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Archytas made a wooden model of a dove with such mechanical ingenuity and art that it flew; so nicely balanced was it, you see, with weights and moved by a current of air enclosed and hidden within it. About so improbable a story I prefer to give
Favorinus' own words: "Archytas the Tarentine, being
444:
And therefore Plato himself dislikes
Eudoxus, Archytas, and Menaechmus for endeavoring to bring down the doubling the cube to mechanical operations; for by this means all that was good in geometry would be lost and corrupted, it falling back again to sensible things, and not rising upward and
261:("general") seven years in a row, a step that required them to violate their own rule against successive appointments. Archytas was allegedly undefeated as a general in Tarentine campaigns against their southern Italian neighbors.
499:, and were extensively used by musicologists of the Greek classical period, of which Archytas was one among several. Examples of supernummerary ratios seen frequently in musical analysis of intonation even to the present day are
215:
As a
Pythagorean, Archytas believed that arithmetic (logistic), rather than geometry, provided the basis for satisfactory proofs, and developed the most famous argument for the infinity of the universe in antiquity.
381:
considered
Archytas the most sophisticated Pythagorean music theorist, and scholars believe Archytas gave a mathematical account of the musical scales used by practicing musicians of his day.
678:
1513:
402:. Tradition also has it that Archytas built a mechanical flying dove. The sole mention of this from antiquity comes some five centuries after Archytas, when
2847:
1074:
833:
710:
351:, the first in which mechanical motions entered geometry. The topic of proportions, which Archytas seems to have worked on extensively, is treated in
1506:
3951:
1406:
1256:
Archytas' dove in context: an investigation of the non-human agency between paradoxography, encyclopedism, and mechanics in the ancient world
347:. Archytas' demonstration uses lines generated by moving figures to construct the two proportionals between magnitudes and was, according to
1499:
419:
Aulus
Gellius views the reporting of the tradition as problematic, since it spreads implausible beliefs even if accompanied by skepticism.
320:. He is thought to have written a great number of works in the sciences, but only four fragments are generally believed to be authentic.
3551:
4125:
1922:
4029:
247:
Politically and militarily, Archytas appears to have been the dominant figure in
Tarentum in his generation, somewhat comparable to
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392:
includes him in a list of twelve authors who wrote works on mechanics. T.N. Winter presents evidence that the pseudo-Aristotelian
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2147:
1254:
775:
1080:
340:
109:
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2710:
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in other lines also a mechanician, made a flying dove out of wood. Whenever it lit, it did not rise again."
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790:
Morris Kline, Mathematical
Thought from Ancient to Modern Times Oxford University Press, 1972 p. 49
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Aulus
Gellius und die >Noctus Atticae< — die literarische Konstruktion einer Sammlung
1098:
352:
336:
288:
1356:
1033:
Masià, R. (2016). "A new reading of
Archytas' doubling of the cube and its implications".
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348:
208:
school and famous for being the reputed founder of mathematical mechanics and a friend of
8:
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2015:
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996:
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43:
1001:
Pythagoras
Redivivus: Studies on the texts attributed to Pythagoras and the Pythagoreans
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cannot be divided by a mean proportional – an important result in ancient harmonics.
328:
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126:
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considering immaterial and immortal images, in which God being versed is always God.
264:
In his public career, Archytas had a reputation for virtue as well as efficacy. The
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283:
282:. Some scholars have argued that Archytas may have served as one model for Plato's
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Archytas is said to be the first ancient Greek to have spoken of the sciences of
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274:, asserts that Archytas attempted to rescue Plato during his difficulties with
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1977:
1827:
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2407:
2246:
2084:
1634:
1150:"Ptolemy's Pythagoreans, Archytas, and Plato's conception of mathematics"
936:
47:
16:
4th-century BC Greek philosopher, mathematician, astronomer and statesman
1020:
The Frontiers of Ancient Science: Essays in honor of Heinrich von Staden
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1935:
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358:, where the construction for two proportional means can also be found.
317:
301:
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51:
286:, and that he influenced Plato's political philosophy as expressed in
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1930:
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864:
815:(Winter 2020 ed.), Metaphysics Research Lab, Stanford University
407:
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344:
309:
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233:
1393:. Vol. 1. New York: Charles Scribner's Sons. pp. 231–233.
37:
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1967:
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130:
438:
blamed Archytas for his contamination of geometry with mechanics:
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3156:
3056:
3046:
3021:
2747:
2005:
1972:
1945:
1280:. Vol. X. Translated by J. C. Rolfe. Loeb Classical Library.
398:
might have been authored by Archytas and later mis-attributed to
384:
Later tradition regarded Archytas as the founder of mathematical
378:
197:
65:
3131:
3006:
2800:
2717:
2576:
2485:
2397:
2213:
1320:
The Role of Favorinus in the "Attic Nights" of Aulus Gellius".
1094:
252:
3507:
3485:
3141:
2634:
2609:
2303:
1903:
435:
271:
209:
232:, and was the son of Hestiaeus. He was presumably taught by
154:
1771:
971:
The Origin of the History of Science in Classical Antiquity
166:
937:"Classification of the sciences in Greco-Roman antiquity"
683:
Sito ufficiale del Museo Archeologico Nazionale di Napoli
335:) with an ingenious geometric construction. Before this,
204:. He was a scientist and philosopher affiliated with the
160:
1521:
1122:(Report). The MacTutor History of Mathematics archive.
997:"Archytas: Author and authenticator of Pythagoreanism"
196:, statesman, and strategist from the ancient city of
169:
157:
1482:
Complete fragments (Greek–Spanish bilingual edition)
1273:
339:
had reduced this problem to the finding of two mean
163:
491:; they are the "atoms" of mathematical theories of
255:a half-century earlier. The Tarentines elected him
224:Archytas was born in Tarentum, a Greek city in the
151:
1236:The Mechanical Problems in the Corpus of Aristotle
999:. In Macris, C.; Dorandi, T.; Brisson, L. (eds.).
709:
1450:
1188:
1113:
1079:. Book VIII, Question 2. Archived from
327:, Archytas was the first to solve the problem of
50:, once identified as Archytas, now thought to be
4107:
1387:von Fritz, Kurt (1970). "Archytas of Tarentum".
373:, though he did not discover it. He proved that
1375:(Two volume ed.). Loeb Classical Library.
1261:Ancient Medicine and Technology Seminar Series
2855:
2841:
1507:
831:
2237:
1252:
1120:www-history.mcs.st-andrews.ac.uk/Biographies
1022:. pp. 407–436 – via Google books.
890:"Plato and Archytas in the "Seventh Letter""
2848:
2834:
1550:
1514:
1500:
36:
1386:
1355:
1238:(Report). Digital Commons. Lincoln, NB:
1194:
1018:. In Holmes, B.; Fischer, K.-D. (eds.).
865:"Sources for the Philosophy of Archytas"
832:Despotopoulos, Constantin (2004-11-01).
316:as kin, which later became the medieval
1462:MacTutor History of Mathematics Archive
862:
813:The Stanford Encyclopedia of Philosophy
806:
730:10.1093/gmo/9781561592630.article.01183
707:
4108:
3877:Latin translations of the 12th century
1688:
1253:Vespa, Marco; Ruffell, Isabel (2020).
1233:
1147:
934:
3607:Straightedge and compass construction
2829:
1611:
1495:
1315:
1209:
1036:Archive for History of Exact Sciences
1032:
994:
974:. Walter de Gruyter. pp. 62–63.
967:
887:
3572:Incircle and excircles of a triangle
1478:– Greek text and English translation
1414:, Cambridge University Press, 2005,
1290:
1069:
1013:
802:
800:
798:
796:
698:, Bloomsbury Academic, 2015, p. 154.
1523:Ancient Greek schools of philosophy
1443:Stanford Encyclopedia of Philosophy
1431:
1274:A. Cornelius Gellius (1927). "12".
13:
1390:Dictionary of Scientific Biography
1380:
1093:
834:"Archytas' Logismos and Logistika"
343:, equivalent to the extraction of
14:
4182:
4126:4th-century BC Greek philosophers
1425:
1368:Lives of the Eminent Philosophers
1322:The American Journal of Philology
793:
696:Science: Antiquity and its Legacy
406:discusses a report by his mentor
4089:
4076:
1349:
1114:O'Connor, J.J.; Robertson, E.F.
147:
1371:. Vol. 2:8. Translated by
1343:
1309:
1284:
1267:
1246:
1227:
1203:
1141:
1107:
1087:
1063:
1026:
1016:"How Archytas doubled the cube"
1007:
988:
961:
928:
460:are integer ratios of the form
451:
429:
3909:A History of Greek Mathematics
3422:The Quadrature of the Parabola
1487:Fragments and Life of Archytas
1362:"Pythagoreans: Archytas"
1234:Winter, Thomas Nelson (2007).
881:
856:
825:
784:
760:
701:
688:
672:
270:, traditionally attributed to
1:
4171:4th-century BC mathematicians
4166:5th-century BC mathematicians
4161:Pythagoreans of Magna Graecia
4141:Ancient Greek music theorists
1277:Noctes Atticae (Attic Nights)
811:, in Zalta, Edward N. (ed.),
685:, retrieved 25 September 2012
666:
185:; 435/410–360/350 BC) was an
4136:Ancient Greek mathematicians
3690:Intersecting secants theorem
850:10.5840/philinquiry200426311
754:UK public library membership
236:, and taught mathematics to
7:
3685:Intersecting chords theorem
3552:Doctrine of proportionality
1316:Beall, Stephen M. (2001). "
10:
4187:
3381:On the Sphere and Cylinder
3334:On the Sizes and Distances
1295:. De Gruyter. p. 88.
1166:10.1163/156852894321052135
365:, important much later in
93:Classical Greek philosophy
18:
4083:Ancient Greece portal
4072:
4022:
3900:
3887:Philosophy of mathematics
3857:
3850:
3824:
3802:Ptolemy's table of chords
3746:
3728:
3627:
3620:
3476:
3438:
3255:
2863:
2857:Ancient Greek mathematics
2776:
2691:
2648:
2590:
2552:
2504:
2431:
2388:
2379:
2327:
2294:
2184:
2156:
2113:
2075:
2047:
1996:
1953:
1944:
1921:
1889:
1863:
1854:
1813:
1790:
1697:
1648:
1620:
1602:
1529:
1223:] (in Latin). vii.14.
1128:University of St. Andrews
1049:10.1007/s00407-015-0165-9
984:– via Google books.
955:10.5771/0943-7444-7-8-499
240:and to Eudoxus' student,
182:
136:
120:
108:
98:
88:
84:
76:
58:
35:
28:
21:Archytas (disambiguation)
4146:Ancient Greek physicists
3754:Aristarchus's inequality
3327:On Conoids and Spheroids
2362:Alexander of Aphrodisias
1467:University of St Andrews
888:Lloyd, G. E. R. (1990).
422:
295:
4151:Ancient Greek inventors
3862:Ancient Greek astronomy
3675:Inscribed angle theorem
3665:Greek geometric algebra
3320:Measurement of a Circle
2471:Lucius Annaeus Cornutus
2204:Thrasymachus of Corinth
1882:Metrodorus of Lampsacus
1318:Homo Fandi Dulcissimus:
906:10.1163/156852890X00097
863:Johnson, M. R. (2008).
722:Oxford University Press
708:Barbera, André (2001).
219:
4131:Ancient Greek generals
4096:Mathematics portal
3882:Non-Euclidean geometry
3837:Mouseion of Alexandria
3710:Tangent-secant theorem
3660:Geometric mean theorem
3645:Exterior angle theorem
3640:Angle bisector theorem
3344:On Sizes and Distances
2128:Aristippus the Younger
1240:University of Nebraska
942:Knowledge Organization
807:Huffman, Carl (2020),
711:"Archytas of Tarentum"
417:
3784:Pappus's area theorem
3720:Theorem of the gnomon
3597:Quadratrix of Hippias
3520:Circles of Apollonius
3468:Problem of Apollonius
3446:Constructible numbers
3270:Archimedes Palimpsest
2605:Eudorus of Alexandria
2176:Asclepiades of Phlius
2133:Theodorus the Atheist
1334:10.1353/ajp.2001.0001
1124:St. Andrews, Scotland
838:Philosophical Inquiry
458:Supernummerary ratios
412:
375:supernummerary ratios
4000:prehistoric counting
3797:Ptolemy's inequality
3738:Apollonius's theorem
3577:Method of exhaustion
3547:Diophantine equation
3537:Circumscribed circle
3354:On the Moving Sphere
2539:Diogenes of Oenoanda
1453:Robertson, Edmund F.
1412:Archytas of Tarentum
1291:Beer, Beate (2020).
1116:Archytas of Tarentum
995:Horky, P.S. (2021).
337:Hippocrates of Chios
19:For other uses, see
4086: •
3892:Neusis construction
3812:Spiral of Theodorus
3705:Pythagorean theorem
3650:Euclidean algorithm
3592:Lune of Hippocrates
3461:Squaring the circle
3217:Theon of Alexandria
2892:Aristaeus the Elder
2663:Apollonius of Tyana
2610:Philo of Alexandria
2413:Agrippa the Skeptic
2352:Strato of Lampsacus
1451:O'Connor, John J.;
1199:Vitae philosophorum
1148:Barker, A. (1994).
935:Furner, J. (2021).
768:The People of Plato
395:Mechanical Problems
367:projective geometry
361:Archytas named the
44:Villa of the Papyri
4156:Ancient Tarantines
3779:Menelaus's theorem
3769:Irrational numbers
3582:Parallel postulate
3557:Euclidean geometry
3525:Apollonian circles
3067:Isidore of Miletus
2738:Plutarch of Athens
2678:Numenius of Apamea
2668:Moderatus of Gades
2138:Hegesias of Cyrene
1473:Pseudo-Aristotle,
1373:Hicks, Robert Drew
1357:Laërtius, Diogenes
968:Zhmud, L. (2008).
717:Grove Music Online
103:Western philosophy
4103:
4102:
4068:
4067:
3820:
3819:
3807:Ptolemy's theorem
3680:Intercept theorem
3530:Apollonian gasket
3456:Doubling the cube
3429:The Sand Reckoner
2823:
2822:
2819:
2818:
2786:Nicetes of Smyrna
2375:
2374:
2290:
2289:
2252:Apollonius Cronus
2043:
2042:
2039:
2038:
1917:
1916:
1841:
1840:
1762:Metrodorus of Cos
1684:
1683:
1671:
1670:
1598:
1597:
1410:Huffman, Carl A.
1103:. book VIII.
1014:Menn, S. (2015).
981:978-3-11-019432-6
752:(subscription or
739:978-1-56159-263-0
679:Archita; Pitagora
349:Diogenes Laërtius
329:doubling the cube
292:and other works.
238:Eudoxus of Cnidus
228:that was part of
226:Italian Peninsula
140:
139:
131:Infinite universe
127:Doubling the cube
4178:
4094:
4093:
4081:
4080:
4079:
3855:
3854:
3842:Platonic Academy
3789:Problem II.8 of
3759:Crossbar theorem
3715:Thales's theorem
3655:Euclid's theorem
3625:
3624:
3542:Commensurability
3503:Axiomatic system
3451:Angle trisection
3416:
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3348:
3338:
3314:
3304:
3287:
2850:
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2827:
2826:
2778:Second Sophistic
2753:Ammonius Hermiae
2658:Nigidius Figulus
2572:Philo of Larissa
2554:Academic Skeptic
2418:Sextus Empiricus
2386:
2385:
2235:
2234:
2194:Euclid of Megara
2073:
2072:
1951:
1950:
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1860:
1695:
1694:
1686:
1685:
1618:
1617:
1609:
1608:
1548:
1547:
1530:Proto-philosophy
1516:
1509:
1502:
1493:
1492:
1469:
1447:
1438:Zalta, Edward N.
1404:
1376:
1364:
1353:
1352:
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959:
958:
949:(7–8): 499–534.
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455:
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433:
284:philosopher king
184:
176:
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172:
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168:
165:
162:
159:
156:
153:
40:
26:
25:
4186:
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4177:
4176:
4175:
4106:
4105:
4104:
4099:
4088:
4077:
4075:
4064:
4030:Arabian/Islamic
4018:
4007:numeral systems
3896:
3846:
3816:
3764:Heron's formula
3742:
3724:
3616:
3612:Triangle center
3602:Regular polygon
3479:and definitions
3478:
3472:
3434:
3414:
3404:
3366:
3356:
3346:
3336:
3312:
3302:
3285:
3251:
3222:Theon of Smyrna
2867:
2859:
2854:
2824:
2815:
2772:
2701:Ammonius Saccas
2687:
2644:
2592:Middle Platonic
2586:
2548:
2500:
2491:Marcus Aurelius
2427:
2403:Timon of Phlius
2371:
2341:Aristotelianism
2323:
2286:
2267:Diodorus Cronus
2233:
2180:
2152:
2109:
2071:
2035:
1992:
1940:
1913:
1885:
1850:
1837:
1809:
1786:
1680:
1667:
1644:
1594:
1546:
1525:
1520:
1432:Huffman, Carl.
1428:
1401:
1383:
1381:Further reading
1350:
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1314:
1310:
1303:
1289:
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1272:
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1247:
1232:
1228:
1221:On Architecture
1216:De architectura
1208:
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1193:
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869:philarchive.org
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694:Philippa Lang,
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331:(the so-called
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150:
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129:
123:
72:
63:
54:
31:
24:
17:
12:
11:
5:
4184:
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3898:
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3872:Greek numerals
3869:
3867:Attic numerals
3864:
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3852:
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3707:
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3695:Law of cosines
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3662:
3657:
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3587:Platonic solid
3584:
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3567:Greek numerals
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3395:Planisphaerium
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2865:Mathematicians
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2689:
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2654:
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2650:Neopythagorean
2646:
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2627:
2622:
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2476:Musonius Rufus
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2441:Zeno of Citium
2437:
2435:
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1426:External links
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1160:(2): 113–135.
1140:
1106:
1086:
1083:on 2008-08-15.
1062:
1043:(2): 175–204.
1025:
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880:
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493:musical scales
489:natural number
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421:
333:Delian problem
297:
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267:Seventh Letter
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202:Southern Italy
200:(Tarentum) in
194:music theorist
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115:Pythagoreanism
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4121:347 BC deaths
4119:
4117:
4116:428 BC births
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3700:Pons asinorum
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3670:Hinge theorem
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2239:Dialecticians
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2017:
2014:
2012:
2009:
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1995:
1989:
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1420:0-521-83746-4
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1400:0-684-10114-9
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1196:
1195:Laërtius 1925
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766:Debra Nails,
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468:
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416:
411:
409:
405:
404:Aulus Gellius
401:
397:
396:
391:
387:
382:
380:
376:
372:
371:number theory
368:
364:
363:harmonic mean
359:
357:
356:
350:
346:
342:
341:proportionals
338:
334:
330:
326:
323:According to
321:
319:
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311:
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293:
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290:
285:
281:
277:
273:
269:
268:
262:
260:
259:
254:
250:
245:
243:
239:
235:
231:
230:Magna Graecia
227:
217:
213:
211:
207:
203:
199:
195:
191:
190:mathematician
188:
187:Ancient Greek
180:
174:
144:
135:
132:
128:
125:
122:Notable ideas
119:
116:
113:
111:
107:
104:
101:
97:
94:
91:
87:
83:
79:
75:
71:
70:Magna Graecia
67:
61:
57:
53:
49:
45:
39:
34:
27:
22:
4087:
4074:
3916:Thomas Heath
3907:
3790:
3774:Law of sines
3630:
3562:Golden ratio
3427:
3420:
3411:
3405:(Theodosius)
3401:
3393:
3386:
3379:
3372:
3363:
3353:
3347:(Hipparchus)
3343:
3333:
3325:
3318:
3309:
3299:
3291:
3286:(Apollonius)
3282:
3274:
3262:
3237:Zeno of Elea
2997:Eratosthenes
2987:Dionysodorus
2886:
2806:Philostratus
2693:Neoplatonist
2347:Theophrastus
2021:Dionysodorus
1978:Thrasymachus
1721:
1604:Pre-Socratic
1474:
1460:
1441:
1411:
1388:
1366:
1325:
1321:
1317:
1311:
1292:
1286:
1276:
1269:
1260:
1255:
1248:
1229:
1220:
1215:
1205:
1198:
1190:
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1153:
1143:
1131:. Retrieved
1119:
1109:
1099:
1089:
1081:the original
1075:
1065:
1040:
1034:
1028:
1019:
1009:
1000:
990:
970:
963:
946:
940:
930:
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893:
883:
872:. Retrieved
868:
858:
841:
837:
827:
817:, retrieved
812:
786:
767:
762:
745:25 September
743:. Retrieved
715:
703:
695:
690:
682:
674:
475:
466:
457:
453:
443:
431:
418:
413:
393:
383:
374:
360:
354:
332:
322:
304:(logistic),
299:
289:The Republic
287:
276:Dionysius II
265:
263:
256:
246:
223:
214:
142:
141:
3983:mathematics
3791:Arithmetica
3388:Ostomachion
3357:(Autolycus)
3276:Arithmetica
3052:Hippocrates
2982:Dinostratus
2967:Dicaearchus
2897:Aristarchus
2408:Aenesidemus
2381:Hellenistic
2329:Peripatetic
2247:Clinomachus
2085:Antisthenes
1699:Pythagorean
1650:Heraclitean
1635:Anaximander
1552:Seven Sages
1003:. Academia.
206:Pythagorean
48:Herculaneum
4110:Categories
4035:Babylonian
3935:arithmetic
3901:History of
3730:Apollonius
3415:(Menelaus)
3374:On Spirals
3293:Catoptrics
3232:Xenocrates
3227:Thymaridas
3212:Theodosius
3197:Theaetetus
3177:Simplicius
3167:Pythagoras
3152:Posidonius
3137:Philonides
3097:Nicomachus
3092:Metrodorus
3082:Menaechmus
3037:Hipparchus
3027:Heliodorus
2977:Diophantus
2962:Democritus
2942:Chrysippus
2912:Archimedes
2907:Apollonius
2877:Anaxagoras
2869:(timeline)
2763:Simplicius
2728:Iamblichus
2673:Nicomachus
2562:Arcesilaus
2529:Philodemus
2519:Metrodorus
2461:Posidonius
2451:Chrysippus
2390:Pyrrhonist
2314:Xenocrates
2309:Speusippus
2282:Panthoides
2123:Aristippus
2026:Euthydemus
1963:Protagoras
1936:Democritus
1899:Empedocles
1872:Anaxagoras
1823:Parmenides
1800:Xenophanes
1757:Hermotimus
1707:Pythagoras
1658:Heraclitus
1640:Anaximenes
1542:Pherecydes
1537:Epimenides
1457:"Archytas"
1434:"Archytas"
1344:References
1076:Symposiacs
874:2023-10-30
844:(3): 1–9.
819:2023-10-28
809:"Archytas"
776:1603844031
720:. Oxford:
667:References
345:cube roots
318:quadrivium
302:arithmetic
242:Menaechmus
80:360/350 BC
62:435/410 BC
52:Pythagoras
42:Bust from
3496:Inscribed
3256:Treatises
3247:Zenodorus
3207:Theodorus
3182:Sosigenes
3127:Philolaus
3112:Oenopides
3107:Nicoteles
3102:Nicomedes
3062:Hypsicles
2957:Ctesibius
2947:Cleomedes
2932:Callippus
2917:Autolycus
2902:Aristotle
2882:Anthemius
2796:Favorinus
2758:Damascius
2600:Antiochus
2567:Carneades
2534:Lucretius
2506:Epicurean
2481:Epictetus
2456:Panaetius
2446:Cleanthes
2337:Aristotle
2262:Dionysius
2257:Euphantus
2209:Eubulides
2171:Menedemus
2143:Anniceris
2049:Classical
2016:Lycophron
2011:Callicles
1931:Leucippus
1909:Pausanias
1877:Archelaus
1856:Pluralist
1752:Calliphon
1737:Brontinus
1717:Philolaus
1585:Cleobulus
1580:Periander
1475:Mechanica
1328:(1): 87.
1211:Vitruvius
1174:0031-8868
1154:Phronesis
1133:11 August
1100:Elements
1057:1432-0657
914:0031-8868
894:Phronesis
756:required)
408:Favorinus
400:Aristotle
390:Vitruvius
386:mechanics
353:Euclid's
314:harmonics
310:astronomy
258:strategos
234:Philolaus
4060:Japanese
4045:Egyptian
3988:timeline
3976:timeline
3964:timeline
3959:geometry
3952:timeline
3947:calculus
3940:timeline
3928:timeline
3631:Elements
3477:Concepts
3439:Problems
3412:Spherics
3402:Spherics
3367:(Euclid)
3313:(Euclid)
3310:Elements
3303:(Euclid)
3264:Almagest
3172:Serenus
3147:Porphyry
3087:Menelaus
3042:Hippasus
3017:Eutocius
2992:Domninus
2887:Archytas
2743:Syrianus
2723:Porphyry
2711:students
2706:Plotinus
2630:Alcinous
2625:Apuleius
2615:Plutarch
2514:Epicurus
2296:Platonic
2277:Alexinus
2224:Pasicles
2219:Nicarete
2199:Ichthyas
2186:Megarian
2158:Eretrian
2115:Cyrenaic
2100:Menippus
2090:Diogenes
2067:Xenophon
2061:students
2057:Socrates
1968:Prodicus
1833:Melissus
1805:Xeniades
1767:Arignote
1732:Alcmaeon
1727:Lamiskos
1722:Archytas
1712:Hippasus
1676:Diogenes
1663:Cratylus
1622:Milesian
1570:Pittacus
1405:on line
1359:(1925).
1197:, § 83:
1071:Plutarch
487:is some
483:, where
355:Elements
325:Eutocius
306:geometry
280:Syracuse
249:Pericles
143:Archytas
66:Tarentum
30:Archytas
4040:Chinese
3995:numbers
3923:algebra
3851:Related
3825:Centers
3621:Results
3491:Central
3162:Ptolemy
3157:Proclus
3122:Perseus
3077:Marinus
3057:Hypatia
3047:Hippias
3022:Geminus
3012:Eudoxus
3002:Eudemus
2972:Diocles
2811:more...
2768:more...
2748:Proclus
2683:more...
2640:more...
2582:more...
2544:more...
2496:more...
2423:more...
2367:more...
2319:more...
2148:more...
2105:more...
2031:more...
2006:Gorgias
1998:Italian
1988:more...
1973:Hippias
1946:Sophist
1923:Atomist
1891:Italian
1815:Eleatic
1792:Skeptic
1782:more...
1777:Eurytus
1690:Italian
1440:(ed.).
1182:4182463
922:4182355
657:
645:
641:
629:
625:
613:
609:
597:
593:
581:
577:
565:
561:
549:
545:
533:
529:
517:
513:
501:
480:
463:
379:Ptolemy
183:Ἀρχύτας
4055:Indian
3832:Cyrene
3364:Optics
3283:Conics
3202:Theano
3192:Thales
3187:Sporus
3132:Philon
3117:Pappus
3007:Euclid
2937:Carpus
2927:Bryson
2801:Lucian
2733:Julian
2718:Origen
2577:Cicero
2486:Arrian
2466:Seneca
2398:Pyrrho
2229:Bryson
2214:Stilpo
2095:Crates
1955:Ionian
1865:Ionian
1742:Theano
1630:Thales
1613:Ionian
1590:Chilon
1560:Thales
1418:
1397:
1354:
1299:
1180:
1172:
1095:Euclid
1055:
978:
920:
912:
774:
736:
643:, and
497:tuning
312:, and
253:Athens
110:School
99:Region
4050:Incan
3971:logic
3747:Other
3515:Chord
3508:Axiom
3486:Angle
3142:Plato
3032:Heron
2952:Conon
2635:Galen
2620:Gaius
2433:Stoic
2304:Plato
2272:Philo
2077:Cynic
1983:Damon
1904:Acron
1846:Hippo
1565:Solon
1436:. In
1219:[
1178:JSTOR
918:JSTOR
780:p. 44
436:Plato
423:Notes
296:Works
272:Plato
210:Plato
198:Taras
179:Greek
4012:list
3300:Data
3072:Leon
2922:Bion
1828:Zeno
1772:Myia
1747:Damo
1575:Bias
1416:ISBN
1395:ISBN
1297:ISBN
1170:ISSN
1135:2011
1053:ISSN
976:ISBN
910:ISSN
772:ISBN
747:2021
734:ISBN
495:and
369:and
220:Life
77:Died
59:Born
3914:by
3628:In
1330:doi
1326:122
1162:doi
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542:15
536:16
526:24
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469:+ 1
278:of
251:in
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