinations into which all things fall. The One produces the Forms through the activity of thinking. The One itself does not think, but instead produces a divine mind, Intellect, whose thoughts are themselves the Forms. Intellect is both Thinking and Being. It is a mind which has its own contents as its object. All things relate to the first principle as both One and Good. As Being, Intellect is the product of the One. But it also seeks to return to its cause, and so in Thinking it attempts to grasp the One as its Good. But because the simplicity of the One/Good does not allow Intellect to grasp it, what Intellect does is generate a succession of perspectives around its simple source. Each of these perspectives is itself a Form, and is how Intellect generates for itself its own content.

Plotinus speaks about the generation of Intellect from the One, and Intellect's attempt to return to the One in a thinking which is also a desiring. Proclus systematises this production through a threefold movement of remaining, procession, and return (mone, proodos, epistrophe). Intellect remains in the One, which means that it has the One as its origin. It proceeds from the One, which means that it comes to be as a separate entity. But it returns to the One, which means that it does not cut itself off from its source, but receives the good which is its identity from the One. This threefold motion is used by Proclus to structure all levels of his system below the One and above material reality, so that all things except those mentioned remain, proceed, and return.

Proclus also gives a much more elaborate account of Intellect than does Plotinus. In Plotinus we find the distinction between Being and Thinking in Intellect. Proclus, in keeping with his triadic structure of remaining, procession, and return, distinguishes three moments in Intellect: Intelligible, Intelligible-Intellectual, and Intellectual. They correspond to the object of thought, the power of the object to be grasped by the subject, and the thinking subject. These three divisions are elaborated further, so that the intelligible moment consists of three triads (Being, Eternity, and the Living Being or Paradigm from Plato's Timaeus). The intelligible-intellectual moment also consists of three triads, and the intellectual moment is a hebdomad (seven elements), among which is numbered the Demiurge from Plato's Timaeus and also the monad of Time (which is before temporal things). In this elaboration of Intellect as a whole, Proclus is attempting to give a hierarchical ordering to the various metaphysical elements and principles that other philosophers have discussed, by containing them within a single triadic logic of unfolding.

Proclus's universe unfolds according to the smallest steps possible, from unity to multiplicity. With Intellect emerges the multiplicity which allows one being to be different from another being. But as a divine mind, Intellect has a complete grasp of all its moments in one act of thought. For this reason, Intellect is outside of Time.

Intellect as the second principle also gives rise to individual intellects, which hold various places within Proclus's cosmos.

In terms of his sources, Intellect is like taking the Platonic Forms and placing them in the self-thinking thought which is Aristotle's Unmoved Mover.
Soul

Soul (Psyche) is produced by Intellect, and so is the third principle in the Neoplatonic system. It is a mind, like Intellect, but it does not grasp all of its own content as one. Therefore, with Soul, Time comes to be, as a measure of Soul's movement from one object of thought to another. Intellect tries to grasp the One, and ends up producing its own ideas as its content. Soul attempts to grasp Intellect in its return, and ends up producing its own secondary unfoldings of the Forms in Intellect. Soul, in turn, produces Body, the material world.

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. The Soul is constructed through certain proportions, described mathematically in the Timaeus, which allow it to make Body as a divided image of its own arithmetical and geometrical ideas.

Individual souls have the same overall structure as the principle of Soul, but they are weaker. They have a tendency to be fascinated with the material world, and be overpowered by it. It is at this point that individual souls are united with a material body (i.e. when they are born). Once in the body, our passions have a tendency to overwhelm our reason. 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.

Because the soul's attention, while inhabiting a body, is turned so far away from its origin in the intelligible world, Proclus thinks that we need to make use of bodily reminders of our spiritual origin. In this he agrees with the doctrines of theurgy put forward by Iamblichus. Theurgy is possible because the powers of the gods (the henads) extend through their series of causation even down to the material world. And by certain power-laden words, acts, and objects, the soul can be drawn back up the series, so to speak. Proclus himself was a devotee of many of the religions in Athens, considering that the power of the gods could be present in these various approaches.

For Proclus, philosophy is important because it is one of the primary ways to rescue the soul from a fascination with the body and restore it to its station. However, beyond its own station, the soul has Intellect as its goal, and ultimately has unification with the One as its goal. So higher than philosophy is the non-discursive reason of Intellect, and the pre-intellectual unity of the One. Philosophy is therefore a means of its own overcoming, in that it points the soul beyond itself.
Influence

Proclus can be considered as the spokesman of mature Neoplatonism. His works had a great influence on the history of western philosophy. The extent of this influence, however, is obscured by the channels through which it was exercised. An important source of Procline ideas was through the Pseudo-Dionysius.[6] This late-5th- or early-6th-century Christian Greek author wrote under the pseudonym Dionysius the Areopagite, the figure converted by St. Paul in Athens. Because of this fiction, his writings were taken to have almost apostolic authority. He is an original Christian writer, and in his works can be found a great number of Proclus's metaphysical principles.[7]

Another important source for the influence of Proclus on the Middle Ages is Boethius's Consolation of Philosophy, which has a number of Proclus principles and motifs. The central poem of Book III is a summary of Proclus's 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.

A summary of Proclus's Elements of Theology circulated under the name Liber de Causis (the Book of Causes). This book is of uncertain origin, but circulated in the Arabic world as a work of Aristotle, and was translated into Latin as such. It had great authority because of its supposed Aristotelian origin, and it was only when Proclus's Elements were translated into Latin that Thomas Aquinas realised its true origin.

Proclus's works also exercised an influence during the Renaissance through figures such as Georgius Gemistus Pletho and Marsilio Ficino. 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.

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."

Modern scholarship on Proclus essentially begins with E. R. Dodds edition of the Elements of Theology in 1933. Since then he has attracted considerable attention, especially in the French-speaking world. Procline scholarship, however, still (2006) falls far short of the attention paid to Plotinus.

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

"I am Proclus,
Lycian whom Syrianus brought up to teach his doctrine after him.
This tomb reunites both our bodies.
May an identical sojourn be reserved to our both souls!"

The crater Proclus on the Moon is named after him.
Bibliography
Proclus's works

Platonic Theology: A long (six volumes in the Budé edition) systematic work, using evidence from Plato's dialogues to describe the character of the various divine orders
Elements of Theology: A systematic work, with 211 propositions and proofs, describing the universe from the first principle, the One, to the descent of souls into bodies
Elements of Physics
Commentary on Plato's "Alcibiades I" (it is disputed whether or not this dialogue was written by Plato, but the Neoplatonists thought it was)
Commentary on Plato's "Cratylus"
Commentary on Plato's "Parmenides"
Commentary on Plato's "Republic"
Commentary on Plato's "Timaeus"
A Commentary on the First Book of Euclid's "Elements"
Three small works: Ten doubts concerning providence; On providence and fate; On the existence of evils
Various Hymns (fragments)
Commentary on the Chaldaean Oracles (fragments)
The Life of Proclus, or On Happiness: written by his pupil, Marinus of Samaria

A number of other minor works or fragments of works survive. A number of major commentaries have been lost.

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. It was mistakenly thought in the Middle Ages to be a work of Aristotle, but was recognised by Aquinas not to be so.

A list of modern editions and translations of his surviving works is available at:

"Editions and Translations: Proclus (after 1900)". De Wulf–Mansion Centre for Ancient, Medieval and Renaissance Philosophy.

See also

Allegorical interpretations of Plato

Notes and references

Rosan, Laurence (1981). Harris, R. Baine (ed.). Neoplatonism and Indian Thought. State University of New York Press. pp. 45–49. ISBN 978-0873955461.
Marinus of Samaria, "The Life of Proclus or Concerning Happiness", Translated by Kenneth S. GUTHRIE (1925), pp.15–55:30, retrieved 21 May 2007.
Calian, Florin George (2013), ""Clarifications" of Obscurity: Conditions for Proclus's Allegorical Reading of Plato's Parmenides", Obscurity in medieval texts, pp. 15–31
James Gow, A Short History of Greek Mathematics (1884)
Heath (1908). "Proclus and His Sources". The Thirteen Books of Euclid's Elements Vol. 1. p. 29. "It is well known that the commentary of Proclus on Eucl. Book I is one of the two main sources of information as to the history of Greek geometry which we possess, the other being the Collection of Pappus"
Pseudo-Dionysius, the Areopagite, by Pope Benedict XVI, General Audience Address for May 14, 2008

Dodds, E. R. (1992). The Elements of Theology: A Revised Text with Translation, Introduction, and Commentary. Oxford University Press UK.

Further reading

Monographs

Proklos: Grundzüge seiner Metaphysik, by Werner Beierwaltes
L'Un et L'Âme selon Proclos, by Jean Trouillard
La mystagogie de Proclos, by Jean Trouillard
KINESIS AKINETOS: A study of spiritual motion in the philosophy of Proclus, by Stephen Gersh
From Iamblichus to Eriugena. An investigation of the prehistory and evolution of the Pseudo-Dionysius tradition, by Stephen Gersh
L'architecture du divin. Mathématique et Philosophie chez Plotin et Proclus, by Annick Charles-Saget
Proclus: Neoplatonic philosophy and science, by Lucas Siorvanes
The Philosophy of Proclus – the Final Phase of Ancient Thought, by L J Rosan
The Logical Principles of Proclus' Stoicheiôsis Theologikê as Systematic Ground of the Cosmos, by James Lowry

Collections of essays

Proclus et son influence, actes du Colloque de Neuchâtel, Juin, 1985. Zürich: Éditions du Grand Midi, 1987.
Proclus lecteur et interprète des anciens. Actes du Colloque internationale du C.N.R.S., Paris 2–4 October 1985. J. Pépin et H.-D. Saffrey. Paris: C.N.R.S., 1987.
On Proclus and his Influence in Medieval Philosophy, ed. by E.P. Bos and P.A. Meijer (Philosophia antiqua 53), Leiden-Köln-New York: Brill, 1992.
The perennial tradition of neoplatonism, ed. by J. Cleary (Ancient and medieval philosophy, Series I, 24), Leuven: Leuven University Press, 1997.
Proclus et la Théologie platonicienne: actes du colloque international de Louvain (13–16 mai 1998) en l'honneur de H. D. Saffrey et L. G. Westerink, éd. par A.-Ph. Segonds et C. Steel (Ancient and medieval philosophy, Series I 26), Leuven-Paris: Leuven University Press / Les Belles Lettres, 2000.
Stephen Gersh (ed.), Interpreting Proclus from Antiquity to the Renaissance, Cambridge: Cambridge University Press, 2014.

Studies on particular aspects of Proclus' philosophy

Gertz, S.R.P., "A Testimonium on Proclus' Views about the Rationality of Animals", Classical Quarterly 68.1, 352-357.

Bibliographic resources

Proclo, negli ultimi quarant' anni. Bibliografia ragionata delle letteratura primaria e secondaria riguardante il pensiero procliano e i suoi influssi storici (anni 1949–1992), by Nicoletta Scotti Muth
"Proclus Bibliography (covering the years 1990–2016)".

External links
Wikisource has original works written by or about:
Proclus
Wikiquote has quotations related to: Proclus
Library resources about
Proclus

Online books
Resources in your library
Resources in other libraries

By Proclus

Online books
Resources in your library
Resources in other libraries

Helmig, Christoph; Steel, Carlos. "Proclus". In Zalta, Edward N. (ed.). Stanford Encyclopedia of Philosophy.
Helmig, Christoph; Steel, Carlos. "Proclus' Complete Works (extant, lost, and spurious)". In Zalta, Edward N. (ed.). Stanford Encyclopedia of Philosophy.
Article by Encyclopædia Britannica
O'Connor, John J.; Robertson, Edmund F., "Proclus", MacTutor History of Mathematics archive, University of St Andrews.
Editions and Translations Proclus – Hoger Instituut voor Wijsbegeerte
Article at "The Encyclopedia of Goddess Athena"
Wikisource-logo.svg The Six Books of Proclus, the Platonic Successor, on the Theology of Plato Thomas Taylor translation.
Wikisource-logo.svg Five Hymns of Proclus Thomas Taylor translation.
Fragments that Remain of the Lost Writings of Proclus Thomas Taylor translation.
Commentaries of Proclus on the Timaeus of Plato, in Five Books Thomas Taylor translation.
Ten Doubts Concerning Providence and On the Existence of Evils Thomas Taylor translation.
Proclus's Life and Teachings
Index page of the Proclus section for the "Plato Transformed" project at the University Leuven, Belgium.
Commentary on Plato's Parmenides – (Greek text, scans of Cousin's edition)
Catalogue of the Prometheus Trust "Thomas Taylor Series" which includes translations of many of the works of Proclus. The site has lengthy extracts of these.
Proclus's Commentary on Euclid, Book I. PDF scans of Friedlein's Greek edition, now in the public domain (Classical Greek)
On the Signs of Divine Possession – (partial translation of Proclus's work)
On the Sacred Art – (translation and discussion of this surviving extract from a larger work by Proclus)
On the Sacred Art (French introduction and Greek text)
On the Sacred Art - Greek text and English translation
Hypotyposis Astronomicon Hypotheseon - Greek text
Proclus in English and Greek, Select Online Resources
Works by Proclus at LibriVox (public domain audiobooks)
Guide to Proclus, Elementa theologica. Manuscript, 1582 at the University of Chicago Special Collections Research Center

vte

Platonists
Academic
Old

Plato Aristotle Eudoxus Philip of Opus Aristonymus Coriscus and Erastus of Scepsis Demetrius of Amphipolis Euaeon of Lampsacus Heraclides and Python of Aenus Hestiaeus of Perinthus Lastheneia of Mantinea Timolaus of Cyzicus Speusippus Axiothea of Phlius Heraclides Ponticus Menedemus of Pyrrha Xenocrates Crantor Polemon Crates of Athens

Skeptic
Middle

Arcesilaus Diocles of Cnidus Lacydes Telecles and Evander Hegesinus

New

Carneades Hagnon of Tarsus Metrodorus of Stratonicea Clitomachus Charmadas Aeschines of Neapolis Philo of Larissa Cicero Dio of Alexandria

Middle Platonist

Antiochus Philo of Alexandria Plutarch Justin Martyr Gaius Albinus Alcinous Apuleius Atticus Maximus of Tyre Numenius of Apamea Longinus Clement of Alexandria Origen the Pagan Calcidius

Neoplatonist
Ancient

Ammonius Saccas Plotinus
Disciples Origen Amelius Porphyry Iamblichus Sopater Eustathius of Cappadocia Sosipatra Aedesius Dexippus Chrysanthius Theodorus of Asine Julian Sallustius Maximus of Ephesus Eusebius of Myndus Priscus of Epirus Antoninus Gregory of Nyssa Hypatia Gaius Marius Victorinus Augustine Macrobius

Academy

Plutarch of Athens Asclepigenia Hierocles Syrianus Hermias Aedesia Proclus Ammonius Hermiae Asclepiodotus Hegias Zenodotus Marinus Agapius Isidore Damascius Simplicius Priscian

Medieval

Boethius John Philoponus Olympiodorus Pseudo-Dionysius the Areopagite John Scotus Eriugena

Islamic Golden Age

Al-Farabi

Anselm Peter Abelard

Chartres

Bernard Gilbert Thierry

Henry of Ghent Bonaventure Theodoric of Freiberg Meister Eckhart Berthold of Moosburg Paul of Venice

Modern
Renaissance
Florentine Academy

Plethon Marsilio Ficino Cristoforo Landino Giovanni Pico della Mirandola

Cambridge

Ralph Cudworth Henry More Anne Conway

Petrus Ramus Giordano Bruno Blaise Pascal Emanuel Swedenborg

German idealist

Gottfried Wilhelm Leibniz Christian Wolff Moses Mendelssohn Immanuel Kant Johann Gottlieb Fichte Friedrich Wilhelm Joseph Schelling Arthur Schopenhauer G. W. F. Hegel Hermann Lotze Otto Weininger

Thomas Taylor Ralph Waldo Emerson Josiah Royce Søren Kierkegaard Henri Bergson Aleksei Losev

Contemporary
Analytic
Gottlob Frege G. E. Moore Kurt Gödel Alonzo Church Roderick Chisholm Michael Dummett W. V. O. Quine David Kaplan Saul Kripke Alvin Plantinga Peter van Inwagen Nicholas Wolterstorff Crispin Wright Edward N. Zalta
Continental

Edmund Husserl Roman Ingarden Leo Strauss

Miscellaneous

Philip K. Dick Joseph Ratzinger Bernard Bolzano

----

Ancient Greek and Hellenistic mathematics (Euclidean geometry)
Mathematicians
(timeline)
Anaxagoras Anthemius Archytas Aristaeus the Elder Aristarchus Apollonius Archimedes Autolycus Bion Bryson Callippus Carpus Chrysippus Cleomedes Conon Ctesibius Democritus Dicaearchus Diocles Diophantus Dinostratus Dionysodorus Domninus Eratosthenes Eudemus Euclid Eudoxus Eutocius Geminus Heliodorus Heron Hipparchus Hippasus Hippias Hippocrates Hypatia Hypsicles Isidore of Miletus Leon Marinus Menaechmus Menelaus Metrodorus Nicomachus Nicomedes Nicoteles Oenopides Pappus Perseus Philolaus Philon Philonides Porphyry Posidonius Proclus Ptolemy Pythagoras Serenus Simplicius Sosigenes Sporus Thales Theaetetus Theano Theodorus Theodosius Theon of Alexandria Theon of Smyrna Thymaridas Xenocrates Zeno of Elea Zeno of Sidon Zenodorus
Treatises
Almagest Archimedes Palimpsest Arithmetica Conics (Apollonius) Catoptrics Data (Euclid) Elements (Euclid) Measurement of a Circle On Conoids and Spheroids On the Sizes and Distances (Aristarchus) On Sizes and Distances (Hipparchus) On the Moving Sphere (Autolycus) Euclid's Optics On Spirals On the Sphere and Cylinder Ostomachion Planisphaerium Sphaerics The Quadrature of the Parabola The Sand Reckoner
Problems
Angle trisection Doubling the cube Squaring the circle Problem of Apollonius
Concepts/definitions
Circles of Apollonius
Apollonian circles Apollonian gasket Circumscribed circle Commensurability Diophantine equation Doctrine of proportionality Golden ratio Greek numerals Incircle and excircles of a triangle Method of exhaustion Parallel postulate Platonic solid Lune of Hippocrates Quadratrix of Hippias Regular polygon Straightedge and compass construction Triangle center
Results
In Elements
Angle bisector theorem Exterior angle theorem Euclidean algorithm Euclid's theorem Geometric mean theorem Greek geometric algebra Hinge theorem Inscribed angle theorem Intercept theorem Pons asinorum Pythagorean theorem Thales's theorem Theorem of the gnomon
Apollonius
Apollonius's theorem
Other
Aristarchus's inequality Crossbar theorem Heron's formula Irrational numbers Menelaus's theorem Pappus's area theorem Problem II.8 of Arithmetica Ptolemy's inequality Ptolemy's table of chords Ptolemy's theorem Spiral of Theodorus
Centers
Cyrene Library of Alexandria Platonic Academy
Other
Ancient Greek astronomy Greek numerals Latin translations of the 12th century Neusis construction

Retrieved from "http://en.wikipedia.org/"
All text is available under the terms of the GNU Free Documentation License