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	PHILOLAUS - LoveToKnow Article on PHILOLAUS
		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 (see Plut.
		Philolaus 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 their view.
		Philolaus supposed that the sphere of the fixed stars, the five planets, the sun, moon and earth, all moved round the central fire, which he called the hearth of the universe, the house of Zeus, and the mother of the gods (see Stob.
	www.1911encyclopedia.org /P/PH/PHILOLAUS.htm (609 words)

	Philolaus - Wikipedia, the free encyclopedia
		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 wither Pythagoras or the younger Hicetas (circa 400 BC – circa 335 BC) of Syracuse.
		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.
		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.
	en.wikipedia.org /wiki/Philolaus (875 words)

	Philolaus
		Philolaus' primary example of such a harmonia of limiters and unlimiteds is a musical scale, in which the continuum of sound is limited according to whole number ratios, so that the octave, fifth, and fourth are defined by the ratios 2 : 1, 4 : 3 and 3 : 2, respectively.
		Philolaus is one of twenty thinkers whose views on the causes of disease are presented in the papyrus, and the relatively detailed presentation of Philolaus' views suggests that Meno had access to his book.
		Philolaus is included among those thinkers who argue that diseases arise from the elements which constitute the body, so that the section on Philolaus begins with his account of the constitution of the human body, which is in effect his account of the nature of the embryo and newborn infant.
	plato.stanford.edu /entries/philolaus (10298 words)

	Philolaus
		Philolaus specified that the diesis (by which he meant the diatonic semitone, later also called limma) has the ratio 256:243, and noted that the difference between those numbers is 13.
		Philolaus makes much ado about the fact that the difference between these differences (14 and 13) is 1 ("unity"), and he equates the "comma", which is the difference in pitch-size between the apotome and limma (which he calls diesis), to 1.
		Philolaus, a Pythagorean, tried to divide the tone in another manner, postulating that the tone had its origin in the number that constitutes the first cube of the first odd number -- for that number was highly revered among the Pythagoreans.
	tonalsoft.com /enc/p/philolaus.aspx (1934 words)

	Philolaus -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-11-07)
		Philolaus (circa 480 BC – circa 405 BC) was a (A native or inhabitant of Greece) Greek (A person skilled in mathematics) mathematician and (A specialist in philosophy) philosopher.
		Philolaus was probably born in (Tropical Asiatic shrub; source of croton oil) Croton (after a Greek historian (Click link for more info and facts about Diogenes Laërtius) Diogenes Laërtius) or in (Click link for more info and facts about Tarentum) Tarentum or (Click link for more info and facts about Heraclea) Heraclea.
		Philolaus was perhaps also connected with the Pythagorean exiles at Phlius mentioned in (Ancient Athenian philosopher; pupil of Socrates; teacher of Aristotle (428-347 BC)) Plato's (Click link for more info and facts about Phaedo) Phaedo.
	www.absoluteastronomy.com /encyclopedia/p/ph/philolaus.htm (796 words)

	Dictionary of Greek and Roman Biography and Mythology, page 304 (v. 3) (Site not responding. Last check: 2007-11-07)
		The statements that Philolaus was the instructor of Gorgias, and a disciple of Lysis, for the purpose of paying sepulchral honours to whom he came to Thebes (Olympiodorus ad Plat.
		In all probability, what Philolaus had written was comprised in one treatise, divided into three books, though this division was doubtless made not b}T the author, but by the copyists.
		The name was very likely given, not by Philolaus himself, but by some admirer of him, who regarded his treatise as the fruit of a sort of mystic inspiration, and possibly in imitation of the way in which the books of Herodotus were named.
	ancientlibrary.com /smith-bio/2638.html (791 words)

	Dictionary of Greek and Roman Biography and Mythology, page 303 (v. 3) (Site not responding. Last check: 2007-11-07)
		PHILOLAUS (SiAo'Aaos), that is, friend of the people, was a surname of Asclepius, under which he had a temple in Laconia (Paus.
		Philolaus is not mentioned among the Pythagorean teachers of Plato by Cicero, Appuleius, or Hieronymus (In-terpr.
		Philolaus lived for some time at Heracleia, where he was the pupil of Aresas, or (as Plutarch calls him) Arcesus (lamblich.
	ancientlibrary.com /smith-bio/2637.html (988 words)

	Bryn Mawr Classical Review 94.03.14
		The first book devoted to Philolaus alone since A. Boeckh's Philolaus des Pythagoreers Lehren nebst den Bruchstuecken seines Werkes of 1819, Philolaus of Croton is a clear and well- argued book in which Huffman provides an important reevaluation of the Philolaus fragments and testimonia and a significant rethinking of Philolaus' views.
		Philolaus might well argue that, although there are a plurality of entities, they each individually are completely determinate in the way required by Parmenides.
		Huffman begins with a series of interpretive essays and then goes on to commentaries on all the fragments and testimonia he accepts as genuine, and discussions of all those that he rejects as spurious or doubtful (and he is careful to draw distinctions between the two classes).
	omega.cohums.ohio-state.edu /mailing_lists/BMCR-L/Mirror/1994/94.03.14.html (1766 words)

	PYTHAGORAS - LoveToKnow Article on PYTHAGORAS
		Philolaus, who resided at Thebes in the end of the 5th century (cf.
		Numbers, in other words, were conceived at that early stage of thought not as relations or qualities predicable of things, but as themselves constituting the substance or essence of the phenomenathe rational reality to which the appearances of sense are reducible.
		Hence it is not possible to separate his work from that of his early disciples, and we must therefore treat the geometry of the early Pythagorean school as a whole.
	www.1911encyclopedia.org /P/PY/PYTHAGORAS.htm (6595 words)

	[No title]
		Anaxagoras and Philolaus both lived from the early fifth to the late fifth century BCE; Zeno, Melissus, and Empedocles were their contemporaries.
		Anaxagoras was born in Clazomenae, in Asia Minor; Philolaus was from Tarentum, in southern Italy.
		Philolaus tried to show that multiple things have their source, in some sense, in "the One" or in unity, and that "the One" or unity can itself be analyzed or further understood in some way.
	www.gmu.edu /courses/phil/ancient/anph2.htm (3486 words)

	PYTHAGOREAN :::: SOURCES :: AND : FRAGMENTS.
		Nevertheless, the Pythagorean Philolaus has tried to divide the tone otherwise; his tone's starting-point is the first uneven number which forms a cube, and you know that the first uneven number was an object of veneration among these Pythagoreans.
		Philolaus divides this number 27 in two parts, the one greater than half, which he calls apotome, the other one smaller than half he calls sharp, but which latterly has become known as a minor half-tone.
		He supposes that this sharp contain thirteen unities, because 13 is the difference between 256 and 243, and that this same number is the sum of 9, 3, and unity, in which unity plays the part of the point, 3 the odd first line, and 9 of the first odd square.
	www.spirasolaris.ca /sbb5s1.html (4060 words)

	Nicolaus Copernicus - Wikipedia, the free encyclopedia
		Philolaus (4th century BC) was one of the first to hypothesize movement by the Earth, probably inspired by Pythagoras' theories about a spherical Globe.
		Aristarchus of Samos in the 3rd century BC had developed some theories of Heraclides Ponticus (speaking of a revolution by Earth on its axis) to propose what was, so far as is known, the first serious model of a heliocentric solar system.
		Copernicus cited Aristarchus and Philolaus in an early manuscript of his book which survives, stating: "Philolaus believed in the mobility of the earth, and some even say that Aristarchus of Samos was of that opinion." For reasons unknown, he struck this passage before publication of his book.
	en.wikipedia.org /wiki/Copernicus (3373 words)

	Presocratic philosophy: Pythagorean esotericism
		For Philolaus, as for his predecessors, the Universe was made of pairs of opposites, the Limited (the Monad) and the Unlimited (the Decad) (9).
		Philolaus specified the notes of the scale by defining the major fifth and the major fourth, as well as the composition of the octave (five tones and two semi-tones), thus laying the foundation for modern music.
		Philolaus justified this choice through an anthropological argument, as reported in fragment DK A13, commenting that not only the Greeks but all nations gave a special role to the figure 10 in their counting systems.
	www.pasteur.fr /recherche/unites/REG/causeries/Pythagoreans.html (3866 words)

	The Pythagoreans (Site not responding. Last check: 2007-11-07)
		Philolaus and Lysis, the latter of whom had escaped as a young man from the massacre of Croton, had already found their way to Thebes.
		Philolaus wrote on medicine and, while apparently influenced by the theories of the Sicilian school, he opposed them from the Pythagorean standpoint.
		Philolaus made bile, blood, and phlegm the causes of disease and, in accordance with this theory, he had to deny that the phlegm was cold, as the Sicilian school held.
	www.askwhy.co.uk /judaism/Pythagoreans.html (6489 words)

	A Treatise on Government by Aristotle: Part 2 Chapter 12 (continued) - The Literature Page
		Philolaus also, of the family of the Bacchiades, was a Theban legislator.
		As Philolaus gave them laws concerning many other things, so did he upon adoption, which they call adoptive laws; and this he in particular did to preserve the number of families.
		Philolaus introduced the law for the equal distribution of goods; Plato that for the community of women, children, and goods, and also for public tables for the women; and one concerning drunkenness, that they might observe sobriety in their symposiums.
	www.literaturepage.com /read/treatiseongovernment-68.html (265 words)

	Pythagoras
		The first such cosmic model in the Pythagorean tradition is that of Philolaus in the second half of the fifth century, a model which still shows traces of the connection to the moral cosmos of Pythagoras in its account of the counter-earth and the central fire (see Philolaus).
		Philolaus' cosmos and his metaphysical system, in which all things arise from limiters and unlimiteds and are known through numbers, are not stolen from Pythagoras.
		Philolaus' system is nonetheless an intelligible development of the reverence for mathematical truth found in Pythagoras' own cosmological scheme, which is embodied in the acusmata.
	plato.stanford.edu /entries/pythagoras (10548 words)

	TMTh:: PHILOLAUS
		When the house where the disciples of Pythagoras met was burned to the ground, Philolaus was one of the three who escaped (the others were Archippus and Lyses).
		Philolaus wrote two books ("Bacchae" and "On setting") in Doric dialect, of which unfortunately only a few fragments have survived.
		Philolaus used myths in his teaching, as the Pythagoreans were accustomed to do.
	www.tmth.edu.gr /en/aet/1/80.html (307 words)

	Philolaus of Croton: Pythagorean and Presocratic - Cambridge University Press (Site not responding. Last check: 2007-11-07)
		This is the first comprehensive study for nearly 200 years of what remains of the writings of the Presocratic philosopher Philolaus of Croton (c.
		These fragments are crucial to our understanding of one of the most influential schools of ancient philosophy, the Pythagoreans; they also show close ties with the main lines of development of Presocratic thought, and represent a significant response to thinkers such as Parmenides and Anaxagoras.
		Philolaus’ use of archai and the method of hypothesis; Part III.
	www.cambridge.org /catalogue/print.asp?isbn=052141525X&print=y (252 words)

	Earth & Sky : Frequently Asked Science Questions (Site not responding. Last check: 2007-11-07)
		The idea of a counter-earth first came from Philolaus of Croton, in Italy, around 450 B.C. His are the earliest known texts that detail the structure of the cosmos.
		Philolaus developed a geometric portrait of the cosmos that moved the earth from the center of the cosmos and replaced it with an invisible Central Fire.
		Philolaus also contrived an invisible counter-earth, which, he wrote, travels in a circular orbit inside our orbit, directly between earth and the Central Fire.
	www.earthsky.org /faqs?c=a348110d50&f=358 (253 words)

	Philolaus and Euclid (Site not responding. Last check: 2007-11-07)
		With the exception of Philolaus, all ancient Greek and modern theorists refer to ratio 256/243 as a limma (lit.
		For a second perspective, refer to Figure 9, which illustrates Philolaus’ diatonic scale distributed over the entire GPS, and in the context of the Dorian and Lydian Modes.
		Finally, observe that in the Dorian Mode, Philolaus’ diatonic scale forms a sequence of five descending 3/2’s, and in the Lydian Mode, a sequence of five ascending 3/2’s.
	www.chrysalis-foundation.org /Philolaus_&_Euclid.htm (3187 words)

	Diogenes Laertius: Life of Philolaus, from Lives of the Philosophers, translated by C.D. Yonge (Site not responding. Last check: 2007-11-07)
		BY DIOGENES LAERTIUS, TRANSLATED BY C.D. PHILOLAUS was a native of Crotona, and a pupil of Pythagoras, it was from him that Plato wrote to Dion to take care and purchase the books of Pythagoras.
		And he was the first person who affirmed that the earth moved in a circle; though some attribute the assertion of this principle to Icetas of Syracuse.
		He wrote one book, which Hermippus reports, on the authority of some unknown writer, that Plato the philosopher purchased when he was in Sicily (having come thither to the court of Dionysius), of the relations of Philolaus, for forty Alexandrian minae of silver; and that from this book he copied his Timaeus.
	classicpersuasion.org /pw/diogenes/dlphilolaus.htm (322 words)

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