Philolaus (circa 480 BC – circa 405 BC) was a Greek mathematician and philosopher. Centuries: 6th century BC - 5th century BC - 4th century BC Decades: 530s BC 520s BC 510s BC 500s BC 490s BC - 480s BC - 470s BC 460s BC 450s BC 440s BC 430s BC Years: 485 BC 484 BC 483 BC 482 BC 481 BC _ 480 BC _ 479 BC... Jump to: navigation, search Centuries: 6th century BC - 5th century BC - 4th century BC Decades: 450s BC 440s BC 430s BC 420s BC 410s BC - 400s BC - 390s BC 380s BC 370s BC 360s BC 350s BC Years: 410 BC 409 BC 408 BC 407 BC 406 BC - 405 BC... A mathematician is a person whose area of study and research is mathematics. ... Jump to: navigation, search A philosopher is a person devoted to studying and producing results in philosophy. ...

A classic philologist, August Boeckh (1785–1867) places his life between the 70th and 95th Olympiads (496 BC–396 BC). Philolaus was a contemporary of Socrates and Democritus, but senior to them, and was probably somewhat junior to Empedocles, and a contemporary of Zeno of Elea, Melissus and Thucydides, so that his birth may be placed at about 480 BC. Philology is the study of ancient texts and languages. ... Jump to: navigation, search Philipp August Böckh (November 24, 1785 - August 3, 1867), was a German classical scholar and antiquarian. ... Jump to: navigation, search 1785 was a common year starting on Saturday (see link for calendar). ... Jump to: navigation, search 1867 was a common year starting on Tuesday (see link for calendar). ... Jump to: navigation, search The Olympic Games, or Olympics, is an international multi-sport event taking place every two years and alternating between Summer and Winter Games. ... Centuries: 6th century BC - 5th century BC - 4th century BC Decades: 540s BC 530s BC 520s BC 510s BC 500s BC - 490s BC - 480s BC 470s BC 460s BC 450s BC 440s BC Years: 499 BC 498 BC 497 BC - 496 BC - 495 BC 490 BC 489 BC 488 BC... Jump to: navigation, search Centuries: 5th century BC - 4th century BC - 3rd century BC Decades: 440s BC 430s BC 420s BC 410s BC 400s BC - 390s BC - 380s BC 370s BC 360s BC 350s BC 340s BC Years: 401 BC 400 BC 399 BC 398 BC 397 BC - 396 BC... Jump to: navigation, search Socrates This article is about the ancient Greek philosopher, for all other uses see: Socrates (disambiguation) Socrates (June 4, ca. ... Jump to: navigation, search Bust of Democritus Democritus was a pre-Socratic Greek philosopher (born at Abdera in Thrace around 460 BC; died in 370 BC). ... Empedocles of Agrigentum Empedocles (c. ... Zeno of Elea should not be confused with Zeno of Citium. ... In Greek mythology, Melissus was a King of Crete, whose only role was to provide a patriarchal father-figure for Melissa and Amaltheia. ... Bust of Thucydides Thucydides (between 460 and 455 BC–circa 400 BC, Greek Θουκυδίδης, Thoukudídês) was an ancient Greek historian, and the author of the History of the Peloponnesian War, which recounts the 5th century BC war between Sparta and Athens. ... Centuries: 6th century BC - 5th century BC - 4th century BC Decades: 530s BC 520s BC 510s BC 500s BC 490s BC - 480s BC - 470s BC 460s BC 450s BC 440s BC 430s BC Years: 485 BC 484 BC 483 BC 482 BC 481 BC _ 480 BC _ 479 BC...

Philolaus was probably born in Croton (after a Greek historian Diogenes Laërtius) or in Tarentum or Heraclea. He lived around 475 BC and he was in Croton during the persecution of the Pythagoreans. Croton may also refer to a plant genus. ... Diogenes Laërtius, the biographer of the Greek philosophers, is supposed by some to have received his surname from the town of Laerte in Cilicia, and by others from the Roman family of the Laërtii. ... Map of Italy showing Taranto in the bottom right Taranto is a coastal city in Apulia, southern Italy. ... Heraclea was the name of a large number of ancient cities founded by the Greeks. ... Centuries: 4th century BC - 5th century BC - 6th century BC Decades: 520s BC 510s BC 500s BC 490s BC 480s BC - 470s BC - 460s BC 450s BC 440s BC 430s BC 420s BC Years: 480 BC 479 BC 478 BC 477 BC 476 BC - 475 BC - 474 BC 473 BC... The Pythagoreans were an Hellenic organization of astronomers, musicians, mathematicians, and philosophers; who believed that all things are, essentially, numeric. ...

He was said to have been intimate with Democritus, and was probably one of his teachers. He was an immediate pupil and transcriber of Pythagoras and after the death of his teacher great dissensions prevailed in the cities of lower Italy. According to some accounts, Philolaus, obliged to flee, took refuge first in Lucania and then at Thebes, where he had as pupils Simmias and Cebes (Crito), who, being young men, were subsequently present at the death of Socrates in 399 BC. Before this Philolaus had returned to Italy, where he was the teacher of Archytas (428 BC–347 BC). Philolaus was perhaps also connected with the Pythagorean exiles at Phlius mentioned in Plato's Phaedo. Jump to: navigation, search This topic is considered to be an essential subject on Wikipedia. ... For the mountain in Canada named after Lucania, see Mount Lucania. ... For the ancient capital of Upper Egypt, see Thebes, Egypt. ... Jump to: navigation, search Simmias (in Greek Σιμμιας; lived 4th century BC) was a Macedonian, son of Andromenes, and brother of Attalus and Amyntas, the officers of Alexander the Great (336–323 BC). ... Cebes was the name of two Greek philosophers. ... The Crito is a well-known dialogue by the ancient Greek philosopher, Plato, between Socrates and his follower Crito, regarding the source and nature of political obligation. ... Jump to: navigation, search Centuries: 5th century BC - 4th century BC - 3rd century BC Decades: 440s BC 430s BC 420s BC 410s BC 400s BC - 390s BC - 380s BC 370s BC 360s BC 350s BC 340s BC Years: 404 BC 403 BC 402 BC 401 BC 400 BC - 399 BC... Archytas (428 BC - 347 BC), was a Greek philosopher, mathematician, astronomer, statesman, strategist and commander-in-chief. ... Centuries: 6th century BC - 5th century BC - 4th century BC Decades: 470s BC 460s BC 450s BC 440s BC 430s BC - 420s BC - 410s BC 400s BC 390s BC 380s BC 370s BC Years: 433 BC 432 BC 431 BC 430 BC 429 BC - 428 BC - 427 BC 426 BC... Centuries: 5th century BC - 4th century BC - 3rd century BC Decades: 390s BC 380s BC 370s BC 360s BC 350s BC - 340s BC - 330s BC 320s BC 310s BC 300s BC 290s BC 352 BC 351 BC 350 BC 349 BC 348 BC 347 BC 346 BC 345 BC 344... Jump to: navigation, search Statue of a philosopher, presumably Plato, in Delphi. ... The Phaedo is the fourth and last dialogue detailing the final days of Socrates and contains the death scene. ...

Philolaus spoke and wrote in a Greek Doric dialect and was the first to propound the doctrine of the motion of the Earth; some attribute this doctrine to Pythagoras, but there is no evidence in support of either Pythagoras or the younger Hicetas (circa 400 BC – circa 335 BC) of Syracuse. Philolaus supposed that the sphere of the fixed stars, the five planets, the Sun, Moon and Earth, all moved round the central fire, but as these made up only nine revolving bodies, he conceived in accordance with his number theory a tenth, which he called counter-earth. The central holy fire was not the Sun for him, but some mysterious thing between the Earth and counter-earth. He named it "estia", the hearth of the universe, the house of Zeus, and the mother of the gods, after the goddess of fire and hearth Hestia. He kept an idea of the Earth's rotation around its axis. Probably he misunderstood his teacher, because he entangled the idea and he introduced a certain "primordial Earth", the "antichthon", for these numerological reasons, which together with the Earth and the Sun revolve around the central fire. In this model the Earth and the Sun lie always opposite to each other. His idea was restored and resumed around 345 BC by Heraclides of Heraclea (circa 388 BC – 310 BC). This mysterious counter-earth was never seen, because its position in relation to the Earth was parallel to the relative positions of the Earth and the Sun; that of two spheres, connected at fixed points along a circle. He further advanced ideas about the Earth's rotation around its axis: this influenced Aristarchus dramatically. Such a theory about the solar system quite well explained the movement of the Sun and the differing lengths of days through the year. It is not known how accurate it was. Doric, a synonym of Dorian, may refer to any of the following: The Dorians, one of the ancient Hellenic races, Doric Greek, the dialect of the former, the Doric order and its distinctive Doric column, in ancient Greek architecture, the Dorian mode in music, also called the Doric mode, or... Jump to: navigation, search Earth, also known as the Earth, Terra, and (mostly in the 19th century) Tellus, is the third-closest planet to the Sun. ... Hicetas (around 400 BC – around 335 BC) was a Greek philosopher of the Pythagorean School. ... Centuries: 5th century BC - 4th century BC - 3rd century BC Decades: 450s BC 440s BC 430s BC 420s BC 410s BC - 400s BC - 390s BC 380s BC 370s BC 360s BC 350s BC Years: 405 BC 404 BC 403 BC 402 BC 401 BC - 400 BC - 399 BC 398 BC... Centuries: 5th century BC - 4th century BC - 3rd century BC Decades: 380s BC 370s BC 360s BC 350s BC 340s BC - 330s BC - 320s BC 310s BC 300s BC 290s BC 280s BC Years: 340 BC 339 BC 338 BC 337 BC 336 BC - 335 BC - 334 BC 333 BC... Map of central Mediterranean Sea, showing location of Syracuse on the island of Sicily. ... Jump to: navigation, search The Pleiades star cluster A star is a massive body of plasma in outer space that is currently producing or has produced energy through nuclear fusion. ... Jump to: navigation, search A planet in common parlance is a large object in orbit around a star that is not a star itself. ... Jump to: navigation, search The Sun is the star at the centre of our Solar system. ... Jump to: navigation, search Crust composition Oxygen 43% Silicon 21% Aluminium 10% Calcium 9% Iron 9% Magnesium 5% Titanium 2% Nickel 0. ... Jump to: navigation, search Traditionally, number theory is that branch of pure mathematics concerned with the properties of integers. ... Jump to: navigation, search The deepest visible-light image of the cosmos. ... Jump to: navigation, search Statue of Zeus Phidias created the 12-m (40-ft) tall statue of Zeus at Olympia about 435 BC. The statue was perhaps the most famous sculpture in ancient Greece, imagined here in a 16th-century engraving. ... Jump to: navigation, search The term God is capitalized in the English language as a proper noun when used to refer to a specific monotheistic concept of a supernatural Supreme Being in accordance with Christian, Jewish (sometimes as G-d - cf. ... A goddess is a female deity, in contrast with a male deity known as a god. A great many cultures have goddesses, sometimes alone, but more often as part of a larger pantheon that includes both of the conventional genders and in some cases even hermaphroditic (or gender neutral) deities. ... Jump to: navigation, search A large bonfire Fire is a form of combustion. ... In common historic and modern usage, a hearth is a brick- or stone-lined fireplace or oven used for cooking and/or heating. ... Statue of Hestia. ... The axis of rotation of a rotating body is a line such that the distance between any point on the line and any point of the body remains constant under the rotation. ... Jump to: navigation, search Numerology is the study of the purported mystical or esoteric relationship between numbers and the character or action of physical objects and living things. ... Jump to: navigation, search The Sun is the star at the centre of our Solar system. ... Centuries: 5th century BC - 4th century BC - 3rd century BC Decades: 390s BC 380s BC 370s BC 360s BC 350s BC - 340s BC - 330s BC 320s BC 310s BC 300s BC 290s BC Years: 350 BC 349 BC 348 BC 347 BC 346 BC - 345 BC - 344 BC 343 BC... Heraclides Ponticus (387 - 312 BCE), also known as Heraklides, was a Greek philosopher who lived and died at Heraclea, now Eregli, Turkey. ... Centuries: 5th century BC - 4th century BC - 3rd century BC Decades: 430s BC 420s BC 410s BC 400s BC 390s BC - 380s BC - 370s BC 360s BC 350s BC 340s BC 330s BC 393 BC 392 BC 391 BC 390 BC 389 BC 388 BC 387 BC 386 BC 385... Centuries: 5th century BC - 4th century BC - 3rd century BC Decades: 360s BC 350s BC 340s BC 330s BC 320s BC 310s BC 300s BC 290s BC 280s BC 270s BC 260s BC Years: 315 BC 314 BC 313 BC 312 BC 311 BC _ 310 BC _ 309 BC... Aristarchus (310 BC - circa 230 BC) was a Greek astronomer and mathematician, born in Samos, Greece. ... Jump to: navigation, search Presentation of the solar system (not to scale) The solar system is the retinue of objects gravitationally bound to our Sun. ... See also Day (language) A day (symbol: d) is a unit of time. ... Jump to: navigation, search A year is the time between two recurrences of an event related to the orbit of the Earth around the Sun. ...

According to Nicolaus Copernicus, Philolaus already knew about the Earth's revolution in a circular orbit around the Sun. Jump to: navigation, search Nicolaus Copernicus (in Latin; German: ; Polish: ; February 19, 1473 – May 24, 1543) was a German astronomer, mathematician and economist who developed the heliocentric (Sun-centered) theory of the solar system in a form detailed enough to make it scientifically useful. ... In physics, an orbit is the path that an object makes, around another object, whilst under the influence of a source of centripetal force, such as gravity. ...

He supposed the Sun to be a disk of glass which reflects the light of the universe. He made the lunar month consist of 29 1/2 days, the lunar year of 354, and the solar year of 365 1/2 days. Jump to: navigation, search Prism splitting light Light is electromagnetic radiation with a wavelength that is visible to the eye (visible light) or, in a technical or scientific setting, electromagnetic radiation of any wavelength. ... Jump to: navigation, search In lunar calendars, a lunar month is the time between two successive similar syzygies (new moons or full moons). ... Since there are about twelve lunations (synodic months) in a solar year, this period (354. ... A tropical year is the length of time that the Sun, as viewed from the Earth, takes to return to the same position along the ecliptic (its path among the stars on the celestial sphere). ...

He was the first to publish a book on the Pythagorean doctrines, a treatise of which Plato made use in the composition of his Timaeus. Philolaus represented the philosophical system of his school in a work Peri fyseos (About the nature). Speusipus, the Plato's successor at the Academy summarized Philolaus's work. Timaeus is a theoretical treatise of Plato in the form of a Socratic dialogue, written circa 360 B.C. The work puts forward speculation on the nature of the physical world. ... An academy is an institution for the study of higher learning. ...

Philolaus was deeply involved in the distinctively Pythagorean number theory, dwelling particularly on the properties inherent in the decad – the sum of the first four numbers, consequently the fourth triangular number, the tetractys – which he called great, all-powerful, and all-producing. The great Pythagorean oath was taken by the sacred tetractys. The discovery of the regular solids is attributed to Pythagoras by Eudemus, and Empedocles is stated to have been the first who maintained that there are four classical elements. Philolaus, connecting these ideas, held that the elementary nature of bodies depends on their form, and assigned the tetrahedron to fire, the octahedron to air, the icosahedron to water, and the cube to earth; the dodecahedron he assigned to a fifth element, aether, or, as some think, to the universe. This theory, however superficial from the standpoint of observation, indicates considerable knowledge of geometry and gave a motivating boost to the study of science. Following Parmenides' philosophy, Philolaus regarded the soul as a "mixture and harmony" of the bodily parts; he also assumed a substantial soul, whose existence in the body is an exile on account of sin. A number is an abstract entity used originally to describe quantity. ... A triangular number is a number that can be arranged in the shape of an equilateral triangle. ... The Tetractys, also known as the decad, is a triangular figure consisting of ten points arranged in four rows: one, two, three, and four points in each row. ... The Tetractys, also known as the decad, is a triangular figure consisting of ten points arranged in four rows: one, two, three, and four points in each row. ... Jump to: navigation, search In solid geometry and some ancient physical theories, a Platonic solid is a convex polyhedron with all its faces being congruent regular polygons, and the same number of faces meeting at each of its vertices. ... Jump to: navigation, search Many ancient philosophies use a set of archetypal classical elements to explain patterns in nature. ... Jump to: navigation, search For academic journal, see Tetrahedron A tetrahedron (plural: tetrahedra) is a polyhedron composed of four triangular faces, three of which meet at each vertex. ... Jump to: navigation, search This article needs to be cleaned up to conform to a higher standard of quality. ... Jump to: navigation, search An octahedron (plural: octahedra) is a polyhedron with eight faces. ... Air is one of the four classical elements, and is associated with many other concepts, such as the sword suit in the tarot. ... Jump to: navigation, search An icosahedron [ËŒaıkÉ™sÉ™hiːdrÉ™n] noun (plural: -drons, -dra [-drÉ™]) is a polyhedron having 20 faces, but usually a regular icosahedron is meant. ... Water is one of the four classical elements in ancient Greek philosophy and science. ... Jump to: navigation, search A cube (or regular hexahedron) is a three-dimensional Platonic solid composed of six square faces, with three meeting at each vertex. ... This article needs to be cleaned up to conform to a higher standard of quality. ... Jump to: navigation, search A dodecahedron is literally a polyhedron with 12 faces, but usually a regular dodecahedron is meant: a Platonic solid composed of twelve pentagonal faces, with three meeting at each vertex. ... Jump to: navigation, search Many ancient philosophies use a set of archetypal classical elements to explain patterns in nature. ... The aether (also spelled ether) is a substance concept, historically used in science and philosophy. ... Jump to: navigation, search The deepest visible-light image of the cosmos. ... Jump to: navigation, search Geometry (Greek γεωμετρία; geo = earth, metria = measure) arose as the field of knowledge dealing with spatial relationships. ... // What is science? There are various understandings of the word science. According to empiricism, scientific theories are objective, empirically testable, and predictive — they predict empirical results that can be checked and possibly contradicted. ... Parmenides of Elea (5th century BC) was an ancient Greek philosopher born in Elea, a Greek city on the Southern coast of Italy. ...

This article incorporates text from the 1911 Encyclopædia Britannica, which is in the public domain. Jump to: navigation, search Supporters contend that the Eleventh Edition of the Encyclopædia Britannica (1910-1911) represents the sum of human knowledge at the beginning of the 20th century; indeed, it was advertised as such. ... The public domain comprises the body of all creative works and other knowledge—writing, artwork, music, science, inventions, and others—in which no person or organization has any proprietary interest. ...

External links

• Stanford Encyclopedia of Philosophy entry