XenocratesXenocrates (zəˈnɒkrəˌtiːz; Ξενοκράτης; c. 396/5 - 314/3 BC) of Chalcedon was a Greek philosopher, mathematician, and leader (scholarch) of the Platonic Academy from 339/8 to 314/3 BC. His teachings followed those of Plato, which he attempted to define more closely, often with mathematical elements. He distinguished three forms of being: the sensible, the intelligible, and a third compounded of the two, to which correspond respectively, sense, intellect and opinion.
AristoxenusAristoxenus of Tarentum (Ἀριστόξενος ὁ Ταραντῖνος; born 375, fl. 335 BC) was a Greek Peripatetic philosopher, and a pupil of Aristotle. Most of his writings, which dealt with philosophy, ethics and music, have been lost, but one musical treatise, Elements of Harmony (Greek: Ἁρμονικὰ στοιχεῖα; Latin: Elementa harmonica), survives incomplete, as well as some fragments concerning rhythm and meter. The Elements is the chief source of our knowledge of ancient Greek music.
QuadriviumFrom the time of Plato through the Middle Ages, the quadrivium (plural: quadrivia) was a grouping of four subjects or arts—arithmetic, geometry, music, and astronomy—that formed a second curricular stage following preparatory work in the trivium, consisting of grammar, logic, and rhetoric. Together, the trivium and the quadrivium comprised the seven liberal arts, and formed the basis of a liberal arts education in Western society until gradually displaced as a curricular structure by the studia humanitatis and its later offshoots, beginning with Petrarch in the 14th century.
RegiomontanusJohannes Müller von Königsberg (6 June 1436 – 6 July 1476), better known as Regiomontanus (ˌriːdʒioʊmɒnˈteɪnəs), was a mathematician, astrologer and astronomer of the German Renaissance, active in Vienna, Buda and Nuremberg. His contributions were instrumental in the development of Copernican heliocentrism in the decades following his death. Regiomontanus wrote under the Latinized name of Ioannes de Monteregio (or Monte Regio; Regio Monte); the toponym Regiomontanus was first used by Philipp Melanchthon in 1534.
HermeticaThe Hermetica are texts attributed to the legendary Hellenistic figure Hermes Trismegistus, a syncretic combination of the Greek god Hermes and the Egyptian god Thoth. These texts may vary widely in content and purpose, but are usually subdivided into two main categories, the "technical" and "religio-philosophical" Hermetica. The category of "technical" Hermetica encompasses a broad variety of treatises dealing with astrology, medicine and pharmacology, alchemy, and magic, the oldest of which were written in Greek and may go back as far as the second or third century BCE.
PlatonismPlatonism is the philosophy of Plato and philosophical systems closely derived from it, though contemporary Platonists do not necessarily accept all doctrines of Plato. Platonism had a profound effect on Western thought. In its most basic fundamentals, Platonism affirms the existence of abstract objects, which are asserted to exist in a third realm distinct from both the sensible external world and from the internal world of consciousness, and is the opposite of nominalism.
GorgiasGorgias (ˈɡɔrdʒiəs; Γοργίας; 483–375 BC) was an ancient Greek sophist, pre-Socratic philosopher, and rhetorician who was a native of Leontinoi in Sicily. Along with Protagoras, he forms the first generation of Sophists. Several doxographers report that he was a pupil of Empedocles, although he would only have been a few years younger. W. K. C. Guthrie writes that "Like other Sophists, he was an itinerant that practiced in various cities and giving public exhibitions of his skill at the great pan-Hellenic centers of Olympia and Delphi, and charged fees for his instruction and performances.
RatioIn mathematics, a ratio (ˈreɪʃ(i)oʊ) shows how many times one number contains another. For example, if there are eight oranges and six lemons in a bowl of fruit, then the ratio of oranges to lemons is eight to six (that is, 8:6, which is equivalent to the ratio 4:3). Similarly, the ratio of lemons to oranges is 6:8 (or 3:4) and the ratio of oranges to the total amount of fruit is 8:14 (or 4:7). The numbers in a ratio may be quantities of any kind, such as counts of people or objects, or such as measurements of lengths, weights, time, etc.
Apollonius of TyanaApollonius of Tyana (Ἀπολλώνιος; بلينس; अपालुन्यःc. 15 – c. 100 AD) was a first-century Greek philosopher and religious leader from the town of Tyana, Cappadocia in Roman Anatolia, who spent his life travelling and teaching in the Middle East, North Africa and South Asia. He is a central figure in Neopythagoreanism and was one of the most famous "miracle workers" of his day. His exceptional personality and his mystical way of life, which was regarded as exemplary, impressed his contemporaries and had a lasting cultural influence.
EmpedoclesEmpedocles (ɛmˈpɛdəkliːz; Ἐμπεδοκλῆς; 494-434 BC, 444–443 BC) was a Greek pre-Socratic philosopher and a native citizen of Akragas, a Greek city in Sicily. Empedocles' philosophy is best known for originating the cosmogonic theory of the four classical elements. He also proposed forces he called Love and Strife which would mix and separate the elements, respectively. Empedocles challenged the practice of animal sacrifice and killing animals for food. He developed a distinctive doctrine of reincarnation.
