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Greek mathematics

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215: 5184: 1048: 8073: 3904: 5171: 31: 8083: 8093: 1034: 751: 368: 359:, often used mathematics to illustrate many of his theories, as when he used geometry in his theory of the rainbow and the theory of proportions in his analysis of motion. Much of the knowledge about ancient Greek mathematics in this period is thanks to records referenced by Aristotle in his own works. 552:
480–540 AD), who wrote commentaries on treatises by Archimedes and Apollonius. Although none of these mathematicians, save perhaps Diophantus, had notable original works, they are distinguished for their commentaries and expositions. These commentaries have preserved valuable extracts from works
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Despite the lack of original manuscripts, the dates for some Greek mathematicians are more certain than the dates of surviving Babylonian or Egyptian sources because a number of overlapping chronologies exist, though many dates remain uncertain.
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supposedly believed that "all is number" and were keen in looking for mathematical relations between numbers and things. Pythagoras himself was given credit for many later discoveries, including the construction of the
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civilizations, both of which flourished during the 2nd millennium BC. While these civilizations possessed writing and were capable of advanced engineering, including four-story palaces with drainage and
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mathematical texts that have been found were written after the Hellenistic period, most are considered to be copies of works written during and before the Hellenistic period. The two major sources are
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in the span of 800 to 600 BC, not much is known about Greek mathematics in this early period—nearly all of the information was passed down through later authors, beginning in the mid-4th century BC.
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Ancient Greek mathematics was not limited to theoretical works but was also used in other activities, such as business transactions and in land mensuration, as evidenced by extant texts where
505:, among others). Although few in number, Hellenistic mathematicians actively communicated with each other; publication consisted of passing and copying someone's work among colleagues. 556:
Most of the mathematical texts written in Greek survived through the copying of manuscripts over the centuries. While some fragments dating from antiquity have been found above all in
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ideas about number and believed that the elements of matter could be broken down into geometric solids. He also believed that geometrical proportions bound the
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to reach answers to problems with an arbitrary degree of accuracy, while specifying the limits within which the answers lay. Known as the
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Prolegomena Mathematica: From Apollonius of Perga to the Late Neoplatonism. With an Appendix on Pappus and the History of Platonism
8027: 6776: 6203: 6198: 3870: 3751: 3704: 343:, mentions mathematics in several of his dialogues. While not considered a mathematician, Plato seems to have been influenced by 3836: 553:
which have perished, or historical allusions which, in the absence of original documents, are precious because of their rarity.
6670: 6530: 6525: 5802: 3907: 3646: 3533: 1386:"Sub-scientific mathematics: Undercurrents and missing links in the mathematical technology of the Hellenistic and Roman world" 560:, as a rule they do not add anything significant to our knowledge of Greek mathematics preserved in the manuscript tradition. 247:, he traveled to Babylon from where he learned mathematics and other subjects, coming up with the proof of what is now called 8054: 6695: 5206: 5068: 5001: 4634: 4514: 3697: 3685: 3443: 1549: 1515: 624:, who presumably wrote on optics, astronomy, and harmonics, collected many previous mathematical results and theorems in the 7606: 3851: 800:(2011) has counted 144 ancient authors in the mathematical or exact sciences, from whom only 29 works are extant in Greek: 8049: 7099: 6615: 6535: 6233: 5943: 3680: 3619: 122: 8022: 6551: 6005: 5137: 4894: 4782: 3957: 3800: 1094: 7077: 6685: 6561: 6223: 6177: 6132: 5908: 5597: 4777: 3319: 869: 7616: 4846: 3515: 1115: 2264: 115: 8117: 7738: 7611: 6744: 6739: 6715: 6625: 6142: 5240: 4473: 4289: 4264: 901: 688: 467: 321: 8096: 8039: 6995: 6798: 6783: 6705: 6640: 6109: 5960: 5855: 5329: 5263: 5008: 4979: 4339: 4194: 3712: 1212:"The Creation of Second-Order Knowledge in Ancient Greek Science as a Process in the Globalization of Knowledge" 6793: 6756: 6690: 6356: 6243: 5142: 4419: 3641: 1566: 240: 4876: 3141: 2642: 3021: 2924: 239:(c. 624–548 BC). Very little is known about his life, although it is generally agreed that he was one of the 8076: 7200: 7000: 6985: 6788: 6771: 6751: 6720: 6620: 6556: 6172: 6157: 6127: 6088: 5965: 5817: 5319: 5104: 5080: 4954: 4889: 4830: 4767: 4757: 4493: 4412: 4274: 4184: 4064: 3675: 3663: 3634: 3560: 2830: 1383: 950: 849: 670: 481:
Several centers of learning appeared during the Hellenistic period, of which the most important one was the
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Pappus Reborn : Pappus of Alexandria and the Changing Face of Analysis and Synthesis in Late Antiquity
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of scholarship throughout the Hellenistic world, and the mathematics of the Classical period merged with
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is customarily attributed to the Pythagoreans, including the discovery of irrationals, attributed to
284: 223: 134: 3520: 2458:"Eudoxos and Dedekind: On the ancient Greek theory of ratios and its relation to modern mathematics" 2079: 1411: 1350:
On the early history of axiomatics: The interaction of mathematics and philosophy in Greek Antiquity
7689: 7659: 7047: 6942: 6937: 6374: 5689: 5602: 5572: 5526: 5289: 5132: 5051: 5039: 5020: 4984: 4904: 4822: 4807: 4797: 4747: 4742: 4684: 4553: 4445: 4374: 4309: 4299: 4199: 4169: 4109: 4084: 4009: 3999: 3984: 3810: 3658: 3609: 3580: 3311: 3290: 2549: 1078: 905: 817: 805: 545: 531: 475: 459: 447: 390: 293: 248: 179: 89: 39: 8082: 2925:"The Hyperbola-Construction in the Conics, Book II: Ancient Variations on a Theorem of Apollonius" 2605: 7906: 7803: 7709: 7353: 7270: 7158: 6660: 6484: 6000: 5980: 5837: 5708: 5592: 5387: 5314: 5188: 5147: 5087: 5015: 4881: 4674: 4649: 4617: 4214: 4159: 4124: 4019: 3815: 3575: 3241: 3202: 3114: 2997: 2905: 2858: 2811: 2764: 2756: 2485: 2060: 2012: 1965: 1853: 1751: 1685: 1488: 1273: 1053: 845: 809: 739: 710: 635: 417:, leading to the spread of the Greek language and culture across these regions. Greek became the 386: 356: 170:
The origins of Greek mathematics are not well documented. The earliest advanced civilizations in
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Companion Encyclopedia of the History and Philosophy of the Mathematical Sciences: Volume One
7911: 7443: 7408: 7225: 7082: 6960: 6847: 6842: 6167: 6122: 5953: 5860: 5476: 5309: 5294: 5284: 5063: 4934: 4851: 4607: 4595: 4543: 4279: 3692: 3268: 3233: 3176: 3106: 3041: 2979: 2944: 2889: 2842: 2795: 2740: 2701: 2617: 2469: 2400: 2245: 2210: 2169: 2126: 2122: 2085: 2004: 1949: 1880: 1798: 1669: 1578: 1472: 1417: 1265: 1253: 1199:. Greek Thought: A Guide to Classical Knowledge: Harvard University Press. pp. 386–413. 1126: 1009: 615: 513: 340: 332: 316:. Other mathematicians active in this period, not fully affiliated with any school, include 203: 183: 7951: 296:(fl. 450 BC). The greatest mathematician associated with the group, however, may have been 96:
is an important difference between Greek mathematics and those of preceding civilizations.
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Hans-Joachim Waschkies, "Introduction" to "Part 1: The Beginning of Greek Mathematics" in
1567:"A review of Aristotle's claim regarding Pythagoreans fundamental Beliefs: All is number?" 853: 778: 406: 1704: 202:
civilizations had an influence on the younger Greek tradition. Unlike the flourishing of
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periods, mostly from the 5th century BC to the 6th century AD, around the shores of the
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Collineations and Conic Sections: An Introduction to Projective Geometry in its History
2948: 2199:"Practicing algebra in late antiquity: The problem-solving of Diophantus of Alexandria" 1321: 1072: 1018: 938: 772: 765: 502: 344: 272: 267: 140: 85: 53: 163:
could be any branch of learning, or anything learnt; however, since antiquity certain
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Toomer, G. J. (January 1984). "Lost greek mathematical works in arabic translation".
3245: 3118: 3001: 2862: 2768: 2346: 2016: 1969: 1689: 1211: 1039: 706: 589: 581: 493:, which attracted scholars from across the Hellenistic world (mostly Greek, but also 490: 419: 398: 305: 263: 258:(c. 580–500 BC), who supposedly visited Egypt and Babylon, and ultimately settled in 199: 194:
Though no direct evidence is available, it is generally thought that the neighboring
167:(mainly arithmetic, geometry, astronomy, and harmonics) were granted special status. 3525: 3206: 2489: 1877:
The Forgotten Revolution: How Science Was Born in 300 BC and Why It Had to Be Reborn
1857: 1837: 1492: 1368:. Science and Philosophy in Classical Greece: Garland Publishing Inc. pp. 1–10. 1218:, MPRL – Studies, Berlin: Max-Planck-Gesellschaft zur Förderung der Wissenschaften, 7861: 7813: 7679: 7533: 7403: 7042: 6878: 6384: 6346: 6045: 4866: 4654: 4329: 4089: 4079: 3315: 3068: 2972:"Conics in Greek Geometry: Apollonius, Harmonic Division, and Later Greek Geometry" 1277: 728: 611: 577: 471: 435: 410: 188: 77: 61: 17: 2846: 2705: 2659:"Spherical Interpretation of Plane Geometry in Menelaus of Alexandria's Sphaerica" 2289: 434:
Greek mathematics and astronomy reached its acme during the Hellenistic and early
3380: 2578: 2008: 1953: 7881: 7773: 7753: 7586: 7581: 7089: 7067: 7057: 7052: 6975: 6932: 6479: 6389: 6379: 6266: 6256: 6020: 5397: 5372: 4480: 4368: 4074: 4059: 3461: 3438: 2983: 2404: 2239: 1884: 961: 797: 756: 664:, Archimedes employed it in several of his works, including an approximation to 607: 606:
developed a theory of proportion that bears resemblance to the modern theory of
569: 518: 402: 49: 30: 3222:"Greek-Arabic-Latin: The Transmission of Mathematical Texts in the Middle Ages" 1984: 750: 7818: 7788: 7783: 7768: 7654: 7621: 7290: 7260: 6927: 6655: 6489: 6331: 6326: 6316: 6301: 6286: 6276: 6251: 5627: 5382: 5337: 4466: 4385: 4324: 4319: 4259: 4244: 4189: 4174: 4129: 4069: 4054: 4034: 4004: 3969: 3237: 3181: 3164: 2971: 2658: 2392: 1872: 1673: 1130: 1029: 885: 861: 821: 732: 714: 653: 509: 486: 451: 443: 255: 218: 3190: 3053: 2956: 2901: 2854: 2807: 2752: 2713: 2674: 2629: 2481: 2305: 2224: 2215: 2183: 2174: 2056: 1961: 1747: 1681: 1592: 1484: 1292: 381:(c. 300 BC), considered the most influential mathematics textbook of all time 7793: 7719: 7704: 7674: 7669: 7601: 7525: 7510: 7495: 7438: 7338: 6990: 6922: 6494: 6474: 6444: 6439: 6434: 6399: 6394: 6364: 6311: 6271: 6050: 5916: 5870: 5850: 5657: 5481: 5352: 4219: 4204: 4154: 4049: 4039: 4024: 3994: 3918: 2621: 1583: 1061: 857: 833: 494: 352: 313: 195: 88:. The development of mathematics as a theoretical discipline and the use of 3198: 3022:"The Chord Table of Hipparchus and the Early History of Greek Trigonometry" 68:. Greek mathematicians lived in cities spread over the entire region, from 2322:
Prolegomena Mathematica: From Apollonius of Perga to the Late Neoplatonism
2089: 1476: 1421: 705:
The most characteristic product of Greek mathematics may be the theory of
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around this time include the construction of analogue computers like the
297: 289: 151: 69: 3483: 2909: 2877: 2760: 2728: 2064: 2044: 1755: 1731: 7986: 7976: 7931: 7921: 7916: 7901: 7891: 7876: 7871: 7758: 7646: 7636: 7515: 7490: 7485: 7458: 7453: 7433: 7423: 7413: 7378: 7368: 7358: 7310: 7300: 7275: 7245: 7240: 7235: 7210: 6863: 6645: 6306: 6296: 6055: 6025: 6015: 6010: 5990: 5985: 5865: 5812: 5726: 5521: 5511: 5501: 5496: 5486: 4929: 4254: 4249: 4149: 4139: 4114: 3272: 2815: 2783: 2744: 2473: 2320: 865: 841: 724: 630:, a canon of geometry and elementary number theory for many centuries. 535: 482: 455: 259: 244: 228: 3169:
NTM Zeitschrift fĂŒr Geschichte der Wissenschaften, Technik und Medizin
2290:"Isidore of Miletus and Hypatia: On the Editing of Mathematical Texts" 7956: 7886: 7866: 7828: 7694: 7500: 7393: 7330: 7320: 7265: 6883: 6868: 6464: 6449: 6424: 6419: 6404: 6065: 6060: 5827: 5807: 5551: 5541: 5536: 5407: 5367: 5357: 5342: 4224: 4099: 2457: 1269: 825: 693: 621: 439: 372: 348: 331:
Greek mathematics also drew the attention of philosophers during the
309: 279: 175: 171: 35: 2799: 2729:"Archimedes and the Measurement of the Circle: A New Interpretation" 2350: 1839:
Alexander to Actium: The Historical Evolution of the Hellenistic Age
1460: 1354:
Theory Change, Ancient Axiomatics, and Galileo's Methodology, Vol. 1
568:
Greek mathematics constitutes an important period in the history of
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Eudoxus, the most important mathematician you've never heard of.
8011: 7153: 6582: 6086: 5433: 5253: 5202: 3922: 3529: 2526: 2119:
Oxford Handbook of Science and Medicine in the Classical World
723:. The methods employed in these works made no explicit use of 498: 3165:"The Bibliosphere of Ancient Science (Outside of Alexandria)" 2113:
Acerbi, F. (2018). Keyser, Paul T; Scarborough, John (eds.).
2507:
https://web.stanford.edu/~yuvalwig/math/teaching/Eudoxus.pdf
2399:, Compact Textbooks in Mathematics, Springer, pp. 1–8, 2393:"Axiomatics—Euclid's and Hilbert's: From Material to Formal" 919:
The following works are extant only in Arabic translations:
634:, a later geometer and astronomer, wrote a standard work on 526:(c. 290–350 AD), who compiled many important results in the 2978:, Cham: Springer International Publishing, pp. 45–57, 1630:, Cambridge: Cambridge University Press, pp. 167–184, 1413:
The Origin of the History of Science in Classical Antiquity
1366:
Some remarks on the origins of Greek science and philosophy
775:, written some 500 to 1500 years after their originals, and 665: 474:(276–194 BC), and the mathematical and mechanical works of 127: 1123:
The Cambridge Companion to Ancient Greek and Roman Science
742:
and practical considerations took more of a central role.
3382:
Unknown Quantity: A Real And Imaginary History of Algebra
2531:
Acta Mathematica Academiae Paedagogicae NyĂ­ regyhĂĄziensis
1293:"Classification of the sciences in Greco-Roman antiquity" 1013:(extant in Latin from an Arabic translation of the Greek) 3481:
Sing, Robert; van Berkel Tazuko; Osborne, Robin (2021),
3406:(2nd ed.), Springer Science + Business Media Inc., 2443:
History of Mathematics Special Interest Group of the MAA
2970:
Baltus, Christopher (2020), Baltus, Christopher (ed.),
1985:"The Antikythera mechanism and the mechanical universe" 1323:
A History of Mathematics: From Mesopotamia to Modernity
2158:"Completing Diophantus, De polygonis numeris, prop. 5" 438:, and much of the work represented by authors such as 3095:"Greco-Egyptian Arithmetical Problems: P. Mich. 4966" 1445: 1443: 1441: 1075: â€“ System of writing numbers using Greek letters 717:
and perfected primarily under Apollonius in his work
3076:
DIO: The International Journal of Scientific History
1776:. The University of Chicago Press. pp. 82–110. 1706:
Numbers, Ontologically Speaking: Plato on Numerosity
351:
together rather than physical or mechanical forces.
7852: 7729: 7718: 7645: 7567: 7524: 7471: 7329: 7181: 7172: 7098: 7013: 6951: 6906: 6856: 6807: 6729: 6606: 6544: 6513: 6355: 6242: 6186: 6108: 5934: 5907: 5879: 5836: 5784: 5626: 5565: 5462: 5328: 5277: 5115: 4993: 4943: 4917: 4839: 4821: 4720: 4713: 4569: 4531: 4348: 3956: 3860: 3829: 3788: 3762: 3568: 1571:
Filosofia Unisinos / Unisinos Journal of Philosophy
2784:"Archimedes' Quadrature of the Parabola Revisited" 1320: 3424:(3rd ed.), The McGraw-Hill Companies, Inc., 2610:The British Journal for the Philosophy of Science 1879:, Berlin, Heidelberg: Springer, pp. 31–55, 1461:"Thales and the Origin of Theoretical Reasoning" 1150:Science and Mathematics in Ancient Greek Culture 3132:J J O'Connor and E F Robertson (October 1999). 2441:Powers, J. (2020). Did Archimedes do calculus? 1244:Heath (1931). "A Manual of Greek Mathematics". 656:made use of a technique dependent on a form of 596:, and, at times, approached ideas close to the 2431:. Vita Mathematica: MAA Press. pp. 67–86. 2429:The method of indivisibles in Ancient Geometry 1842:(1 ed.). University of California Press. 1459:Panchenko, D. V. (Dmitrii Vadimovich) (1993). 508:Later mathematicians in the Roman era include 191:, they left behind no mathematical documents. 5214: 3934: 3541: 3324:(3rd ed.), John Wiley & Sons, Inc., 2548:J J O'Connor and E F Robertson (April 1999). 1622:Netz, Reviel (2014), Huffman, Carl A. (ed.), 1174:(2nd ed.). New York: Wiley. p. 48. 8: 3340:Classics in the History of Greek Mathematics 2606:"Euclid's Elements and the Axiomatic Method" 2397:Turning Points in the History of Mathematics 1607:Classics in the History of Greek Mathematics 1352:. D. Reidel Publishing Co. pp. 145–186. 1319:Hodgkin, Luke (2005). "Greeks and origins". 646:, arguably considered the first treatise in 389:began in the late 4th century BC, following 3422:The History of Mathematics: An Introduction 3140:. University of St. Andrews. Archived from 3138:The MacTutor History of Mathematics archive 674:), and a proof that the area enclosed by a 618:, who acknowledged Eudoxus as inspiration. 580:. Greek mathematicians also contributed to 300:(c. 435-360 BC), who solved the problem of 8008: 7726: 7178: 7169: 7150: 6910: 6813: 6603: 6579: 6096: 6083: 5790: 5459: 5430: 5274: 5250: 5221: 5207: 5199: 4947: 4717: 3941: 3927: 3919: 3548: 3534: 3526: 3359:The History of Mathematics: A Brief Course 1938:"Hero of Alexandria's Mechanical Geometry" 1396:Aufstieg und Niedergang der römischen Welt 1081: â€“ Historical development of geometry 1068:Chronology of ancient Greek mathematicians 731:, the latter appearing around the time of 266:, where he started a kind of brotherhood. 3180: 3134:"How do we know about Greek mathematics?" 2214: 2173: 1582: 1416:. Peripatoi. De Gruyter. pp. 23–44. 1377: 1375: 1216:The Globalization of Knowledge in History 1114:Sidoli, Nathan (2020). Taub, Liba (ed.). 746:Transmission and the manuscript tradition 431:to give rise to Hellenistic mathematics. 3069:"The very early history of trigonometry" 2645:The Foundations of Arithmetic in Euclid. 2527:"Proportion theory in Greek mathematics" 2045:"Greek Science in its Hellenistic Phase" 1624:"The problem of Pythagorean mathematics" 1090:Timeline of ancient Greek mathematicians 3484:Numbers and Numeracy in the Greek Polis 2831:"The Goal of Archimedes' Sand Reckoner" 2555:MacTutor History of Mathematics archive 1106: 1064: â€“ 2nd Abbasid caliph (r. 754–775) 235:Greek mathematics allegedly began with 4970:Latin translations of the 12th century 1449:Boyer & Merzbach (2011) pp. 40–89. 1003:Commentary on Euclid's Elements book X 538:(c. 370–415 AD), who edited Ptolemy's 150: 139: 4700:Straightedge and compass construction 2782:Swain, Gordon; Dence, Thomas (1998). 2733:Archive for History of Exact Sciences 2688:Papadopoulos, Athanase (2019-08-09). 2127:10.1093/oxfordhb/9780199734146.013.69 1905: 1903: 1823: 1767: 1765: 1617: 1615: 1393:(Unpublished manuscript, written for 709:, which was largely developed in the 221:with a tablet of ratios, detail from 7: 7622:Illicitanus Limin/Portus Illicitanus 4665:Incircle and excircles of a triangle 2197:Christianidis, J.; Oaks, J. (2013). 1703:Calian, Florin George (2021-12-09). 1314: 1312: 1146:"Greek mathematics: A group picture" 946:Construction of the Regular Heptagon 355:(c. 384–322 BC), the founder of the 339:(c. 428–348 BC), the founder of the 3493:The Beginnings of Greek Mathematics 2294:Greek, Roman, and Byzantine Studies 159:, "to learn". Strictly speaking, a 3163:Netz, Reviel (27 September 2011). 3046:10.1111/j.1600-0498.1974.tb00205.x 2949:10.1111/j.1600-0498.1981.tb00647.x 2663:Journal for the History of Science 2580:Euclid—The Creation of Mathematics 516:and a work in pre-modern algebra ( 466:, the accurate measurement of the 52:texts and ideas stemming from the 25: 2694:The American Mathematical Monthly 2265:"Theon of Alexandria and Hypatia" 1774:The Beginnings of Western Science 1565:Cornelli, Gabriele (2016-05-20). 534:(c. 335–405 AD) and his daughter 108:("mathematics") derives from the 8091: 8081: 8072: 8071: 5182: 5169: 3903: 3902: 3495:, Reidel & Akademiai Kiado, 3338:Jean Christianidis, ed. (2004), 2033:. Berlin: Springer. pp. 273–277. 1826:, "Euclid of Alexandria" p. 119) 1797:Mendell, Henry (26 March 2004). 1046: 1032: 8092: 3487:, Brill, ISBN 978-90-04-46722-4 2391:Grant, H.; Kleiner, I. (2015), 278:Almost half of the material in 254:An equally enigmatic figure is 5002:A History of Greek Mathematics 4515:The Quadrature of the Parabola 3444:A History of Greek Mathematics 3342:, Kluwer Academic Publishers, 3297:, Princeton University Press, 3261:The Mathematical Intelligencer 2923:Knorr, Wilbur Richard (1981). 2378:A History of Greek Mathematics 1210:Schiefsky, Mark (2012-07-20), 512:(c. 214–298 AD), who wrote on 308:, and possibly contributed to 1: 5693: 5680: 5661: 5644: 3466:A Manual of Greek Mathematics 2847:10.1515/APEIRON.2003.36.4.251 2706:10.1080/00029890.2019.1604052 2583:. New York: Springer-Verlag. 1983:Edmunds, M. G. (2014-10-02). 1912:"Greek mathematics to AD 300" 363:Hellenistic and Roman periods 210:Archaic and Classical periods 27:Mathematics of Ancient Greeks 6821:Funeral and burial practices 6006:Military of Mycenaean Greece 4783:Intersecting secants theorem 3220:Lorch, Richard (June 2001). 2690:"Three Theorems of Menelaus" 2502:Wigderson, Y. (April 2019). 2456:Stein, Howard (1990-08-01). 2269:History of the Ancient World 2081:Hellenistic Science at Court 2009:10.1080/00107514.2014.927280 1954:10.1515/APEIRON.2004.37.4.29 1936:Karin Tybjerg (2004-12-01). 1410:Zhmud, Leonid (2008-08-22). 1095:List of Greek mathematicians 713:, starting with the work of 686:with equal base and height ( 572:: fundamental in respect of 128: 4778:Intersecting chords theorem 4645:Doctrine of proportionality 3521:Famous Greek Mathematicians 3404:Mathematics and its History 2984:10.1007/978-3-030-46287-1_4 2878:"The problem of Apollonius" 2657:Amini, Hasan (2013-03-21). 2604:MUELLER, IAN (1969-12-01). 2558:. University of St. Andrews 2405:10.1007/978-1-4939-3264-1_1 1885:10.1007/978-3-642-18904-3_3 1799:"Aristotle and Mathematics" 1628:A History of Pythagoreanism 1327:. Oxford University Press. 1116:"Ancient Greek Mathematics" 8134: 6745:Greek Revival architecture 4474:On the Sphere and Cylinder 4427:On the Sizes and Distances 2829:Reviel Netz (2003-12-01). 689:Quadrature of the Parabola 468:circumference of the Earth 114: 113: 8067: 8018: 8007: 7168: 7149: 6913: 6816: 6602: 6578: 6153:Attalid kings of Pergamon 6099: 6095: 6082: 5961:Antigonid Macedonian army 5793: 5458: 5429: 5273: 5249: 5236: 5176:Ancient Greece portal 5165: 4980:Philosophy of mathematics 4950: 4895:Ptolemy's table of chords 3950:Ancient Greek mathematics 3898: 3420:Burton, David M. (1997), 3238:10.1017/S0269889701000114 3182:10.1007/s00048-011-0057-2 2727:Knorr, Wilbur R. (1976). 2238:Rideout, Bronwyn (2008). 2115:"Hellenistic Mathematics" 1873:"Hellenistic Mathematics" 1736:The Review of Metaphysics 1730:Cherniss, Harold (1951). 1674:10.1017/S0269889705000347 1510:. Wiley. pp. 42–43. 1131:10.1017/9781316136096.010 671:Measurement of the Circle 4847:Aristarchus's inequality 4420:On Conoids and Spheroids 3321:A History of Mathematics 3295:A History of Mathematics 2216:10.1016/j.hm.2012.09.001 2175:10.1016/j.hm.2011.05.002 2031:The Forgotten Revolution 1772:Lindberg, David (2008). 1732:"Plato as Mathematician" 1656:Burnyeat, M. F. (2005). 1508:A History of Mathematics 1172:A History of Mathematics 740:computational procedures 696:, which denoted 10,000 ( 241:Seven Wise Men of Greece 4955:Ancient Greek astronomy 4768:Inscribed angle theorem 4758:Greek geometric algebra 4413:Measurement of a Circle 3093:Robbins, F. E. (1934). 2882:The Mathematics Teacher 2577:Artmann, Benno (1999). 1584:10.4013/fsu.2016.171.06 1530:Heath (2003) pp. 36–111 970:On Divisions of Figures 789:of the Arabic versions. 678:and a straight line is 6187:Artists & scholars 6102:List of ancient Greeks 5739:Second Athenian League 5588:Greco-Bactrian Kingdom 5413:Ancient Greek colonies 5189:Mathematics portal 4975:Non-Euclidean geometry 4930:Mouseion of Alexandria 4803:Tangent-secant theorem 4753:Geometric mean theorem 4738:Exterior angle theorem 4733:Angle bisector theorem 4437:On Sizes and Distances 3821:Medieval Islamic world 3557:History of mathematics 3491:Szabo, Arpad (1978) , 3468:, Dover publications, 3447:, Dover publications, 3385:, Joseph Henry Press, 3362:, Wiley-Interscience, 3020:Toomer, G. J. (1974). 2376:Heath, Thomas (1921). 1085:History of mathematics 932:Cutting Off of a Ratio 764:Although the earliest 761: 658:proof by contradiction 648:non-Euclidean geometry 586:mathematical astronomy 429:Babylonian mathematics 382: 232: 42: 7306:Sybaris on the Traeis 6031:Sacred Band of Thebes 5771:(c. 300 BC–c. 300 AD) 5285:Cycladic civilization 4877:Pappus's area theorem 4813:Theorem of the gnomon 4690:Quadratrix of Hippias 4613:Circles of Apollonius 4561:Problem of Apollonius 4539:Constructible numbers 4363:Archimedes Palimpsest 3890:Future of mathematics 3867:Women in mathematics 3356:Cooke, Roger (1997), 2876:Court, N. A. (1961). 2622:10.1093/bjps/20.4.289 2319:Mansfeld, J. (2016). 2090:10.1515/9783110541939 2029:Russo, Lucio (2004). 1803:Stanford Encyclopedia 1658:"Archytas and Optics" 1544:. Wiley. p. 45. 1477:10.1353/con.1993.0024 1422:10.1515/9783110194326 1144:Netz, Reviel (2002). 754:Cover of Diophantus' 753: 544:and other works, and 464:Antikythera mechanism 454:(c. 190–120 BC), and 395:Eastern Mediterranean 391:Alexander the Great's 370: 324:(c. 417–369 BC), and 217: 100:Origins and etymology 80:, but were united by 33: 6831:mythological figures 6552:Ancient Greek tribes 5677:Peloponnesian League 5093:prehistoric counting 4890:Ptolemy's inequality 4831:Apollonius's theorem 4670:Method of exhaustion 4640:Diophantine equation 4630:Circumscribed circle 4447:On the Moving Sphere 3842:Over Cantor's theory 3462:Heath, Thomas Little 3439:Heath, Thomas Little 2894:10.5951/MT.54.6.0444 2788:Mathematics Magazine 2288:Cameron, A. (1990). 2263:Lambrou, M. (2003). 2203:Historia Mathematica 2162:Historia Mathematica 2121:. pp. 268–292. 2043:Luce, J. V. (1988). 1989:Contemporary Physics 1858:10.1525/j.ctt130jt89 1542:A History of Science 1540:Boyer, Carl (1968). 1506:Boyer, Carl (1968). 1364:Kahn, C. H. (1991). 1170:Boyer, C.B. (1991). 878:Aristides Quintilian 682:times the area of a 662:method of exhaustion 638:in the style of the 594:mathematical physics 576:and for the idea of 524:Pappus of Alexandria 318:Hippocrates of Chios 292:(c. 530–450 BC) and 224:The School of Athens 141:[mĂĄ.tʰɛː.ma] 6943:Tunnel of Eupalinos 6938:Theatre of Dionysus 6562:Ancient Macedonians 6178:Tyrants of Syracuse 5690:Amphictyonic League 5290:Minoan civilization 5179: • 4985:Neusis construction 4905:Spiral of Theodorus 4798:Pythagorean theorem 4743:Euclidean algorithm 4685:Lune of Hippocrates 4554:Squaring the circle 4310:Theon of Alexandria 3985:Aristaeus the Elder 3878:Approximations of π 3789:By ancient cultures 3038:1974Cent...18....6T 2941:1981Cent...25..253K 2643:Pierce, D. (2015). 2550:"Eudoxus of Cnidus" 2380:. Humphrey Milford. 2156:Acerbi, F. (2011). 2078:Berrey, M. (2017). 2001:2014ConPh..55..263E 1382:HĂžyrup, J. (1990). 1291:Furner, J. (2020). 1262:1931Natur.128..739T 1079:History of geometry 906:Theon of Alexandria 785:of Greek works and 783:Arabic translations 546:Eutocius of Ascalon 532:Theon of Alexandria 460:applied mathematics 273:five regular solids 256:Pythagoras of Samos 152:[ˈma.Ξi.ma] 90:deductive reasoning 40:Pythagorean theorem 34:An illustration of 18:Ancient mathematics 7617:Menestheus's Limin 7271:Pandosia (Lucania) 7159:Greek colonisation 6521:Athenian statesmen 6282:Diogenes of Sinope 6143:Kings of Macedonia 6133:Kings of Commagene 6001:Macedonian phalanx 5981:Hellenistic armies 5729:(c. 424–c. 395 BC) 5593:Indo-Greek Kingdom 5315:Hellenistic Greece 4872:Menelaus's theorem 4862:Irrational numbers 4675:Parallel postulate 4650:Euclidean geometry 4618:Apollonian circles 4160:Isidore of Miletus 3681:Information theory 3273:10.1007/BF03024153 3226:Science in Context 3144:on 30 January 2000 2745:10.1007/BF00348496 2525:Filep, L. (2003). 2512:2021-07-28 at the 2474:10.1007/BF00485377 2427:Knorr, W. (1996). 1910:Jones, A. (1994). 1871:Russo, L. (2004), 1836:Green, P. (1990). 1662:Science in Context 1348:Knorr, W. (1981). 1195:Knorr, W. (2000). 1152:. pp. 196–216 1054:Mathematics portal 955:On Burning Mirrors 810:Philo of Byzantium 787:Latin translations 762: 711:Hellenistic period 636:spherical geometry 383: 357:Peripatetic school 233: 43: 8118:Greek mathematics 8105: 8104: 8063: 8062: 8003: 8002: 7999: 7998: 7995: 7994: 7569:Iberian Peninsula 7501:Lipara/Meligounis 7467: 7466: 7145: 7144: 7141: 7140: 7118:Cypriot syllabary 7009: 7008: 6918:Athenian Treasury 6902: 6901: 6574: 6573: 6570: 6569: 6163:Ptolemaic dynasty 6123:Archons of Athens 6078: 6077: 6074: 6073: 5949:Athenian military 5930: 5929: 5763:League of Corinth 5745:Thessalian League 5721:Chalcidian League 5703:Acarnanian League 5613:Ptolemaic Kingdom 5425: 5424: 5421: 5420: 5196: 5195: 5161: 5160: 4913: 4912: 4900:Ptolemy's theorem 4773:Intercept theorem 4623:Apollonian gasket 4549:Doubling the cube 4522:The Sand Reckoner 3916: 3915: 3752:Separation axioms 3502:978-963-05-1416-3 3475:978-0-486-43231-1 3454:978-0-486-24073-2 3431:978-0-07-009465-9 3413:978-0-387-95336-6 3392:978-0-309-09657-7 3369:978-0-471-18082-1 3349:978-1-4020-0081-2 3331:978-0-471-54397-8 3304:978-0-691-02391-5 3067:Duke, D. (2011). 2993:978-3-030-46287-1 2590:978-0-387-98423-0 2414:978-1-4939-3264-1 2362:978-90-04-32105-2 2332:978-90-04-32105-2 2136:978-0-19-973414-6 2099:978-3-11-054193-9 1894:978-3-642-18904-3 1849:978-0-520-08349-3 1716:978-90-04-46722-4 1637:978-1-107-01439-8 1431:978-3-11-019432-6 1334:978-0-19-852937-8 1225:978-3-945561-23-2 773:Byzantine codices 699:The Sand-Reckoner 604:Eudoxus of Cnidus 598:integral calculus 514:polygonal numbers 450:(c. 240–190 BC), 446:(c. 287–212 BC), 328:(c. 408–355 BC). 320:(c. 470–410 BC), 304:, identified the 302:doubling the cube 237:Thales of Miletus 126: 46:Greek mathematics 16:(Redirected from 8125: 8095: 8094: 8085: 8075: 8074: 8009: 7727: 7226:Heraclea Lucania 7179: 7170: 7151: 6911: 6843:Twelve Olympians 6814: 6604: 6580: 6168:Seleucid dynasty 6148:Kings of Paionia 6097: 6084: 5954:Scythian archers 5861:Graphe paranomon 5791: 5698: 5695: 5685: 5682: 5666: 5663: 5653: 5649: 5646: 5460: 5431: 5310:Classical Greece 5295:Mycenaean Greece 5275: 5251: 5223: 5216: 5209: 5200: 5187: 5186: 5174: 5173: 5172: 4948: 4935:Platonic Academy 4882:Problem II.8 of 4852:Crossbar theorem 4808:Thales's theorem 4748:Euclid's theorem 4718: 4635:Commensurability 4596:Axiomatic system 4544:Angle trisection 4509: 4499: 4461: 4451: 4441: 4431: 4407: 4397: 4380: 3943: 3936: 3929: 3920: 3906: 3905: 3626:Category theory 3550: 3543: 3536: 3527: 3505: 3478: 3457: 3434: 3416: 3395: 3377:Derbyshire, John 3372: 3352: 3334: 3316:Merzbach, Uta C. 3307: 3277: 3276: 3256: 3250: 3249: 3232:(1–2): 313–331. 3217: 3211: 3210: 3184: 3160: 3154: 3153: 3151: 3149: 3129: 3123: 3122: 3090: 3084: 3083: 3073: 3064: 3058: 3057: 3017: 3011: 3010: 3009: 3008: 2967: 2961: 2960: 2920: 2914: 2913: 2873: 2867: 2866: 2826: 2820: 2819: 2779: 2773: 2772: 2724: 2718: 2717: 2685: 2679: 2678: 2654: 2648: 2640: 2634: 2633: 2601: 2595: 2594: 2574: 2568: 2567: 2565: 2563: 2545: 2539: 2538: 2522: 2516: 2500: 2494: 2493: 2453: 2447: 2439: 2433: 2432: 2424: 2418: 2417: 2388: 2382: 2381: 2373: 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7464: 7462: 7461: 7456: 7451: 7446: 7441: 7436: 7431: 7426: 7421: 7419:Megara Hyblaea 7416: 7411: 7406: 7401: 7399:Hybla Gereatis 7396: 7391: 7389:Heraclea Minoa 7386: 7381: 7376: 7371: 7366: 7361: 7356: 7351: 7346: 7341: 7335: 7333: 7327: 7326: 7324: 7323: 7318: 7313: 7308: 7303: 7298: 7293: 7288: 7283: 7278: 7273: 7268: 7263: 7258: 7253: 7248: 7243: 7238: 7233: 7228: 7223: 7218: 7213: 7208: 7203: 7198: 7193: 7187: 7185: 7176: 7166: 7165: 7162: 7161: 7155: 7154: 7147: 7146: 7143: 7142: 7139: 7138: 7136: 7135: 7133:Attic numerals 7130: 7128:Greek numerals 7125: 7123:Greek alphabet 7120: 7115: 7110: 7104: 7102: 7096: 7095: 7093: 7092: 7087: 7086: 7085: 7080: 7075: 7070: 7065: 7060: 7055: 7050: 7045: 7035: 7030: 7025: 7019: 7017: 7011: 7010: 7007: 7006: 7004: 7003: 6998: 6993: 6988: 6983: 6978: 6973: 6968: 6963: 6957: 6955: 6949: 6948: 6946: 6945: 6940: 6935: 6930: 6925: 6920: 6914: 6908: 6904: 6903: 6900: 6899: 6897: 6896: 6891: 6886: 6881: 6876: 6871: 6866: 6860: 6858: 6854: 6853: 6851: 6850: 6845: 6840: 6835: 6834: 6833: 6823: 6817: 6811: 6805: 6804: 6802: 6801: 6796: 6791: 6786: 6781: 6780: 6779: 6777:Musical system 6769: 6764: 6759: 6754: 6749: 6748: 6747: 6736: 6734: 6727: 6726: 6724: 6723: 6718: 6713: 6708: 6703: 6698: 6693: 6688: 6683: 6678: 6673: 6668: 6663: 6658: 6653: 6648: 6643: 6638: 6633: 6628: 6623: 6618: 6612: 6610: 6600: 6599: 6596: 6595: 6590: 6584: 6583: 6576: 6575: 6572: 6571: 6568: 6567: 6565: 6564: 6559: 6554: 6548: 6546: 6542: 6541: 6539: 6538: 6533: 6528: 6523: 6517: 6515: 6511: 6510: 6508: 6507: 6502: 6497: 6492: 6487: 6482: 6477: 6472: 6467: 6462: 6457: 6452: 6447: 6442: 6437: 6432: 6427: 6422: 6417: 6412: 6407: 6402: 6397: 6392: 6387: 6382: 6377: 6372: 6367: 6361: 6359: 6353: 6352: 6350: 6349: 6344: 6339: 6334: 6329: 6324: 6319: 6314: 6309: 6304: 6299: 6294: 6289: 6284: 6279: 6274: 6269: 6264: 6259: 6254: 6248: 6246: 6240: 6239: 6237: 6236: 6231: 6226: 6221: 6216: 6211: 6209:Mathematicians 6206: 6201: 6196: 6190: 6188: 6184: 6183: 6181: 6180: 6175: 6170: 6165: 6160: 6155: 6150: 6145: 6140: 6135: 6130: 6125: 6120: 6118:Kings of Argos 6114: 6112: 6106: 6105: 6100: 6093: 6092: 6087: 6080: 6079: 6076: 6075: 6072: 6071: 6069: 6068: 6063: 6058: 6053: 6048: 6043: 6038: 6033: 6028: 6023: 6018: 6013: 6008: 6003: 5998: 5993: 5988: 5983: 5978: 5976:Cretan archers 5973: 5968: 5963: 5958: 5957: 5956: 5946: 5940: 5938: 5932: 5931: 5928: 5927: 5925: 5924: 5919: 5913: 5911: 5905: 5904: 5902: 5901: 5896: 5891: 5885: 5883: 5877: 5876: 5874: 5873: 5868: 5863: 5858: 5853: 5848: 5842: 5840: 5834: 5833: 5831: 5830: 5825: 5820: 5815: 5810: 5805: 5800: 5794: 5788: 5782: 5781: 5779: 5778: 5775:Achaean League 5772: 5769:Euboean League 5766: 5760: 5757:Epirote League 5754: 5748: 5742: 5736: 5730: 5724: 5718: 5712: 5706: 5705:(c. 500–31 BC) 5700: 5687: 5674: 5668: 5655: 5637: 5635: 5633:Confederations 5624: 5623: 5621: 5620: 5615: 5610: 5605: 5600: 5595: 5590: 5585: 5580: 5575: 5569: 5567: 5563: 5562: 5560: 5559: 5557:Lissus (Crete) 5554: 5549: 5544: 5539: 5534: 5529: 5524: 5519: 5514: 5509: 5504: 5499: 5494: 5489: 5484: 5479: 5474: 5468: 5466: 5456: 5455: 5452: 5451: 5446: 5441: 5435: 5434: 5427: 5426: 5423: 5422: 5419: 5418: 5416: 5415: 5410: 5405: 5400: 5395: 5390: 5385: 5380: 5375: 5370: 5365: 5360: 5355: 5350: 5345: 5340: 5334: 5332: 5326: 5325: 5323: 5322: 5317: 5312: 5307: 5305:Archaic Greece 5302: 5297: 5292: 5287: 5281: 5279: 5271: 5270: 5267: 5266: 5261: 5255: 5254: 5247: 5246: 5244: 5243: 5237: 5234: 5233: 5230:Ancient Greece 5228: 5226: 5225: 5218: 5211: 5203: 5194: 5193: 5166: 5163: 5162: 5159: 5158: 5156: 5155: 5150: 5145: 5140: 5135: 5130: 5125: 5119: 5117: 5116:Other cultures 5113: 5112: 5110: 5109: 5108: 5107: 5097: 5096: 5095: 5085: 5084: 5083: 5073: 5072: 5071: 5061: 5060: 5059: 5049: 5048: 5047: 5037: 5036: 5035: 5025: 5024: 5023: 5013: 5012: 5011: 4997: 4995: 4991: 4990: 4988: 4987: 4982: 4977: 4972: 4967: 4965:Greek numerals 4962: 4960:Attic numerals 4957: 4951: 4945: 4941: 4940: 4938: 4937: 4932: 4927: 4921: 4919: 4915: 4914: 4911: 4910: 4908: 4907: 4902: 4897: 4892: 4887: 4879: 4874: 4869: 4864: 4859: 4854: 4849: 4843: 4841: 4837: 4836: 4834: 4833: 4827: 4825: 4819: 4818: 4816: 4815: 4810: 4805: 4800: 4795: 4790: 4788:Law of cosines 4785: 4780: 4775: 4770: 4765: 4760: 4755: 4750: 4745: 4740: 4735: 4729: 4727: 4715: 4711: 4710: 4708: 4707: 4702: 4697: 4692: 4687: 4682: 4680:Platonic solid 4677: 4672: 4667: 4662: 4660:Greek numerals 4657: 4652: 4647: 4642: 4637: 4632: 4627: 4626: 4625: 4620: 4610: 4605: 4604: 4603: 4593: 4592: 4591: 4586: 4575: 4573: 4567: 4566: 4564: 4563: 4558: 4557: 4556: 4551: 4546: 4535: 4533: 4529: 4528: 4526: 4525: 4518: 4511: 4501: 4491: 4488:Planisphaerium 4484: 4477: 4470: 4463: 4453: 4443: 4433: 4423: 4416: 4409: 4399: 4389: 4382: 4372: 4365: 4360: 4352: 4350: 4346: 4345: 4343: 4342: 4337: 4332: 4327: 4322: 4317: 4312: 4307: 4302: 4297: 4292: 4287: 4282: 4277: 4272: 4267: 4262: 4257: 4252: 4247: 4242: 4237: 4232: 4227: 4222: 4217: 4212: 4207: 4202: 4197: 4192: 4187: 4182: 4177: 4172: 4167: 4162: 4157: 4152: 4147: 4142: 4137: 4132: 4127: 4122: 4117: 4112: 4107: 4102: 4097: 4092: 4087: 4082: 4077: 4072: 4067: 4062: 4057: 4052: 4047: 4042: 4037: 4032: 4027: 4022: 4017: 4012: 4007: 4002: 3997: 3992: 3987: 3982: 3977: 3972: 3966: 3964: 3958:Mathematicians 3954: 3953: 3948: 3946: 3945: 3938: 3931: 3923: 3914: 3913: 3911: 3910: 3899: 3896: 3895: 3893: 3892: 3887: 3886: 3885: 3875: 3874: 3873: 3864: 3862: 3858: 3857: 3855: 3854: 3849: 3847:Leibniz–Newton 3844: 3839: 3833: 3831: 3827: 3826: 3824: 3823: 3818: 3813: 3808: 3806:Ancient Greece 3803: 3798: 3792: 3790: 3786: 3785: 3783: 3782: 3777: 3772: 3766: 3764: 3760: 3759: 3757: 3756: 3755: 3754: 3749: 3748: 3747: 3734: 3733: 3732: 3727: 3717: 3716: 3715: 3709:Number theory 3707: 3702: 3701: 3700: 3690: 3689: 3688: 3678: 3673: 3672: 3671: 3666: 3656: 3655: 3654: 3644: 3639: 3638: 3637: 3632: 3624: 3623: 3622: 3617: 3607: 3606: 3605: 3595: 3594: 3593: 3585: 3584: 3583: 3572: 3570: 3566: 3565: 3555: 3553: 3552: 3545: 3538: 3530: 3524: 3523: 3518: 3511: 3510:External links 3508: 3507: 3506: 3501: 3488: 3479: 3474: 3458: 3453: 3435: 3430: 3417: 3412: 3396: 3391: 3373: 3368: 3353: 3348: 3335: 3330: 3312:Boyer, Carl B. 3308: 3303: 3291:Boyer, Carl B. 3285: 3282: 3279: 3278: 3251: 3212: 3175:(3): 239–269. 3155: 3124: 3111:10.1086/346874 3085: 3059: 3012: 2992: 2962: 2935:(3): 253–291. 2915: 2888:(6): 444–452. 2868: 2841:(4): 251–290. 2821: 2794:(2): 123–130. 2774: 2739:(2): 115–140. 2719: 2700:(7): 610–619. 2680: 2649: 2635: 2616:(4): 289–309. 2596: 2589: 2569: 2540: 2517: 2495: 2468:(2): 163–211. 2448: 2434: 2419: 2413: 2383: 2368: 2361: 2338: 2331: 2311: 2300:(1): 103–127. 2280: 2255: 2230: 2209:(2): 127–163. 2189: 2168:(4): 548–560. 2148: 2135: 2105: 2098: 2084:. De Gruyter. 2070: 2051:(145): 23–38. 2035: 2022: 1995:(4): 263–285. 1975: 1928: 1899: 1893: 1863: 1848: 1828: 1815: 1789: 1782: 1761: 1742:(3): 395–425. 1722: 1715: 1695: 1648: 1636: 1611: 1598: 1557: 1550: 1532: 1523: 1516: 1498: 1471:(3): 387–414. 1465:Configurations 1451: 1437: 1430: 1402: 1371: 1356: 1340: 1333: 1308: 1283: 1236: 1224: 1202: 1187: 1180: 1162: 1136: 1105: 1104: 1102: 1099: 1098: 1097: 1092: 1087: 1082: 1076: 1073:Greek numerals 1070: 1065: 1058: 1057: 1043: 1027: 1024: 1023: 1022: 1019:Planisphaerium 1014: 1005: 999: 990: 984: 978: 972: 966: 957: 948: 942: 939:Book of Lemmas 934: 928: 927:books V to VII 791: 790: 776: 747: 744: 707:conic sections 565: 562: 442:(fl. 300 BC), 364: 361: 211: 208: 101: 98: 86:Greek language 26: 24: 14: 13: 10: 9: 6: 4: 3: 2: 8130: 8119: 8116: 8115: 8113: 8098: 8090: 8088: 8084: 8080: 8078: 8070: 8069: 8066: 8056: 8053: 8051: 8048: 8046: 8043: 8041: 8038: 8036: 8033: 8029: 8026: 8025: 8024: 8021: 8020: 8017: 8010: 8006: 7988: 7985: 7983: 7980: 7978: 7975: 7973: 7970: 7968: 7965: 7963: 7960: 7958: 7955: 7953: 7950: 7948: 7945: 7943: 7940: 7938: 7935: 7933: 7930: 7928: 7925: 7923: 7920: 7918: 7915: 7913: 7910: 7908: 7905: 7903: 7900: 7898: 7895: 7893: 7890: 7888: 7885: 7883: 7880: 7878: 7875: 7873: 7870: 7868: 7865: 7863: 7860: 7859: 7857: 7851: 7845: 7842: 7840: 7837: 7835: 7832: 7830: 7827: 7825: 7822: 7820: 7817: 7815: 7812: 7810: 7807: 7805: 7802: 7800: 7797: 7795: 7792: 7790: 7787: 7785: 7782: 7780: 7777: 7775: 7772: 7770: 7767: 7765: 7762: 7760: 7757: 7755: 7752: 7750: 7747: 7745: 7742: 7740: 7737: 7736: 7734: 7728: 7725: 7721: 7717: 7711: 7708: 7706: 7703: 7701: 7698: 7696: 7693: 7691: 7688: 7686: 7683: 7681: 7678: 7676: 7673: 7671: 7668: 7666: 7663: 7661: 7658: 7656: 7653: 7652: 7650: 7648: 7644: 7638: 7635: 7633: 7630: 7628: 7625: 7623: 7620: 7618: 7615: 7613: 7610: 7608: 7605: 7603: 7600: 7598: 7597:Hemeroscopion 7595: 7593: 7590: 7588: 7585: 7583: 7580: 7578: 7575: 7574: 7572: 7570: 7566: 7560: 7557: 7554: 7550: 7547: 7545: 7542: 7540: 7537: 7535: 7532: 7531: 7529: 7527: 7523: 7517: 7514: 7512: 7509: 7507: 7504: 7502: 7499: 7497: 7494: 7492: 7489: 7487: 7484: 7482: 7479: 7478: 7476: 7474: 7470: 7460: 7457: 7455: 7452: 7450: 7447: 7445: 7442: 7440: 7437: 7435: 7432: 7430: 7427: 7425: 7422: 7420: 7417: 7415: 7412: 7410: 7407: 7405: 7402: 7400: 7397: 7395: 7392: 7390: 7387: 7385: 7382: 7380: 7377: 7375: 7372: 7370: 7367: 7365: 7362: 7360: 7357: 7355: 7352: 7350: 7347: 7345: 7342: 7340: 7337: 7336: 7334: 7332: 7328: 7322: 7319: 7317: 7314: 7312: 7309: 7307: 7304: 7302: 7299: 7297: 7294: 7292: 7289: 7287: 7284: 7282: 7279: 7277: 7274: 7272: 7269: 7267: 7264: 7262: 7259: 7257: 7254: 7252: 7249: 7247: 7244: 7242: 7239: 7237: 7234: 7232: 7229: 7227: 7224: 7222: 7219: 7217: 7214: 7212: 7209: 7207: 7204: 7202: 7199: 7197: 7194: 7192: 7189: 7188: 7186: 7180: 7177: 7175: 7174:Magna Graecia 7171: 7167: 7160: 7157: 7156: 7152: 7148: 7134: 7131: 7129: 7126: 7124: 7121: 7119: 7116: 7114: 7111: 7109: 7106: 7105: 7103: 7101: 7097: 7091: 7088: 7084: 7081: 7079: 7076: 7074: 7071: 7069: 7066: 7064: 7061: 7059: 7056: 7054: 7051: 7049: 7048:Arcadocypriot 7046: 7044: 7041: 7040: 7039: 7036: 7034: 7031: 7029: 7026: 7024: 7021: 7020: 7018: 7016: 7012: 7002: 7001:Zeus, Olympia 6999: 6997: 6994: 6992: 6989: 6987: 6986:Hera, Olympia 6984: 6982: 6979: 6977: 6974: 6972: 6969: 6967: 6964: 6962: 6959: 6958: 6956: 6954: 6950: 6944: 6941: 6939: 6936: 6934: 6931: 6929: 6926: 6924: 6921: 6919: 6916: 6915: 6912: 6909: 6905: 6895: 6892: 6890: 6889:Mount Olympus 6887: 6885: 6882: 6880: 6877: 6875: 6872: 6870: 6867: 6865: 6862: 6861: 6859: 6857:Sacred places 6855: 6849: 6846: 6844: 6841: 6839: 6836: 6832: 6829: 6828: 6827: 6824: 6822: 6819: 6818: 6815: 6812: 6810: 6806: 6800: 6797: 6795: 6792: 6790: 6787: 6785: 6782: 6778: 6775: 6774: 6773: 6770: 6768: 6765: 6763: 6760: 6758: 6755: 6753: 6750: 6746: 6743: 6742: 6741: 6738: 6737: 6735: 6732: 6728: 6722: 6719: 6717: 6714: 6712: 6709: 6707: 6704: 6702: 6699: 6697: 6694: 6692: 6689: 6687: 6684: 6682: 6681:Olympic Games 6679: 6677: 6674: 6672: 6671:Homosexuality 6669: 6667: 6664: 6662: 6659: 6657: 6654: 6652: 6649: 6647: 6644: 6642: 6639: 6637: 6634: 6632: 6629: 6627: 6624: 6622: 6619: 6617: 6614: 6613: 6611: 6609: 6605: 6601: 6594: 6591: 6589: 6586: 6585: 6581: 6577: 6563: 6560: 6558: 6555: 6553: 6550: 6549: 6547: 6543: 6537: 6534: 6532: 6529: 6527: 6524: 6522: 6519: 6518: 6516: 6512: 6506: 6503: 6501: 6498: 6496: 6493: 6491: 6488: 6486: 6483: 6481: 6478: 6476: 6473: 6471: 6468: 6466: 6463: 6461: 6458: 6456: 6453: 6451: 6448: 6446: 6443: 6441: 6438: 6436: 6433: 6431: 6428: 6426: 6423: 6421: 6418: 6416: 6413: 6411: 6408: 6406: 6403: 6401: 6398: 6396: 6393: 6391: 6388: 6386: 6383: 6381: 6378: 6376: 6373: 6371: 6368: 6366: 6363: 6362: 6360: 6358: 6354: 6348: 6345: 6343: 6340: 6338: 6335: 6333: 6330: 6328: 6325: 6323: 6320: 6318: 6315: 6313: 6310: 6308: 6305: 6303: 6300: 6298: 6295: 6293: 6290: 6288: 6285: 6283: 6280: 6278: 6275: 6273: 6270: 6268: 6265: 6263: 6260: 6258: 6255: 6253: 6250: 6249: 6247: 6245: 6241: 6235: 6232: 6230: 6227: 6225: 6222: 6220: 6217: 6215: 6212: 6210: 6207: 6205: 6202: 6200: 6197: 6195: 6192: 6191: 6189: 6185: 6179: 6176: 6174: 6171: 6169: 6166: 6164: 6161: 6159: 6156: 6154: 6151: 6149: 6146: 6144: 6141: 6139: 6136: 6134: 6131: 6129: 6126: 6124: 6121: 6119: 6116: 6115: 6113: 6111: 6107: 6103: 6098: 6094: 6090: 6085: 6081: 6067: 6064: 6062: 6059: 6057: 6054: 6052: 6049: 6047: 6044: 6042: 6041:Seleucid army 6039: 6037: 6034: 6032: 6029: 6027: 6024: 6022: 6019: 6017: 6014: 6012: 6009: 6007: 6004: 6002: 5999: 5997: 5994: 5992: 5989: 5987: 5984: 5982: 5979: 5977: 5974: 5972: 5969: 5967: 5964: 5962: 5959: 5955: 5952: 5951: 5950: 5947: 5945: 5942: 5941: 5939: 5937: 5933: 5923: 5920: 5918: 5915: 5914: 5912: 5910: 5906: 5900: 5897: 5895: 5892: 5890: 5887: 5886: 5884: 5882: 5878: 5872: 5869: 5867: 5864: 5862: 5859: 5857: 5854: 5852: 5849: 5847: 5844: 5843: 5841: 5839: 5835: 5829: 5826: 5824: 5821: 5819: 5816: 5814: 5811: 5809: 5806: 5804: 5801: 5799: 5796: 5795: 5792: 5789: 5787: 5783: 5776: 5773: 5770: 5767: 5764: 5761: 5758: 5755: 5752: 5749: 5746: 5743: 5740: 5737: 5734: 5731: 5728: 5725: 5722: 5719: 5716: 5715:Delian League 5713: 5710: 5707: 5704: 5701: 5691: 5688: 5678: 5675: 5672: 5671:Ionian League 5669: 5659: 5656: 5652: 560 BC 5642: 5639: 5638: 5636: 5634: 5629: 5625: 5619: 5616: 5614: 5611: 5609: 5606: 5604: 5601: 5599: 5596: 5594: 5591: 5589: 5586: 5584: 5581: 5579: 5576: 5574: 5571: 5570: 5568: 5564: 5558: 5555: 5553: 5550: 5548: 5545: 5543: 5540: 5538: 5535: 5533: 5530: 5528: 5525: 5523: 5520: 5518: 5515: 5513: 5510: 5508: 5505: 5503: 5500: 5498: 5495: 5493: 5490: 5488: 5485: 5483: 5480: 5478: 5475: 5473: 5470: 5469: 5467: 5465: 5461: 5457: 5450: 5447: 5445: 5442: 5440: 5437: 5436: 5432: 5428: 5414: 5411: 5409: 5406: 5404: 5401: 5399: 5396: 5394: 5393:Magna Graecia 5391: 5389: 5386: 5384: 5381: 5379: 5376: 5374: 5371: 5369: 5366: 5364: 5361: 5359: 5356: 5354: 5351: 5349: 5346: 5344: 5341: 5339: 5336: 5335: 5333: 5331: 5327: 5321: 5318: 5316: 5313: 5311: 5308: 5306: 5303: 5301: 5298: 5296: 5293: 5291: 5288: 5286: 5283: 5282: 5280: 5276: 5272: 5265: 5262: 5260: 5257: 5256: 5252: 5248: 5242: 5239: 5238: 5235: 5231: 5224: 5219: 5217: 5212: 5210: 5205: 5204: 5201: 5191: 5190: 5185: 5178: 5177: 5164: 5154: 5151: 5149: 5146: 5144: 5141: 5139: 5136: 5134: 5131: 5129: 5126: 5124: 5121: 5120: 5118: 5114: 5106: 5103: 5102: 5101: 5098: 5094: 5091: 5090: 5089: 5086: 5082: 5079: 5078: 5077: 5074: 5070: 5067: 5066: 5065: 5062: 5058: 5055: 5054: 5053: 5050: 5046: 5043: 5042: 5041: 5038: 5034: 5031: 5030: 5029: 5026: 5022: 5019: 5018: 5017: 5014: 5010: 5006: 5005: 5004: 5003: 4999: 4998: 4996: 4992: 4986: 4983: 4981: 4978: 4976: 4973: 4971: 4968: 4966: 4963: 4961: 4958: 4956: 4953: 4952: 4949: 4946: 4942: 4936: 4933: 4931: 4928: 4926: 4923: 4922: 4920: 4916: 4906: 4903: 4901: 4898: 4896: 4893: 4891: 4888: 4886: 4885: 4880: 4878: 4875: 4873: 4870: 4868: 4865: 4863: 4860: 4858: 4855: 4853: 4850: 4848: 4845: 4844: 4842: 4838: 4832: 4829: 4828: 4826: 4824: 4820: 4814: 4811: 4809: 4806: 4804: 4801: 4799: 4796: 4794: 4793:Pons asinorum 4791: 4789: 4786: 4784: 4781: 4779: 4776: 4774: 4771: 4769: 4766: 4764: 4763:Hinge theorem 4761: 4759: 4756: 4754: 4751: 4749: 4746: 4744: 4741: 4739: 4736: 4734: 4731: 4730: 4728: 4726: 4725: 4719: 4716: 4712: 4706: 4703: 4701: 4698: 4696: 4693: 4691: 4688: 4686: 4683: 4681: 4678: 4676: 4673: 4671: 4668: 4666: 4663: 4661: 4658: 4656: 4653: 4651: 4648: 4646: 4643: 4641: 4638: 4636: 4633: 4631: 4628: 4624: 4621: 4619: 4616: 4615: 4614: 4611: 4609: 4606: 4602: 4599: 4598: 4597: 4594: 4590: 4587: 4585: 4582: 4581: 4580: 4577: 4576: 4574: 4568: 4562: 4559: 4555: 4552: 4550: 4547: 4545: 4542: 4541: 4540: 4537: 4536: 4534: 4530: 4524: 4523: 4519: 4517: 4516: 4512: 4510: 4506: 4502: 4500: 4496: 4492: 4490: 4489: 4485: 4483: 4482: 4478: 4476: 4475: 4471: 4469: 4468: 4464: 4462: 4458: 4454: 4452: 4448: 4444: 4442: 4438: 4434: 4432: 4430:(Aristarchus) 4428: 4424: 4422: 4421: 4417: 4415: 4414: 4410: 4408: 4404: 4400: 4398: 4394: 4390: 4388: 4387: 4383: 4381: 4377: 4373: 4371: 4370: 4366: 4364: 4361: 4359: 4358: 4354: 4353: 4351: 4347: 4341: 4338: 4336: 4335:Zeno of Sidon 4333: 4331: 4328: 4326: 4323: 4321: 4318: 4316: 4313: 4311: 4308: 4306: 4303: 4301: 4298: 4296: 4293: 4291: 4288: 4286: 4283: 4281: 4278: 4276: 4273: 4271: 4268: 4266: 4263: 4261: 4258: 4256: 4253: 4251: 4248: 4246: 4243: 4241: 4238: 4236: 4233: 4231: 4228: 4226: 4223: 4221: 4218: 4216: 4213: 4211: 4208: 4206: 4203: 4201: 4198: 4196: 4193: 4191: 4188: 4186: 4183: 4181: 4178: 4176: 4173: 4171: 4168: 4166: 4163: 4161: 4158: 4156: 4153: 4151: 4148: 4146: 4143: 4141: 4138: 4136: 4133: 4131: 4128: 4126: 4123: 4121: 4118: 4116: 4113: 4111: 4108: 4106: 4103: 4101: 4098: 4096: 4093: 4091: 4088: 4086: 4083: 4081: 4078: 4076: 4073: 4071: 4068: 4066: 4063: 4061: 4058: 4056: 4053: 4051: 4048: 4046: 4043: 4041: 4038: 4036: 4033: 4031: 4028: 4026: 4023: 4021: 4018: 4016: 4013: 4011: 4008: 4006: 4003: 4001: 3998: 3996: 3993: 3991: 3988: 3986: 3983: 3981: 3978: 3976: 3973: 3971: 3968: 3967: 3965: 3963: 3959: 3955: 3951: 3944: 3939: 3937: 3932: 3930: 3925: 3924: 3921: 3909: 3901: 3900: 3897: 3891: 3888: 3884: 3881: 3880: 3879: 3876: 3872: 3869: 3868: 3866: 3865: 3863: 3859: 3853: 3852:Hobbes–Wallis 3850: 3848: 3845: 3843: 3840: 3838: 3835: 3834: 3832: 3830:Controversies 3828: 3822: 3819: 3817: 3814: 3812: 3809: 3807: 3804: 3802: 3801:Ancient Egypt 3799: 3797: 3794: 3793: 3791: 3787: 3781: 3778: 3776: 3773: 3771: 3768: 3767: 3765: 3761: 3753: 3750: 3746: 3743: 3742: 3741: 3738: 3737: 3735: 3731: 3728: 3726: 3723: 3722: 3721: 3718: 3714: 3711: 3710: 3708: 3706: 3705:Math notation 3703: 3699: 3696: 3695: 3694: 3691: 3687: 3684: 3683: 3682: 3679: 3677: 3674: 3670: 3667: 3665: 3662: 3661: 3660: 3657: 3653: 3650: 3649: 3648: 3645: 3643: 3642:Combinatorics 3640: 3636: 3633: 3631: 3628: 3627: 3625: 3621: 3618: 3616: 3613: 3612: 3611: 3608: 3604: 3601: 3600: 3599: 3596: 3592: 3589: 3588: 3586: 3582: 3579: 3578: 3577: 3574: 3573: 3571: 3567: 3562: 3558: 3551: 3546: 3544: 3539: 3537: 3532: 3531: 3528: 3522: 3519: 3517: 3514: 3513: 3509: 3504: 3498: 3494: 3489: 3486: 3485: 3480: 3477: 3471: 3467: 3463: 3459: 3456: 3450: 3446: 3445: 3440: 3436: 3433: 3427: 3423: 3418: 3415: 3409: 3405: 3401: 3397: 3394: 3388: 3384: 3383: 3378: 3374: 3371: 3365: 3361: 3360: 3354: 3351: 3345: 3341: 3336: 3333: 3327: 3323: 3322: 3317: 3313: 3309: 3306: 3300: 3296: 3292: 3288: 3287: 3283: 3274: 3270: 3266: 3262: 3255: 3252: 3247: 3243: 3239: 3235: 3231: 3227: 3223: 3216: 3213: 3208: 3204: 3200: 3196: 3192: 3188: 3183: 3178: 3174: 3171:(in German). 3170: 3166: 3159: 3156: 3143: 3139: 3135: 3128: 3125: 3120: 3116: 3112: 3108: 3105:(1): 95–103. 3104: 3100: 3096: 3089: 3086: 3081: 3077: 3070: 3063: 3060: 3055: 3051: 3047: 3043: 3039: 3035: 3031: 3027: 3023: 3016: 3013: 3003: 2999: 2995: 2989: 2985: 2981: 2977: 2973: 2966: 2963: 2958: 2954: 2950: 2946: 2942: 2938: 2934: 2930: 2926: 2919: 2916: 2911: 2907: 2903: 2899: 2895: 2891: 2887: 2883: 2879: 2872: 2869: 2864: 2860: 2856: 2852: 2848: 2844: 2840: 2836: 2832: 2825: 2822: 2817: 2813: 2809: 2805: 2801: 2797: 2793: 2789: 2785: 2778: 2775: 2770: 2766: 2762: 2758: 2754: 2750: 2746: 2742: 2738: 2734: 2730: 2723: 2720: 2715: 2711: 2707: 2703: 2699: 2695: 2691: 2684: 2681: 2676: 2672: 2668: 2664: 2660: 2653: 2650: 2647: 2646: 2639: 2636: 2631: 2627: 2623: 2619: 2615: 2611: 2607: 2600: 2597: 2592: 2586: 2582: 2581: 2573: 2570: 2557: 2556: 2551: 2544: 2541: 2536: 2532: 2528: 2521: 2518: 2515: 2511: 2508: 2505: 2499: 2496: 2491: 2487: 2483: 2479: 2475: 2471: 2467: 2463: 2459: 2452: 2449: 2446: 2444: 2438: 2435: 2430: 2423: 2420: 2416: 2410: 2406: 2402: 2398: 2394: 2387: 2384: 2379: 2372: 2369: 2364: 2358: 2354: 2353: 2348: 2342: 2339: 2334: 2328: 2324: 2323: 2315: 2312: 2307: 2303: 2299: 2295: 2291: 2284: 2281: 2270: 2266: 2259: 2256: 2251: 2250:10.26021/3834 2247: 2243: 2242: 2234: 2231: 2226: 2222: 2217: 2212: 2208: 2204: 2200: 2193: 2190: 2185: 2181: 2176: 2171: 2167: 2163: 2159: 2152: 2149: 2138: 2132: 2128: 2124: 2120: 2116: 2109: 2106: 2101: 2095: 2091: 2087: 2083: 2082: 2074: 2071: 2066: 2062: 2058: 2054: 2050: 2046: 2039: 2036: 2032: 2026: 2023: 2018: 2014: 2010: 2006: 2002: 1998: 1994: 1990: 1986: 1979: 1976: 1971: 1967: 1963: 1959: 1955: 1951: 1947: 1943: 1939: 1932: 1929: 1917: 1913: 1906: 1904: 1900: 1896: 1890: 1886: 1882: 1878: 1874: 1867: 1864: 1859: 1855: 1851: 1845: 1841: 1840: 1832: 1829: 1825: 1819: 1816: 1804: 1800: 1793: 1790: 1785: 1783:9780226482057 1779: 1775: 1768: 1766: 1762: 1757: 1753: 1749: 1745: 1741: 1737: 1733: 1726: 1723: 1718: 1712: 1708: 1707: 1699: 1696: 1691: 1687: 1683: 1679: 1675: 1671: 1667: 1663: 1659: 1652: 1649: 1639: 1633: 1629: 1625: 1618: 1616: 1612: 1608: 1602: 1599: 1594: 1590: 1585: 1580: 1576: 1572: 1568: 1561: 1558: 1553: 1547: 1543: 1536: 1533: 1527: 1524: 1519: 1513: 1509: 1502: 1499: 1494: 1490: 1486: 1482: 1478: 1474: 1470: 1466: 1462: 1455: 1452: 1446: 1444: 1442: 1438: 1433: 1427: 1423: 1419: 1415: 1414: 1406: 1403: 1398: 1397: 1389: 1388: 1385: 1378: 1376: 1372: 1367: 1360: 1357: 1351: 1344: 1341: 1336: 1330: 1325: 1324: 1315: 1313: 1309: 1298: 1294: 1287: 1284: 1279: 1275: 1271: 1267: 1263: 1259: 1255: 1251: 1247: 1240: 1237: 1227: 1221: 1217: 1213: 1206: 1203: 1198: 1191: 1188: 1183: 1181:0-471-09763-2 1177: 1173: 1166: 1163: 1151: 1147: 1140: 1137: 1132: 1128: 1124: 1117: 1110: 1107: 1100: 1096: 1093: 1091: 1088: 1086: 1083: 1080: 1077: 1074: 1071: 1069: 1066: 1063: 1060: 1059: 1055: 1049: 1044: 1041: 1040:Greece portal 1030: 1025: 1021: 1020: 1015: 1012: 1011: 1006: 1004: 1000: 998: 994: 991: 989: 985: 983: 979: 977: 973: 971: 967: 964: 963: 958: 956: 952: 949: 947: 943: 941: 940: 935: 933: 929: 926: 922: 921: 920: 917: 915: 911: 907: 903: 899: 895: 891: 887: 883: 879: 875: 871: 867: 863: 859: 855: 851: 847: 843: 839: 835: 831: 827: 823: 819: 815: 811: 807: 803: 799: 795: 788: 784: 780: 777: 774: 771: 770: 769: 767: 759: 758: 752: 745: 743: 741: 736: 734: 730: 726: 722: 721: 716: 712: 708: 703: 701: 700: 695: 691: 690: 685: 677: 673: 672: 667: 663: 659: 655: 651: 649: 645: 641: 637: 633: 629: 628: 623: 619: 617: 613: 609: 605: 601: 599: 595: 591: 590:combinatorics 587: 583: 582:number theory 579: 575: 571: 563: 561: 559: 554: 547: 543: 542: 537: 533: 529: 525: 521: 520: 515: 511: 506: 504: 500: 496: 492: 488: 484: 479: 477: 473: 469: 465: 461: 457: 453: 449: 445: 441: 437: 436:Roman periods 432: 430: 426: 422: 421: 420:lingua franca 416: 412: 408: 404: 400: 396: 392: 388: 380: 379: 374: 369: 362: 360: 358: 354: 350: 346: 342: 338: 334: 329: 327: 323: 319: 315: 311: 307: 306:harmonic mean 303: 299: 295: 291: 287: 286: 281: 276: 274: 269: 265: 264:Magna Graecia 261: 257: 252: 250: 246: 242: 238: 230: 226: 225: 220: 216: 209: 207: 205: 201: 197: 192: 190: 189:beehive tombs 185: 181: 177: 173: 168: 166: 162: 158: 153: 147: 142: 136: 130: 124: 117: 111: 110:Ancient Greek 107: 99: 97: 95: 91: 87: 83: 82:Greek culture 79: 75: 71: 67: 66:Mediterranean 63: 59: 55: 51: 47: 41: 37: 32: 19: 7892:Dionysopolis 7862:Abonoteichos 7814:Pantikapaion 7404:Hybla Heraea 6761: 6740:Architecture 6696:Prostitution 6385:Aristophanes 6244:Philosophers 6214:Philosophers 6046:Spartan army 5777:(280–146 BC) 5765:(338–322 BC) 5759:(370–168 BC) 5747:(374–196 BC) 5741:(378–355 BC) 5723:(430–348 BC) 5717:(478–404 BC) 5711:(499–449 BC) 5398:Peloponnesus 5320:Roman Greece 5180: 5167: 5009:Thomas Heath 5000: 4883: 4867:Law of sines 4723: 4655:Golden ratio 4520: 4513: 4504: 4498:(Theodosius) 4494: 4486: 4479: 4472: 4465: 4456: 4446: 4440:(Hipparchus) 4436: 4426: 4418: 4411: 4402: 4392: 4384: 4379:(Apollonius) 4375: 4367: 4355: 4330:Zeno of Elea 4090:Eratosthenes 4080:Dionysodorus 3949: 3805: 3780:Hindu-Arabic 3676:Group theory 3664:Trigonometry 3635:Topos theory 3492: 3482: 3465: 3442: 3421: 3403: 3381: 3358: 3339: 3320: 3294: 3267:(2): 32–38. 3264: 3260: 3254: 3229: 3225: 3215: 3172: 3168: 3158: 3146:. Retrieved 3142:the original 3137: 3127: 3102: 3098: 3088: 3079: 3075: 3062: 3029: 3025: 3015: 3005:, retrieved 2975: 2965: 2932: 2928: 2918: 2885: 2881: 2871: 2838: 2834: 2824: 2791: 2787: 2777: 2736: 2732: 2722: 2697: 2693: 2683: 2669:(1): 31–46. 2666: 2662: 2652: 2644: 2638: 2613: 2609: 2599: 2579: 2572: 2560:. Retrieved 2553: 2543: 2534: 2530: 2520: 2503: 2498: 2465: 2461: 2451: 2442: 2437: 2428: 2422: 2396: 2386: 2377: 2371: 2351: 2347:Mansfeld, J. 2341: 2321: 2314: 2297: 2293: 2283: 2272:. Retrieved 2268: 2258: 2240: 2233: 2206: 2202: 2192: 2165: 2161: 2151: 2140:. Retrieved 2118: 2108: 2080: 2073: 2048: 2038: 2030: 2025: 1992: 1988: 1978: 1948:(4): 29–56. 1945: 1941: 1931: 1920:. Retrieved 1915: 1876: 1866: 1838: 1831: 1818: 1806:. Retrieved 1802: 1792: 1773: 1739: 1735: 1725: 1705: 1698: 1668:(1): 35–53. 1665: 1661: 1651: 1641:, retrieved 1627: 1606: 1601: 1577:(1): 50–57. 1574: 1570: 1560: 1541: 1535: 1526: 1507: 1501: 1468: 1464: 1454: 1412: 1405: 1394: 1387: 1384: 1365: 1359: 1349: 1343: 1322: 1300:. Retrieved 1297:www.isko.org 1296: 1286: 1249: 1245: 1239: 1229:, retrieved 1215: 1205: 1196: 1190: 1171: 1165: 1154:. Retrieved 1149: 1139: 1122: 1109: 1017: 1008: 1002: 996: 987: 981: 975: 969: 960: 959:Diophantus, 954: 945: 944:Archimedes, 937: 936:Archimedes, 931: 930:Apollonius, 924: 923:Apollonius, 918: 796: 792: 763: 755: 737: 729:trigonometry 718: 704: 697: 687: 669: 652: 643: 639: 625: 620: 612:Dedekind cut 608:real numbers 602: 578:formal proof 567: 564:Achievements 555: 539: 527: 517: 507: 480: 472:Eratosthenes 433: 418: 411:Central Asia 384: 376: 330: 283: 277: 268:Pythagoreans 253: 234: 222: 193: 169: 164: 160: 156: 105: 103: 78:North Africa 56:through the 45: 44: 8040:Place names 7952:Salmydessus 7774:Kalos Limen 7754:Chersonesus 7744:Borysthenes 7449:Tauromenion 7261:Metapontion 7023:Proto-Greek 6976:Erechtheion 6971:Athena Nike 6933:Philippeion 6762:Mathematics 6733:and science 6616:Agriculture 6480:Stesichorus 6390:Bacchylides 6380:Archilochus 6267:Antisthenes 6257:Anaximander 6229:Seven Sages 6219:Playwrights 6199:Geographers 6194:Astronomers 6021:Pezhetairos 5648: 1100 5628:Federations 5527:Megalopolis 5464:City states 5439:City states 5076:mathematics 4884:Arithmetica 4481:Ostomachion 4450:(Autolycus) 4369:Arithmetica 4145:Hippocrates 4075:Dinostratus 4060:Dicaearchus 3990:Aristarchus 3796:Mesopotamia 3770:Prehistoric 3730:Probability 3587:Algorithms 3032:(1): 6–28. 1609:, pp. 11–12 1197:Mathematics 1125:: 190–191. 962:Arithmetica 850:Apollodorus 802:Aristarchus 757:Arithmetica 570:mathematics 519:Arithmetica 403:Mesopotamia 345:Pythagorean 146:Koinē Greek 135:Attic Greek 106:mathēmatikē 58:Hellenistic 50:mathematics 7942:Polemonion 7819:Phanagoria 7789:Kimmerikon 7784:Kerkinitis 7769:Hermonassa 7759:Dioscurias 7655:Aspalathos 7602:Kalathousa 7577:Akra Leuke 7506:Phoenicusa 7291:Scylletium 7276:Poseidonia 7196:Brentesion 7083:Pamphylian 7078:Macedonian 6996:Samothrace 6981:Hephaestus 6928:Long Walls 6907:Structures 6848:Underworld 6794:Technology 6757:Literature 6691:Philosophy 6656:Euergetism 6545:By culture 6490:Thucydides 6332:Pythagoras 6327:Protagoras 6317:Parmenides 6302:Heraclitus 6287:Empedocles 6277:Democritus 6262:Anaximenes 6252:Anaxagoras 6204:Historians 5697: 595 5684: 550 5665: 800 5650: â€“ c. 5578:Cappadocia 5383:Ionian Sea 5373:Hellespont 5338:Aegean Sea 5128:Babylonian 5028:arithmetic 4994:History of 4823:Apollonius 4508:(Menelaus) 4467:On Spirals 4386:Catoptrics 4325:Xenocrates 4320:Thymaridas 4305:Theodosius 4290:Theaetetus 4270:Simplicius 4260:Pythagoras 4245:Posidonius 4230:Philonides 4190:Nicomachus 4185:Metrodorus 4175:Menaechmus 4130:Hipparchus 4120:Heliodorus 4070:Diophantus 4055:Democritus 4035:Chrysippus 4005:Archimedes 4000:Apollonius 3970:Anaxagoras 3962:(timeline) 3720:Statistics 3652:Logarithms 3598:Arithmetic 3284:References 3007:2021-03-27 2537:: 167–174. 2274:2021-05-26 2244:(Thesis). 2142:2021-05-26 2049:Hermathena 1922:2021-05-26 1824:Boyer 1991 1643:2021-05-26 1551:0471543977 1517:0471543977 1302:2023-01-09 1231:2021-03-27 1156:2024-03-04 982:Catoptrica 976:On Weights 886:Diophantus 870:Gaudentius 862:Nicomachus 830:Theodosius 822:Archimedes 818:Apollonius 733:Hipparchus 715:Menaechmus 654:Archimedes 610:using the 528:Collection 510:Diophantus 487:Alexandria 452:Hipparchus 448:Apollonius 444:Archimedes 322:Theaetetus 219:Pythagoras 196:Babylonian 182:and later 157:manthanein 48:refers to 8028:in Epirus 7977:Trapezous 7922:Mesambria 7907:Eupatoria 7877:Apollonia 7872:Anchialos 7834:Theodosia 7804:Nymphaion 7794:Myrmekion 7764:Gorgippia 7720:Black Sea 7705:Tragurion 7690:Nymphaion 7675:Epidauros 7670:Epidamnos 7660:Apollonia 7637:Zacynthos 7559:Ptolemais 7553:Apollonia 7526:Cyrenaica 7516:TherassĂ­a 7511:Strongyle 7491:Ereikousa 7414:Leontinoi 7354:Apollonia 7231:Hipponion 7028:Mycenaean 6991:Parthenon 6923:Lion Gate 6826:Mythology 6789:Sculpture 6752:Astronomy 6686:Pederasty 6661:Festivals 6646:Education 6526:Lawgivers 6495:Timocreon 6475:Sophocles 6470:Simonides 6445:Philocles 6440:Panyassis 6435:Mimnermus 6400:Herodotus 6395:Euripides 6365:Aeschylus 6312:Leucippus 6272:Aristotle 6051:Strategos 5917:Synedrion 5871:Ostracism 5851:Areopagus 5803:Free city 5598:Macedonia 5482:Byzantion 5388:Macedonia 5353:Cyrenaica 5330:Geography 5264:Geography 4589:Inscribed 4349:Treatises 4340:Zenodorus 4300:Theodorus 4275:Sosigenes 4220:Philolaus 4205:Oenopides 4200:Nicoteles 4195:Nicomedes 4155:Hypsicles 4050:Ctesibius 4040:Cleomedes 4025:Callippus 4010:Autolycus 3995:Aristotle 3975:Anthemius 3740:Manifolds 3736:Topology 3647:Functions 3464:(2003) , 3441:(1981) , 3246:146539132 3191:1420-9144 3119:144052363 3054:1600-0498 3026:Centaurus 3002:226745369 2957:1600-0498 2929:Centaurus 2902:0025-5769 2863:147307969 2855:2156-7093 2808:0025-570X 2769:120954547 2753:0003-9519 2714:0002-9890 2675:1735-0573 2630:0007-0882 2482:1573-0964 2355:. Brill. 2325:. Brill. 2306:2159-3159 2225:0315-0860 2184:0315-0860 2057:0018-0750 2017:122403901 1970:170916259 1962:2156-7093 1748:0034-6632 1709:. Brill. 1690:146652622 1682:1474-0664 1593:1984-8234 1485:1080-6520 1062:Al-Mansur 1016:Ptolemy, 1007:Ptolemy, 997:Sphaerica 988:Mechanica 910:Anthemius 874:Anatolius 858:Cleomedes 838:Athenaeus 834:Hypsicles 806:Autolycus 353:Aristotle 314:mechanics 294:Theodorus 184:Mycenaean 178:were the 165:mathēmata 123:romanized 8112:Category 8077:Category 8055:Theatres 7982:Tripolis 7917:Kerasous 7912:Heraclea 7844:Tyritake 7799:Nikonion 7710:Thronion 7632:Salauris 7587:Emporion 7544:Berenice 7534:Balagrae 7486:Euonymos 7459:Tyndaris 7444:Syracuse 7439:Selinous 7409:Kamarina 7364:Casmenae 7349:Akrillai 7266:NeĂĄpolis 7201:Caulonia 7182:Mainland 7113:Linear B 7108:Linear A 7038:Dialects 7015:Language 6809:Religion 6767:Medicine 6701:Religion 6666:Folklore 6651:Emporium 6626:Clothing 6621:Calendar 6505:Xenophon 6500:Tyrtaeus 6485:Theognis 6460:Polybius 6455:Plutarch 6430:Menander 6410:Hipponax 6337:Socrates 6292:Epicurus 6138:Diadochi 6036:Sciritae 5996:Hetairoi 5971:Ballista 5936:Military 5899:Gerousia 5889:Ekklesia 5856:Ecclesia 5838:Athenian 5786:Politics 5699:–279 BC) 5686:–366 BC) 5667:–389 BC) 5603:Pergamon 5573:Bithynia 5566:Kingdoms 5507:Pergamon 5449:Military 5444:Politics 5241:Timeline 5153:Japanese 5138:Egyptian 5081:timeline 5069:timeline 5057:timeline 5052:geometry 5045:timeline 5040:calculus 5033:timeline 5021:timeline 4724:Elements 4570:Concepts 4532:Problems 4505:Spherics 4495:Spherics 4460:(Euclid) 4406:(Euclid) 4403:Elements 4396:(Euclid) 4357:Almagest 4265:Serenus 4240:Porphyry 4180:Menelaus 4135:Hippasus 4110:Eutocius 4085:Domninus 3980:Archytas 3908:Category 3883:timeline 3871:timeline 3745:timeline 3725:timeline 3713:timeline 3698:timeline 3686:timeline 3669:timeline 3659:Geometry 3630:timeline 3615:timeline 3610:Calculus 3603:timeline 3591:timeline 3581:timeline 3569:By topic 3561:timeline 3402:(2004), 3379:(2006), 3318:(2011), 3293:(1985), 3207:21519829 3199:21946891 3148:18 April 3082:: 34–42. 2910:27956431 2761:41133444 2562:18 April 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6536:Tyrants 6375:Alcaeus 6357:Authors 6307:Hypatia 6297:Gorgias 6234:Writers 6056:Toxotai 6026:Sarissa 6016:Peltast 6011:Phalanx 5991:Hoplite 5986:Hippeis 5909:Macedon 5881:Spartan 5866:Heliaia 5813:Proxeny 5522:Larissa 5517:Kerkyra 5512:Eretria 5502:Miletus 5497:Ephesus 5492:Corinth 5487:Chalcis 5408:Taurica 5278:Periods 5259:History 5133:Chinese 5088:numbers 5016:algebra 4944:Related 4918:Centers 4714:Results 4584:Central 4255:Ptolemy 4250:Proclus 4215:Perseus 4170:Marinus 4150:Hypatia 4140:Hippias 4115:Geminus 4105:Eudoxus 4095:Eudemus 4065:Diocles 3775:Ancient 3576:Algebra 3034:Bibcode 2937:Bibcode 2835:Apeiron 2816:2691014 1997:Bibcode 1942:Apeiron 1278:3994109 1258:Bibcode 986:Heron, 980:Heron, 951:Diocles 902:Serenus 890:Alypius 866:Ptolemy 842:Geminus 725:algebra 536:Hypatia 503:Persian 456:Ptolemy 326:Eudoxus 245:Proclus 229:Raphael 161:mĂĄthēma 129:mĂĄthēma 125::  54:Archaic 8087:Portal 8035:People 8023:Cities 7962:Sinope 7947:Rhizos 7937:Phasis 7887:Bathus 7882:Athina 7867:Amisos 7829:Tanais 7824:Pityus 7749:Charax 7700:Pharos 7695:Orikon 7592:Helike 7582:Alonis 7549:Cyrene 7481:Didyme 7394:Himera 7369:Catana 7331:Sicily 7321:Thurii 7316:Terina 7281:Pixous 7236:Hydrus 7211:Croton 7043:Aeolic 6961:Aphaea 6884:Dodona 6869:Delphi 6838:Temple 6514:Others 6465:Sappho 6450:Pindar 6425:Lucian 6420:Ibycus 6405:Hesiod 6342:Thales 6110:Rulers 6089:People 6066:Xyston 6061:Xiphos 5922:Koinon 5828:Tyrant 5818:Stasis 5808:Koinon 5608:Pontus 5583:Epirus 5552:Sparta 5542:Rhodes 5537:Megara 5532:Thebes 5477:Athens 5403:Pontus 5368:Epirus 5358:Cyprus 5343:Aeolis 5148:Indian 4925:Cyrene 4457:Optics 4376:Conics 4295:Theano 4285:Thales 4280:Sporus 4225:Philon 4210:Pappus 4100:Euclid 4030:Carpus 4020:Bryson 3499:  3472:  3451:  3428:  3410:  3389:  3366:  3346:  3328:  3301:  3244:  3205:  3197:  3189:  3117:  3052:  3000:  2990:  2955:  2908:  2900:  2861:  2853:  2814:  2806:  2767:  2759:  2751:  2712:  2673:  2628:  2587:  2488:  2480:  2411:  2359:  2329:  2304:  2223:  2182:  2133:  2096:  2063:  2055:  2015:  1968:  1960:  1891:  1856:  1846:  1780:  1754:  1746:  1713:  1688:  1680:  1634:  1591:  1548:  1514:  1491:  1483:  1428:  1331:  1276:  1246:Nature 1222:  1178:  1010:Optics 925:Conics 912:, and 898:Pappus 826:Euclid 779:Syriac 727:, nor 720:Conics 694:myriad 642:, the 622:Euclid 499:Jewish 440:Euclid 405:, the 373:Euclid 349:cosmos 310:optics 280:Euclid 260:Croton 231:(1509) 180:Minoan 176:Europe 172:Greece 116:ÎŒÎŹÎžÎ·ÎŒÎ± 104:Greek 94:proofs 36:Euclid 8045:Stoae 8013:Lists 7932:OinĂČe 7855:coast 7853:South 7839:Tyras 7809:Olbia 7779:Kepoi 7732:coast 7730:North 7723:basin 7665:Aulon 7627:Rhode 7539:Barca 7429:Naxos 7384:Henna 7344:Akrai 7311:Taras 7296:Siris 7256:Medma 7251:Locri 7216:Cumae 7206:Chone 7184:Italy 7090:Koine 7068:Ionic 7058:Doric 7053:Attic 6874:Delos 6772:Music 6415:Homer 6370:Aesop 6322:Plato 6224:Poets 5894:Ephor 5846:Agora 5823:Tagus 5798:Boule 5547:Samos 5472:Argos 5378:Ionia 5363:Doris 5348:Crete 5143:Incan 5064:logic 4840:Other 4608:Chord 4601:Axiom 4579:Angle 4235:Plato 4125:Heron 4045:Conon 3861:Other 3816:India 3811:China 3693:Logic 3242:S2CID 3203:S2CID 3115:S2CID 3072:(PDF) 2998:S2CID 2906:JSTOR 2859:S2CID 2812:JSTOR 2765:S2CID 2757:JSTOR 2486:S2CID 2061:JSTOR 2013:S2CID 1966:S2CID 1854:JSTOR 1752:JSTOR 1686:S2CID 1489:S2CID 1391:(PDF) 1274:S2CID 1119:(PDF) 1101:Notes 846:Heron 814:Biton 766:Greek 558:Egypt 491:Egypt 476:Heron 415:India 399:Egypt 337:Plato 74:Italy 62:Roman 7972:Tium 7739:Akra 7680:Issa 7374:Gela 7246:LaĂŒs 7221:Elea 6879:Dion 6731:Arts 6721:Wine 6347:Zeno 5944:Wars 5105:list 4393:Data 4165:Leon 4015:Bion 3497:ISBN 3470:ISBN 3449:ISBN 3426:ISBN 3408:ISBN 3387:ISBN 3364:ISBN 3344:ISBN 3326:ISBN 3299:ISBN 3195:PMID 3187:ISSN 3150:2011 3099:Isis 3050:ISSN 2988:ISBN 2953:ISSN 2898:ISSN 2851:ISSN 2804:ISSN 2749:ISSN 2710:ISSN 2671:ISSN 2626:ISSN 2585:ISBN 2564:2011 2478:ISSN 2409:ISBN 2357:ISBN 2327:ISBN 2302:ISSN 2221:ISSN 2180:ISSN 2131:ISBN 2094:ISBN 2053:ISSN 1958:ISSN 1889:ISBN 1844:ISBN 1810:2021 1778:ISBN 1744:ISSN 1711:ISBN 1678:ISSN 1632:ISBN 1589:ISSN 1546:ISBN 1512:ISBN 1481:ISSN 1426:ISBN 1329:ISBN 1220:ISBN 1176:ISBN 798:Netz 427:and 385:The 312:and 198:and 174:and 76:and 60:and 6676:Law 5007:by 4721:In 3269:doi 3234:doi 3177:doi 3107:doi 3042:doi 2980:doi 2945:doi 2890:doi 2843:doi 2796:doi 2741:doi 2702:doi 2698:126 2618:doi 2470:doi 2401:doi 2246:doi 2211:doi 2170:doi 2123:doi 2086:doi 2005:doi 1950:doi 1881:doi 1670:doi 1579:doi 1473:doi 1418:doi 1266:doi 1250:128 1127:doi 781:or 702:). 680:4/3 522:), 485:in 470:by 375:'s 282:'s 227:by 92:in 72:to 8114:: 5694:c. 5681:c. 5662:c. 5645:c. 3314:; 3263:. 3240:. 3230:14 3228:. 3224:. 3201:. 3193:. 3185:. 3173:19 3167:. 3136:. 3113:. 3103:22 3101:. 3097:. 3080:17 3078:. 3074:. 3048:. 3040:. 3030:18 3028:. 3024:. 2996:, 2986:, 2974:, 2951:. 2943:. 2933:25 2931:. 2927:. 2904:. 2896:. 2886:54 2884:. 2880:. 2857:. 2849:. 2839:36 2837:. 2833:. 2810:. 2802:. 2792:71 2790:. 2786:. 2763:. 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Index

Ancient mathematics

Euclid
Pythagorean theorem
mathematics
Archaic
Hellenistic
Roman
Mediterranean
Anatolia
Italy
North Africa
Greek culture
Greek language
deductive reasoning
proofs
Ancient Greek
ÎŒÎŹÎžÎ·ÎŒÎ±
romanized
Attic Greek
[mĂĄ.tʰɛː.ma]
Koinē Greek
[ˈma.Ξi.ma]
Greece
Europe
Minoan
Mycenaean
beehive tombs
Babylonian
Egyptian

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