| Refs | {'start': {'reference': '3.18', 'human_reference': 'Book 3 Section 18'}, 'end': {'reference': '3.22', 'human_reference': 'Book 3 Section 22'}} |
|---|---|
| Ancestors | [{'reference': '3'}] |
| Children | [] |
[*] [*]
| μετελθόντες | 1 | w | 11 |
| δὲ | 1 | w | 13 |
| ἑξῆς | 1 | w | 17 |
| διδάσκωμεν | 1 | w | 27 |
| ὅτι | 1 | w | 30 |
| ψευδεῖς | 1 | w | 37 |
| καὶ | 1 | w | 40 |
| ἀπιθάνους | 1 | w | 49 |
| αὐτῶν | 1 | w | 54 |
| συμβέβηκεν | 1 | w | 64 |
| εἶναι | 1 | w | 69 |
| τὰς | 1 | w | 72 |
| ἀρχὰς | 1 | w | 77 |
| τῆς | 1 | w | 80 |
| τέχνης | 1 | w | 86 |
| καὶ | 2 | w | 90 |
| δὴ | 1 | w | 92 |
| πολλῶν | 1 | w | 98 |
| 14 | 1 | w | 101 |
| M | 1 | w | 102 |
| VIII375 | 1 | w | 109 |
| 16 | 1 | w | 111 |
| M | 2 | w | 112 |
| VIII376 | 1 | w | 119 |
| 16 | 2 | w | 121 |
| M | 3 | w | 122 |
| VIII | 3 | w | 126 |
| 377 | 1 | w | 129 |
| in | 1 | w | 131 |
| marg | 1 | w | 135 |
| codd | 1 | w | 139 |
| haec | 1 | w | 144 |
| figura | 1 | w | 150 |
| πετόμενον | 1 | w | 161 |
| 17 | 1 | w | 163 |
| M | 4 | w | 164 |
| VIII | 4 | w | 168 |
| 378 | 1 | w | 171 |
| 8 | 2 | w | 172 |
| ἐξ | 1 | w | 174 |
| ὧν | 1 | w | 176 |
| G | 1 | w | 177 |
| sec | 1 | w | 181 |
| Herv | 1 | w | 186 |
| corr | 1 | w | 191 |
| Bekk | 1 | w | 196 |
| 10 | 1 | w | 199 |
| ἐξ | 2 | w | 201 |
| αὐτοῦ | 1 | w | 206 |
| τοῦ | 2 | w | 209 |
| π | 4 | w | 210 |
| LVr | 1 | w | 214 |
| ἐξ | 3 | w | 217 |
| αὐτοῦ | 2 | w | 222 |
| cett | 1 | w | 226 |
| 14 | 2 | w | 229 |
| πεπιστωμένων | 1 | w | 241 |
| dub | 1 | w | 244 |
| Bekk | 2 | w | 249 |
| Bury | 1 | w | 254 |
| 18 | 1 | w | 256 |
| Bekk | 3 | w | 262 |
| 25 | 1 | w | 265 |
| ἐπιδεδόσθω | 1 | w | 275 |
| VC | 1 | w | 277 |
| εἰς | 1 | w | 280 |
| τοῦτο | 1 | w | 285 |
| δυναμένων | 1 | w | 294 |
| λέγεσθαι | 1 | w | 302 |
| ὡς | 1 | w | 305 |
| ἐναρχόμενοι | 1 | w | 316 |
| τῆς | 2 | w | 319 |
| ὑφη- | 1 | w | 323 |
| γήσεως | 1 | w | 329 |
| εἴπομεν | 1 | w | 336 |
| τούτοις | 1 | w | 344 |
| προσαχθήσεται | 1 | w | 357 |
| τὰ | 2 | w | 359 |
| τῆς | 3 | w | 362 |
| ἀπορίας | 1 | w | 369 |
| ὧν | 2 | w | 371 |
| ἀναιρουμένων | 1 | w | 383 |
| καὶ | 3 | w | 386 |
| τὰ | 3 | w | 388 |
| λοιπὰ | 1 | w | 393 |
| συναναιρεθήσεται | 1 | w | 409 |
| ἐπεὶ | 1 | w | 414 |
| οὖν | 1 | w | 417 |
| τῶν | 2 | w | 420 |
| ἀρχῶν | 1 | w | 425 |
| διαβληθεισῶν | 1 | w | 437 |
| οὐδέ | 1 | w | 441 |
| αἱ | 1 | w | 443 |
| κατὰ | 1 | w | 447 |
| μέρος | 1 | w | 452 |
| ἀπο- | 1 | w | 456 |
| δείξεις | 1 | w | 463 |
| αὐτοῖς | 1 | w | 469 |
| δύνανται | 1 | w | 477 |
| προκόπτειν | 1 | w | 487 |
| λέγωμεν | 1 | w | 495 |
| τὰ | 5 | w | 497 |
| ἁρμό- | 1 | w | 502 |
| ζοντα | 1 | w | 507 |
| πρὸς | 1 | w | 511 |
| τὰς | 2 | w | 514 |
| ἀρχάς | 1 | w | 519 |
| Εὐθέως | 1 | w | 526 |
| τοίνυν | 1 | w | 532 |
| ὡς | 2 | w | 534 |
| πρῶτόν | 1 | w | 540 |
| τι | 2 | w | 542 |
| καὶ | 4 | w | 545 |
| στοιχειωδέστατον | 1 | w | 561 |
| δι- | 1 | w | 564 |
| δάσκουσιν | 1 | w | 573 |
| ἡμᾶς | 1 | w | 577 |
| ὅτι | 2 | w | 580 |
| σῶμα | 1 | w | 584 |
| μέν | 4 | w | 587 |
| ἐστι | 1 | w | 591 |
| τὸ | 1 | w | 593 |
| τὰς | 3 | w | 596 |
| τρεῖς | 1 | w | 601 |
| ἔχον | 1 | w | 605 |
| διαστάσεις | 1 | w | 615 |
| μῆκος | 1 | w | 621 |
| πλάτος | 1 | w | 627 |
| βάθος | 1 | w | 632 |
| ὧν | 3 | w | 635 |
| πρώτη | 1 | w | 640 |
| μὲν | 1 | w | 643 |
| διάστα- | 1 | w | 650 |
| σίς | 1 | w | 653 |
| ἐστιν | 1 | w | 658 |
| ἡ | 2 | w | 659 |
| κατὰ | 2 | w | 663 |
| μῆκος | 2 | w | 668 |
| ἄνωθεν | 1 | w | 674 |
| κάτω | 1 | w | 678 |
| δευτέρα | 1 | w | 686 |
| δὲ | 2 | w | 688 |
| ἡ | 3 | w | 689 |
| κατὰ | 3 | w | 693 |
| πλάτος | 2 | w | 699 |
| ἀπὸ | 1 | w | 702 |
| δεξιῶν | 1 | w | 708 |
| ἐπʼ | 1 | w | 711 |
| ἀριστερά | 1 | w | 719 |
| τρίτη | 1 | w | 725 |
| δὲ | 3 | w | 727 |
| ἡ | 4 | w | 728 |
| κατὰ | 4 | w | 732 |
| βάθος | 2 | w | 737 |
| ἀπὸ | 2 | w | 740 |
| τῶν | 3 | w | 743 |
| πρόσω | 1 | w | 748 |
| εἰς | 2 | w | 751 |
| τοὐπίσω | 1 | w | 758 |
| ὥστε | 1 | w | 763 |
| ὄν | 1 | w | 766 |
| των | 1 | w | 770 |
| τριῶν | 1 | w | 775 |
| τούτων | 1 | w | 781 |
| ἓξ | 1 | w | 783 |
| γίνεσθαι | 1 | w | 791 |
| παρατάσεις | 1 | w | 801 |
| δύο | 1 | w | 805 |
| καθʼ | 1 | w | 809 |
| ἑκάστην | 1 | w | 816 |
| τῆς | 4 | w | 820 |
| μὲν | 2 | w | 823 |
| πρώτης | 1 | w | 829 |
| τὴν | 1 | w | 832 |
| ἄνω | 2 | w | 835 |
| καὶ | 5 | w | 838 |
| κάτω | 2 | w | 842 |
| τῆς | 5 | w | 846 |
| δὲ | 4 | w | 848 |
| δευτέρας | 1 | w | 856 |
| τὴν | 2 | w | 859 |
| ἐν | 2 | w | 861 |
| ἀριστερᾷ | 1 | w | 869 |
| καὶ | 6 | w | 872 |
| ἐν | 3 | w | 874 |
| δεξιᾷ | 1 | w | 879 |
| τῆς | 6 | w | 883 |
| δὲ | 5 | w | 885 |
| τρίτης | 1 | w | 891 |
| τὴν | 3 | w | 894 |
| πρόσω | 2 | w | 899 |
| καὶ | 7 | w | 902 |
| ὀπίσω | 1 | w | 907 |
| Στιγμῆς | 1 | w | 915 |
| μὲν | 3 | w | 918 |
| γὰρ | 1 | w | 921 |
| ῥυείσης | 1 | w | 928 |
| γραμμὴν | 1 | w | 935 |
| γίνεσθαί | 1 | w | 943 |
| φασι | 1 | w | 947 |
| γραμ- | 1 | w | 953 |
| μῆς | 2 | w | 956 |
| δʼ | 1 | w | 958 |
| ἐπιφάνειαν | 1 | w | 968 |
| ἐπιφανείας | 1 | w | 979 |
| δὲ | 6 | w | 981 |
| στερεὸν | 1 | w | 988 |
| σῶμα | 2 | w | 992 |
| παρὸ | 1 | w | 997 |
| καὶ | 8 | w | 1000 |
| ὑπογράφοντες | 1 | w | 1012 |
| λέγουσι | 1 | w | 1019 |
| στιγμὴν | 1 | w | 1026 |
| μὲν | 4 | w | 1029 |
| εἶναι | 2 | w | 1034 |
| σημεῖον | 1 | w | 1041 |
| ἀμε- | 1 | w | 1045 |
| ρὲς | 1 | w | 1048 |
| καὶ | 9 | w | 1051 |
| ἀδιάστατον | 1 | w | 1061 |
| ἢ | 1 | w | 1062 |
| πέρας | 1 | w | 1067 |
| γραμμῆς | 1 | w | 1074 |
| γραμμὴν | 2 | w | 1082 |
| δέ | 3 | w | 1084 |
| μῆκος | 3 | w | 1089 |
| ἀπλατὲς | 1 | w | 1096 |
| ἢ | 2 | w | 1097 |
| πέρας | 2 | w | 1102 |
| ἐπιφανείας | 2 | w | 1112 |
| ἐπιφάνειαν | 2 | w | 1123 |
| δὲ | 7 | w | 1125 |
| πέρας | 3 | w | 1130 |
| σώ- | 1 | w | 1133 |
| ματος | 1 | w | 1138 |
| ἢ | 3 | w | 1139 |
| πλάτος | 3 | w | 1145 |
| ἀβαθές | 1 | w | 1151 |
| τάξει | 1 | w | 1157 |
| οὖν | 2 | w | 1160 |
| ἀναλαβόντες | 1 | w | 1171 |
| περὶ | 1 | w | 1175 |
| στιγ- | 1 | w | 1180 |
| μῆς | 4 | w | 1183 |
| λέγωμεν | 2 | w | 1190 |
| πρῶτον | 1 | w | 1196 |
| εἶτα | 1 | w | 1201 |
| περὶ | 2 | w | 1205 |
| γραμμῆς | 2 | w | 1212 |
| τὸ | 2 | w | 1215 |
| δὲ | 8 | w | 1217 |
| μετὰ | 1 | w | 1221 |
| τοῦτο | 2 | w | 1226 |
| περὶ | 3 | w | 1230 |
| ἐπιφανείας | 3 | w | 1240 |
| καὶ | 10 | w | 1243 |
| σώματος | 1 | w | 1250 |
| τούτων | 2 | w | 1257 |
| γὰρ | 2 | w | 1260 |
| ἀναι- | 1 | w | 1265 |
| ρουμένων | 2 | w | 1273 |
| οὐδʼ | 1 | w | 1277 |
| ἡ | 5 | w | 1278 |
| γεωμετρία | 1 | w | 1287 |
| γενήσεται | 1 | w | 1296 |
| τέχνη | 2 | w | 1301 |
| μὴ | 4 | w | 1304 |
| ἔχουσα | 1 | w | 1310 |
| τὰ | 12 | w | 1312 |
| ἐφʼ | 1 | w | 1315 |
| οἷς | 1 | w | 1318 |
| ἡ | 6 | w | 1319 |
| σύστασις | 1 | w | 1327 |
| αὐτῆς | 1 | w | 1332 |
| δοκεῖ | 1 | w | 1337 |
| προκόπτειν | 2 | w | 1347 |
| Ἡ | 1 | w | 1349 |
| τοίνυν | 2 | w | 1355 |
| στιγμή | 1 | w | 1361 |
| ἥν | 1 | w | 1364 |
| φασι | 2 | w | 1368 |
| σημεῖον | 2 | w | 1375 |
| ἀδιάστατον | 2 | w | 1385 |
| ὑπ- | 1 | w | 1388 |
| άρχειν | 1 | w | 1394 |
| ἤτοι | 1 | w | 1399 |
| σῶμα | 3 | w | 1403 |
| νοεῖται | 1 | w | 1410 |
| ἢ | 4 | w | 1411 |
| ἀσώματον | 1 | w | 1419 |
| καὶ | 11 | w | 1423 |
| σῶμα | 4 | w | 1427 |
| μέν | 6 | w | 1430 |
| 18 | 2 | w | 1433 |
| ἐναρχόμενοι | 2 | w | 1444 |
| τῆς | 8 | w | 1447 |
| ὑφηγ | 1 | w | 1451 |
| εἴπ | 2 | w | 1455 |
| argumentum | 1 | w | 1466 |
| libri | 1 | w | 1471 |
| confusum | 1 | w | 1479 |
| esse | 1 | w | 1483 |
| et | 2 | w | 1485 |
| hic | 1 | w | 1488 |
| locum | 1 | w | 1493 |
| 10 | 2 | w | 1495 |
| 23 | 1 | w | 1498 |
| commemorari | 1 | w | 1509 |
| ostendit | 1 | w | 1517 |
| Heintz | 1 | w | 1523 |
| p | 1 | w | 1524 |
| 270 | 1 | w | 1528 |
| 19 | 1 | w | 1530 |
| M | 5 | w | 1531 |
| IX | 1 | w | 1533 |
| 367 | 1 | w | 1536 |
| σῶμα | 5 | w | 1540 |
| μέν | 7 | w | 1543 |
| ἐστι | 3 | w | 1547 |
| Eucl | 1 | w | 1551 |
| el | 1 | w | 1554 |
| XI | 1 | w | 1557 |
| def | 1 | w | 1560 |
| 1 | 11 | w | 1562 |
| στιγμῆς | 1 | w | 1569 |
| ῥυείσης | 2 | w | 1576 |
| cf | 1 | w | 1578 |
| schol | 1 | w | 1584 |
| in | 3 | w | 1587 |
| Euclid | 1 | w | 1593 |
| el | 2 | w | 1596 |
| I | 15 | w | 1598 |
| p | 2 | w | 1599 |
| 78 | 2 | w | 1602 |
| 15 | 1 | w | 1605 |
| vol | 1 | w | 1608 |
| 5 | 4 | w | 1610 |
| Heiberg | 1 | w | 1617 |
| 20 | 1 | w | 1619 |
| πέρας | 4 | w | 1624 |
| σώμ | 3 | w | 1627 |
| Eucl | 3 | w | 1632 |
| el | 3 | w | 1635 |
| XI | 2 | w | 1638 |
| def | 2 | w | 1641 |
| 2 | 5 | w | 1643 |
| I | 17 | w | 1645 |
| def | 3 | w | 1648 |
| 2 | 6 | w | 1650 |
| 3 | 7 | w | 1652 |
| 22 | 1 | w | 1654 |
| M | 6 | w | 1655 |
| IX | 2 | w | 1657 |
| 377-378 | 1 | w | 1664 |
| φασι | 3 | w | 1668 |
| schol | 2 | w | 1673 |
| in | 4 | w | 1676 |
| Eucl | 4 | w | 1680 |
| el | 4 | w | 1683 |
| l | 14 | w | 1685 |
| p | 3 | w | 1686 |
| 75 | 2 | w | 1689 |
| 23 | 2 | w | 1692 |
| Heiberg | 2 | w | 1699 |
| vol | 2 | w | 1702 |
| 5 | 6 | w | 1704 |
| 7 | 14 | w | 1705 |
| στοχειωδέστατον | 1 | w | 1720 |
| ζ | 2 | w | 1721 |
| edd | 1 | w | 1724 |
| 12 | 1 | w | 1727 |
| τῶν | 4 | w | 1730 |
| τριῶν | 2 | w | 1735 |
| G | 2 | w | 1736 |
| ex | 1 | w | 1739 |
| his | 1 | w | 1742 |
| Herv | 2 | w | 1746 |
| Harder | 1 | w | 1756 |
| 13 | 1 | w | 1758 |
| διαστάσεις | 2 | w | 1768 |
| G | 3 | w | 1769 |
| corr | 2 | w | 1774 |
| Bekk | 4 | w | 1779 |
| cl | 5 | w | 1782 |
| p | 4 | w | 1784 |
| 463 | 1 | w | 1788 |
| 6 | 6 | w | 1790 |
| p | 5 | w | 1792 |
| II | 9 | w | 1795 |
| 288 | 1 | w | 1798 |
| Mutschmann | 1 | w | 1808 |
| ubi | 1 | w | 1813 |
| coniectura | 1 | w | 1823 |
| codice | 1 | w | 1829 |
| N | 1 | w | 1830 |
| affirmatur | 1 | w | 1840 |
| 15 | 2 | w | 1842 |
| lacunosa | 1 | w | 1850 |
| argumentorum | 1 | w | 1863 |
| series | 1 | w | 1869 |
| iis | 1 | w | 1872 |
| quae | 1 | w | 1877 |
| leguntur | 1 | w | 1885 |
| M | 8 | w | 1886 |
| IX | 3 | w | 1888 |
| 368 | 1 | w | 1891 |
| 276 | 1 | w | 1895 |
| supple- | 1 | w | 1903 |
| tur | 4 | w | 1906 |
| 18 | 3 | w | 1908 |
| μέν | 8 | w | 1911 |
| om | 2 | w | 1913 |
| V | 7 | w | 1915 |
| C | 2 | w | 1916 |
| οὐκ | 1 | w | 1919 |
| ἂν | 1 | w | 1921 |
| εἴη | 1 | w | 1924 |
| κατ | 5 | w | 1927 |
| αὐτούς | 1 | w | 1934 |
| τὰ | 13 | w | 1937 |
| γὰρ | 3 | w | 1940 |
| μὴ | 5 | w | 1942 |
| ἔχοντα | 1 | w | 1948 |
| διάστασιν | 1 | w | 1957 |
| οὐε | 1 | w | 1960 |
| ἦν | 1 | w | 1962 |
| σώματα | 1 | w | 1968 |
| λείπεται | 1 | w | 1977 |
| οὖν | 3 | w | 1980 |
| ἀσώματον | 2 | w | 1988 |
| αὐτὴν | 1 | w | 1993 |
| ὑπάρχειν | 1 | w | 2001 |
| ὃ | 1 | w | 2003 |
| πάλιν | 1 | w | 2008 |
| ἐστὶν | 1 | w | 2013 |
| ἀπίθανον | 1 | w | 2021 |
| τὸ | 3 | w | 2024 |
| μέν | 9 | w | 2027 |
| γὰρ | 4 | w | 2030 |
| ἀσώματον | 3 | w | 2038 |
| οὐδενὸς | 1 | w | 2045 |
| νοεῖται | 2 | w | 2052 |
| γεννητικὸν | 1 | w | 2062 |
| ὡσανεὶ | 1 | w | 2068 |
| ἀθιγὲς | 1 | w | 2074 |
| καθεστώς | 1 | w | 2082 |
| ἡ | 7 | w | 2084 |
| δὲ | 9 | w | 2086 |
| στιγμὴ | 2 | w | 2092 |
| νοεῖται | 3 | w | 2099 |
| τῆς | 9 | w | 2102 |
| γραμμῆς | 3 | w | 2109 |
| γεννητική | 1 | w | 2118 |
| οὐ | 7 | w | 2121 |
| τοίνυν | 3 | w | 2127 |
| ἐστὶ | 2 | w | 2131 |
| σημεῖον | 3 | w | 2138 |
| ἀδιάστατον | 3 | w | 2148 |
| ἡ | 8 | w | 2149 |
| στιγμή | 2 | w | 2155 |