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Pythagoreanism
Pythagoreanism originated in the 6th century BC, based on and around the teachings and beliefs held by Pythagoras and his followers, the Pythagoreans. Pythagoras established the first Pythagorean community in the ancient Greek colony of Kroton, in modern Calabria (Italy). Early Pythagorean communities spread throughout Magna Graecia. Pythagoras' death and disputes about his teachings led to the development of two philosophical traditions within Pythagoreanism.
Western philosophy
Western philosophy encompasses the philosophical thought and work of the Western world. Historically, the term refers to the philosophical thinking of Western culture, beginning with the ancient Greek philosophy of the pre-Socratics. The word philosophy itself originated from the Ancient Greek (φιλοσοφία), literally, "the love of wisdom" φιλεῖν , "to love" and σοφία sophía, "wisdom").
Philosophy
Philosophy (love of wisdom in ancient Greek) is a systematic study of general and fundamental questions concerning topics like existence, reason, knowledge, values, mind, and language. It is a rational and critical inquiry that reflects on its own methods and assumptions. Historically, many of the individual sciences, like physics and psychology, formed part of philosophy. But they are considered separate academic disciplines in the modern sense of the term.
Nicomachus
Nicomachus of Gerasa (Νικόμαχος; 60-120 AD) was an Ancient Greek Neopythagorean philosopher from Gerasa, in the Roman province of Syria (now Jerash, Jordan). Like many Pythagoreans, Nicomachus wrote about the mystical properties of numbers, best known for his works Introduction to Arithmetic and Manual of Harmonics, which are an important resource on Ancient Greek mathematics and Ancient Greek music in the Roman period.
Platonic Academy
The Academy (Akademía) was founded by Plato in 387 BC in Athens. Aristotle studied there for twenty years (367–347 BC) before founding his own school, the Lyceum. The Academy persisted throughout the Hellenistic period as a skeptical school, until coming to an end after the death of Philo of Larissa in 83 BC. The Platonic Academy was destroyed by the Roman dictator Sulla in 86 BC. The Akademia was a school outside the city walls of ancient Athens.
Philolaus
Philolaus (ˌfɪləˈleɪəs; Φιλόλαος, Philólaos; 470-385 BCE) was a Greek Pythagorean and pre-Socratic philosopher. He was born in a Greek colony in Italy and migrated to Greece. Philolaus has been called one of three most prominent figures in the Pythagorean tradition and the most outstanding figure in the Pythagorean school. Pythagoras developed a school of philosophy that was dominated by both mathematics and mysticism. Most of what is known today about the Pythagorean astronomical system is derived from Philolaus's views.
Aristoxenus
Aristoxenus 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.
Hellenistic period
In classical antiquity, the Hellenistic period covers the time in Mediterranean history after Classical Greece, between the death of Alexander the Great in 323 BC to the death of Cleopatra VII (30 BC) followed by the emergence of the Roman Empire, as signified by the Battle of Actium in 31 BC and the conquest of Ptolemaic Egypt the following year. The Ancient Greek word Hellas (Ἑλλάς, Hellás) was gradually recognized as the name for Greece, from which the word Hellenistic was derived.
Eudoxus of Cnidus
Eudoxus of Cnidus (ˈjuːdəksəs; Εὔδοξος ὁ Κνίδιος, Eúdoxos ho Knídios; 408-355 BC) was an ancient Greek astronomer, mathematician, scholar, and student of Archytas and Plato. All of his original works are lost, though some fragments are preserved in Hipparchus' commentary on Aratus's poem on astronomy. Sphaerics by Theodosius of Bithynia may be based on a work by Eudoxus. Eudoxus was born and died in Cnidus (also spelled Knidos), which was a city on the southwest coast of Asia Minor.
Euclid's Elements
Euclid's Elements (Στοιχεῖα Stoikheîa) is a mathematical treatise consisting of 13 books attributed to the ancient Greek mathematician Euclid in Alexandria, Ptolemaic Egypt 300 BC. It is a collection of definitions, postulates, propositions (theorems and constructions), and mathematical proofs of the propositions. The books cover plane and solid Euclidean geometry, elementary number theory, and incommensurable lines. Elements is the oldest extant large-scale deductive treatment of mathematics.