Knowledge

Philolaus

Source 📝

536:
three forged treatises of Pythagoras. Burkert's arguments (1972a, 238–277), supported by further study (Huffman 1993), have led to a consensus that some 11 fragments are genuine (Frs. 1–6, 6a, 7, 13, 16 and 17 in the numbering of Huffman 1993) and derive from Philolaus' book On Nature (Barnes 1982; Kahn 1993 and 2001; Kirk, Raven and Schofield 1983; Nussbaum 1979; Zhmud 1997). Fragments 1, 6a and 13 are identified as coming from the book On Nature by ancient sources. Stobaeus cites fragments 2 and 4–7 as coming from a work On the Cosmos, but this appears to be an alternate title for On Nature, which probably arose because the chapter heading in Stobaeus under which the fragments are cited is 'On the Cosmos.'
435: 3107: 1273: 3094: 556: 1185: 49: 1261: 1224: 642:, and after all of them the fire of the hearth which holds position at the centre. The highest part of the surrounding, where the elements are found in their purity, he calls Olympus; the regions beneath the orbit of Olympus, where are the five planets with the sun and the moon, he calls the world; the part under them, being beneath the moon and around the earth, in which are found generation and change, he calls the sky. 1288: 1015: 523:, he was hardly likely to feel much reluctance in publishing them; and amid the conflicting and improbable accounts preserved in the authorities above referred to, little more can be regarded as trustworthy, except that Philolaus was the first who published a book on the Pythagorean doctrines, and that Plato read and made use of it. Historians from the 577:
essence was not the internal foundation of the principles of which the world was founded, that is, of the limiting and unlimited elements. Now since these principles are not mutually similar, neither of similar nature, it would be impossible that the order of the world should have been formed by them, unless the harmony intervened .
591:
Philolaus is trying to show how the ordered universe that we know came into its present condition. It arose, he says, by the action of harmony on a basic substance, which we do not know but must infer. This substance consisted of different primary elements, and harmony fitted these together in such a
503:
as a book for teaching theology by means of mathematics. It appears, in fact, from this, as well as from the extant fragments, that the first book of the work contained a general account of the origin and arrangement of the universe. The second book appears to have been an exposition of the nature of
567:
Philolaus argued at the foundation of everything is the part played by the ideas of limit and the unlimited. One of the first declarations in the work of Philolaus was that all things in the universe result from a combination of the unlimited and the limiting; for if all things had been unlimited,
535:
It is implied that these books were not by Philolaus himself, and it seems likely that the statement refers to three spurious works assigned to Pythagoras at D.L. VIII 6 (Burkert 1972a, 224–5). The story of Plato's purchase of these books from Philolaus was probably invented to authenticate the
576:
This is the state of affairs about nature and harmony. The essence of things is eternal; it is a unique and divine nature, the knowledge of which does not belong to Man. Still it would not be possible that any of the things that are, and are known by us, should arrive to our knowledge, if this
450:
collected in a written form some of the principal Pythagorean doctrines, which were handed down as heirlooms in their families, under strict injunctions that they should not be made public. But amid the different and inconsistent accounts of the matter, the first publication of the Pythagorean
515:, who purchased it from Philolaus, who was at the time in deep poverty. Other versions of the story represent Plato as purchasing it himself from Philolaus or his relatives when in Sicily. Out of the materials which he derived from these books Plato is said to have composed his 637:
Philolaus says that there is fire in the middle at the centre and again more fire at the highest point and surrounding everything. By nature the middle is first, and around it dance ten divine bodies—the sky, the planets, then the sun, next the moon, next the earth, next the
262:
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. He may have been the first to write about Pythagorean doctrine. According to
257:
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.
425:
As to his death, Diogenes Laërtius reports a dubious story that Philolaus was put to death at Croton on account of being suspected of wanting to be the tyrant; a story which Diogenes Laërtius even chose to put into verse.
778:"The most likely date for Philolaus' birth would then appear to be around 470, although he could have been born as early as 480 or as late as 440. He appears to have lived into the 380s and at the very least until 399." 624:
According to Stobaeus, Philolaus did away with the ideas of fixed direction in space and developed one of the first non-geocentric views of the universe and in his new way of thinking, the universe revolved around a
705:
It has been pointed out, however, that Stobaeus betrays a tendency to confound the dogmas of the early Ionian philosophers, and in his accounts, he occasionally mixes up Platonism with Pythagoreanism.
382:
The writings of much later writers are the sources of further reports about his life. They are scattered and of dubious value in reconstructing his life. Apparently, he lived for some time at
620:) in the world-order (cosmos) was fitted together out of things which are unlimited and out of things which are limiting, both the world-order as a whole and everything in it. 3143: 466:. It might have been one treatise divided into three books. Plato is said to have procured a copy of his book. Later, it was claimed that Plato composed much of his 519:. But in the age of Plato the leading features of the Pythagorean doctrines had long ceased to be a secret; and if Philolaus taught the Pythagorean doctrines at 419: 1029: 1020: 1200: 1090:(Diog. Laert. viii. 15, 55, 84, 85, iii. 9; A. Gellius, iV. iii. 17; lamblichus, Vit. Fyth. 31. p. 172; Tzetzes, Chiliad, x. 792, &c. xi. 38, &c.) 442:
Pythagoras and his earliest successors do not appear to have committed any of their doctrines to writing. According to Porphyrius (Vit. Pyth. p. 40)
1863: 3136: 1355: 1165: 2967: 3129: 2567: 1325: 1205: 4465: 3552: 398:
is the only authority for the claim that shortly after the death of Socrates, Plato traveled to Italy where he met with Philolaus and
4480: 3045: 2348: 1884: 1626: 1856: 1830: 692:
The system that Philolaus described predated the idea of spheres by hundreds of years, however. Nearly two-thousand years later,
4520: 4515: 4495: 2892: 4470: 4148: 4052: 2622: 1348: 979:"The story at D.L. 84 that Philolaus was killed because he was thought to be aiming at a tyranny is clearly a confusion with 689:
required a tenth. However, Greek scholar George Burch asserts his belief that Aristotle was lampooning Philolaus's addition.
2587: 3511: 2955: 2358: 1820: 1616: 1309: 876: 507:
He composed a work on the Pythagorean philosophy in three books, which Plato is said to have procured at the cost of 100
17: 3022: 1849: 4490: 4475: 3996: 1372: 1240: 1341: 4485: 550: 4173: 3777: 2991: 2924: 2557: 2437: 1753: 1024: 113: 331: 4340: 3060: 2817: 2705: 1880: 1162: 4500: 4440: 3690: 3627: 3520: 3319: 2769: 2700: 4397: 4269: 4211: 4125: 3948: 3734: 3678: 3584: 3494: 3251: 3242: 2396: 2212: 1292: 2187: 4312: 2931: 2902: 2262: 2117: 1550: 278:, which combine in a harmony. With his assertions that the Earth was not the center of the universe ( 568:
nothing could have been the object of knowledge. Limiters and unlimiteds are combined in a harmony (
3991: 3421: 3386: 3152: 3065: 2799: 2342: 1234: 734: 1145: 762: 4510: 4505: 4100: 3833: 3506: 3233: 3027: 3003: 2877: 2812: 2753: 2690: 2680: 2416: 2335: 2197: 2107: 1987: 1545: 1364: 803: 677: 546: 96: 2297: 342:, perhaps while fleeing the second burning of the Pythagorean meeting-place around 454 BC. 4352: 4259: 4010: 3901: 3891: 3757: 3650: 3485: 3050: 2998: 2897: 2725: 2675: 2660: 2655: 2426: 2227: 2162: 2152: 2102: 1692: 1565: 1500: 227: 4392: 4234: 3805: 3762: 3706: 3411: 3406: 3305: 3269: 3181: 3166: 3098: 2950: 2794: 2735: 2612: 2535: 2483: 2285: 2192: 2042: 1728: 1657: 1395: 487:
and from which he has preserved a series of passages. Other writers refer to a work entitled
399: 1190:
One or more of the preceding sentences incorporates text from a publication now in the
1110: 434: 4229: 4168: 3371: 3209: 3199: 3075: 3015: 2979: 2822: 2645: 2592: 2562: 2552: 2461: 2324: 2217: 2132: 2087: 2067: 1912: 1897: 1799: 1540: 1490: 1410: 1385: 411: 31: 1272: 1229: 455: 395: 8: 4292: 4249: 4183: 4042: 3981: 3655: 3645: 3538: 3475: 3381: 3214: 3171: 3055: 2974: 2962: 2943: 2907: 2827: 2745: 2730: 2720: 2670: 2665: 2607: 2476: 2368: 2232: 2222: 2122: 2092: 2032: 2007: 1932: 1922: 1907: 1570: 1475: 1425: 1400: 1319: 1277: 719: 693: 797: 4367: 4307: 4297: 4095: 3958: 3853: 3848: 3767: 3376: 3361: 3111: 3070: 3010: 2938: 2804: 2779: 2597: 2572: 2540: 2378: 2137: 2082: 2047: 1942: 1804: 1718: 714: 468: 298:
as the center of the universe and that spheres (including the Sun) revolved around it.
282:), he is credited with the earliest known discussion of concepts in the development of 106: 54: 3121: 458:
speaks of Philolaus composing one book, but elsewhere he speaks of three books, as do
274:
He argued that at the foundation of everything is the part played by the limiting and
4415: 4279: 3881: 3660: 3617: 3462: 3391: 3259: 3189: 3106: 2784: 2695: 2545: 2471: 2444: 2207: 2027: 2017: 1952: 1872: 1713: 1560: 1465: 1420: 1245: 1064:
Diogenes Laërtius, viii. 15, 55, 84, 85, iii. 9; Aulus Gellius, iii. 17; Iamblichus,
698: 626: 415: 356: 983:
who is mentioned in the context and did have such a death." Carl A. Huffman, (1993)
4407: 4382: 4362: 4287: 4221: 4201: 4047: 3858: 3823: 3724: 3219: 2986: 2857: 2774: 2530: 2518: 2466: 2202: 1825: 1778: 1748: 1738: 1687: 1662: 980: 903:
Not to be confused with the first burning of the meeting place, in the lifetime of
512: 504:
numbers, which in the Pythagorean theory are the essence and source of all things.
491:, which may have been another name for the same work, and which may originate from 447: 407: 383: 188: 1265: 4330: 4120: 4032: 3970: 3896: 3868: 3815: 3787: 3612: 3194: 2627: 2617: 2511: 2237: 1773: 1708: 1677: 1575: 1505: 1304: 1169: 871: 779: 364: 327: 1300: 867: 702:
that Philolaus already knew about the Earth's revolution around a central fire.
264: 4420: 4105: 4070: 3795: 3328: 3204: 2887: 2882: 2710: 2602: 2582: 2410: 1967: 1937: 1636: 1515: 1450: 1430: 1233: 685:, as without it there would be only nine revolving bodies, and the Pythagorean 520: 443: 323: 250: 118: 4459: 4153: 3986: 2847: 2715: 2685: 2506: 2314: 2257: 1758: 1743: 1723: 1196: 1191: 686: 682: 639: 459: 319: 283: 161: 1841: 4435: 4322: 4135: 3976: 3607: 3457: 2789: 2577: 2252: 2012: 2002: 1606: 1455: 742: 630: 295: 254: 156: 48: 1333: 4037: 3876: 3714: 3264: 2403: 2291: 1997: 1982: 1445: 1390: 508: 279: 167: 133: 4357: 4302: 4191: 4158: 4090: 4080: 4019: 3943: 3938: 3911: 3752: 3592: 3565: 3528: 3501: 3452: 3429: 3336: 3287: 3279: 2389: 2308: 2247: 2242: 2182: 2167: 2112: 2097: 2052: 1992: 1977: 1957: 1927: 1892: 1763: 1580: 1525: 1485: 1415: 1281: 904: 729: 724: 463: 403: 376: 315: 268: 259: 58: 952:
13, although the account given by Plutarch involves great inaccuracies
799:
Philolaos des Pythagoreers Lehren nebst den Bruchstücken seines Werkes
555: 338:
settlers). It is most likely that he came from Croton. He migrated to
4425: 4387: 4196: 4163: 4110: 4085: 4075: 3966: 3925: 3886: 3838: 3800: 3772: 3744: 3640: 3560: 3366: 2127: 2077: 1972: 1962: 1947: 1917: 1667: 1510: 1495: 1440: 1435: 1380: 672: 138: 4372: 4335: 4254: 4244: 4143: 4062: 3906: 3828: 3729: 3719: 3696: 3686: 3597: 3444: 3434: 3396: 3356: 3351: 3341: 3292: 2279: 2057: 1902: 1768: 1596: 1460: 647: 492: 480: 391: 372: 371:
takes place, in 399 BC. That would make him a contemporary of
291: 4377: 3635: 3602: 3575: 2852: 2177: 2172: 2072: 2062: 2037: 1672: 1535: 1530: 1480: 1470: 1260: 496: 311: 307: 275: 1318: 438:
Discussion of Philolaus in a book by Charles Peter Mason (1870)
4430: 4347: 4206: 4115: 4027: 3843: 2147: 2022: 1783: 1733: 1682: 1555: 1405: 1287: 660: 617: 387: 351: 339: 335: 1042: 1040: 4264: 4239: 3933: 3533: 2523: 2501: 2157: 602: 594: 360: 346: 287: 3401: 1173:. Osirus, vol. 11. Saint Catherines Press, 1954. p. 267-294 1037: 671:, and Earth, all moved around a Central Fire. According to 668: 656: 306:
Various reports give the birthplace of Philolaus as either
215: 212: 203: 664: 375:, and would agree with the statement that Philolaus and 197: 30:"Philolaos" redirects here. For the Greek sculptor, see 3151: 808:
Pythagoras Lehren nebst den Bruchstücken seines Werkes.
451:
doctrines is pretty uniformly attributed to Philolaus.
1009: 1007: 1005: 1030:
Dictionary of Greek and Roman Biography and Mythology
402:. The pupils of Philolaus were said to have included 218: 194: 191: 587:
Robert Scoon explained Philolaus' universe in 1922:
294:, but rather that the Sun is. Philolaus discussed a 209: 200: 1019: 1002: 206: 1329:. Vol. 21 (11th ed.). 1911. p. 414. 1147:Philolaus, Fragment 6, Diels. Stobaeus i. 21. 460 681:, Philolaus added a tenth unseen body, he called 612:The book by Philolaus begins with the following: 529:Philolaus' Book: Genuine Fragments and Testimonia 4457: 985:Philolaus of Croton: Pythagorean and Presocratic 892:Philolaus of Croton: Pythagorean and Presocratic 784:Philolaus of Croton: Pythagorean and Presocratic 61:and Philolaus conducting musical investigations 1248:(Two volume ed.). Loeb Classical Library. 861: 859: 857: 855: 3137: 1871: 1857: 1349: 271:, Philolaus was the successor of Pythagoras. 3867: 1209:(11th ed.). Cambridge University Press. 655:In Philolaus's system a sphere of the fixed 1363: 852: 3180: 3144: 3130: 1864: 1850: 1356: 1342: 802:. In der Vossischen Buchhandlung. p.  47: 1108: 996:Diogenes Laërtius, iii. p. 84; cf. Suda, 935:Apollodorus ap. Diogenes Laërtius, ix. 38 475:One of the works of Philolaus was called 1228: 1195: 865: 836:, p. 267; Diogenes Laërtius, viii, p. 46 554: 433: 786:, pages 5–6. Cambridge University Press 767:The Stanford Encyclopedia of Philosophy 760: 547:Pythagoreanism § Music and harmony 14: 4458: 3318: 2893:Latin translations of the 12th century 495:. However, it has been mentioned that 27:Greek philosopher (c. 470 – c. 385 BC) 3241: 3125: 2623:Straightedge and compass construction 1845: 1337: 1154: 1143: 795: 2588:Incircle and excircles of a triangle 479:. It seems to be the same work that 3153:Ancient Greek schools of philosophy 1310:Stanford Encyclopedia of Philosophy 1298: 1055:Diogenes Laërtius, iii. 9, viii. 15 877:Stanford Encyclopedia of Philosophy 525:Stanford Encyclopedia of Philosophy 24: 987:, p. 6. Cambridge University Press 894:, p. 6. Cambridge University Press 472:based upon the book by Philolaus. 322:(the name of the coastal areas of 25: 4532: 4466:5th-century BC Greek philosophers 1253: 1241:Lives of the Eminent Philosophers 600:turns out to be an ordered world 4481:Ancient Greek political refugees 3105: 3092: 1286: 1271: 1259: 1222: 1183: 1013: 627:hypothetical astronomical object 187: 1244:. Vol. 2:8. Translated by 1235:"Pythagoreans: Philolaus"  1176: 1137: 1128: 1119: 1102: 1093: 1084: 1075: 1058: 1049: 990: 973: 964: 955: 938: 929: 916: 551:Pythagorean astronomical system 2925:A History of Greek Mathematics 2438:The Quadrature of the Parabola 1109:Gaffurius, Franchinus (1492). 897: 884: 839: 826: 813: 789: 772: 754: 582:Philolaus, Fragment DK 44B 6a. 13: 1: 4521:4th-century BC mathematicians 4516:5th-century BC mathematicians 4496:Pythagoreans of Magna Graecia 1754:Inferior and superior planets 1216: 908: 540: 239: 81: 70: 4471:Ancient Greek mathematicians 2706:Intersecting secants theorem 386:, where he was the pupil of 301: 7: 2701:Intersecting chords theorem 2568:Doctrine of proportionality 1046:Diogenes Laërtius, viii. 85 970:Diogenes Laërtius, viii. 46 708: 429: 355:, he was the instructor of 10: 4537: 2397:On the Sphere and Cylinder 2350:On the Sizes and Distances 1831:Medieval Islamic astronomy 1628:On the Sizes and Distances 603: 595: 544: 231: 29: 4406: 4321: 4278: 4220: 4182: 4134: 4061: 4018: 4009: 3957: 3924: 3814: 3786: 3743: 3705: 3677: 3626: 3583: 3574: 3551: 3519: 3493: 3484: 3443: 3420: 3327: 3278: 3250: 3232: 3159: 3099:Ancient Greece portal 3088: 3038: 2916: 2903:Philosophy of mathematics 2873: 2866: 2840: 2818:Ptolemy's table of chords 2762: 2744: 2643: 2636: 2492: 2454: 2271: 1879: 1873:Ancient Greek mathematics 1821:Medieval European science 1813: 1792: 1701: 1650: 1589: 1551:Sosigenes the Peripatetic 1371: 961:Diogenes Laërtius, iii. 6 290:is not the center of the 176: 147: 124: 112: 102: 92: 88: 77: 66: 46: 39: 4491:Presocratic philosophers 4476:Ancient Greek physicists 3992:Alexander of Aphrodisias 2770:Aristarchus's inequality 2343:On Conoids and Spheroids 1160:Burch, George Bosworth. 1081:DK 44 B 2, 3, 4, 5, 6, 7 1023:(1870). "Philolaus". In 890:Carl A. Huffman, (1993) 748: 4101:Lucius Annaeus Cornutus 3834:Thrasymachus of Corinth 3512:Metrodorus of Lampsacus 2878:Ancient Greek astronomy 2691:Inscribed angle theorem 2681:Greek geometric algebra 2336:Measurement of a Circle 1546:Sosigenes of Alexandria 1365:Ancient Greek astronomy 1326:Encyclopædia Britannica 1206:Encyclopædia Britannica 531:, noted the following: 97:Pre-Socratic philosophy 4486:Ancient Thebes, Greece 3758:Aristippus the Younger 3112:Mathematics portal 2898:Non-Euclidean geometry 2853:Mouseion of Alexandria 2726:Tangent-secant theorem 2676:Geometric mean theorem 2661:Exterior angle theorem 2656:Angle bisector theorem 2360:On Sizes and Distances 1618:On Sizes and Distances 1264:Quotations related to 1150:. Classical Philology. 1144:Scoon, Robert (1922). 796:Böckh, August (1819). 761:Huffman, Carl (2020), 653: 622: 610: 585: 564: 538: 439: 367:, around the time the 286:, the theory that the 4235:Eudorus of Alexandria 3806:Asclepiades of Phlius 3763:Theodorus the Atheist 2800:Pappus's area theorem 2736:Theorem of the gnomon 2613:Quadratrix of Hippias 2536:Circles of Apollonius 2484:Problem of Apollonius 2462:Constructible numbers 2286:Archimedes Palimpsest 1729:Deferent and epicycle 1658:Antikythera mechanism 635: 614: 589: 574: 558: 533: 437: 379:were contemporaries. 4169:Diogenes of Oenoanda 3016:prehistoric counting 2813:Ptolemy's inequality 2754:Apollonius's theorem 2593:Method of exhaustion 2563:Diophantine equation 2553:Circumscribed circle 2370:On the Moving Sphere 1800:Babylonian astronomy 1491:Hippocrates of Chios 1295:at Wikimedia Commons 1099:(Böckh, I.e. p. 22.) 394:calls him) Arcesus. 53:Medieval woodcut by 32:Philolaos (sculptor) 4293:Apollonius of Tyana 4240:Philo of Alexandria 4043:Agrippa the Skeptic 3982:Strato of Lampsacus 3102: • 2908:Neusis construction 2828:Spiral of Theodorus 2721:Pythagorean theorem 2666:Euclidean algorithm 2608:Lune of Hippocrates 2477:Squaring the circle 2233:Theon of Alexandria 1908:Aristaeus the Elder 1571:Theon of Alexandria 1021:Charles Peter Mason 694:Nicolaus Copernicus 18:Philolaus of Croton 4501:Ancient Crotonians 4368:Plutarch of Athens 4308:Numenius of Apamea 4298:Moderatus of Gades 3768:Hegesias of Cyrene 2795:Menelaus's theorem 2785:Irrational numbers 2598:Parallel postulate 2573:Euclidean geometry 2541:Apollonian circles 2083:Isidore of Miletus 1805:Egyptian astronomy 1719:Circle of latitude 1276:Works by or about 1246:Hicks, Robert Drew 1230:Laërtius, Diogenes 1168:2013-10-29 at the 948:; comp. Plutarch, 912: 509 BC 715:Alcmaeon of Croton 565: 440: 267:(1819), who cites 247: 385 BC 107:Western philosophy 55:Franchino Gaffurio 4453: 4452: 4449: 4448: 4416:Nicetes of Smyrna 4005: 4004: 3920: 3919: 3882:Apollonius Cronus 3673: 3672: 3669: 3668: 3547: 3546: 3471: 3470: 3392:Metrodorus of Cos 3314: 3313: 3301: 3300: 3228: 3227: 3119: 3118: 3084: 3083: 2836: 2835: 2823:Ptolemy's theorem 2696:Intercept theorem 2546:Apollonian gasket 2472:Doubling the cube 2445:The Sand Reckoner 1839: 1838: 1714:Celestial spheres 1320:"Philolaus"  1291:Media related to 1201:Stobaeus, Joannes 1163:The Counter-Earth 1134:Fragment DK 44B 3 1125:Fragment DK 44B 1 699:De revolutionibus 696:would mention in 456:Diogenes Laërtius 396:Diogenes Laërtius 180: 179: 16:(Redirected from 4528: 4408:Second Sophistic 4383:Ammonius Hermiae 4288:Nigidius Figulus 4202:Philo of Larissa 4184:Academic Skeptic 4048:Sextus Empiricus 4016: 4015: 3865: 3864: 3824:Euclid of Megara 3703: 3702: 3581: 3580: 3491: 3490: 3325: 3324: 3316: 3315: 3248: 3247: 3239: 3238: 3178: 3177: 3160:Proto-philosophy 3146: 3139: 3132: 3123: 3122: 3110: 3109: 3097: 3096: 3095: 2871: 2870: 2858:Platonic Academy 2805:Problem II.8 of 2775:Crossbar theorem 2731:Thales's theorem 2671:Euclid's theorem 2641: 2640: 2558:Commensurability 2519:Axiomatic system 2467:Angle trisection 2432: 2422: 2384: 2374: 2364: 2354: 2330: 2320: 2303: 1866: 1859: 1852: 1843: 1842: 1826:Indian astronomy 1779:Sublunary sphere 1749:Hipparchic cycle 1688:Mural instrument 1663:Armillary sphere 1642: 1632: 1622: 1612: 1602: 1358: 1351: 1344: 1335: 1334: 1330: 1322: 1314: 1305:Zalta, Edward N. 1290: 1275: 1263: 1249: 1237: 1226: 1225: 1211: 1210: 1189: 1187: 1186: 1180: 1174: 1158: 1152: 1151: 1141: 1135: 1132: 1126: 1123: 1117: 1116: 1112:Theorica musicae 1106: 1100: 1097: 1091: 1088: 1082: 1079: 1073: 1072:, x. 792, xi. 38 1066:Vita Pythagorica 1062: 1056: 1053: 1047: 1044: 1035: 1034: 1017: 1016: 1011: 1000: 994: 988: 977: 971: 968: 962: 959: 953: 946:Vita Pythagorica 942: 936: 933: 927: 920: 914: 913: 910: 901: 895: 888: 882: 881: 872:Zalta, Edward N. 863: 850: 847:Vita Pythagorica 843: 837: 834:Vita Pythagorica 830: 824: 821:Vita Pythagorica 817: 811: 810: 793: 787: 776: 770: 769: 758: 651: 606: 605: 598: 597: 592:way that nature 583: 561:Theorica Musicae 513:Dion of Syracuse 248: 244: 241: 233: 225: 224: 221: 220: 217: 214: 211: 208: 205: 202: 199: 196: 193: 83: 72: 51: 37: 36: 21: 4536: 4535: 4531: 4530: 4529: 4527: 4526: 4525: 4456: 4455: 4454: 4445: 4402: 4331:Ammonius Saccas 4317: 4274: 4222:Middle Platonic 4216: 4178: 4130: 4121:Marcus Aurelius 4057: 4033:Timon of Phlius 4001: 3971:Aristotelianism 3953: 3916: 3897:Diodorus Cronus 3863: 3810: 3782: 3739: 3701: 3665: 3622: 3570: 3543: 3515: 3480: 3467: 3439: 3416: 3310: 3297: 3274: 3224: 3176: 3155: 3150: 3120: 3115: 3104: 3093: 3091: 3080: 3046:Arabian/Islamic 3034: 3023:numeral systems 2912: 2862: 2832: 2780:Heron's formula 2758: 2740: 2632: 2628:Triangle center 2618:Regular polygon 2495:and definitions 2494: 2488: 2450: 2430: 2420: 2382: 2372: 2362: 2352: 2328: 2318: 2301: 2267: 2238:Theon of Smyrna 1883: 1875: 1870: 1840: 1835: 1809: 1788: 1774:Spherical Earth 1709:Callippic cycle 1697: 1678:Equatorial ring 1646: 1640: 1630: 1620: 1610: 1600: 1585: 1576:Theon of Smyrna 1367: 1362: 1317: 1299:Huffman, Carl. 1256: 1223: 1219: 1214: 1199:, ed. (1911). " 1184: 1182: 1181: 1177: 1170:Wayback Machine 1159: 1155: 1142: 1138: 1133: 1129: 1124: 1120: 1107: 1103: 1098: 1094: 1089: 1085: 1080: 1076: 1063: 1059: 1054: 1050: 1045: 1038: 1014: 1012: 1003: 995: 991: 978: 974: 969: 965: 960: 956: 943: 939: 934: 930: 921: 917: 911: 902: 898: 889: 885: 864: 853: 844: 840: 831: 827: 818: 814: 794: 790: 780:Carl A. Huffman 777: 773: 759: 755: 751: 711: 652: 646: 584: 581: 553: 543: 454:In one source, 432: 334:extensively by 304: 246: 242: 190: 186: 172: 150: 143: 127: 62: 42: 35: 28: 23: 22: 15: 12: 11: 5: 4534: 4524: 4523: 4518: 4513: 4511:380s BC deaths 4508: 4506:470s BC births 4503: 4498: 4493: 4488: 4483: 4478: 4473: 4468: 4451: 4450: 4447: 4446: 4444: 4443: 4438: 4433: 4428: 4423: 4421:Dio Chrysostom 4418: 4412: 4410: 4404: 4403: 4401: 4400: 4395: 4390: 4385: 4380: 4375: 4370: 4365: 4360: 4355: 4350: 4345: 4344: 4343: 4333: 4327: 4325: 4319: 4318: 4316: 4315: 4310: 4305: 4300: 4295: 4290: 4284: 4282: 4280:Neopythagorean 4276: 4275: 4273: 4272: 4267: 4262: 4257: 4252: 4247: 4242: 4237: 4232: 4226: 4224: 4218: 4217: 4215: 4214: 4209: 4204: 4199: 4194: 4188: 4186: 4180: 4179: 4177: 4176: 4171: 4166: 4161: 4156: 4151: 4146: 4140: 4138: 4132: 4131: 4129: 4128: 4123: 4118: 4113: 4108: 4106:Musonius Rufus 4103: 4098: 4093: 4088: 4083: 4078: 4073: 4071:Zeno of Citium 4067: 4065: 4059: 4058: 4056: 4055: 4050: 4045: 4040: 4035: 4030: 4024: 4022: 4013: 4007: 4006: 4003: 4002: 4000: 3999: 3994: 3989: 3984: 3979: 3974: 3963: 3961: 3955: 3954: 3952: 3951: 3946: 3941: 3936: 3930: 3928: 3922: 3921: 3918: 3917: 3915: 3914: 3909: 3904: 3899: 3894: 3889: 3884: 3879: 3873: 3871: 3862: 3861: 3856: 3851: 3846: 3841: 3836: 3831: 3826: 3820: 3818: 3812: 3811: 3809: 3808: 3803: 3798: 3796:Phaedo of Elis 3792: 3790: 3784: 3783: 3781: 3780: 3775: 3770: 3765: 3760: 3755: 3749: 3747: 3741: 3740: 3738: 3737: 3732: 3727: 3722: 3717: 3711: 3709: 3700: 3699: 3694: 3683: 3681: 3675: 3674: 3671: 3670: 3667: 3666: 3664: 3663: 3658: 3653: 3648: 3643: 3638: 3632: 3630: 3624: 3623: 3621: 3620: 3615: 3610: 3605: 3600: 3595: 3589: 3587: 3578: 3572: 3571: 3569: 3568: 3563: 3557: 3555: 3549: 3548: 3545: 3544: 3542: 3541: 3536: 3531: 3525: 3523: 3517: 3516: 3514: 3509: 3504: 3499: 3497: 3488: 3482: 3481: 3479: 3478: 3472: 3469: 3468: 3466: 3465: 3460: 3455: 3449: 3447: 3441: 3440: 3438: 3437: 3432: 3426: 3424: 3418: 3417: 3415: 3414: 3409: 3404: 3399: 3394: 3389: 3384: 3379: 3374: 3369: 3364: 3359: 3354: 3349: 3344: 3339: 3333: 3331: 3322: 3312: 3311: 3309: 3308: 3302: 3299: 3298: 3296: 3295: 3290: 3284: 3282: 3276: 3275: 3273: 3272: 3267: 3262: 3256: 3254: 3245: 3236: 3230: 3229: 3226: 3225: 3223: 3222: 3217: 3212: 3207: 3202: 3197: 3192: 3186: 3184: 3175: 3174: 3169: 3163: 3161: 3157: 3156: 3149: 3148: 3141: 3134: 3126: 3117: 3116: 3089: 3086: 3085: 3082: 3081: 3079: 3078: 3073: 3068: 3063: 3058: 3053: 3048: 3042: 3040: 3039:Other cultures 3036: 3035: 3033: 3032: 3031: 3030: 3020: 3019: 3018: 3008: 3007: 3006: 2996: 2995: 2994: 2984: 2983: 2982: 2972: 2971: 2970: 2960: 2959: 2958: 2948: 2947: 2946: 2936: 2935: 2934: 2920: 2918: 2914: 2913: 2911: 2910: 2905: 2900: 2895: 2890: 2888:Greek numerals 2885: 2883:Attic numerals 2880: 2874: 2868: 2864: 2863: 2861: 2860: 2855: 2850: 2844: 2842: 2838: 2837: 2834: 2833: 2831: 2830: 2825: 2820: 2815: 2810: 2802: 2797: 2792: 2787: 2782: 2777: 2772: 2766: 2764: 2760: 2759: 2757: 2756: 2750: 2748: 2742: 2741: 2739: 2738: 2733: 2728: 2723: 2718: 2713: 2711:Law of cosines 2708: 2703: 2698: 2693: 2688: 2683: 2678: 2673: 2668: 2663: 2658: 2652: 2650: 2638: 2634: 2633: 2631: 2630: 2625: 2620: 2615: 2610: 2605: 2603:Platonic solid 2600: 2595: 2590: 2585: 2583:Greek numerals 2580: 2575: 2570: 2565: 2560: 2555: 2550: 2549: 2548: 2543: 2533: 2528: 2527: 2526: 2516: 2515: 2514: 2509: 2498: 2496: 2490: 2489: 2487: 2486: 2481: 2480: 2479: 2474: 2469: 2458: 2456: 2452: 2451: 2449: 2448: 2441: 2434: 2424: 2414: 2411:Planisphaerium 2407: 2400: 2393: 2386: 2376: 2366: 2356: 2346: 2339: 2332: 2322: 2312: 2305: 2295: 2288: 2283: 2275: 2273: 2269: 2268: 2266: 2265: 2260: 2255: 2250: 2245: 2240: 2235: 2230: 2225: 2220: 2215: 2210: 2205: 2200: 2195: 2190: 2185: 2180: 2175: 2170: 2165: 2160: 2155: 2150: 2145: 2140: 2135: 2130: 2125: 2120: 2115: 2110: 2105: 2100: 2095: 2090: 2085: 2080: 2075: 2070: 2065: 2060: 2055: 2050: 2045: 2040: 2035: 2030: 2025: 2020: 2015: 2010: 2005: 2000: 1995: 1990: 1985: 1980: 1975: 1970: 1965: 1960: 1955: 1950: 1945: 1940: 1935: 1930: 1925: 1920: 1915: 1910: 1905: 1900: 1895: 1889: 1887: 1881:Mathematicians 1877: 1876: 1869: 1868: 1861: 1854: 1846: 1837: 1836: 1834: 1833: 1828: 1823: 1817: 1815: 1811: 1810: 1808: 1807: 1802: 1796: 1794: 1790: 1789: 1787: 1786: 1781: 1776: 1771: 1766: 1761: 1756: 1751: 1746: 1741: 1736: 1731: 1726: 1721: 1716: 1711: 1705: 1703: 1699: 1698: 1696: 1695: 1690: 1685: 1680: 1675: 1670: 1665: 1660: 1654: 1652: 1648: 1647: 1645: 1644: 1638:On the Heavens 1634: 1624: 1614: 1611:(Eratosthenes) 1604: 1593: 1591: 1587: 1586: 1584: 1583: 1578: 1573: 1568: 1563: 1558: 1553: 1548: 1543: 1538: 1533: 1528: 1523: 1518: 1516:Philip of Opus 1513: 1508: 1503: 1498: 1493: 1488: 1483: 1478: 1473: 1468: 1463: 1458: 1453: 1448: 1443: 1438: 1433: 1428: 1423: 1418: 1413: 1408: 1403: 1398: 1393: 1388: 1383: 1377: 1375: 1369: 1368: 1361: 1360: 1353: 1346: 1338: 1332: 1331: 1315: 1296: 1284: 1269: 1255: 1254:External links 1252: 1251: 1250: 1218: 1215: 1213: 1212: 1197:Chisholm, Hugh 1175: 1153: 1136: 1127: 1118: 1101: 1092: 1083: 1074: 1057: 1048: 1036: 1025:Smith, William 1001: 989: 972: 963: 954: 937: 928: 915: 896: 883: 866:Carl Huffman. 851: 838: 825: 812: 788: 771: 752: 750: 747: 746: 745: 740: 732: 727: 722: 717: 710: 707: 644: 629:he called the 579: 542: 539: 499:describes the 431: 428: 328:Tarentine Gulf 324:Southern Italy 303: 300: 249:) was a Greek 178: 177: 174: 173: 171: 170: 164: 159: 153: 151: 148: 145: 144: 142: 141: 136: 130: 128: 126:Main interests 125: 122: 121: 119:Pythagoreanism 116: 110: 109: 104: 100: 99: 94: 90: 89: 86: 85: 79: 75: 74: 68: 64: 63: 52: 44: 43: 40: 26: 9: 6: 4: 3: 2: 4533: 4522: 4519: 4517: 4514: 4512: 4509: 4507: 4504: 4502: 4499: 4497: 4494: 4492: 4489: 4487: 4484: 4482: 4479: 4477: 4474: 4472: 4469: 4467: 4464: 4463: 4461: 4442: 4439: 4437: 4434: 4432: 4429: 4427: 4424: 4422: 4419: 4417: 4414: 4413: 4411: 4409: 4405: 4399: 4396: 4394: 4391: 4389: 4386: 4384: 4381: 4379: 4376: 4374: 4371: 4369: 4366: 4364: 4361: 4359: 4356: 4354: 4351: 4349: 4346: 4342: 4339: 4338: 4337: 4334: 4332: 4329: 4328: 4326: 4324: 4320: 4314: 4311: 4309: 4306: 4304: 4301: 4299: 4296: 4294: 4291: 4289: 4286: 4285: 4283: 4281: 4277: 4271: 4268: 4266: 4263: 4261: 4258: 4256: 4253: 4251: 4248: 4246: 4243: 4241: 4238: 4236: 4233: 4231: 4228: 4227: 4225: 4223: 4219: 4213: 4210: 4208: 4205: 4203: 4200: 4198: 4195: 4193: 4190: 4189: 4187: 4185: 4181: 4175: 4172: 4170: 4167: 4165: 4162: 4160: 4157: 4155: 4154:Zeno of Sidon 4152: 4150: 4147: 4145: 4142: 4141: 4139: 4137: 4133: 4127: 4124: 4122: 4119: 4117: 4114: 4112: 4109: 4107: 4104: 4102: 4099: 4097: 4094: 4092: 4089: 4087: 4084: 4082: 4079: 4077: 4074: 4072: 4069: 4068: 4066: 4064: 4060: 4054: 4051: 4049: 4046: 4044: 4041: 4039: 4036: 4034: 4031: 4029: 4026: 4025: 4023: 4021: 4017: 4014: 4012: 4008: 3998: 3995: 3993: 3990: 3988: 3987:Lyco of Troas 3985: 3983: 3980: 3978: 3975: 3972: 3968: 3965: 3964: 3962: 3960: 3956: 3950: 3947: 3945: 3942: 3940: 3937: 3935: 3932: 3931: 3929: 3927: 3923: 3913: 3910: 3908: 3905: 3903: 3900: 3898: 3895: 3893: 3890: 3888: 3885: 3883: 3880: 3878: 3875: 3874: 3872: 3870: 3869:Dialecticians 3866: 3860: 3857: 3855: 3852: 3850: 3847: 3845: 3842: 3840: 3837: 3835: 3832: 3830: 3827: 3825: 3822: 3821: 3819: 3817: 3813: 3807: 3804: 3802: 3799: 3797: 3794: 3793: 3791: 3789: 3785: 3779: 3776: 3774: 3771: 3769: 3766: 3764: 3761: 3759: 3756: 3754: 3751: 3750: 3748: 3746: 3742: 3736: 3733: 3731: 3728: 3726: 3723: 3721: 3718: 3716: 3713: 3712: 3710: 3708: 3704: 3698: 3695: 3692: 3688: 3685: 3684: 3682: 3680: 3676: 3662: 3659: 3657: 3654: 3652: 3649: 3647: 3644: 3642: 3639: 3637: 3634: 3633: 3631: 3629: 3625: 3619: 3616: 3614: 3611: 3609: 3606: 3604: 3601: 3599: 3596: 3594: 3591: 3590: 3588: 3586: 3582: 3579: 3577: 3573: 3567: 3564: 3562: 3559: 3558: 3556: 3554: 3550: 3540: 3537: 3535: 3532: 3530: 3527: 3526: 3524: 3522: 3518: 3513: 3510: 3508: 3505: 3503: 3500: 3498: 3496: 3492: 3489: 3487: 3483: 3477: 3474: 3473: 3464: 3461: 3459: 3456: 3454: 3451: 3450: 3448: 3446: 3442: 3436: 3433: 3431: 3428: 3427: 3425: 3423: 3419: 3413: 3410: 3408: 3405: 3403: 3400: 3398: 3395: 3393: 3390: 3388: 3385: 3383: 3380: 3378: 3375: 3373: 3370: 3368: 3365: 3363: 3360: 3358: 3355: 3353: 3350: 3348: 3345: 3343: 3340: 3338: 3335: 3334: 3332: 3330: 3326: 3323: 3321: 3317: 3307: 3304: 3303: 3294: 3291: 3289: 3286: 3285: 3283: 3281: 3277: 3271: 3268: 3266: 3263: 3261: 3258: 3257: 3255: 3253: 3249: 3246: 3244: 3240: 3237: 3235: 3231: 3221: 3218: 3216: 3213: 3211: 3208: 3206: 3203: 3201: 3198: 3196: 3193: 3191: 3188: 3187: 3185: 3183: 3179: 3173: 3170: 3168: 3165: 3164: 3162: 3158: 3154: 3147: 3142: 3140: 3135: 3133: 3128: 3127: 3124: 3114: 3113: 3108: 3101: 3100: 3087: 3077: 3074: 3072: 3069: 3067: 3064: 3062: 3059: 3057: 3054: 3052: 3049: 3047: 3044: 3043: 3041: 3037: 3029: 3026: 3025: 3024: 3021: 3017: 3014: 3013: 3012: 3009: 3005: 3002: 3001: 3000: 2997: 2993: 2990: 2989: 2988: 2985: 2981: 2978: 2977: 2976: 2973: 2969: 2966: 2965: 2964: 2961: 2957: 2954: 2953: 2952: 2949: 2945: 2942: 2941: 2940: 2937: 2933: 2929: 2928: 2927: 2926: 2922: 2921: 2919: 2915: 2909: 2906: 2904: 2901: 2899: 2896: 2894: 2891: 2889: 2886: 2884: 2881: 2879: 2876: 2875: 2872: 2869: 2865: 2859: 2856: 2854: 2851: 2849: 2846: 2845: 2843: 2839: 2829: 2826: 2824: 2821: 2819: 2816: 2814: 2811: 2809: 2808: 2803: 2801: 2798: 2796: 2793: 2791: 2788: 2786: 2783: 2781: 2778: 2776: 2773: 2771: 2768: 2767: 2765: 2761: 2755: 2752: 2751: 2749: 2747: 2743: 2737: 2734: 2732: 2729: 2727: 2724: 2722: 2719: 2717: 2716:Pons asinorum 2714: 2712: 2709: 2707: 2704: 2702: 2699: 2697: 2694: 2692: 2689: 2687: 2686:Hinge theorem 2684: 2682: 2679: 2677: 2674: 2672: 2669: 2667: 2664: 2662: 2659: 2657: 2654: 2653: 2651: 2649: 2648: 2642: 2639: 2635: 2629: 2626: 2624: 2621: 2619: 2616: 2614: 2611: 2609: 2606: 2604: 2601: 2599: 2596: 2594: 2591: 2589: 2586: 2584: 2581: 2579: 2576: 2574: 2571: 2569: 2566: 2564: 2561: 2559: 2556: 2554: 2551: 2547: 2544: 2542: 2539: 2538: 2537: 2534: 2532: 2529: 2525: 2522: 2521: 2520: 2517: 2513: 2510: 2508: 2505: 2504: 2503: 2500: 2499: 2497: 2491: 2485: 2482: 2478: 2475: 2473: 2470: 2468: 2465: 2464: 2463: 2460: 2459: 2457: 2453: 2447: 2446: 2442: 2440: 2439: 2435: 2433: 2429: 2425: 2423: 2419: 2415: 2413: 2412: 2408: 2406: 2405: 2401: 2399: 2398: 2394: 2392: 2391: 2387: 2385: 2381: 2377: 2375: 2371: 2367: 2365: 2361: 2357: 2355: 2353:(Aristarchus) 2351: 2347: 2345: 2344: 2340: 2338: 2337: 2333: 2331: 2327: 2323: 2321: 2317: 2313: 2311: 2310: 2306: 2304: 2300: 2296: 2294: 2293: 2289: 2287: 2284: 2282: 2281: 2277: 2276: 2274: 2270: 2264: 2261: 2259: 2258:Zeno of Sidon 2256: 2254: 2251: 2249: 2246: 2244: 2241: 2239: 2236: 2234: 2231: 2229: 2226: 2224: 2221: 2219: 2216: 2214: 2211: 2209: 2206: 2204: 2201: 2199: 2196: 2194: 2191: 2189: 2186: 2184: 2181: 2179: 2176: 2174: 2171: 2169: 2166: 2164: 2161: 2159: 2156: 2154: 2151: 2149: 2146: 2144: 2141: 2139: 2136: 2134: 2131: 2129: 2126: 2124: 2121: 2119: 2116: 2114: 2111: 2109: 2106: 2104: 2101: 2099: 2096: 2094: 2091: 2089: 2086: 2084: 2081: 2079: 2076: 2074: 2071: 2069: 2066: 2064: 2061: 2059: 2056: 2054: 2051: 2049: 2046: 2044: 2041: 2039: 2036: 2034: 2031: 2029: 2026: 2024: 2021: 2019: 2016: 2014: 2011: 2009: 2006: 2004: 2001: 1999: 1996: 1994: 1991: 1989: 1986: 1984: 1981: 1979: 1976: 1974: 1971: 1969: 1966: 1964: 1961: 1959: 1956: 1954: 1951: 1949: 1946: 1944: 1941: 1939: 1936: 1934: 1931: 1929: 1926: 1924: 1921: 1919: 1916: 1914: 1911: 1909: 1906: 1904: 1901: 1899: 1896: 1894: 1891: 1890: 1888: 1886: 1882: 1878: 1874: 1867: 1862: 1860: 1855: 1853: 1848: 1847: 1844: 1832: 1829: 1827: 1824: 1822: 1819: 1818: 1816: 1812: 1806: 1803: 1801: 1798: 1797: 1795: 1791: 1785: 1782: 1780: 1777: 1775: 1772: 1770: 1767: 1765: 1762: 1760: 1759:Metonic cycle 1757: 1755: 1752: 1750: 1747: 1745: 1744:Heliocentrism 1742: 1740: 1737: 1735: 1732: 1730: 1727: 1725: 1724:Counter-Earth 1722: 1720: 1717: 1715: 1712: 1710: 1707: 1706: 1704: 1700: 1694: 1691: 1689: 1686: 1684: 1681: 1679: 1676: 1674: 1671: 1669: 1666: 1664: 1661: 1659: 1656: 1655: 1653: 1649: 1643: 1639: 1635: 1633: 1631:(Aristarchus) 1629: 1625: 1623: 1619: 1615: 1613: 1609: 1605: 1603: 1599: 1595: 1594: 1592: 1588: 1582: 1579: 1577: 1574: 1572: 1569: 1567: 1564: 1562: 1559: 1557: 1554: 1552: 1549: 1547: 1544: 1542: 1539: 1537: 1534: 1532: 1529: 1527: 1524: 1522: 1519: 1517: 1514: 1512: 1509: 1507: 1504: 1502: 1499: 1497: 1494: 1492: 1489: 1487: 1484: 1482: 1479: 1477: 1474: 1472: 1469: 1467: 1464: 1462: 1459: 1457: 1454: 1452: 1449: 1447: 1444: 1442: 1439: 1437: 1434: 1432: 1429: 1427: 1424: 1422: 1419: 1417: 1414: 1412: 1409: 1407: 1404: 1402: 1399: 1397: 1394: 1392: 1389: 1387: 1384: 1382: 1379: 1378: 1376: 1374: 1370: 1366: 1359: 1354: 1352: 1347: 1345: 1340: 1339: 1336: 1328: 1327: 1321: 1316: 1312: 1311: 1306: 1302: 1297: 1294: 1289: 1285: 1283: 1279: 1274: 1270: 1267: 1262: 1258: 1257: 1247: 1243: 1242: 1236: 1231: 1221: 1220: 1208: 1207: 1202: 1198: 1193: 1192:public domain 1179: 1172: 1171: 1167: 1164: 1157: 1149: 1148: 1140: 1131: 1122: 1114: 1113: 1105: 1096: 1087: 1078: 1071: 1067: 1061: 1052: 1043: 1041: 1032: 1031: 1026: 1022: 1010: 1008: 1006: 999: 993: 986: 982: 976: 967: 958: 951: 950:de Gen. Socr. 947: 941: 932: 925: 919: 906: 900: 893: 887: 879: 878: 873: 869: 862: 860: 858: 856: 848: 842: 835: 829: 822: 816: 809: 805: 801: 800: 792: 785: 781: 775: 768: 764: 757: 753: 744: 741: 739: 737: 733: 731: 728: 726: 723: 721: 718: 716: 713: 712: 706: 703: 701: 700: 695: 690: 688: 687:number theory 684: 683:Counter-Earth 680: 679: 675:, writing in 674: 670: 666: 662: 658: 649: 643: 641: 634: 632: 628: 621: 619: 613: 609: 607: 599: 588: 578: 573: 571: 562: 557: 552: 548: 537: 532: 530: 526: 522: 518: 514: 510: 505: 502: 498: 494: 490: 486: 482: 478: 473: 471: 470: 465: 461: 460:Aulus Gellius 457: 452: 449: 445: 436: 427: 423: 421: 417: 413: 409: 405: 401: 397: 393: 389: 385: 380: 378: 374: 370: 366: 362: 358: 354: 353: 348: 345:According to 343: 341: 337: 333: 329: 325: 321: 320:Magna Graecia 318:—all part of 317: 313: 309: 299: 297: 293: 289: 285: 284:heliocentrism 281: 277: 272: 270: 266: 261: 256: 252: 237: 229: 228:Ancient Greek 223: 184: 175: 169: 165: 163: 162:Counter-Earth 160: 158: 155: 154: 152: 149:Notable ideas 146: 140: 137: 135: 132: 131: 129: 123: 120: 117: 115: 111: 108: 105: 101: 98: 95: 91: 87: 80: 76: 69: 65: 60: 56: 50: 45: 38: 33: 19: 4436:Philostratus 4323:Neoplatonist 3977:Theophrastus 3651:Dionysodorus 3608:Thrasymachus 3346: 3234:Pre-Socratic 3103: 3090: 2932:Thomas Heath 2923: 2806: 2790:Law of sines 2646: 2578:Golden ratio 2443: 2436: 2427: 2421:(Theodosius) 2417: 2409: 2402: 2395: 2388: 2379: 2369: 2363:(Hipparchus) 2359: 2349: 2341: 2334: 2325: 2315: 2307: 2302:(Apollonius) 2298: 2290: 2278: 2253:Zeno of Elea 2142: 2013:Eratosthenes 2003:Dionysodorus 1637: 1627: 1621:(Hipparchus) 1617: 1608:Catasterismi 1607: 1597: 1520: 1456:Eratosthenes 1324: 1308: 1268:at Wikiquote 1239: 1204: 1178: 1161: 1156: 1146: 1139: 1130: 1121: 1111: 1104: 1095: 1086: 1077: 1069: 1065: 1060: 1051: 1028: 997: 992: 984: 975: 966: 957: 949: 945: 944:Iamblichus, 940: 931: 923: 918: 899: 891: 886: 875: 849:, pp. 266–67 846: 845:Iamblichus, 841: 833: 832:Iamblichus, 828: 820: 819:Iamblichus, 815: 807: 798: 791: 783: 774: 766: 756: 743:Pythagoreans 736:Protrepticus 735: 704: 697: 691: 676: 654: 640:counterearth 636: 631:Central Fire 623: 615: 611: 601: 593: 590: 586: 575: 569: 566: 560: 559:A page from 534: 528: 524: 516: 506: 500: 488: 485:On the World 484: 476: 474: 467: 453: 441: 424: 381: 368: 350: 344: 305: 296:Central Fire 273: 265:August Böckh 255:pre-Socratic 235: 182: 181: 166:discounting 157:Central Fire 57:, depicting 4038:Aenesidemus 4011:Hellenistic 3959:Peripatetic 3877:Clinomachus 3715:Antisthenes 3329:Pythagorean 3280:Heraclitean 3265:Anaximander 3182:Seven Sages 2999:mathematics 2807:Arithmetica 2404:Ostomachion 2373:(Autolycus) 2292:Arithmetica 2068:Hippocrates 1998:Dinostratus 1983:Dicaearchus 1913:Aristarchus 1739:Geocentrism 1651:Instruments 1641:(Aristotle) 1446:Cleostratus 1411:Aristarchus 1391:Anaximander 1373:Astronomers 1301:"Philolaus" 1068:; Tzetzes, 868:"Philolaus" 763:"Philolaus" 738:(Aristotle) 678:Metaphysics 659:, the five 650:, i. 22. 1d 420:Polymnastus 280:geocentrism 251:Pythagorean 168:Geocentrism 134:Metaphysics 4460:Categories 4393:Simplicius 4358:Iamblichus 4303:Nicomachus 4192:Arcesilaus 4159:Philodemus 4149:Metrodorus 4091:Posidonius 4081:Chrysippus 4020:Pyrrhonist 3944:Xenocrates 3939:Speusippus 3912:Panthoides 3753:Aristippus 3656:Euthydemus 3593:Protagoras 3566:Democritus 3529:Empedocles 3502:Anaxagoras 3453:Parmenides 3430:Xenophanes 3387:Hermotimus 3337:Pythagoras 3288:Heraclitus 3270:Anaximenes 3172:Pherecydes 3167:Epimenides 3051:Babylonian 2951:arithmetic 2917:History of 2746:Apollonius 2431:(Menelaus) 2390:On Spirals 2309:Catoptrics 2248:Xenocrates 2243:Thymaridas 2228:Theodosius 2213:Theaetetus 2193:Simplicius 2183:Pythagoras 2168:Posidonius 2153:Philonides 2113:Nicomachus 2108:Metrodorus 2098:Menaechmus 2053:Hipparchus 2043:Heliodorus 1993:Diophantus 1978:Democritus 1958:Chrysippus 1928:Archimedes 1923:Apollonius 1893:Anaxagoras 1885:(timeline) 1814:Influenced 1793:Influences 1764:Octaeteris 1693:Triquetrum 1581:Timocharis 1566:Theodosius 1526:Posidonius 1486:Hipparchus 1476:Heraclides 1416:Aristyllus 1401:Apollonius 1396:Andronicus 1282:Wikisource 1217:References 905:Pythagoras 730:Parmenides 725:Nicomachus 545:See also: 541:Philosophy 527:, Chapter 464:Iamblichus 412:Echecrates 404:Xenophilus 377:Democritus 330:that were 316:Metapontum 269:Nicomachus 260:Pythagoras 245: – c. 243: 470 59:Pythagoras 4426:Favorinus 4388:Damascius 4230:Antiochus 4197:Carneades 4164:Lucretius 4136:Epicurean 4111:Epictetus 4086:Panaetius 4076:Cleanthes 3967:Aristotle 3892:Dionysius 3887:Euphantus 3839:Eubulides 3801:Menedemus 3773:Anniceris 3679:Classical 3646:Lycophron 3641:Callicles 3561:Leucippus 3539:Pausanias 3507:Archelaus 3486:Pluralist 3382:Calliphon 3367:Brontinus 3347:Philolaus 3215:Cleobulus 3210:Periander 2512:Inscribed 2272:Treatises 2263:Zenodorus 2223:Theodorus 2198:Sosigenes 2143:Philolaus 2128:Oenopides 2123:Nicoteles 2118:Nicomedes 2078:Hypsicles 1973:Ctesibius 1963:Cleomedes 1948:Callippus 1933:Autolycus 1918:Aristotle 1898:Anthemius 1668:Astrolabe 1601:(Ptolemy) 1521:Philolaus 1511:Oenopides 1496:Hypsicles 1441:Cleomedes 1436:Callippus 1426:Autolycus 1381:Aglaonice 1293:Philolaus 1278:Philolaus 1266:Philolaus 998:Philolaus 782:, (1993) 673:Aristotle 477:On Nature 448:Archippus 390:, or (as 332:colonized 302:Biography 276:limitless 236:Philólaos 183:Philolaus 139:Astronomy 41:Philolaus 4373:Syrianus 4353:Porphyry 4341:students 4336:Plotinus 4260:Alcinous 4255:Apuleius 4245:Plutarch 4144:Epicurus 3926:Platonic 3907:Alexinus 3854:Pasicles 3849:Nicarete 3829:Ichthyas 3816:Megarian 3788:Eretrian 3745:Cyrenaic 3730:Menippus 3720:Diogenes 3697:Xenophon 3691:students 3687:Socrates 3598:Prodicus 3463:Melissus 3435:Xeniades 3397:Arignote 3362:Alcmaeon 3357:Lamiskos 3352:Archytas 3342:Hippasus 3306:Diogenes 3293:Cratylus 3252:Milesian 3200:Pittacus 3076:Japanese 3061:Egyptian 3004:timeline 2992:timeline 2980:timeline 2975:geometry 2968:timeline 2963:calculus 2956:timeline 2944:timeline 2647:Elements 2493:Concepts 2455:Problems 2428:Spherics 2418:Spherics 2383:(Euclid) 2329:(Euclid) 2326:Elements 2319:(Euclid) 2280:Almagest 2188:Serenus 2163:Porphyry 2103:Menelaus 2058:Hippasus 2033:Eutocius 2008:Domninus 1903:Archytas 1769:Solstice 1702:Concepts 1598:Almagest 1541:Seleucus 1501:Menelaus 1461:Euctemon 1232:(1925). 1166:Archived 823:, p. 148 709:See also 648:Stobaeus 645:—  616:Nature ( 580:—  570:harmonia 511:through 493:Arignote 481:Stobaeus 430:Writings 392:Plutarch 384:Heraclea 373:Socrates 312:Tarentum 292:Universe 232:Φιλόλαος 4441:more... 4398:more... 4378:Proclus 4313:more... 4270:more... 4212:more... 4174:more... 4126:more... 4053:more... 3997:more... 3949:more... 3778:more... 3735:more... 3661:more... 3636:Gorgias 3628:Italian 3618:more... 3603:Hippias 3576:Sophist 3553:Atomist 3521:Italian 3445:Eleatic 3422:Skeptic 3412:more... 3407:Eurytus 3320:Italian 3056:Chinese 3011:numbers 2939:algebra 2867:Related 2841:Centers 2637:Results 2507:Central 2178:Ptolemy 2173:Proclus 2138:Perseus 2093:Marinus 2073:Hypatia 2063:Hippias 2038:Geminus 2028:Eudoxus 2018:Eudemus 1988:Diocles 1673:Dioptra 1536:Pytheas 1531:Ptolemy 1481:Hicetas 1471:Geminus 1466:Eudoxus 1421:Attalus 1386:Agrippa 1307:(ed.). 1194::  1070:Chiliad 1027:(ed.). 922:Plato, 874:(ed.). 720:Apeiron 661:planets 563:(1492) 517:Timaeus 501:Bacchae 497:Proclus 489:Bacchae 469:Timaeus 416:Diocles 400:Eurytus 357:Simmias 326:on the 4431:Lucian 4363:Julian 4348:Origen 4207:Cicero 4116:Arrian 4096:Seneca 4028:Pyrrho 3859:Bryson 3844:Stilpo 3725:Crates 3585:Ionian 3495:Ionian 3372:Theano 3260:Thales 3243:Ionian 3220:Chilon 3190:Thales 3071:Indian 2848:Cyrene 2380:Optics 2299:Conics 2218:Theano 2208:Thales 2203:Sporus 2148:Philon 2133:Pappus 2023:Euclid 1953:Carpus 1943:Bryson 1784:Zodiac 1734:Equant 1683:Gnomon 1561:Thales 1556:Strabo 1406:Aratus 1227:  1188:  1018:  926:, 61DE 924:Phaedo 663:, the 618:physis 604:κόσμος 549:, and 521:Thebes 483:calls 418:, and 408:Phanto 388:Aresas 369:Phaedo 365:Thebes 352:Phaedo 340:Greece 308:Croton 114:School 103:Region 84:385 BC 73:470 BC 4265:Galen 4250:Gaius 4063:Stoic 3934:Plato 3902:Philo 3707:Cynic 3613:Damon 3534:Acron 3476:Hippo 3195:Solon 3066:Incan 2987:logic 2763:Other 2531:Chord 2524:Axiom 2502:Angle 2158:Plato 2048:Heron 1968:Conon 1590:Works 1506:Meton 1451:Conon 1303:. In 870:. In 749:Notes 657:stars 596:φύσις 509:minae 444:Lysis 361:Cebes 347:Plato 336:Greek 314:, or 288:Earth 3458:Zeno 3402:Myia 3377:Damo 3205:Bias 3028:list 2316:Data 2088:Leon 1938:Bion 1431:Bion 981:Dion 669:Moon 462:and 446:and 359:and 253:and 78:Died 67:Born 2930:by 2644:In 1280:at 1203:". 665:Sun 572:): 363:at 349:'s 93:Era 4462:: 1323:. 1238:. 1039:^ 1004:^ 909:c. 907:, 854:^ 806:. 804:14 765:, 667:, 633:. 422:. 414:, 410:, 406:, 310:, 240:c. 238:; 234:, 230:: 226:; 213:eɪ 82:c. 71:c. 3973:) 3969:( 3693:) 3689:( 3145:e 3138:t 3131:v 1865:e 1858:t 1851:v 1357:e 1350:t 1343:v 1313:. 1115:. 1033:. 880:. 608:. 222:/ 219:s 216:ə 210:l 207:ˈ 204:ə 201:l 198:ɪ 195:f 192:ˌ 189:/ 185:( 34:. 20:)

Index

Philolaus of Croton
Philolaos (sculptor)

Franchino Gaffurio
Pythagoras
Pre-Socratic philosophy
Western philosophy
School
Pythagoreanism
Metaphysics
Astronomy
Central Fire
Counter-Earth
Geocentrism
/ˌfɪləˈləs/
Ancient Greek
Pythagorean
pre-Socratic
Pythagoras
August Böckh
Nicomachus
limitless
geocentrism
heliocentrism
Earth
Universe
Central Fire
Croton
Tarentum
Metapontum

Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.