2668:
2655:
421:Θεοδόσιος, φιλόσοφος. ἔγραψε Σφαιρικὰ ἐν βιβλίοις γ', ̔Υπόμνημα εἰς τὰ Θευδα̂ κεφάλαια, Περὶ ἡμερω̂ν καὶ νυκτω̂ν δύο, ̔Υπόμνημα εἰς τὸ ̓Αρχιμήδους ̓Εφόδιον, Διαγραφὰς οἰκιω̂ν ἐν βιβλίοις τρισί, Σκεπτικὰ κεφάλαια, ̓Αστρολογικά, Περὶ οἰκήσεων. Θεοδόσιος: ἔγραψε δι' ἐπω̂ν εἰς τὸ ἔαρ, καὶ ἕτερα διάφορα. ἠ̂ν δὲ Τριπολίτης.
218:
may have been based. However, no mention of this hypothetical earlier work or its author remains today, and it is also plausible that
Theodosius was the first to formalize material which had been previously justified by informal physical demonstrations on a globe or armillary sphere.
504:ἄνδρες δ’ ἀξιόλογοι κατὰ παιδείαν γεγόνασιν ἐν τῇ Βιθυνίᾳ Ξενοκράτης τε ὁ φιλόσοφος καὶ Διονύσιος ὁ διαλεκτικὸς καὶ Ἵππαρχος καὶ Θεοδόσιος καὶ οἱ παῖδες αὐτοῦ μαθηματικοὶ Κλεοφάνης τε ῥήτωρ ὁ Μυρλεανὸς Ἀσκληπιάδης τε ἰατρός ὁ Προυσιεύς.
124:(1st century BC) mentioned a sundial invented by Theodosius. Thus Theodosius lived sometime after Archimedes and before Vitruvius, likely contemporaneously with or after Hipparchus, probably sometime between 200–50 BC.
425:
This text was historically taken to refer to a single person, but the sentences about the
Theodosius from Tripoli who wrote verses about the spring were likely intended to represent a separate entry. Furthermore,
356:
was continuously copied and studied in Greek manuscript throughout the
Byzantine period, and was a foundational text for medieval Islamic astronomy and for European astronomy starting in the 12th century.
377:
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210:, so it has been speculated that they may have expected readers to be familiar with a treatise on elementary spherical geometry, perhaps by
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1909:
1445:
1187:
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was widely copied and highly influential, serving as a theoretical foundation for spherical geometry and astronomy for millennia.
135:
which probably fused the entries about separate people named
Theodosius, and was interpreted to mean that he came either from the
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were written by someone else, perhaps a different
Theodosius. The other listed works were by the Theodosius who wrote the
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1919:
1381:
1177:
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143:. Some sources claim he moved from Bithynia to Tripolis, or came from a hypothetical city called Tripolis in Bithynia.
933:
863:
774:
710:
94:
721:
The Little
Astronomy and Middle Books between the 2nd and 13th Centuries CE: Transmissions of Astronomical Curricula
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1998:
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All three of
Theodosius' extant treatises were transmitted together, as part of a collection now called the
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474:(in Greek). Vol. 3. Göttingen: Vandenhoeck & Ruprecht. IB ¶4.9, C.566, p. 490 lines 19–22.
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120:) and "Theodosius and his sons" as among the residents of Bithynia distinguished for their learning.
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769:. Vol. 13 (Staudinger–Veronese). New York: Charles Scribner's Sons. pp. 319–321.
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418:. Theodosius wrote verses on the spring and other types of works. He was from Tripolis.
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Clavius's
Commentary on the Sphericks of Theodosius Tripolitae: or, Spherical Elements
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450:, a separate now-lost work on astronomy, or perhaps a lost work on architecture.
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Tripolis, Greek for "three cities", was the name of several ancient cities. See
263:, an assortment of shorter works on geometry and astronomy building on Euclid's
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1971:
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The
Mathematics of the Heavens and the Earth: The Early History of Trigonometry
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23:
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1319:
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807:. Vol. 26 (11th ed.). Cambridge University Press. pp. 771–772.
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493:, the mathematicians Hipparchus and Theodosius and his sons, and the
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suitable for any place on Earth, but nothing else is known about it.
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522:(in Greek). Vol. 2. Leibzig: Teubner. p. 795 lines 13–14.
386:(in Greek). Vol. 2. p. 693, §Θ.142–143 (Translation from
293:
49:
430:
lived after
Theodosius of Bithynia; the commentary on Theudas and
398:
in three books, a commentary on the chapter of Theudas, two books
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317:. Theodosius' works were published in Latin in the 16th century.
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438:, including presumably the (now-lost) commentary on Archimedes'
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529:"Greek High Culture in Hellenistic and Early Imperial Bithynia"
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332:, which proved many additional theorems of spherical geometry.
309:, and translated from Arabic into Latin in the 12th century by
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185:
180:, establishes a formal foundation for the mathematics of Greek
99:
279:, and with the addition of a few new works, were known as the
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27:
846:
Sidoli, Nathan; Thomas, Robert Spencer David, eds. (2023).
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80:
230:, describing the appearances of the heavens at different
728:
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823:
623:. Translated by Shenitzer, Abe. Springer. p. 3.
88:
encyclopedia) mentioned him writing a commentary on
674:
336:(4th century) commented extensively on Theodosius'
2684:
606:(in Latin). Rome: Ex Typographia Dominici Basae.
697:The History & Practice of Ancient Astronomy
226:, two other works by Theodosius have survived:
880:. Princeton University Press. pp. 49–56.
562:, "Theodosios's time and works", pp. 3–5.
1432:
1418:
910:
872:
749:
668:
252:
238:, a study of the apparent motion of the Sun.
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78:Little is known about Theodosius' life. The
924:
817:A History of Ancient Mathematical Astronomy
603:Theodosii Tripolitae Sphaericorum Libri III
194:provides for geometry in general. Euclid's
1425:
1411:
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571:
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544:
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482:from Bithynia have been the philosopher
835:MacTutor History of Mathematics Archive
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497:Cleophanes from Myrleia and the doctor
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2454:Latin translations of the 12th century
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2184:Straightedge and compass construction
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526:
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328:(c. 100 AD) extended it with his own
234:and different times of the year, and
2149:Incircle and excircles of a triangle
617:Rozenfeld, Boris Abramovich (1988).
131:due to a confusing paragraph in the
620:A History of Non-Euclidean Geometry
366:
13:
876:(2009). "Theodosius of Bithynia".
766:Dictionary of Scientific Biography
724:(PhD thesis). New York University.
640:(in Russian). Moscow: Nauka. 1976.
389:Dictionary of Scientific Biography
14:
2724:
2666:
2653:
701:. Oxford University Press. "The
686:
638:Istoriya Neevklidovoi Geometrii
394:Theodosius, philosopher, wrote
214:(4th century BC), on which the
2486:A History of Greek Mathematics
1999:The Quadrature of the Parabola
794:"Theodosius of Tripolis"
644:
454:
301:was translated into Arabic by
283:, intended to fit between the
1:
2708:2nd-century BC mathematicians
1315:Inferior and superior planets
743:
2267:Intersecting secants theorem
593:. London: J. Senex. Preface.
172:
157:Theodosius' chief work, the
37:; 2nd–1st century BC) was a
33:
7:
2703:2nd-century BC Greek people
2262:Intersecting chords theorem
2129:Doctrine of proportionality
761:Gillispie, Charles Coulston
718:Roughan, Christine (2023).
127:Historically he was called
98:(late 3rd century BC), and
10:
2729:
2713:2nd-century BC astronomers
1958:On the Sphere and Cylinder
1911:On the Sizes and Distances
1392:Medieval Islamic astronomy
1189:On the Sizes and Distances
848:The Spherics of Theodosios
446:is a mangled reference to
253:Transmission and influence
184:similar to the foundation
167:
150:
28:
2693:Ancient Greek astronomers
2660:Ancient Greece portal
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2464:Philosophy of mathematics
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2379:Ptolemy's table of chords
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2015:
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1434:Ancient Greek mathematics
1382:Medieval European science
1374:
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1211:
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1112:Sosigenes the Peripatetic
932:
652:Tripolis (disambiguation)
546:10.1163/1568525X-bja10120
108:mentioned mathematicians
2331:Aristarchus's inequality
1904:On Conoids and Spheroids
840:University of St Andrews
830:"Theodosius of Bithynia"
756:"Theodosius of Bithynia"
560:Sidoli & Thomas 2023
503:
442:. It is unclear whether
420:
376:Adler, Ada, ed. (1931).
360:
241:Theodosius was cited by
146:
16:Ancient Greek astronomer
2698:Ancient Greek geometers
2439:Ancient Greek astronomy
2252:Inscribed angle theorem
2242:Greek geometric algebra
1897:Measurement of a Circle
1107:Sosigenes of Alexandria
926:Ancient Greek astronomy
804:Encyclopædia Britannica
73:
2673:Mathematics portal
2459:Non-Euclidean geometry
2414:Mouseion of Alexandria
2287:Tangent-secant theorem
2237:Geometric mean theorem
2222:Exterior angle theorem
2217:Angle bisector theorem
1921:On Sizes and Distances
1179:On Sizes and Distances
476:Men notable for their
444:Descriptions of Houses
414:, astrological works,
408:Descriptions of Houses
402:, a commentary on the
326:Menelaus of Alexandria
129:Theodosius of Tripolis
20:Theodosius of Bithynia
2361:Pappus's area theorem
2297:Theorem of the gnomon
2174:Quadratrix of Hippias
2097:Circles of Apollonius
2045:Problem of Apollonius
2023:Constructible numbers
1847:Archimedes Palimpsest
1290:Deferent and epicycle
1219:Antikythera mechanism
856:10.4324/9781003142164
850:. London: Routledge.
693:Evans, James (1998).
519:Strabonis Geographica
275:were translated into
245:as having invented a
137:Tripolis in Phoenicia
2577:prehistoric counting
2374:Ptolemy's inequality
2315:Apollonius's theorem
2154:Method of exhaustion
2124:Diophantine equation
2114:Circumscribed circle
1931:On the Moving Sphere
1361:Babylonian astronomy
1052:Hippocrates of Chios
826:Robertson, Edmund F.
789:Heath, Thomas Little
784:at Encyclopedia.com.
598:Clavius, Christopher
527:Bowie, Ewen (2022).
471:Strabons Geographika
334:Pappus of Alexandria
204:On the Moving Sphere
153:Theodosius' Spherics
2663: •
2469:Neusis construction
2389:Spiral of Theodorus
2282:Pythagorean theorem
2227:Euclidean algorithm
2169:Lune of Hippocrates
2038:Squaring the circle
1794:Theon of Alexandria
1469:Aristaeus the Elder
1132:Theon of Alexandria
874:Van Brummelen, Glen
824:O'Connor, John J.;
751:Bulmer-Thomas, Ivor
737:, pp. 771–772.
705:", pp. 89–91.
271:, the books in the
222:In addition to the
182:spherical astronomy
58:, a treatise about
2356:Menelaus's theorem
2346:Irrational numbers
2159:Parallel postulate
2134:Euclidean geometry
2102:Apollonian circles
1644:Isidore of Miletus
1366:Egyptian astronomy
1280:Circle of latitude
669:Bulmer-Thomas 1976
432:Skeptical Chapters
412:Skeptical Chapters
400:On Days and Nights
342:On Days and Nights
269:Islamic Golden Age
236:On Days and Nights
178:spherical geometry
68:On Days and Nights
60:spherical geometry
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2257:Intercept theorem
2107:Apollonian gasket
2033:Doubling the cube
2006:The Sand Reckoner
1400:
1399:
1275:Celestial spheres
887:978-0-691-12973-0
630:978-0-387-96458-4
525:Translation from
315:Gerard of Cremona
212:Eudoxus of Cnidus
141:the one in Africa
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2336:Crossbar theorem
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1199:On the Heavens
1195:
1185:
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1172:(Eratosthenes)
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1077:Philip of Opus
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893:
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864:
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821:
809:
799:Chisholm, Hugh
785:
782:Online version
775:
745:
742:
740:
739:
727:
711:
685:
683:, p. 771.
673:
656:
643:
629:
609:
576:
574:, p. 750.
564:
552:
453:
448:On Habitations
416:On Habitations
383:Suidae Lexicon
364:
362:
359:
303:Qusṭā ibn Lūqā
254:
251:
228:On Habitations
148:
145:
84:(10th-century
75:
72:
64:On Habitations
52:who wrote the
15:
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2277:Pons asinorum
2275:
2273:
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2255:
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2250:
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2247:Hinge theorem
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1914:(Aristarchus)
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1819:Zeno of Sidon
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1326:
1323:
1321:
1320:Metonic cycle
1318:
1316:
1313:
1311:
1308:
1306:
1305:Heliocentrism
1303:
1301:
1298:
1296:
1293:
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1288:
1286:
1285:Counter-Earth
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1196:
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1192:(Aristarchus)
1190:
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865:9780367557300
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776:0-684-12925-6
772:
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747:
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731:
723:
722:
714:
712:0-19-509539-1
708:
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605:
604:
599:
592:
591:
586:
585:Stone, Edmund
580:
573:
568:
561:
556:
547:
542:
539:(1): 73–112.
538:
534:
530:
521:
520:
515:
511:
502:
501:from Prusias.
500:
496:
492:
489:
485:
481:
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472:
467:
463:
457:
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318:
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308:
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296:
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278:
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270:
267:. During the
266:
262:
261:
250:
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244:
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229:
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217:
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205:
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97:
96:
91:
87:
83:
82:
71:
69:
65:
61:
57:
56:
51:
47:
46:mathematician
43:
40:
35:
25:
21:
2664:
2651:
2493:Thomas Heath
2484:
2367:
2351:Law of sines
2207:
2139:Golden ratio
2004:
1997:
1988:
1982:(Theodosius)
1978:
1970:
1963:
1956:
1949:
1940:
1930:
1924:(Hipparchus)
1920:
1910:
1902:
1895:
1886:
1876:
1868:
1863:(Apollonius)
1859:
1851:
1839:
1814:Zeno of Elea
1788:
1574:Eratosthenes
1564:Dionysodorus
1198:
1188:
1182:(Hipparchus)
1178:
1169:Catasterismi
1168:
1158:
1126:
1017:Eratosthenes
877:
847:
833:
816:
802:
764:
730:
720:
702:
696:
688:
676:
646:
637:
619:
612:
602:
589:
579:
567:
555:
536:
532:
518:
494:
487:
477:
475:
470:
466:Radt, Stefan
456:
447:
443:
439:
435:
431:
424:
415:
411:
407:
403:
399:
395:
393:
387:
381:
378:"Theodosius"
353:
345:
341:
337:
329:
321:
319:
298:
292:
284:
281:Middle Books
280:
272:
264:
258:
256:
240:
235:
227:
223:
221:
215:
207:
203:
195:
190:
173:tá sphairiká
158:
156:
132:
128:
126:
103:
93:
79:
77:
67:
63:
53:
19:
18:
2560:mathematics
2368:Arithmetica
1965:Ostomachion
1934:(Autolycus)
1853:Arithmetica
1629:Hippocrates
1559:Dinostratus
1544:Dicaearchus
1474:Aristarchus
1300:Geocentrism
1212:Instruments
1202:(Aristotle)
1007:Cleostratus
972:Aristarchus
952:Anaximander
934:Astronomers
819:. Springer.
499:Asclepiades
488:dialecticus
168:τὰ σφαιρικά
105:Geographica
39:Hellenistic
2687:Categories
2612:Babylonian
2512:arithmetic
2478:History of
2307:Apollonius
1992:(Menelaus)
1951:On Spirals
1870:Catoptrics
1809:Xenocrates
1804:Thymaridas
1789:Theodosius
1774:Theaetetus
1754:Simplicius
1744:Pythagoras
1729:Posidonius
1714:Philonides
1674:Nicomachus
1669:Metrodorus
1659:Menaechmus
1614:Hipparchus
1604:Heliodorus
1554:Diophantus
1539:Democritus
1519:Chrysippus
1489:Archimedes
1484:Apollonius
1454:Anaxagoras
1446:(timeline)
1375:Influenced
1354:Influences
1325:Octaeteris
1254:Triquetrum
1142:Timocharis
1127:Theodosius
1087:Posidonius
1047:Hipparchus
1037:Heraclides
977:Aristyllus
962:Apollonius
957:Andronicus
744:References
735:Heath 1911
681:Heath 1911
484:Xenocrates
346:Collection
151:See also:
110:Hipparchus
90:Archimedes
42:astronomer
34:Theodosios
2073:Inscribed
1833:Treatises
1824:Zenodorus
1784:Theodorus
1759:Sosigenes
1704:Philolaus
1689:Oenopides
1684:Nicoteles
1679:Nicomedes
1639:Hypsicles
1534:Ctesibius
1524:Cleomedes
1509:Callippus
1494:Autolycus
1479:Aristotle
1459:Anthemius
1229:Astrolabe
1162:(Ptolemy)
1082:Philolaus
1072:Oenopides
1057:Hypsicles
1002:Cleomedes
997:Callippus
987:Autolycus
942:Aglaonice
533:Mnemosyne
491:Dionysius
396:Sphaerics
243:Vitruvius
200:Autolycus
196:Phenomena
176:), about
122:Vitruvius
118:c. 120 BC
86:Byzantine
29:Θεοδόσιος
2637:Japanese
2622:Egyptian
2565:timeline
2553:timeline
2541:timeline
2536:geometry
2529:timeline
2524:calculus
2517:timeline
2505:timeline
2208:Elements
2054:Concepts
2016:Problems
1989:Spherics
1979:Spherics
1944:(Euclid)
1890:(Euclid)
1887:Elements
1880:(Euclid)
1841:Almagest
1749:Serenus
1724:Porphyry
1664:Menelaus
1619:Hippasus
1594:Eutocius
1569:Domninus
1464:Archytas
1330:Solstice
1263:Concepts
1159:Almagest
1102:Seleucus
1062:Menelaus
1022:Euctemon
828:(1999),
815:(1975).
791:(1911).
753:(1976).
600:(1586).
587:(1721).
512:(1852).
464:(2004).
436:Spherics
354:Spherics
338:Spherics
330:Spherics
322:Spherics
299:Spherics
294:Almagest
285:Elements
265:Elements
224:Spherics
216:Spherics
208:Spherics
191:Elements
159:Spherics
55:Spherics
50:Bithynia
2617:Chinese
2572:numbers
2500:algebra
2428:Related
2402:Centers
2198:Results
2068:Central
1739:Ptolemy
1734:Proclus
1699:Perseus
1654:Marinus
1634:Hypatia
1624:Hippias
1599:Geminus
1589:Eudoxus
1579:Eudemus
1549:Diocles
1234:Dioptra
1097:Pytheas
1092:Ptolemy
1042:Hicetas
1032:Geminus
1027:Eudoxus
982:Attalus
947:Agrippa
801:(ed.).
763:(ed.).
516:(ed.).
479:paideia
468:(ed.).
428:Theudas
350:Book VI
344:in his
289:Ptolemy
247:sundial
2632:Indian
2409:Cyrene
1941:Optics
1860:Conics
1779:Theano
1769:Thales
1764:Sporus
1709:Philon
1694:Pappus
1584:Euclid
1514:Carpus
1504:Bryson
1345:Zodiac
1295:Equant
1244:Gnomon
1122:Thales
1117:Strabo
967:Aratus
884:
862:
773:
709:
627:
510:Strabo
495:rhetor
486:, the
462:Strabo
440:Method
404:Method
277:Arabic
232:climes
186:Euclid
114:c. 190
100:Strabo
95:Method
2627:Incan
2548:logic
2324:Other
2092:Chord
2085:Axiom
2063:Angle
1719:Plato
1609:Heron
1529:Conon
1151:Works
1067:Meton
1012:Conon
797:. In
759:. In
361:Notes
163:Greek
147:Works
48:from
24:Greek
2589:list
1877:Data
1649:Leon
1499:Bion
992:Bion
882:ISBN
860:ISBN
771:ISBN
707:ISBN
625:ISBN
340:and
320:The
313:and
305:and
287:and
198:and
133:Suda
81:Suda
74:Life
66:and
44:and
2491:by
2205:In
852:doi
541:doi
392:):
291:'s
202:'s
188:'s
139:or
102:'s
2689::
858:.
838:,
832:,
659:^
537:75
535:.
531:.
380:.
368:^
352:.
348:,
297:.
165::
116:–
92:'
70:.
26::
1426:e
1419:t
1412:v
918:e
911:t
904:v
890:.
868:.
854::
779:.
715:.
671:.
654:.
633:.
549:.
543::
161:(
112:(
22:(
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.