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On Conoids and Spheroids

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of any segment cut off by a plane with the volume of a
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A history of the conic sections and quadric surfaces
78:. The principal result of the work is comparing the 1689: 1567: 1517: 1491: 1413: 1395: 1294: 1287: 1143: 1105: 922: 530: 436: 405: 369: 271: 189:ON CONOIDS AND SPHEROIDS - The Works of Archimedes 89:The work is addressed to Dositheus of Pelusium. 25:A page from Archimedes' On Conoids and Spheroids 1877: 1820: 508: 249: 8: 1884: 1870: 1827: 1813: 1521: 1291: 515: 501: 493: 256: 242: 234: 105: 98: 1544:Latin translations of the 12th century 1274:Straightedge and compass construction 423:List of things named after Archimedes 7: 1838: 1836: 1778: 1776: 1239:Incircle and excircles of a triangle 1856:. You can help Knowledge (XXG) by 1799:. You can help Knowledge (XXG) by 14: 343:The Method of Mechanical Theorems 139:(3) On Conoids and Spheroids..... 1903:Ancient Greek mathematical works 1840: 1780: 1756: 1743: 477: 476: 360: 40:Περὶ κωνοειδέων καὶ σφαιροειδέων 1576:A History of Greek Mathematics 1089:The Quadrature of the Parabola 1: 51: 47: 1928:History of mathematics stubs 1923:Mathematics literature stubs 1357:Intersecting secants theorem 294:On the Equilibrium of Planes 66:about their axes, including 1352:Intersecting chords theorem 1219:Doctrine of proportionality 382:Archimedes's cattle problem 62:generated by revolution of 1944: 1835: 1775: 1048:On the Sphere and Cylinder 1001:On the Sizes and Distances 370:Discoveries and inventions 308:On the Sphere and Cylinder 301:Quadrature of the Parabola 86:with equal base and axis. 54:212 BC). Consisting of 32 39: 1750:Ancient Greece portal 1739: 1554:Philosophy of mathematics 1524: 1469:Ptolemy's table of chords 524:Ancient Greek mathematics 472: 358: 1421:Aristarchus's inequality 994:On Conoids and Spheroids 322:On Conoids and Spheroids 31:On Conoids and Spheroids 1848:This article about the 1529:Ancient Greek astronomy 1342:Inscribed angle theorem 1332:Greek geometric algebra 987:Measurement of a Circle 280:Measurement of a Circle 226:Encyclopædia Britannica 206:Encyclopædia Britannica 155:Coolidge, J.L. (1945). 134:Encyclopædia Britannica 1850:history of mathematics 1763:Mathematics portal 1549:Non-Euclidean geometry 1504:Mouseion of Alexandria 1377:Tangent-secant theorem 1327:Geometric mean theorem 1312:Exterior angle theorem 1307:Angle bisector theorem 1011:On Sizes and Distances 161:. Dover Publications. 26: 1788:This article about a 1451:Pappus's area theorem 1387:Theorem of the gnomon 1264:Quadratrix of Hippias 1187:Circles of Apollonius 1135:Problem of Apollonius 1113:Constructible numbers 937:Archimedes Palimpsest 418:Archimedes Palimpsest 387:Archimedes' principle 24: 1667:prehistoric counting 1464:Ptolemy's inequality 1405:Apollonius's theorem 1244:Method of exhaustion 1214:Diophantine equation 1204:Circumscribed circle 1021:On the Moving Sphere 413:Archimedes' heat ray 119:Heath, Thomas Little 1913:Works by Archimedes 1753: • 1559:Neusis construction 1479:Spiral of Theodorus 1372:Pythagorean theorem 1317:Euclidean algorithm 1259:Lune of Hippocrates 1128:Squaring the circle 884:Theon of Alexandria 559:Aristaeus the Elder 464:Eutocius of Ascalon 454:Apollonius of Perga 1908:Euclidean geometry 1446:Menelaus's theorem 1436:Irrational numbers 1249:Parallel postulate 1224:Euclidean geometry 1192:Apollonian circles 734:Isidore of Miletus 459:Hero of Alexandria 397:Claw of Archimedes 392:Archimedes's screw 329:On Floating Bodies 124:"Archimedes"  27: 16:Work by Archimedes 1865: 1864: 1808: 1807: 1770: 1769: 1735: 1734: 1487: 1486: 1474:Ptolemy's theorem 1347:Intercept theorem 1197:Apollonian gasket 1123:Doubling the cube 1096:The Sand Reckoner 490: 489: 449:Eudoxus of Cnidus 428:Pseudo-Archimedes 377:Archimedean solid 287:The Sand Reckoner 1935: 1886: 1879: 1872: 1844: 1837: 1829: 1822: 1815: 1784: 1777: 1761: 1760: 1748: 1747: 1746: 1522: 1509:Platonic Academy 1456:Problem II.8 of 1426:Crossbar theorem 1382:Thales's theorem 1322:Euclid's theorem 1292: 1209:Commensurability 1170:Axiomatic system 1118:Angle trisection 1083: 1073: 1035: 1025: 1015: 1005: 981: 971: 954: 517: 510: 503: 494: 480: 479: 364: 258: 251: 244: 235: 230: 222: 220:"Spheroid"  210: 202: 178: 176: 175: 142: 141: 126: 115: 109: 103: 53: 49: 41: 1943: 1942: 1938: 1937: 1936: 1934: 1933: 1932: 1893: 1892: 1891: 1890: 1834: 1833: 1773: 1771: 1766: 1755: 1744: 1742: 1731: 1697:Arabian/Islamic 1685: 1674:numeral systems 1563: 1513: 1483: 1431:Heron's formula 1409: 1391: 1283: 1279:Triangle center 1269:Regular polygon 1146:and definitions 1145: 1139: 1101: 1081: 1071: 1033: 1023: 1013: 1003: 979: 969: 952: 918: 889:Theon of Smyrna 534: 526: 521: 491: 486: 468: 432: 401: 365: 356: 267: 262: 213: 193: 185: 173: 171: 169: 154: 151: 146: 145: 117: 116: 112: 104: 100: 95: 17: 12: 11: 5: 1941: 1939: 1931: 1930: 1925: 1920: 1915: 1910: 1905: 1895: 1894: 1889: 1888: 1881: 1874: 1866: 1863: 1862: 1845: 1832: 1831: 1824: 1817: 1809: 1806: 1805: 1785: 1768: 1767: 1740: 1737: 1736: 1733: 1732: 1730: 1729: 1724: 1719: 1714: 1709: 1704: 1699: 1693: 1691: 1690:Other cultures 1687: 1686: 1684: 1683: 1682: 1681: 1671: 1670: 1669: 1659: 1658: 1657: 1647: 1646: 1645: 1635: 1634: 1633: 1623: 1622: 1621: 1611: 1610: 1609: 1599: 1598: 1597: 1587: 1586: 1585: 1571: 1569: 1565: 1564: 1562: 1561: 1556: 1551: 1546: 1541: 1539:Greek numerals 1536: 1534:Attic numerals 1531: 1525: 1519: 1515: 1514: 1512: 1511: 1506: 1501: 1495: 1493: 1489: 1488: 1485: 1484: 1482: 1481: 1476: 1471: 1466: 1461: 1453: 1448: 1443: 1438: 1433: 1428: 1423: 1417: 1415: 1411: 1410: 1408: 1407: 1401: 1399: 1393: 1392: 1390: 1389: 1384: 1379: 1374: 1369: 1364: 1362:Law of cosines 1359: 1354: 1349: 1344: 1339: 1334: 1329: 1324: 1319: 1314: 1309: 1303: 1301: 1289: 1285: 1284: 1282: 1281: 1276: 1271: 1266: 1261: 1256: 1254:Platonic solid 1251: 1246: 1241: 1236: 1234:Greek numerals 1231: 1226: 1221: 1216: 1211: 1206: 1201: 1200: 1199: 1194: 1184: 1179: 1178: 1177: 1167: 1166: 1165: 1160: 1149: 1147: 1141: 1140: 1138: 1137: 1132: 1131: 1130: 1125: 1120: 1109: 1107: 1103: 1102: 1100: 1099: 1092: 1085: 1075: 1065: 1062:Planisphaerium 1058: 1051: 1044: 1037: 1027: 1017: 1007: 997: 990: 983: 973: 963: 956: 946: 939: 934: 926: 924: 920: 919: 917: 916: 911: 906: 901: 896: 891: 886: 881: 876: 871: 866: 861: 856: 851: 846: 841: 836: 831: 826: 821: 816: 811: 806: 801: 796: 791: 786: 781: 776: 771: 766: 761: 756: 751: 746: 741: 736: 731: 726: 721: 716: 711: 706: 701: 696: 691: 686: 681: 676: 671: 666: 661: 656: 651: 646: 641: 636: 631: 626: 621: 616: 611: 606: 601: 596: 591: 586: 581: 576: 571: 566: 561: 556: 551: 546: 540: 538: 532:Mathematicians 528: 527: 522: 520: 519: 512: 505: 497: 488: 487: 485: 484: 473: 470: 469: 467: 466: 461: 456: 451: 446: 440: 438: 437:Related people 434: 433: 431: 430: 425: 420: 415: 409: 407: 403: 402: 400: 399: 394: 389: 384: 379: 373: 371: 367: 366: 359: 357: 355: 354: 350:Book of Lemmas 346: 339: 332: 325: 318: 311: 304: 297: 290: 283: 275: 273: 269: 268: 263: 261: 260: 253: 246: 238: 232: 231: 217:, ed. (1911). 215:Chisholm, Hugh 211: 200:"Conoid"  197:, ed. (1911). 195:Chisholm, Hugh 191: 184: 183:External links 181: 180: 179: 167: 150: 147: 144: 143: 129:Chisholm, Hugh 110: 97: 96: 94: 91: 64:conic sections 15: 13: 10: 9: 6: 4: 3: 2: 1940: 1929: 1926: 1924: 1921: 1919: 1916: 1914: 1911: 1909: 1906: 1904: 1901: 1900: 1898: 1887: 1882: 1880: 1875: 1873: 1868: 1867: 1861: 1859: 1855: 1851: 1846: 1843: 1839: 1830: 1825: 1823: 1818: 1816: 1811: 1810: 1804: 1802: 1798: 1794: 1791: 1786: 1783: 1779: 1774: 1765: 1764: 1759: 1752: 1751: 1738: 1728: 1725: 1723: 1720: 1718: 1715: 1713: 1710: 1708: 1705: 1703: 1700: 1698: 1695: 1694: 1692: 1688: 1680: 1677: 1676: 1675: 1672: 1668: 1665: 1664: 1663: 1660: 1656: 1653: 1652: 1651: 1648: 1644: 1641: 1640: 1639: 1636: 1632: 1629: 1628: 1627: 1624: 1620: 1617: 1616: 1615: 1612: 1608: 1605: 1604: 1603: 1600: 1596: 1593: 1592: 1591: 1588: 1584: 1580: 1579: 1578: 1577: 1573: 1572: 1570: 1566: 1560: 1557: 1555: 1552: 1550: 1547: 1545: 1542: 1540: 1537: 1535: 1532: 1530: 1527: 1526: 1523: 1520: 1516: 1510: 1507: 1505: 1502: 1500: 1497: 1496: 1494: 1490: 1480: 1477: 1475: 1472: 1470: 1467: 1465: 1462: 1460: 1459: 1454: 1452: 1449: 1447: 1444: 1442: 1439: 1437: 1434: 1432: 1429: 1427: 1424: 1422: 1419: 1418: 1416: 1412: 1406: 1403: 1402: 1400: 1398: 1394: 1388: 1385: 1383: 1380: 1378: 1375: 1373: 1370: 1368: 1367:Pons asinorum 1365: 1363: 1360: 1358: 1355: 1353: 1350: 1348: 1345: 1343: 1340: 1338: 1337:Hinge theorem 1335: 1333: 1330: 1328: 1325: 1323: 1320: 1318: 1315: 1313: 1310: 1308: 1305: 1304: 1302: 1300: 1299: 1293: 1290: 1286: 1280: 1277: 1275: 1272: 1270: 1267: 1265: 1262: 1260: 1257: 1255: 1252: 1250: 1247: 1245: 1242: 1240: 1237: 1235: 1232: 1230: 1227: 1225: 1222: 1220: 1217: 1215: 1212: 1210: 1207: 1205: 1202: 1198: 1195: 1193: 1190: 1189: 1188: 1185: 1183: 1180: 1176: 1173: 1172: 1171: 1168: 1164: 1161: 1159: 1156: 1155: 1154: 1151: 1150: 1148: 1142: 1136: 1133: 1129: 1126: 1124: 1121: 1119: 1116: 1115: 1114: 1111: 1110: 1108: 1104: 1098: 1097: 1093: 1091: 1090: 1086: 1084: 1080: 1076: 1074: 1070: 1066: 1064: 1063: 1059: 1057: 1056: 1052: 1050: 1049: 1045: 1043: 1042: 1038: 1036: 1032: 1028: 1026: 1022: 1018: 1016: 1012: 1008: 1006: 1004:(Aristarchus) 1002: 998: 996: 995: 991: 989: 988: 984: 982: 978: 974: 972: 968: 964: 962: 961: 957: 955: 951: 947: 945: 944: 940: 938: 935: 933: 932: 928: 927: 925: 921: 915: 912: 910: 909:Zeno of Sidon 907: 905: 902: 900: 897: 895: 892: 890: 887: 885: 882: 880: 877: 875: 872: 870: 867: 865: 862: 860: 857: 855: 852: 850: 847: 845: 842: 840: 837: 835: 832: 830: 827: 825: 822: 820: 817: 815: 812: 810: 807: 805: 802: 800: 797: 795: 792: 790: 787: 785: 782: 780: 777: 775: 772: 770: 767: 765: 762: 760: 757: 755: 752: 750: 747: 745: 742: 740: 737: 735: 732: 730: 727: 725: 722: 720: 717: 715: 712: 710: 707: 705: 702: 700: 697: 695: 692: 690: 687: 685: 682: 680: 677: 675: 672: 670: 667: 665: 662: 660: 657: 655: 652: 650: 647: 645: 642: 640: 637: 635: 632: 630: 627: 625: 622: 620: 617: 615: 612: 610: 607: 605: 602: 600: 597: 595: 592: 590: 587: 585: 582: 580: 577: 575: 572: 570: 567: 565: 562: 560: 557: 555: 552: 550: 547: 545: 542: 541: 539: 537: 533: 529: 525: 518: 513: 511: 506: 504: 499: 498: 495: 483: 475: 474: 471: 465: 462: 460: 457: 455: 452: 450: 447: 445: 442: 441: 439: 435: 429: 426: 424: 421: 419: 416: 414: 411: 410: 408: 406:Miscellaneous 404: 398: 395: 393: 390: 388: 385: 383: 380: 378: 375: 374: 372: 368: 363: 352: 351: 347: 345: 344: 340: 338: 337: 333: 331: 330: 326: 324: 323: 319: 317: 316: 312: 310: 309: 305: 303: 302: 298: 296: 295: 291: 289: 288: 284: 282: 281: 277: 276: 274: 272:Written works 270: 266: 259: 254: 252: 247: 245: 240: 239: 236: 228: 227: 221: 216: 212: 208: 207: 201: 196: 192: 190: 187: 186: 182: 170: 168:9780486619125 164: 160: 159: 153: 152: 148: 140: 136: 135: 130: 125: 120: 114: 111: 107: 106:Coolidge 1945 102: 99: 92: 90: 87: 85: 81: 77: 73: 69: 65: 61: 57: 45: 37: 36:Ancient Greek 33: 32: 23: 19: 1858:expanding it 1847: 1801:expanding it 1790:mathematical 1787: 1772: 1754: 1741: 1583:Thomas Heath 1574: 1457: 1441:Law of sines 1297: 1229:Golden ratio 1094: 1087: 1078: 1072:(Theodosius) 1068: 1060: 1053: 1046: 1039: 1030: 1020: 1014:(Hipparchus) 1010: 1000: 993: 992: 985: 976: 966: 958: 953:(Apollonius) 949: 941: 929: 904:Zeno of Elea 664:Eratosthenes 654:Dionysodorus 353:(apocryphal) 348: 341: 334: 327: 321: 320: 313: 306: 299: 292: 285: 278: 224: 204: 172:. Retrieved 157: 138: 132: 113: 101: 88: 72:hyperboloids 56:propositions 30: 29: 28: 18: 1793:publication 1650:mathematics 1458:Arithmetica 1055:Ostomachion 1024:(Autolycus) 943:Arithmetica 719:Hippocrates 649:Dinostratus 634:Dicaearchus 564:Aristarchus 336:Ostomachion 68:paraboloids 1897:Categories 1702:Babylonian 1602:arithmetic 1568:History of 1397:Apollonius 1082:(Menelaus) 1041:On Spirals 960:Catoptrics 899:Xenocrates 894:Thymaridas 879:Theodosius 864:Theaetetus 844:Simplicius 834:Pythagoras 819:Posidonius 804:Philonides 764:Nicomachus 759:Metrodorus 749:Menaechmus 704:Hipparchus 694:Heliodorus 644:Diophantus 629:Democritus 609:Chrysippus 579:Archimedes 574:Apollonius 544:Anaxagoras 536:(timeline) 315:On Spirals 265:Archimedes 174:2018-12-16 149:References 44:Archimedes 1163:Inscribed 923:Treatises 914:Zenodorus 874:Theodorus 849:Sosigenes 794:Philolaus 779:Oenopides 774:Nicoteles 769:Nicomedes 729:Hypsicles 624:Ctesibius 614:Cleomedes 599:Callippus 584:Autolycus 569:Aristotle 549:Anthemius 93:Footnotes 76:spheroids 50:287 BC – 1727:Japanese 1712:Egyptian 1655:timeline 1643:timeline 1631:timeline 1626:geometry 1619:timeline 1614:calculus 1607:timeline 1595:timeline 1298:Elements 1144:Concepts 1106:Problems 1079:Spherics 1069:Spherics 1034:(Euclid) 980:(Euclid) 977:Elements 970:(Euclid) 931:Almagest 839:Serenus 814:Porphyry 754:Menelaus 709:Hippasus 684:Eutocius 659:Domninus 554:Archytas 482:Category 121:(1911). 1707:Chinese 1662:numbers 1590:algebra 1518:Related 1492:Centers 1288:Results 1158:Central 829:Ptolemy 824:Proclus 789:Perseus 744:Marinus 724:Hypatia 714:Hippias 689:Geminus 679:Eudoxus 669:Eudemus 639:Diocles 131:(ed.). 1918:225 BC 1722:Indian 1499:Cyrene 1031:Optics 950:Conics 869:Theano 859:Thales 854:Sporus 799:Philon 784:Pappus 674:Euclid 604:Carpus 594:Bryson 444:Euclid 165:  80:volume 74:, and 60:solids 1852:is a 1795:is a 1717:Incan 1638:logic 1414:Other 1182:Chord 1175:Axiom 1153:Angle 809:Plato 699:Heron 619:Conon 127:. In 1854:stub 1797:stub 1679:list 967:Data 739:Leon 589:Bion 163:ISBN 84:cone 1581:by 1295:In 1899:: 223:. 203:. 108::7 70:, 52:c. 48:c. 38:: 1885:e 1878:t 1871:v 1860:. 1828:e 1821:t 1814:v 1803:. 516:e 509:t 502:v 257:e 250:t 243:v 177:. 46:( 34:(

Index


Ancient Greek
Archimedes
propositions
solids
conic sections
paraboloids
hyperboloids
spheroids
volume
cone
Coolidge 1945
Heath, Thomas Little
"Archimedes" 
Chisholm, Hugh
Encyclopædia Britannica
A history of the conic sections and quadric surfaces
ISBN
9780486619125
ON CONOIDS AND SPHEROIDS - The Works of Archimedes
Chisholm, Hugh
"Conoid" 
Encyclopædia Britannica
Chisholm, Hugh
"Spheroid" 
Encyclopædia Britannica
v
t
e
Archimedes

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