| Refs | {'start': {'reference': '86', 'human_reference': 'Paragraph 86'}, 'end': {'reference': '90', 'human_reference': 'Paragraph 90'}} |
|---|---|
| Ancestors | [] |
| Children | [] |
| Ἡμισφαίριον | 1 | w | 11 |
| μετρῆσαι | 1 | w | 19 |
| οὗ | 1 | w | 21 |
| ἡ | 1 | w | 22 |
| διάμετρος | 1 | w | 31 |
| ιγ | 1 | w | 33 |
| εὑρεῖν | 1 | w | 40 |
| αὐτοῦ | 1 | w | 45 |
| τὸ | 1 | w | 47 |
| στερεόν | 1 | w | 54 |
| ποίει | 1 | w | 60 |
| οὕτως | 1 | w | 65 |
| τὰ | 1 | w | 68 |
| ιγ | 2 | w | 70 |
| κύβισον | 1 | w | 77 |
| γίνονται | 1 | w | 86 |
| βρ | 1 | w | 88 |
| ζ | 1 | w | 91 |
| ταῦτα | 1 | w | 97 |
| ἐνδεκάκις | 1 | w | 106 |
| γίνονται | 2 | w | 115 |
| β | 3 | w | 116 |
| δρξζ | 1 | w | 121 |
| τοῦ | 2 | w | 125 |
| αὐτοῦ | 2 | w | 130 |
| μβʹ | 1 | w | 133 |
| γίνονται | 3 | w | 142 |
| φοε | 1 | w | 145 |
| δ | 4 | w | 146 |
| η | 1 | w | 147 |
| τοσοῦτον | 1 | w | 156 |
| τὸ | 2 | w | 158 |
| στερεόν | 2 | w | 165 |
| Εύρεῖν | 1 | w | 172 |
| αὐτοῦ | 3 | w | 177 |
| καὶ | 1 | w | 180 |
| τὴν | 1 | w | 183 |
| ἐπιφάνειαν | 1 | w | 193 |
| τὰ | 2 | w | 196 |
| ιγ | 3 | w | 198 |
| ἐφʼἑαυτά | 1 | w | 206 |
| 1 | 1 | w | 207 |
| ὧν | 1 | w | 209 |
| γʹ | 1 | w | 211 |
| delevi | 1 | w | 217 |
| sed | 1 | w | 221 |
| nondum | 1 | w | 227 |
| locus | 1 | w | 232 |
| sanatus | 1 | w | 239 |
| est | 1 | w | 242 |
| 4 | 1 | w | 244 |
| τῶν | 1 | w | 249 |
| delevi | 2 | w | 255 |
| et | 1 | w | 257 |
| lacunam | 1 | w | 264 |
| statui | 1 | w | 270 |
| 5 | 1 | w | 272 |
| ταῦτα | 2 | w | 277 |
| nempe | 1 | w | 283 |
| τὰ | 3 | w | 285 |
| ζ | 3 | w | 286 |
| diametri | 1 | w | 294 |
| 17 | 1 | w | 297 |
| αρν | 1 | w | 300 |
| U | 1 | w | 301 |
| 2220 | 1 | w | 305 |
| δʹ | 1 | w | 307 |
| αρλ | 1 | w | 311 |
| A | 1 | w | 312 |
| 26 | 1 | w | 315 |
| φοε | 2 | w | 318 |
| δ | 6 | w | 319 |
| η | 2 | w | 320 |
| Neglecta | 1 | w | 329 |
| videntur | 1 | w | 337 |
| πδ | 1 | w | 339 |
| τλϛ | 1 | w | 342 |
| 27 | 1 | w | 345 |
| Lacunam | 1 | w | 352 |
| indicavi | 1 | w | 360 |
| Μεῖζον | 1 | w | 367 |
| τμῆμα | 1 | w | 372 |
| ἡμισφαιρίου | 1 | w | 383 |
| οὗ | 2 | w | 385 |
| ἡ | 3 | w | 386 |
| βάσις | 1 | w | 391 |
| ιβ | 1 | w | 393 |
| ἡ | 4 | w | 395 |
| δὲ | 1 | w | 397 |
| κάθετος | 1 | w | 404 |
| θ | 2 | w | 405 |
| εὑρεῖν | 2 | w | 412 |
| αὐτοῦ | 4 | w | 417 |
| τὸ | 3 | w | 419 |
| στερεόν | 3 | w | 426 |
| λαμβάνω | 1 | w | 434 |
| τὸ | 4 | w | 436 |
| ἥμισυ | 1 | w | 441 |
| τῆς | 1 | w | 444 |
| βάσεως | 1 | w | 450 |
| ἐφʼ | 2 | w | 454 |
| ἑαυτά | 2 | w | 459 |
| γίνονται | 4 | w | 468 |
| λϛ | 2 | w | 470 |
| ταῦτα | 3 | w | 476 |
| τρισσάκις | 1 | w | 485 |
| γίνονται | 5 | w | 494 |
| ρη | 1 | w | 496 |
| καὶ | 2 | w | 500 |
| τὴν | 2 | w | 503 |
| κάθετον | 1 | w | 510 |
| ἐφʼ | 3 | w | 513 |
| ἑαυτήν | 1 | w | 519 |
| γίνονται | 6 | w | 528 |
| κα | 3 | w | 530 |
| σύνθες | 1 | w | 537 |
| ὁμοῦ | 1 | w | 541 |
| γίνονται | 7 | w | 550 |
| ρπθ | 1 | w | 553 |
| ταῦτα | 4 | w | 559 |
| ἐπὶ | 1 | w | 562 |
| κάθετον | 2 | w | 569 |
| ἐπὶ | 2 | w | 573 |
| τὰ | 4 | w | 575 |
| θ | 7 | w | 576 |
| γίνονται | 8 | w | 585 |
| αψα | 1 | w | 588 |
| ταῦτα | 5 | w | 594 |
| ἑνδεκάκις | 1 | w | 603 |
| γίνονται | 9 | w | 612 |
| α | 40 | w | 613 |
| ηψια | 1 | w | 618 |
| τούτωον | 1 | w | 626 |
| τὸ | 5 | w | 628 |
| κα | 4 | w | 630 |
| γίνονται | 10 | w | 639 |
| ω | 5 | w | 640 |
| α | 44 | w | 643 |
| τοσοῦτον | 2 | w | 652 |
| ἔσται | 1 | w | 657 |
| τὸ | 6 | w | 659 |
| στερεόν | 4 | w | 666 |
| Εὑρεῖν | 1 | w | 673 |
| αὐτοῦ | 5 | w | 678 |
| καὶ | 3 | w | 681 |
| τὴν | 3 | w | 684 |
| ἐπιφάνειαν | 2 | w | 694 |
| τῆς | 2 | w | 698 |
| βάσεως | 2 | w | 704 |
| τὸ | 7 | w | 706 |
| ἥμισυ | 2 | w | 711 |
| ἐφʼ | 4 | w | 714 |
| ἑαυτό | 1 | w | 719 |
| γίνονται | 11 | w | 728 |
| λϚ | 1 | w | 730 |
| καὶ | 4 | w | 734 |
| τὴν | 4 | w | 737 |
| κάθετον | 3 | w | 744 |
| ἐφʼ | 5 | w | 748 |
| ἑαυτά | 3 | w | 753 |
| γίνονται | 12 | w | 762 |
| πα | 1 | w | 764 |
| ὁμοῦ | 2 | w | 769 |
| γίνονται | 13 | w | 777 |
| ριζ | 1 | w | 780 |
| ταῦτα | 6 | w | 786 |
| τετράκις | 1 | w | 794 |
| γίνονται | 14 | w | 803 |
| υξη | 1 | w | 806 |
| ταῦτα | 7 | w | 812 |
| ἑνδεκάκις | 2 | w | 821 |
| γίνονται | 15 | w | 830 |
| ερμη | 1 | w | 834 |
| τούτων | 1 | w | 841 |
| τὸ | 8 | w | 843 |
| ιδʹ | 1 | w | 846 |
| τξζ | 1 | w | 850 |
| U | 2 | w | 851 |
| 2220 | 2 | w | 855 |
| τοσοῦτον | 3 | w | 864 |
| ἡ | 5 | w | 865 |
| ἐπιφάνεια | 3 | w | 874 |
| τοῦ | 7 | w | 877 |
| μείζονος | 1 | w | 885 |
| τμήματος | 1 | w | 893 |
| τοῦ | 8 | w | 896 |
| ἡμισφαιρίου | 2 | w | 907 |
| Σφαίρας | 1 | w | 915 |
| ἔσται | 2 | w | 920 |
| ἡ | 7 | w | 921 |
| διάμετρος | 2 | w | 930 |
| δ | 13 | w | 931 |
| εὑρεῖν | 3 | w | 938 |
| αὐτῆς | 1 | w | 943 |
| τὸ | 9 | w | 945 |
| στερεὸν | 1 | w | 952 |
| ἀπὸ | 1 | w | 955 |
| τοῦ | 9 | w | 958 |
| κυλίνδρου | 1 | w | 967 |
| ποιῶ | 1 | w | 972 |
| οὕτως | 2 | w | 977 |
| ἐν | 2 | w | 980 |
| τῇ | 1 | w | 982 |
| βάσει | 1 | w | 987 |
| μέτρει | 1 | w | 993 |
| κύκλον | 1 | w | 999 |
| ἀπὸ | 2 | w | 1002 |
| τῆς | 4 | w | 1005 |
| διαμέτρου | 1 | w | 1014 |
| τὸ | 10 | w | 1017 |
| ἐμβαδὸν | 1 | w | 1024 |
| εὑρήσομεν | 1 | w | 1033 |
| οὕτως | 3 | w | 1038 |
| ποιοῦμεν | 1 | w | 1047 |
| τὴν | 5 | w | 1050 |
| διάμετρον | 1 | w | 1059 |
| τὰ | 5 | w | 1062 |
| δ | 18 | w | 1063 |
| ἐφʼ | 6 | w | 1067 |
| ἑαυτά | 4 | w | 1072 |
| γίνονται | 16 | w | 1081 |
| ιϚ | 1 | w | 1083 |
| ταῦτα | 8 | w | 1088 |
| ἑνδεκάκις | 3 | w | 1097 |
| γίνονται | 17 | w | 1106 |
| ρο | 6 | w | 1108 |
| τούτων | 2 | w | 1114 |
| τὸ | 11 | w | 1116 |
| ιδʹ | 2 | w | 1119 |
| γίνονται | 18 | w | 1128 |
| ιβ | 2 | w | 1130 |
| U | 3 | w | 1131 |
| 2220 | 3 | w | 1135 |
| ιδ | 3 | w | 1137 |
| τοσοῦτον | 4 | w | 1146 |
| τὸ | 12 | w | 1148 |
| ἐμβαδόν | 1 | w | 1155 |
| ταῦτα | 9 | w | 1161 |
| ποίει | 2 | w | 1166 |
| ἐπὶ | 3 | w | 1169 |
| τὴν | 6 | w | 1172 |
| διάμετρον | 2 | w | 1181 |
| ἐπὶ | 4 | w | 1185 |
| τὰ | 6 | w | 1187 |
| δ | 24 | w | 1188 |
| τὰ | 7 | w | 1191 |
| γὰρ | 1 | w | 1194 |
| ἐστὶ | 1 | w | 1198 |
| τὸ | 13 | w | 1200 |
| ὕψος | 1 | w | 1204 |
| τοῦ | 10 | w | 1207 |
| περιλαμβάνοντος | 1 | w | 1222 |
| κυλίνδρου | 2 | w | 1231 |
| τὴν | 7 | w | 1234 |
| σφαῖραν | 1 | w | 1241 |
| δύο | 1 | w | 1245 |
| ὄντων | 1 | w | 1250 |
| διαμέτρων | 1 | w | 1259 |
| τῆς | 5 | w | 1262 |
| σφαίρας | 1 | w | 1269 |
| καὶ | 5 | w | 1272 |
| τοῦ | 11 | w | 1275 |
| κυλίνδρου | 3 | w | 1284 |
| ἐποίησα | 1 | w | 1292 |
| οὖν | 1 | w | 1295 |
| τὰ | 8 | w | 1297 |
| δ | 29 | w | 1298 |
| ἐπὶ | 5 | w | 1301 |
| τὸ | 14 | w | 1303 |
| ἐμβαδόν | 2 | w | 1310 |
| ἐπὶ | 6 | w | 1314 |
| τὰ | 9 | w | 1316 |
| ιβ | 3 | w | 1318 |
| U | 4 | w | 1319 |
| 2220 | 4 | w | 1323 |
| ιδʹ | 3 | w | 1326 |
| γίνονται | 19 | w | 1335 |
| ν | 104 | w | 1336 |
| καὶ | 6 | w | 1339 |
| δύο | 2 | w | 1342 |
| ἕβδομα | 1 | w | 1348 |
| τοσοῦτον | 5 | w | 1357 |
| ὁ | 3 | w | 1358 |
| 48 | 1 | w | 1360 |
| Cf | 1 | w | 1362 |
| Mens | 1 | w | 1367 |
| 47 | 1 | w | 1370 |
| unde | 1 | w | 1374 |
| initium | 1 | w | 1381 |
| supplevi | 1 | w | 1389 |
| 50 | 1 | w | 1393 |
| Cf | 2 | w | 1396 |
| Ster | 1 | w | 1401 |
| l | 7 | w | 1403 |
| 9 | 1 | w | 1405 |
| 4 | 4 | w | 1407 |
| ρη | 2 | w | 1409 |
| om | 1 | w | 1411 |
| A | 2 | w | 1413 |
| 7 | 4 | w | 1415 |
| A | 3 | w | 1416 |
| 13 | 1 | w | 1419 |
| τξζ | 2 | w | 1422 |
| U | 5 | w | 1423 |
| 2220 | 5 | w | 1427 |
| Addendum | 1 | w | 1436 |
| erat | 1 | w | 1440 |
| ζ | 9 | w | 1441 |
| κη | 1 | w | 1443 |
| 16 | 1 | w | 1446 |
| ἀπὸ | 3 | w | 1449 |
| addidi | 1 | w | 1455 |
| 17 | 2 | w | 1458 |
| μέτρει | 2 | w | 1464 |
| scripsi | 1 | w | 1471 |
| μείζονα | 1 | w | 1479 |
| A | 5 | w | 1480 |
| τῆς | 6 | w | 1484 |
| διαμέτρου | 2 | w | 1493 |
| scripsi | 2 | w | 1500 |
| τοῦ | 12 | w | 1504 |
| ἐμβαδοῦ | 1 | w | 1511 |
| A | 6 | w | 1512 |
| 21 | 1 | w | 1515 |
| τὰ | 10 | w | 1517 |
| δ | 36 | w | 1518 |
| τὰ | 11 | w | 1521 |
| ιδ | 5 | w | 1523 |
| A | 7 | w | 1524 |
| 23 | 1 | w | 1527 |
| καὶ | 7 | w | 1530 |
| addidi | 2 | w | 1536 |
| 25 | 1 | w | 1539 |
| ἕβδομον | 1 | w | 1546 |
| A | 8 | w | 1547 |
| κύλινδρος | 1 | w | 1557 |
| ὅσον | 1 | w | 1562 |
| ἡ | 8 | w | 1563 |
| ἐπιφάνεια | 4 | w | 1572 |
| τῆς | 7 | w | 1575 |
| σφαίρας | 2 | w | 1582 |
| δέδειχε | 1 | w | 1590 |
| δὲ | 2 | w | 1592 |
| Ἀρχιμήδης | 1 | w | 1601 |
| ὅτι | 1 | w | 1604 |
| κύλινδρος | 2 | w | 1613 |
| ὁ | 4 | w | 1614 |
| περιλαμβάνων | 1 | w | 1626 |
| τὴν | 8 | w | 1629 |
| σφαῖραν | 2 | w | 1636 |
| ἡμιόλιός | 1 | w | 1644 |
| ἐστι | 1 | w | 1648 |
| τῆς | 8 | w | 1651 |
| σφαίρας | 3 | w | 1658 |
| εἰ | 1 | w | 1661 |
| οὖν | 2 | w | 1664 |
| U | 6 | w | 1665 |
| 2220 | 6 | w | 1669 |
| πρόσθεμα | 1 | w | 1677 |
| γʹ | 2 | w | 1680 |
| ἀφαίρεμα | 1 | w | 1688 |
| ἀφαιρῶ | 1 | w | 1695 |
| οὖν | 3 | w | 1698 |
| τοῦ | 13 | w | 1701 |
| κυλίνδρου | 4 | w | 1710 |
| ὅ | 3 | w | 1712 |
| ἐστιν | 1 | w | 1717 |
| ἐπιφάνεια | 5 | w | 1726 |
| τῆς | 9 | w | 1729 |
| σφαίρας | 4 | w | 1736 |
| τῶν | 2 | w | 1740 |
| καὶ | 8 | w | 1743 |
| β | 21 | w | 1744 |
| ἑβδόμων | 1 | w | 1751 |
| τὸ | 15 | w | 1753 |
| γʹ | 3 | w | 1755 |
| καταλείπεται | 1 | w | 1768 |
| λγ | 1 | w | 1770 |
| γ | 28 | w | 1771 |
| ζ | 11 | w | 1772 |
| κα | 12 | w | 1774 |
| τοσοῦτον | 6 | w | 1783 |
| τὸ | 16 | w | 1785 |
| στερεὸν | 2 | w | 1792 |
| τῆς | 10 | w | 1795 |
| σφαίρας | 5 | w | 1802 |
| ἐὰν | 1 | w | 1806 |
| δὲ | 3 | w | 1808 |
| τὸ | 17 | w | 1810 |
| λάβωμεν | 1 | w | 1819 |
| τῶν | 3 | w | 1822 |
| ν | 128 | w | 1823 |
| καὶ | 9 | w | 1826 |
| δύο | 3 | w | 1829 |
| ἑβδόμων | 2 | w | 1836 |
| γίνονται | 20 | w | 1845 |
| ὁμοίως | 1 | w | 1851 |
| λγ | 2 | w | 1853 |
| γʹ | 4 | w | 1855 |
| ζʹ | 1 | w | 1857 |
| κα | 14 | w | 1859 |
| ἔσται | 3 | w | 1865 |
| ἄρα | 1 | w | 1868 |
| ἡ | 10 | w | 1869 |
| μὲν | 1 | w | 1872 |
| ἐπιφάνεια | 6 | w | 1881 |
| τῆς | 11 | w | 1884 |
| σφαίρας | 6 | w | 1891 |
| ν | 134 | w | 1892 |
| καὶ | 10 | w | 1895 |
| δύο | 4 | w | 1898 |
| ἑβδόμων | 3 | w | 1905 |
| τὸ | 18 | w | 1908 |
| δὲ | 4 | w | 1910 |
| στερεὸν | 3 | w | 1917 |
| λγ | 3 | w | 1919 |
| γ | 33 | w | 1920 |
| ζ | 13 | w | 1921 |
| κα | 16 | w | 1923 |