1672:
1659:
428:
1532:
1132:
116:, possibly as early as 525. From his testimony, it seems he traveled to other cultural centers of his time to find missing manuscripts.
1726:
1610:
913:
449:
421:
395:
317:
of
Apollonius was dedicated to Anthemius of Tralles (t534), an able mathematician and architect of St. Sophia of Constantinople."
1721:
1457:
1706:
1187:
368:
1711:
1152:
1716:
1520:
923:
194:
Historians owe much of their knowledge of
Archimedes' solution of a cubic by means of intersecting conics, alluded to in
1587:
414:
347:
309:. It is to Eutocius that we owe the Archimedean solution of a cubic through intersecting conics, referred to in
1556:
1489:
1122:
1002:
1625:
1382:
1270:
445:
167:
305:
Boyer, p. 193. "Eutocius (born ca. 480), commented on several
Archimedean treatises and on the Apollonian
1334:
1265:
961:
777:
148:
752:
313:
but not otherwise extant except through the commentary of
Eutocius. The commentary by Eutocius on the
1496:
1467:
827:
682:
1630:
1364:
907:
400:
113:
390:
1592:
1568:
1442:
1377:
1318:
1255:
1245:
981:
900:
762:
672:
552:
156:
862:
1615:
1563:
1462:
1290:
1240:
1225:
1220:
991:
792:
727:
717:
667:
132:
281:
1663:
1515:
1359:
1300:
1177:
1100:
1048:
850:
757:
607:
1640:
1580:
1544:
1387:
1210:
1157:
1127:
1117:
1026:
889:
782:
697:
652:
632:
477:
462:
203:
8:
1701:
1696:
1620:
1539:
1527:
1508:
1472:
1392:
1310:
1295:
1285:
1235:
1230:
1172:
1041:
933:
797:
787:
687:
657:
572:
497:
487:
472:
386:
331:
120:
78:
1676:
1635:
1575:
1503:
1369:
1344:
1162:
1137:
1105:
943:
702:
647:
612:
507:
105:
1671:
1349:
1260:
1110:
1036:
1009:
772:
592:
582:
517:
437:
364:
343:
336:
198:, to Eutocius and his commentaries. Eutocius dedicated his commentary on Apollonius'
1551:
1422:
1339:
1095:
1083:
1031:
767:
265:
109:
25:
1192:
1182:
1076:
802:
97:
1452:
1447:
1275:
1167:
1147:
975:
532:
502:
211:
58:
1690:
1412:
1280:
1250:
1071:
879:
822:
406:
1354:
1142:
817:
577:
567:
207:
240:
968:
856:
562:
547:
101:
954:
873:
812:
807:
747:
732:
677:
662:
617:
557:
542:
522:
492:
457:
124:
74:
707:
692:
642:
537:
527:
512:
482:
844:
622:
467:
186:
93:
73:
520s) was a Greek mathematician who wrote commentaries on several
1417:
742:
737:
637:
627:
602:
181:
712:
587:
137:
1088:
1066:
722:
31:
92:
Little is known about the life of
Eutocius. He was born in
46:
40:
43:
28:
361:
City and School in Late
Antique Athens and Alexandria
49:
37:
34:
335:
384:
1688:
206:, also a mathematician and the architect of the
342:(Second ed.). John Wiley & Sons, Inc.
436:
422:
112:, and he was succeeded in this position by
429:
415:
104:Eutocius probably became the head of the
396:MacTutor History of Mathematics Archive
1689:
1458:Latin translations of the 12th century
1188:Straightedge and compass construction
410:
358:
330:
1153:Incircle and excircles of a triangle
16:5th–6th century Greek mathematician
13:
363:. University of California Press.
144:Commentaries on Archimedes' work:
127:. The surviving commentaries are:
14:
1738:
378:
162:In Archimedis Dimensionem Circuli
1727:6th-century Byzantine scientists
1670:
1657:
267:Eutocii Ascalonitae commentarius
87:
24:
135:on the first four books of the
119:Eutocius wrote commentaries on
1490:A History of Greek Mathematics
1003:The Quadrature of the Parabola
299:
274:
258:
233:
224:
100:and lived during the reign of
1:
1722:6th-century Byzantine writers
217:
180:An introduction to Book I of
70:
66:
1707:Ancient Greek mathematicians
1271:Intersecting secants theorem
7:
1712:Ancient Greeks from Ascalon
1266:Intersecting chords theorem
1133:Doctrine of proportionality
10:
1743:
1717:6th-century mathematicians
962:On the Sphere and Cylinder
915:On the Sizes and Distances
324:
196:On the Sphere and Cylinder
149:On the Sphere and Cylinder
1664:Ancient Greece portal
1653:
1603:
1481:
1468:Philosophy of mathematics
1438:
1431:
1405:
1383:Ptolemy's table of chords
1327:
1309:
1208:
1201:
1057:
1019:
836:
444:
438:Ancient Greek mathematics
359:Watts, Edward J. (2006).
157:Measurement of the Circle
62:
1335:Aristarchus's inequality
908:On Conoids and Spheroids
401:University of St Andrews
338:A History of Mathematics
1443:Ancient Greek astronomy
1256:Inscribed angle theorem
1246:Greek geometric algebra
901:Measurement of a Circle
311:The Sphere and Cylinder
1677:Mathematics portal
1463:Non-Euclidean geometry
1418:Mouseion of Alexandria
1291:Tangent-secant theorem
1241:Geometric mean theorem
1226:Exterior angle theorem
1221:Angle bisector theorem
925:On Sizes and Distances
282:"Eutocius – Biography"
63:Εὐτόκιος ὁ Ἀσκαλωνίτης
1365:Pappus's area theorem
1301:Theorem of the gnomon
1178:Quadratrix of Hippias
1101:Circles of Apollonius
1049:Problem of Apollonius
1027:Constructible numbers
851:Archimedes Palimpsest
391:"Eutocius of Ascalon"
77:treatises and on the
1581:prehistoric counting
1378:Ptolemy's inequality
1319:Apollonius's theorem
1158:Method of exhaustion
1128:Diophantine equation
1118:Circumscribed circle
935:On the Moving Sphere
387:Robertson, Edmund F.
332:Boyer, Carl Benjamin
204:Anthemius of Tralles
1667: •
1473:Neusis construction
1393:Spiral of Theodorus
1286:Pythagorean theorem
1231:Euclidean algorithm
1173:Lune of Hippocrates
1042:Squaring the circle
798:Theon of Alexandria
473:Aristaeus the Elder
385:O'Connor, John J.;
20:Eutocius of Ascalon
1360:Menelaus's theorem
1350:Irrational numbers
1163:Parallel postulate
1138:Euclidean geometry
1106:Apollonian circles
648:Isidore of Miletus
169:On the Equilibrium
106:Alexandrian school
1684:
1683:
1649:
1648:
1401:
1400:
1388:Ptolemy's theorem
1261:Intercept theorem
1111:Apollonian gasket
1037:Doubling the cube
1010:The Sand Reckoner
370:978-0-520-25816-7
245:whistleralley.com
230:Watts, p. 233-234
1734:
1675:
1674:
1662:
1661:
1660:
1436:
1435:
1423:Platonic Academy
1370:Problem II.8 of
1340:Crossbar theorem
1296:Thales's theorem
1236:Euclid's theorem
1206:
1205:
1123:Commensurability
1084:Axiomatic system
1032:Angle trisection
997:
987:
949:
939:
929:
919:
895:
885:
868:
431:
424:
417:
408:
407:
403:
374:
353:
341:
318:
303:
297:
296:
294:
292:
278:
272:
271:
262:
256:
255:
253:
251:
237:
231:
228:
72:
68:
64:
56:
55:
52:
51:
48:
45:
42:
39:
36:
33:
30:
1742:
1741:
1737:
1736:
1735:
1733:
1732:
1731:
1687:
1686:
1685:
1680:
1669:
1658:
1656:
1645:
1611:Arabian/Islamic
1599:
1588:numeral systems
1477:
1427:
1397:
1345:Heron's formula
1323:
1305:
1197:
1193:Triangle center
1183:Regular polygon
1060:and definitions
1059:
1053:
1015:
995:
985:
947:
937:
927:
917:
893:
883:
866:
832:
803:Theon of Smyrna
448:
440:
435:
381:
371:
350:
327:
322:
321:
304:
300:
290:
288:
280:
279:
275:
264:
263:
259:
249:
247:
239:
238:
234:
229:
225:
220:
98:Palestina Prima
90:
27:
23:
17:
12:
11:
5:
1740:
1730:
1729:
1724:
1719:
1714:
1709:
1704:
1699:
1682:
1681:
1654:
1651:
1650:
1647:
1646:
1644:
1643:
1638:
1633:
1628:
1623:
1618:
1613:
1607:
1605:
1604:Other cultures
1601:
1600:
1598:
1597:
1596:
1595:
1585:
1584:
1583:
1573:
1572:
1571:
1561:
1560:
1559:
1549:
1548:
1547:
1537:
1536:
1535:
1525:
1524:
1523:
1513:
1512:
1511:
1501:
1500:
1499:
1485:
1483:
1479:
1478:
1476:
1475:
1470:
1465:
1460:
1455:
1453:Greek numerals
1450:
1448:Attic numerals
1445:
1439:
1433:
1429:
1428:
1426:
1425:
1420:
1415:
1409:
1407:
1403:
1402:
1399:
1398:
1396:
1395:
1390:
1385:
1380:
1375:
1367:
1362:
1357:
1352:
1347:
1342:
1337:
1331:
1329:
1325:
1324:
1322:
1321:
1315:
1313:
1307:
1306:
1304:
1303:
1298:
1293:
1288:
1283:
1278:
1276:Law of cosines
1273:
1268:
1263:
1258:
1253:
1248:
1243:
1238:
1233:
1228:
1223:
1217:
1215:
1203:
1199:
1198:
1196:
1195:
1190:
1185:
1180:
1175:
1170:
1168:Platonic solid
1165:
1160:
1155:
1150:
1148:Greek numerals
1145:
1140:
1135:
1130:
1125:
1120:
1115:
1114:
1113:
1108:
1098:
1093:
1092:
1091:
1081:
1080:
1079:
1074:
1063:
1061:
1055:
1054:
1052:
1051:
1046:
1045:
1044:
1039:
1034:
1023:
1021:
1017:
1016:
1014:
1013:
1006:
999:
989:
979:
976:Planisphaerium
972:
965:
958:
951:
941:
931:
921:
911:
904:
897:
887:
877:
870:
860:
853:
848:
840:
838:
834:
833:
831:
830:
825:
820:
815:
810:
805:
800:
795:
790:
785:
780:
775:
770:
765:
760:
755:
750:
745:
740:
735:
730:
725:
720:
715:
710:
705:
700:
695:
690:
685:
680:
675:
670:
665:
660:
655:
650:
645:
640:
635:
630:
625:
620:
615:
610:
605:
600:
595:
590:
585:
580:
575:
570:
565:
560:
555:
550:
545:
540:
535:
530:
525:
520:
515:
510:
505:
500:
495:
490:
485:
480:
475:
470:
465:
460:
454:
452:
446:Mathematicians
442:
441:
434:
433:
426:
419:
411:
405:
404:
380:
379:External links
377:
376:
375:
369:
355:
354:
348:
326:
323:
320:
319:
298:
273:
257:
232:
222:
221:
219:
216:
212:Constantinople
192:
191:
178:
177:
176:
165:
153:
142:
141:of Apollonius.
89:
86:
15:
9:
6:
4:
3:
2:
1739:
1728:
1725:
1723:
1720:
1718:
1715:
1713:
1710:
1708:
1705:
1703:
1700:
1698:
1695:
1694:
1692:
1679:
1678:
1673:
1666:
1665:
1652:
1642:
1639:
1637:
1634:
1632:
1629:
1627:
1624:
1622:
1619:
1617:
1614:
1612:
1609:
1608:
1606:
1602:
1594:
1591:
1590:
1589:
1586:
1582:
1579:
1578:
1577:
1574:
1570:
1567:
1566:
1565:
1562:
1558:
1555:
1554:
1553:
1550:
1546:
1543:
1542:
1541:
1538:
1534:
1531:
1530:
1529:
1526:
1522:
1519:
1518:
1517:
1514:
1510:
1507:
1506:
1505:
1502:
1498:
1494:
1493:
1492:
1491:
1487:
1486:
1484:
1480:
1474:
1471:
1469:
1466:
1464:
1461:
1459:
1456:
1454:
1451:
1449:
1446:
1444:
1441:
1440:
1437:
1434:
1430:
1424:
1421:
1419:
1416:
1414:
1411:
1410:
1408:
1404:
1394:
1391:
1389:
1386:
1384:
1381:
1379:
1376:
1374:
1373:
1368:
1366:
1363:
1361:
1358:
1356:
1353:
1351:
1348:
1346:
1343:
1341:
1338:
1336:
1333:
1332:
1330:
1326:
1320:
1317:
1316:
1314:
1312:
1308:
1302:
1299:
1297:
1294:
1292:
1289:
1287:
1284:
1282:
1281:Pons asinorum
1279:
1277:
1274:
1272:
1269:
1267:
1264:
1262:
1259:
1257:
1254:
1252:
1251:Hinge theorem
1249:
1247:
1244:
1242:
1239:
1237:
1234:
1232:
1229:
1227:
1224:
1222:
1219:
1218:
1216:
1214:
1213:
1207:
1204:
1200:
1194:
1191:
1189:
1186:
1184:
1181:
1179:
1176:
1174:
1171:
1169:
1166:
1164:
1161:
1159:
1156:
1154:
1151:
1149:
1146:
1144:
1141:
1139:
1136:
1134:
1131:
1129:
1126:
1124:
1121:
1119:
1116:
1112:
1109:
1107:
1104:
1103:
1102:
1099:
1097:
1094:
1090:
1087:
1086:
1085:
1082:
1078:
1075:
1073:
1070:
1069:
1068:
1065:
1064:
1062:
1056:
1050:
1047:
1043:
1040:
1038:
1035:
1033:
1030:
1029:
1028:
1025:
1024:
1022:
1018:
1012:
1011:
1007:
1005:
1004:
1000:
998:
994:
990:
988:
984:
980:
978:
977:
973:
971:
970:
966:
964:
963:
959:
957:
956:
952:
950:
946:
942:
940:
936:
932:
930:
926:
922:
920:
918:(Aristarchus)
916:
912:
910:
909:
905:
903:
902:
898:
896:
892:
888:
886:
882:
878:
876:
875:
871:
869:
865:
861:
859:
858:
854:
852:
849:
847:
846:
842:
841:
839:
835:
829:
826:
824:
823:Zeno of Sidon
821:
819:
816:
814:
811:
809:
806:
804:
801:
799:
796:
794:
791:
789:
786:
784:
781:
779:
776:
774:
771:
769:
766:
764:
761:
759:
756:
754:
751:
749:
746:
744:
741:
739:
736:
734:
731:
729:
726:
724:
721:
719:
716:
714:
711:
709:
706:
704:
701:
699:
696:
694:
691:
689:
686:
684:
681:
679:
676:
674:
671:
669:
666:
664:
661:
659:
656:
654:
651:
649:
646:
644:
641:
639:
636:
634:
631:
629:
626:
624:
621:
619:
616:
614:
611:
609:
606:
604:
601:
599:
596:
594:
591:
589:
586:
584:
581:
579:
576:
574:
571:
569:
566:
564:
561:
559:
556:
554:
551:
549:
546:
544:
541:
539:
536:
534:
531:
529:
526:
524:
521:
519:
516:
514:
511:
509:
506:
504:
501:
499:
496:
494:
491:
489:
486:
484:
481:
479:
476:
474:
471:
469:
466:
464:
461:
459:
456:
455:
453:
451:
447:
443:
439:
432:
427:
425:
420:
418:
413:
412:
409:
402:
398:
397:
392:
388:
383:
382:
372:
366:
362:
357:
356:
351:
349:0-471-54397-7
345:
340:
339:
333:
329:
328:
316:
312:
308:
302:
287:
286:Maths History
283:
277:
269:
268:
261:
246:
242:
236:
227:
223:
215:
213:
209:
205:
201:
197:
189:
188:
183:
179:
174:
173:
170:
166:
163:
159:
158:
154:
151:
150:
146:
145:
143:
140:
139:
134:
130:
129:
128:
126:
122:
117:
115:
111:
107:
103:
99:
95:
88:Life and work
85:
83:
80:
76:
60:
54:
21:
1668:
1655:
1497:Thomas Heath
1488:
1371:
1355:Law of sines
1211:
1143:Golden ratio
1008:
1001:
992:
986:(Theodosius)
982:
974:
967:
960:
953:
944:
934:
928:(Hipparchus)
924:
914:
906:
899:
890:
880:
872:
867:(Apollonius)
863:
855:
843:
818:Zeno of Elea
597:
578:Eratosthenes
568:Dionysodorus
394:
360:
337:
314:
310:
306:
301:
289:. Retrieved
285:
276:
270:. 1401–1500.
266:
260:
248:. Retrieved
244:
235:
226:
208:Hagia Sophia
199:
195:
193:
185:
171:
168:
161:
155:
147:
136:
118:
114:Olympiodorus
91:
81:
19:
18:
1564:mathematics
1372:Arithmetica
969:Ostomachion
938:(Autolycus)
857:Arithmetica
633:Hippocrates
563:Dinostratus
548:Dicaearchus
478:Aristarchus
250:25 February
75:Archimedean
1702:540 deaths
1697:480 births
1691:Categories
1616:Babylonian
1516:arithmetic
1482:History of
1311:Apollonius
996:(Menelaus)
955:On Spirals
874:Catoptrics
813:Xenocrates
808:Thymaridas
793:Theodosius
778:Theaetetus
758:Simplicius
748:Pythagoras
733:Posidonius
718:Philonides
678:Nicomachus
673:Metrodorus
663:Menaechmus
618:Hipparchus
608:Heliodorus
558:Diophantus
543:Democritus
523:Chrysippus
493:Archimedes
488:Apollonius
458:Anaxagoras
450:(timeline)
291:27 October
218:References
133:Commentary
125:Archimedes
121:Apollonius
108:following
102:Justinian.
96:, then in
79:Apollonian
1077:Inscribed
837:Treatises
828:Zenodorus
788:Theodorus
763:Sosigenes
708:Philolaus
693:Oenopides
688:Nicoteles
683:Nicomedes
643:Hypsicles
538:Ctesibius
528:Cleomedes
513:Callippus
498:Autolycus
483:Aristotle
463:Anthemius
172:of Planes
1641:Japanese
1626:Egyptian
1569:timeline
1557:timeline
1545:timeline
1540:geometry
1533:timeline
1528:calculus
1521:timeline
1509:timeline
1212:Elements
1058:Concepts
1020:Problems
993:Spherics
983:Spherics
948:(Euclid)
894:(Euclid)
891:Elements
884:(Euclid)
845:Almagest
753:Serenus
728:Porphyry
668:Menelaus
623:Hippasus
598:Eutocius
573:Domninus
468:Archytas
334:(1991).
241:"Conica"
187:Almagest
160:(Latin:
110:Ammonius
1621:Chinese
1576:numbers
1504:algebra
1432:Related
1406:Centers
1202:Results
1072:Central
743:Ptolemy
738:Proclus
703:Perseus
658:Marinus
638:Hypatia
628:Hippias
603:Geminus
593:Eudoxus
583:Eudemus
553:Diocles
325:Sources
182:Ptolemy
123:and on
94:Ascalon
69:480s –
1636:Indian
1413:Cyrene
945:Optics
864:Conics
783:Theano
773:Thales
768:Sporus
713:Philon
698:Pappus
588:Euclid
518:Carpus
508:Bryson
367:
346:
315:Conics
307:Conics
200:Conics
138:Conics
82:Conics
1631:Incan
1552:logic
1328:Other
1096:Chord
1089:Axiom
1067:Angle
723:Plato
613:Heron
533:Conon
175:I-II.
152:I-II.
59:Greek
1593:list
881:Data
653:Leon
503:Bion
365:ISBN
344:ISBN
293:2021
252:2021
1495:by
1209:In
210:in
202:to
184:'s
1693::
399:,
393:,
389:,
284:.
243:.
214:.
164:).
131:A
84:.
71:c.
67:c.
65:;
61::
57:;
41:oʊ
32:uː
430:e
423:t
416:v
373:.
352:.
295:.
254:.
190:.
53:/
50:s
47:ə
44:ʃ
38:t
35:ˈ
29:j
26:/
22:(
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.