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Leo the Mathematician

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156:, the caliph, upon receiving Leo's letter of refusal, sent a letter requesting answers to some difficult questions of geometry and astrology, which Leo obliged. Al-Mamun then offered two thousands pounds of gold and a perpetual peace to Theophilos, if only he could borrow Leo's services briefly; the request was declined. The emperor then honoured Leo by having John the Grammarian consecrate him 164:, which post he held from the spring of 840 to 843. There is a discrepancy in this account, however, in that the caliph died in 833. It has been suggested that either the connection between the caliph's final letter and Leo's appointment as metropolitan is in error, or the caliph in question was actually al-Mutasim. This latter option squares with the account of 119:, where he could obtain rare manuscripts and was taught mathematics by an old monk. He originally taught privately in obscurity in Constantinople. The story goes that when one of his students was captured during the 175:
in 843. Despite this, he delivered a sermon favourable of icons within months of Theophilos' death. Around 855, Leo was appointed at the head of a newly established Magnaura School by
130:
was so impressed by his knowledge of mathematics, providing proofs that his own scholars were unable to complete, and predictive abilities that he offered Leo great riches to come to
372: 179:. He was renowned for his philosophical, mathematical, medical, scientific, literary, philological, seismological, astronomic, and astrological learning, and was patronised by 1280: 1020: 663:
Treadgold, "Chronological Accuracy ", 187, believes, on the basis of the Logothete's account, that this occurred in 843 and was a re-founding of Theophilos' school.
223:, and was also a compiler, who brought together a wide range of philosophical, medical, and astronomic texts. His library can at least partially be reconstructed: 1098: 115:
descent. In his youth he was educated at Constantinople, but found higher education options limited in the city and thus travelled to the monasteries of
855: 1386: 207:, such as trees with moving birds, roaring lions, and a levitating imperial throne. The throne was in operation a century later, when 1416: 1401: 1371: 1411: 537:
Byzantine Humanism: The First Phase: Notes and Remarks on Education and Culture in Byzantium from Its Origins to the 10th Century
1396: 778: 848: 441: 203:
to Constantinople, which gave advance warning of Arab raids, as well as diplomatic communication. Leo also invented several
1376: 826: 1381: 806: 757: 682: 396: 1211: 841: 283:
Recent years have seen the first translations into English of a number of primary sources about Leo and his times.
1266: 1228: 1406: 1291: 263:. He composed his own medical encyclopaedia. Later Byzantine scholars sometimes confused Leo with the scholar 1391: 1307: 483: 1366: 1191: 1168: 713:
Treadgold, Warren T. (1979). "The Revival of Byzantine Learning and the Revival of the Byzantine State".
184: 104: 1118: 1066: 864: 188: 108: 76: 319:
Chronographiae quae Theophanis Continuati nomine fertur Liber quo Vita Basilii Imperatoris amplectitur
1093: 1079: 1071: 822: 797:
Among them are some centos preserved in the Palatine Anthology; see Prieto Domínguez, Óscar (2011),
619:
Symeon says the Magnaura, Continuatus the Forty Martyrs (Treadgold, "Chronological Accuracy ", 186).
1299: 938: 146: 192: 120: 1160: 570: 322: 292: 248: 153: 60: 171:
Leo, an iconoclast sometimes accused of paganism, lost his metropolitancy with the end of the
997: 700:
The Entry of the Slavs into Christendom: An Introduction to the Medieval History of the Slavs
585: 433: 427: 773:
For a detailed discussion of Leo's telegraph and his automata, see Leone Montagnini (2002),
314:), Canberra: Australian Association for Byzantine Studies; Byzantina Australiensia 11, 1998. 1361: 987: 208: 172: 165: 138: 64: 52: 168:, who makes Leo teach at the Magnaura from late 838 to early 840 and was paid handsomely. 8: 252: 240: 157: 409: 1144: 730: 602: 296: 264: 236: 577:
and puts the invitation after the Islamic conquest of Amorium in the fall of 838, cf.
802: 753: 678: 437: 392: 135: 124: 1139: 1046: 774: 722: 594: 517: 497:
The Glory of Byzantium: Art and Culture of the Middle Byzantine Era, A.D. 843—1261.
219:
Most of Leo's writings have been lost. He wrote book-length works, poems, and many
1134: 1126: 782: 566: 550: 311: 268: 1152: 344: 84: 27: 458:История отечественной математики. Том 1. С древнейших времен до конца XVIII в. 336:, Liverpool University Press; Translated Texts for Byzantinists, vol. 7, 2019. 1355: 801:. Estudios Filológicos, 328. Salamanca: Ediciones Universidad de Salamanca. 161: 833: 521: 300: 180: 141:, who, impressed by his international repute, conferred on him a school ( 67:. His only preserved writings are some notes contained in manuscripts of 375:, which occurred during the Feast of St. Polyeuktos on January 9th, 869. 734: 606: 574: 332:
Wahlgren, Staffan (translator, writer of introduction and commentary).
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written by Pseudo-Symeon the Logothete mentions that Leo survives the
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Featherstone, Jeffrey Michael and Signes-Codoñer, Juan (translators).
903: 367:
132.4. Symeon the Logothete as well as the separate recension of the
112: 775:"Leone il Matematico, un anello mancante nella storia della scienza" 726: 598: 220: 204: 127: 100: 80: 72: 56: 289:
Chronographiae quae Theophanis Continuati nomine fertur Libri I-IV
75:" and "the cleverest man in Byzantium in the 9th century". He was 553: 326: 244: 200: 131: 88: 579:
Treadgold, Warren T. (1979). "The Chronological Accuracy of the
549:
According to the Pseudo-Symeon, this student was Boïditzes, who
486:, in: Εγκυκλοπαίδεια Μείζονος Ελληνισμού, Κωνσταντινούπολη, 2008 272: 228: 176: 116: 232: 68: 31: 573:
between 829 and 833; Symeon the Logothete makes the caliph
539:. Translated by Helen, Lindsay. Leiden: Brill. p. 172. 675:
The Reign of Leo VI (886–912): Politics and People
799:
De Alieno Nostrum: el Centón profano en el mundo griego
583:
of Symeon the Logothete for the Years 813–845".
702:. Cambridge: Cambridge University Press. p. 33. 721:(5). American Historical Association: 1245–1266 . 512:Browning, Robert (1964). "Byzantine Scholarship". 499:Metropolitan Museum of Art, New York, 1997, p. 351 429:The Oxford illustrated history of medieval Europe 347:, active 1081), Cambridge University Press, 2010. 211:witnessed it during his visit to Constantinople. 16:Byzantine philosopher, mathematician and logician 1353: 750:Heaven on Earth: Art and the Church in Byzantium 821:Katerina Ierodiakonou and Börje Bydén (2008), 191:was his student. Leo has been credited with a 145:) in either the Magnaura or the church of the 849: 706: 134:. Leo took the letter from the caliph to the 752:. Pittsburgh: Penn State Press. p. 30. 639:A history of the Byzantine state and society 863: 666: 432:. Oxford: Oxford University Press. p.  856: 842: 741: 691: 628:Treadgold, "Chronological Accuracy ", 172. 507: 505: 712: 578: 383: 381: 341:A synopsis of Byzantine history, 811-1057 195:(an optical telegraph) stretching across 71:'s dialogues. He has been called a "true 511: 421: 419: 259:of Quirinus and Marcellus, and possibly 152:In the version of the story recorded by 672: 534: 502: 1354: 747: 697: 425: 378: 837: 416: 295:Books I-IV, comprising the reigns of 20:Leo the Mathematician, the Grammarian 652:The Byzantine Revival, 780–842 303:), Berlin, Boston: De Gruyter, 2015. 51:– after January 9, 869) was a 827:Stanford Encyclopedia of Philosophy 460:, Киев, Наукова Думка, 1966, p. 447 13: 389:Daily Life in the Byzantine Empire 278: 14: 1428: 1387:Byzantine bishops of Thessalonica 815: 654:(Stanford University Press), 372. 641:(Stanford University Press), 447. 473:, т. 3, Москва, 1964, pp. 156—157 79:and later became the head of the 1417:9th-century Greek mathematicians 1402:9th-century Byzantine scientists 1372:9th-century Byzantine physicians 764:Records Liutprand's description. 791: 767: 657: 644: 631: 622: 613: 559: 543: 528: 65:the Second Byzantine Iconoclasm 1412:9th-century Greek philosophers 715:The American Historical Review 677:. Leiden: Brill. p. 113. 489: 476: 463: 450: 402: 373:869 AD Earthquake of Byzantium 357: 334:The Chronicle of the Logothete 1: 1397:9th-century Byzantine writers 1080:Constantine III Mesopotamites 1072:Constantine III Mesopotamites 391:(Greenwood Publishing Group, 387:Marcus Louis Rautman (2006), 308:On the reigns of the emperors 45: 786:Studi sull'Oriente Cristiano 650:Warren T. Treadgold (1988), 637:Warren T. Treadgold (1997), 329:), Berlin: De Gruyter, 2011. 7: 484:Armenians in Constantinople 469:Философская Энциклопедия , 185:Photios I of Constantinople 105:Patriarch of Constantinople 10: 1433: 1377:9th-century mathematicians 1281:Joseph III the Hieromartyr 1067:Eustathius of Thessalonica 495:H. C. Evans, W. D. Wixom, 77:archbishop of Thessalonica 32: 871: 317:Ševčenko, Ihor (trans.). 121:Byzantine–Arab Wars 1382:9th-century philosophers 939:Eusebius of Thessalonica 410:"History of the Pianola" 351: 339:Wortley, John (trans.). 306:Kaldellis, A. (trans.). 214: 1199:Joasaph II Argyropoulos 1021:Basil III the Confessor 865:Bishops of Thessalonica 823:"Byzantine Philosophy." 673:Tougher, Shaun (1997). 426:Holmes, George (1990). 325:comprising the Life of 94: 1161:Symeon of Thessalonica 1017:John IV the Thessalian 748:Safran, Linda (1998). 698:Vlasto, A. P. (1970). 571:Theophanes Continuatus 535:Lemerle, Paul (2017). 363:Symeon the Logothete, 323:Theophanes Continuatus 293:Theophanes Continuatus 154:Theophanes Continuatus 61:Macedonian Renaissance 1407:Byzantine astronomers 998:Anthony the Confessor 586:Dumbarton Oaks Papers 271:, and ascribe to him 53:Byzantine philosopher 1392:People from Thessaly 1090:Michael II Palatanos 988:Joseph the Confessor 963:Under Constantinople 482:Trkulja J., Lees C. 412:. Pianola Institute. 209:Liutprand of Cremona 166:Symeon the Logothete 59:associated with the 38:Léōn ho Mathēmatikós 1135:Gregory III Palamas 993:Leo the Philosopher 522:10.1093/past/28.1.3 253:Apollonius of Perga 241:Theon of Alexandria 109:John the Grammarian 1367:9th-century deaths 1145:Nicholas Kabasilas 1099:Joannicius Kydones 781:2013-10-17 at the 297:Leo V the Armenian 265:Leo Choirosphaktes 237:Paul of Alexandria 183:and befriended by 103:, a cousin of the 89:Aristotelian logic 87:, where he taught 33:Λέων ὁ Μαθηματικός 1349: 1348: 1063:Basil IV of Ohrid 443:978-0-19-285435-3 193:system of beacons 136:Byzantine emperor 83:of philosophy in 1424: 1140:Neilos Kabasilas 858: 851: 844: 835: 834: 810: 795: 789: 788:, 6 (2), 89–108. 771: 765: 763: 745: 739: 738: 710: 704: 703: 695: 689: 688: 670: 664: 661: 655: 648: 642: 635: 629: 626: 620: 617: 611: 610: 563: 557: 547: 541: 540: 532: 526: 525: 514:Past and Present 509: 500: 493: 487: 480: 474: 467: 461: 454: 448: 447: 423: 414: 413: 406: 400: 399:), 294–95. 385: 376: 361: 343:(the history of 310:(the history of 267:and the emperor 99:Leo was born in 50: 47: 36:or ὁ Φιλόσοφος, 35: 34: 1432: 1431: 1427: 1426: 1425: 1423: 1422: 1421: 1352: 1351: 1350: 1345: 867: 862: 818: 813: 796: 792: 783:Wayback Machine 772: 768: 760: 746: 742: 727:10.2307/1861467 711: 707: 696: 692: 685: 671: 667: 662: 658: 649: 645: 636: 632: 627: 623: 618: 614: 599:10.2307/1291437 567:Joseph Genesius 564: 560: 548: 544: 533: 529: 510: 503: 494: 490: 481: 477: 468: 464: 456:Штокало И. З., 455: 451: 444: 424: 417: 408: 407: 403: 386: 379: 362: 358: 354: 312:Joseph Genesios 281: 279:Primary sources 269:Leo VI the Wise 217: 97: 81:Magnaura School 73:Renaissance man 63:and the end of 48: 24:the Philosopher 17: 12: 11: 5: 1430: 1420: 1419: 1414: 1409: 1404: 1399: 1394: 1389: 1384: 1379: 1374: 1369: 1364: 1347: 1346: 1344: 1343: 1340: 1339:Panteleimon II 1337: 1334: 1331: 1328: 1325: 1322: 1319: 1316: 1313: 1312:Callinicus III 1310: 1305: 1302: 1297: 1294: 1289: 1286: 1283: 1278: 1275: 1272: 1269: 1264: 1261: 1258: 1255: 1252: 1249: 1246: 1243: 1240: 1237: 1234: 1231: 1226: 1223: 1220: 1217: 1214: 1209: 1206: 1203: 1200: 1197: 1194: 1189: 1186: 1183: 1180: 1177: 1174: 1171: 1166: 1163: 1158: 1155: 1150: 1147: 1142: 1137: 1132: 1129: 1124: 1121: 1116: 1113: 1110: 1107: 1104: 1101: 1096: 1091: 1088: 1085: 1082: 1077: 1074: 1069: 1064: 1061: 1058: 1055: 1054:Constantine II 1052: 1049: 1044: 1043:Constantine II 1041: 1038: 1035: 1032: 1029: 1026: 1023: 1018: 1015: 1012: 1009: 1006: 1003: 1000: 995: 990: 985: 982: 979: 976: 973: 970: 960: 959: 956: 953: 950: 947: 944: 941: 936: 933: 930: 927: 924: 921: 918: 915: 912: 909: 906: 901: 898: 895: 892: 889: 886: 883: 880: 872: 869: 868: 861: 860: 853: 846: 838: 832: 831: 817: 816:External links 814: 812: 811: 790: 766: 758: 740: 705: 690: 683: 665: 656: 643: 630: 621: 612: 558: 556:to the caliph. 542: 527: 501: 488: 475: 462: 449: 442: 415: 401: 377: 355: 353: 350: 349: 348: 345:John Scylitzes 337: 330: 321:(Chronicle of 315: 304: 291:(Chronicle of 280: 277: 216: 213: 143:ekpaideutērion 96: 93: 85:Constantinople 42:ho Philósophos 15: 9: 6: 4: 3: 2: 1429: 1418: 1415: 1413: 1410: 1408: 1405: 1403: 1400: 1398: 1395: 1393: 1390: 1388: 1385: 1383: 1380: 1378: 1375: 1373: 1370: 1368: 1365: 1363: 1360: 1359: 1357: 1341: 1338: 1335: 1333:Panteleimon I 1332: 1329: 1326: 1323: 1321:Athanasius II 1320: 1318:Sophronius II 1317: 1314: 1311: 1309: 1306: 1303: 1301: 1300:Callinicus II 1298: 1295: 1293: 1290: 1287: 1284: 1282: 1279: 1276: 1273: 1271:Damascenus II 1270: 1268: 1267:Theodosius II 1265: 1262: 1259: 1256: 1253: 1250: 1247: 1244: 1241: 1238: 1235: 1233:Anastasius II 1232: 1230: 1227: 1224: 1221: 1218: 1215: 1213: 1210: 1207: 1204: 1201: 1198: 1195: 1193: 1190: 1187: 1184: 1182:Gregory-David 1181: 1179:Theophanes II 1178: 1175: 1172: 1170: 1167: 1164: 1162: 1159: 1156: 1154: 1151: 1148: 1146: 1143: 1141: 1138: 1136: 1133: 1130: 1128: 1125: 1122: 1120: 1117: 1114: 1111: 1108: 1105: 1102: 1100: 1097: 1095: 1092: 1089: 1086: 1083: 1081: 1078: 1075: 1073: 1070: 1068: 1065: 1062: 1059: 1056: 1053: 1050: 1048: 1045: 1042: 1039: 1036: 1033: 1030: 1027: 1024: 1022: 1019: 1016: 1013: 1010: 1007: 1004: 1001: 999: 996: 994: 991: 989: 986: 983: 980: 977: 974: 971: 969:Constantine I 968: 967: 966: 964: 957: 954: 951: 948: 945: 942: 940: 937: 934: 931: 928: 925: 922: 919: 916: 913: 910: 907: 905: 902: 899: 896: 893: 890: 887: 884: 881: 878: 877: 875: 870: 866: 859: 854: 852: 847: 845: 840: 839: 836: 829: 828: 824: 820: 819: 809:, p. 120-179. 808: 807:9788478002085 804: 800: 794: 787: 784: 780: 776: 770: 761: 759:0-271-01670-1 755: 751: 744: 736: 732: 728: 724: 720: 716: 709: 701: 694: 686: 684:90-04-10811-4 680: 676: 669: 660: 653: 647: 640: 634: 625: 616: 608: 604: 600: 596: 592: 588: 587: 582: 576: 572: 568: 565:According to 562: 555: 552: 546: 538: 531: 523: 519: 515: 508: 506: 498: 492: 485: 479: 472: 471:Лев Математик 466: 459: 453: 445: 439: 435: 431: 430: 422: 420: 411: 405: 398: 397:0-313-32437-9 394: 390: 384: 382: 374: 370: 369:Chronographia 366: 365:Chronographia 360: 356: 346: 342: 338: 335: 331: 328: 324: 320: 316: 313: 309: 305: 302: 298: 294: 290: 286: 285: 284: 276: 274: 270: 266: 262: 258: 254: 250: 246: 242: 238: 234: 230: 226: 222: 212: 210: 206: 202: 198: 194: 190: 186: 182: 178: 174: 169: 167: 163: 159: 155: 150: 148: 147:Forty Martyrs 144: 140: 137: 133: 129: 126: 122: 118: 114: 110: 106: 102: 92: 90: 86: 82: 78: 74: 70: 66: 62: 58: 54: 43: 39: 29: 25: 21: 1324:Alexander II 1304:Neophytus II 1288:Macarius III 1219:Callinicus I 1216:Damascenus I 1212:Athanasius I 1202:Sophronius I 1149:Dorotheus II 1034:Theophanes I 992: 962: 961: 935:Theodosius I 914:Anastasius I 873: 825: 798: 793: 785: 769: 749: 743: 718: 714: 708: 699: 693: 674: 668: 659: 651: 646: 638: 633: 624: 615: 590: 584: 580: 561: 545: 536: 530: 513: 496: 491: 478: 470: 465: 457: 452: 428: 404: 388: 368: 364: 359: 340: 333: 318: 307: 288: 282: 256: 218: 170: 162:Thessalonica 158:metropolitan 151: 142: 111:. He was of 98: 41: 37: 23: 19: 18: 1362:790s births 1308:Joachim III 1292:Meletius II 1263:Neophytus I 1257:Gabriel III 1248:Ignatius II 1242:Ignatius II 1188:Metrophanes 1173:Macarius II 1165:Gregory III 1127:Ignatius II 1115:Euphemianus 1084:Nicetas III 1076:Chrysanthus 923:Dorotheus I 888:Alexander I 516:(28): 7–8. 301:Michael III 255:, the lost 181:Theoktistos 1356:Categories 1327:Joachim IV 1315:Gregory IV 1285:Matthew II 1254:Joachim II 1236:Meletius I 1222:Theocletus 1208:Parthenius 1192:Gabriel II 1153:Isidore II 1131:Macarius I 1123:Gregory II 1106:Ignatius I 1051:Nicetas II 1037:Prometheus 981:Theophilus 975:Anastasius 882:Nicholas I 874:Under Rome 575:al-Mutasim 261:Thucydides 225:Archimedes 197:Asia Minor 173:Iconoclasm 139:Theophilos 49: 790 1330:Gennadius 1296:Ieronymus 1277:Gerasimus 1274:James III 1239:Methodius 1229:Dionysius 1225:Joachim I 1196:Matthew I 1185:Joasaph I 1157:Gabriel I 1103:Demetrius 1087:Joseph II 1047:Michael I 1040:Theodulus 1031:Nicetas I 1028:Isidore I 1025:Anatolius 1014:Methodius 1011:Gregory I 932:Thalaleus 926:Aristides 917:Auxitheus 904:Ascholius 581:Chronicle 257:Mechanics 1342:Anthimos 1336:Leonidas 1260:Spyridon 1245:James II 1005:Theodore 1002:Basil II 955:John III 946:Plotinus 900:Paulinus 885:Artemius 779:Archived 551:betrayed 249:Porphyry 221:epigrams 205:automata 128:al-Mamun 113:Armenian 101:Thessaly 57:logician 1251:Ananias 1205:Zosimas 1176:Theonas 1169:Nephon 1060:Romanus 1008:Paul II 978:Basil I 958:Sergius 949:John II 943:John II 908:Anysius 897:Irenius 735:1861467 607:1291437 593:: 162. 554:Amorium 327:Basil I 273:oracles 245:Proclus 201:Cilicia 132:Baghdad 1119:John V 1112:Jeremy 1094:Manuel 984:Thomas 952:Paul I 920:Andrew 894:Aetius 891:John I 805:  756:  733:  681:  605:  440:  395:  229:Euclid 177:Bardas 125:Caliph 123:, the 117:Andros 1109:James 972:Peter 929:Elias 911:Rufus 879:Gaius 731:JSTOR 603:JSTOR 352:Notes 233:Plato 215:Works 199:from 189:Cyril 69:Plato 28:Greek 803:ISBN 754:ISBN 679:ISBN 569:and 438:ISBN 393:ISBN 95:Life 55:and 1057:Leo 723:doi 595:doi 518:doi 299:to 160:of 40:or 22:or 1358:: 965:: 876:: 777:, 729:. 719:84 717:. 601:. 591:33 589:. 504:^ 436:. 434:52 418:^ 380:^ 275:. 251:, 247:, 243:, 239:, 235:, 231:, 227:, 187:. 149:. 107:, 91:. 46:c. 44:; 30:: 857:e 850:t 843:v 830:. 762:. 737:. 725:: 687:. 609:. 597:: 524:. 520:: 446:. 26:(

Index

Greek
Byzantine philosopher
logician
Macedonian Renaissance
the Second Byzantine Iconoclasm
Plato
Renaissance man
archbishop of Thessalonica
Magnaura School
Constantinople
Aristotelian logic
Thessaly
Patriarch of Constantinople
John the Grammarian
Armenian
Andros
Byzantine–Arab Wars
Caliph
al-Mamun
Baghdad
Byzantine emperor
Theophilos
Forty Martyrs
Theophanes Continuatus
metropolitan
Thessalonica
Symeon the Logothete
Iconoclasm
Bardas
Theoktistos

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