| Refs | {'start': {'reference': '3.63', 'human_reference': 'Book 3 Section 63'}, 'end': {'reference': '3.67', 'human_reference': 'Book 3 Section 67'}} |
|---|---|
| Ancestors | [{'reference': '3'}] |
| Children | [] |
| οὐ | 1 | w | 2 |
| μὴν | 1 | w | 5 |
| ἀλλʼ | 1 | w | 9 |
| εἴπερ | 1 | w | 14 |
| αἱ | 1 | w | 16 |
| δύο | 1 | w | 19 |
| γραμμαὶ | 1 | w | 26 |
| μία | 1 | w | 29 |
| γίνονται | 1 | w | 37 |
| δεήσει | 1 | w | 44 |
| τὰ | 1 | w | 46 |
| παρατιθέμενα | 1 | w | 58 |
| ἀλλή- | 1 | w | 63 |
| λοις | 1 | w | 67 |
| σώματα | 1 | w | 73 |
| ἑνὶ | 1 | w | 76 |
| ἄκρῳ | 1 | w | 80 |
| ἐλάσσω | 1 | w | 86 |
| εἶναι | 1 | w | 91 |
| γεγόνασι | 1 | w | 100 |
| γὰρ | 1 | w | 103 |
| αἱ | 2 | w | 105 |
| δύο | 2 | w | 108 |
| μία | 2 | w | 111 |
| ἥτις | 1 | w | 116 |
| ἓν | 1 | w | 118 |
| ἔχειν | 1 | w | 123 |
| ὀφείλει | 1 | w | 130 |
| πέρας | 1 | w | 135 |
| τε | 1 | w | 137 |
| καὶ | 1 | w | 140 |
| ἄκρον | 1 | w | 145 |
| οὐχὶ | 1 | w | 150 |
| δέ | 1 | w | 152 |
| γε | 2 | w | 154 |
| τὰ | 2 | w | 156 |
| παρατιθέμενα | 2 | w | 168 |
| ἀλλήλοις | 1 | w | 176 |
| σώματα | 2 | w | 182 |
| ἑνὶ | 2 | w | 185 |
| ἄκρῳ | 2 | w | 189 |
| γίνεται | 1 | w | 196 |
| ἐλάσ- | 1 | w | 201 |
| σονα | 1 | w | 205 |
| ὥστε | 1 | w | 210 |
| αἱ | 3 | w | 212 |
| δύο | 3 | w | 215 |
| γραμμαὶ | 2 | w | 222 |
| οὐκ | 1 | w | 225 |
| ἂν | 1 | w | 227 |
| γένοιντο | 1 | w | 235 |
| μία | 3 | w | 238 |
| γραμμή | 1 | w | 244 |
| εἰ | 1 | w | 247 |
| δὲ | 1 | w | 249 |
| παράλληλοι | 1 | w | 259 |
| γίνονται | 2 | w | 267 |
| δύο | 4 | w | 270 |
| γραμμαὶ | 3 | w | 277 |
| κατὰ | 1 | w | 281 |
| παράθε- | 1 | w | 288 |
| σιν | 1 | w | 291 |
| δυοῖν | 1 | w | 296 |
| σωμάτων | 1 | w | 303 |
| τὸ | 1 | w | 306 |
| ἐκ | 1 | w | 308 |
| τῶν | 1 | w | 311 |
| δυοῖν | 2 | w | 316 |
| γραμμῶν | 1 | w | 323 |
| μεῖζον | 1 | w | 329 |
| ἔσται | 1 | w | 334 |
| τῆς | 1 | w | 337 |
| μιᾶς | 1 | w | 341 |
| γραμμῆς | 1 | w | 348 |
| εἰ | 2 | w | 351 |
| δὲ | 2 | w | 353 |
| τὸ | 2 | w | 355 |
| ἐκ | 2 | w | 357 |
| τῶν | 2 | w | 360 |
| δυοῖν | 3 | w | 365 |
| γινόμενον | 1 | w | 374 |
| γραμ- | 1 | w | 379 |
| μῶν | 2 | w | 382 |
| μεῖζόν | 1 | w | 388 |
| ἐστι | 1 | w | 392 |
| τῆς | 2 | w | 395 |
| μιᾶς | 2 | w | 399 |
| γραμμῆς | 2 | w | 406 |
| ἔχοι | 1 | w | 411 |
| ἂν | 2 | w | 413 |
| ἑκατέρα | 1 | w | 420 |
| αὐτῶν | 1 | w | 425 |
| πλάτος | 1 | w | 431 |
| ὃ | 1 | w | 433 |
| μεθʼ | 1 | w | 437 |
| ἑτέρας | 1 | w | 443 |
| μείζονα | 1 | w | 450 |
| ποιεῖ | 1 | w | 455 |
| τὴν | 1 | w | 458 |
| διάστασιν | 1 | w | 467 |
| καὶ | 2 | w | 471 |
| οὕτως | 1 | w | 476 |
| οὐκ | 2 | w | 479 |
| ἔστιν | 1 | w | 484 |
| ἀπλατὲς | 1 | w | 491 |
| μῆκος | 1 | w | 496 |
| ἡ | 1 | w | 497 |
| γραμμή | 2 | w | 503 |
| δυοῖν | 4 | w | 509 |
| 62 | 1 | w | 512 |
| M | 1 | w | 513 |
| IX | 1 | w | 515 |
| 416 | 1 | w | 518 |
| 63 | 1 | w | 520 |
| M | 2 | w | 521 |
| IX | 2 | w | 523 |
| 416 | 2 | w | 526 |
| 64 | 1 | w | 528 |
| M | 3 | w | 529 |
| IX | 3 | w | 531 |
| 417 | 1 | w | 534 |
| 2 | 2 | w | 535 |
| τῶν | 4 | w | 538 |
| μὲν | 1 | w | 541 |
| ci | 1 | w | 543 |
| Bekk | 1 | w | 548 |
| τῶν | 5 | w | 553 |
| δὲ | 3 | w | 555 |
| G | 1 | w | 556 |
| 3 | 2 | w | 557 |
| 4 | 5 | w | 559 |
| 6 | 6 | w | 561 |
| δυεῖν | 1 | w | 567 |
| EL | 1 | w | 569 |
| 9 | 1 | w | 570 |
| γενέσθαι | 1 | w | 578 |
| VC | 1 | w | 580 |
| 13 | 1 | w | 582 |
| εἰ | 3 | w | 584 |
| om | 1 | w | 586 |
| VC | 2 | w | 589 |
| 20 | 1 | w | 591 |
| Harder | 1 | w | 599 |
| ἐφαίνοντο | 1 | w | 608 |
| G | 2 | w | 609 |
| corr | 1 | w | 614 |
| dubitans | 1 | w | 623 |
| Bekk | 2 | w | 627 |
| Bury | 1 | w | 632 |
| 28 | 1 | w | 634 |
| 29 | 1 | w | 637 |
| 32 | 1 | w | 640 |
| δυεῖν | 2 | w | 645 |
| EL | 2 | w | 647 |
| 29 | 2 | w | 649 |
| εἰ | 4 | w | 651 |
| 30 | 1 | w | 654 |
| γραμμῆς | 3 | w | 661 |
| om | 2 | w | 663 |
| ζ | 4 | w | 665 |
| οὖν | 1 | w | 668 |
| θάτερον | 1 | w | 675 |
| ἢ | 1 | w | 677 |
| ἀναιρεῖν | 1 | w | 685 |
| δεῖ | 1 | w | 688 |
| τὴν | 2 | w | 691 |
| ἐνάργειαν | 1 | w | 700 |
| ἢ | 2 | w | 702 |
| μενούσης | 1 | w | 710 |
| ταύτης | 1 | w | 716 |
| ἀθετεῖν | 1 | w | 723 |
| τὴν | 3 | w | 726 |
| τῶν | 6 | w | 729 |
| γεωμετρῶν | 1 | w | 738 |
| ἐπίνοιαν | 1 | w | 746 |
| καθʼ | 1 | w | 751 |
| ἣν | 1 | w | 753 |
| οἴονται | 1 | w | 760 |
| τὴν | 4 | w | 763 |
| γραμμὴν | 1 | w | 770 |
| μῆκος | 2 | w | 775 |
| ἀπλατὲς | 2 | w | 782 |
| ὑπάρχειν | 1 | w | 790 |
| Καὶ | 1 | w | 794 |
| δὴ | 1 | w | 796 |
| ταῦτα | 1 | w | 801 |
| μὲν | 2 | w | 804 |
| προηγουμένως | 1 | w | 816 |
| ῥητέον | 1 | w | 822 |
| ἐστὶν | 1 | w | 827 |
| ἡμῖν | 1 | w | 831 |
| πρὸς | 1 | w | 835 |
| τὰς | 1 | w | 838 |
| τῆς | 3 | w | 841 |
| γεωμετρίας | 1 | w | 851 |
| ἀρχάς | 1 | w | 856 |
| μεταβάντες | 1 | w | 867 |
| δὲ | 4 | w | 869 |
| διδά- | 1 | w | 874 |
| σκωμεν | 1 | w | 880 |
| ὅτι | 1 | w | 883 |
| καὶ | 3 | w | 886 |
| κατὰ | 2 | w | 890 |
| τὰς | 2 | w | 893 |
| ἐκείνων | 1 | w | 900 |
| αὐτῶν | 2 | w | 905 |
| ὑποθέσεις | 1 | w | 914 |
| οὐχ | 2 | w | 917 |
| οἷόν | 1 | w | 921 |
| τε | 6 | w | 923 |
| προβαίνειν | 1 | w | 933 |
| τὴν | 5 | w | 936 |
| ζήτησιν | 1 | w | 943 |
| ἀρέσκει | 1 | w | 951 |
| τοίνυν | 1 | w | 957 |
| αὐτοῖς | 1 | w | 963 |
| τὴν | 6 | w | 966 |
| εὐθεῖαν | 1 | w | 973 |
| γραμμήν | 1 | w | 980 |
| ὡς | 1 | w | 983 |
| καὶ | 4 | w | 986 |
| ἀνώτερον | 1 | w | 994 |
| 112 | 1 | w | 998 |
| 26 | 1 | w | 1001 |
| ἐλέγομεν | 1 | w | 1010 |
| στρεφομένην | 1 | w | 1022 |
| πᾶσιν | 1 | w | 1027 |
| αὐτῆς | 1 | w | 1032 |
| τοῖς | 2 | w | 1036 |
| μέρεσι | 1 | w | 1042 |
| κύκλους | 1 | w | 1049 |
| γράφειν | 1 | w | 1056 |
| ᾧπερ | 1 | w | 1061 |
| θεωρήματι | 1 | w | 1070 |
| ὄντι | 1 | w | 1074 |
| συνεκτικωτάτῳ | 1 | w | 1087 |
| μαχόμενόν | 1 | w | 1096 |
| ἐστι | 2 | w | 1100 |
| τὸ | 3 | w | 1102 |
| τὴν | 7 | w | 1105 |
| γραμμὴν | 2 | w | 1112 |
| μῆκος | 3 | w | 1117 |
| ἀπλατὲς | 3 | w | 1124 |
| ὑπάρχειν | 2 | w | 1132 |
| ζητῶμεν | 1 | w | 1140 |
| δὲ | 5 | w | 1142 |
| τὸν | 1 | w | 1145 |
| τρόπον | 1 | w | 1151 |
| τοῦτον | 1 | w | 1157 |
| εἰ | 5 | w | 1160 |
| γὰρ | 2 | w | 1163 |
| κατ | 4 | w | 1166 |
| αὐτοὺς | 1 | w | 1172 |
| πᾶν | 1 | w | 1175 |
| μέρος | 1 | w | 1180 |
| τῆς | 5 | w | 1183 |
| γραμ- | 2 | w | 1188 |
| μῆς | 4 | w | 1191 |
| ἔχει | 2 | w | 1195 |
| σημεῖον | 1 | w | 1202 |
| τὸ | 5 | w | 1205 |
| δὲ | 6 | w | 1207 |
| σημεῖον | 2 | w | 1214 |
| στρεφόμενον | 1 | w | 1225 |
| κύκλον | 1 | w | 1231 |
| γράφει | 2 | w | 1237 |
| δεήσει | 2 | w | 1244 |
| κατ | 5 | w | 1247 |
| αὐτούς | 1 | w | 1253 |
| ὅταν | 1 | w | 1258 |
| ἡ | 3 | w | 1259 |
| εὐθεῖα | 2 | w | 1265 |
| γραμμὴ | 3 | w | 1271 |
| στρε- | 1 | w | 1276 |
| φομένη | 2 | w | 1282 |
| καὶ | 5 | w | 1285 |
| πᾶσι | 2 | w | 1289 |
| τοῖς | 3 | w | 1293 |
| ἑαυτῆς | 1 | w | 1299 |
| μέρεσι | 2 | w | 1305 |
| κυκλογραφοῦσα | 1 | w | 1318 |
| τὸ | 6 | w | 1320 |
| διάστημα | 1 | w | 1328 |
| καταμετρῇ | 1 | w | 1337 |
| τὸ | 7 | w | 1340 |
| τῆς | 7 | w | 1344 |
| ἀπὸ | 1 | w | 1347 |
| τοῦ | 2 | w | 1350 |
| κέντρου | 1 | w | 1357 |
| μέχρι | 1 | w | 1362 |
| τῆς | 8 | w | 1365 |
| ἐξωτάτης | 1 | w | 1373 |
| περιφερείας | 1 | w | 1384 |
| ἐπιπέδου | 1 | w | 1392 |
| τότε | 1 | w | 1397 |
| ἤτοι | 1 | w | 1401 |
| συνεχεῖς | 1 | w | 1409 |
| ἀλλή- | 2 | w | 1414 |
| λοις | 3 | w | 1418 |
| ὑπάρχειν | 3 | w | 1426 |
| τοὺς | 2 | w | 1430 |
| καταγραφομένους | 1 | w | 1445 |
| κύκλους | 2 | w | 1452 |
| ἢ | 3 | w | 1453 |
| διεστῶ- | 1 | w | 1460 |
| τας | 1 | w | 1463 |
| ἀπʼ | 1 | w | 1466 |
| ἀλλήλων | 1 | w | 1473 |
| ἀλλʼ | 2 | w | 1478 |
| εἰ | 6 | w | 1480 |
| μὲν | 3 | w | 1483 |
| διεστᾶσιν | 1 | w | 1492 |
| ἀπʼ | 2 | w | 1495 |
| ἀλλήλων | 2 | w | 1502 |
| ἀκολουθήσει | 1 | w | 1514 |
| μέρος | 2 | w | 1519 |
| τι | 11 | w | 1521 |
| εἶναι | 2 | w | 1526 |
| τῆς | 9 | w | 1529 |
| ἐπιπέδου | 2 | w | 1537 |
| τὸ | 8 | w | 1539 |
| μὴ | 5 | w | 1541 |
| κυκλο- | 1 | w | 1547 |
| γραφούμενον | 1 | w | 1558 |
| καὶ | 6 | w | 1562 |
| τῆς | 10 | w | 1565 |
| εὐθείας | 1 | w | 1572 |
| μέρος | 3 | w | 1577 |
| τὸ | 9 | w | 1579 |
| κατὰ | 3 | w | 1583 |
| τούτου | 1 | w | 1589 |
| μὲν | 4 | w | 1592 |
| φερόμενον | 1 | w | 1601 |
| τοῦ | 3 | w | 1604 |
| διαστήματος | 1 | w | 1615 |
| μὴ | 6 | w | 1618 |
| κυκλογραφοῦν | 1 | w | 1630 |
| δέ | 2 | w | 1632 |
| ὅπερ | 1 | w | 1637 |
| ἐστὶν | 2 | w | 1642 |
| ἄτοπον | 1 | w | 1648 |
| ἢ | 4 | w | 1650 |
| γὰρ | 3 | w | 1653 |
| οὐκ | 3 | w | 1656 |
| ἔχει | 3 | w | 1660 |
| κατὰ | 4 | w | 1664 |
| τοῦτο | 2 | w | 1669 |
| τὸ | 10 | w | 1671 |
| μέρος | 4 | w | 1676 |
| ση- | 1 | w | 1679 |
| μεῖον | 3 | w | 1684 |
| ἡ | 4 | w | 1685 |
| εὐθεῖα | 3 | w | 1691 |
| γραμμή | 4 | w | 1697 |
| ἢ | 5 | w | 1699 |
| ἔχουσα | 1 | w | 1705 |
| οὐ | 7 | w | 1707 |
| καταγράφει | 1 | w | 1717 |
| κύκλον | 2 | w | 1723 |
| ὧν | 1 | w | 1726 |
| ἑκάτερον | 1 | w | 1734 |
| παρὰ | 1 | w | 1738 |
| τὸν | 2 | w | 1741 |
| γεωμετρικόν | 1 | w | 1752 |
| ἐστι | 3 | w | 1756 |
| λόγον | 1 | w | 1761 |
| καὶ | 7 | w | 1765 |
| πᾶν | 2 | w | 1768 |
| γὰρ | 4 | w | 1771 |
| μέρος | 5 | w | 1776 |
| τῆς | 11 | w | 1779 |
| γραμμῆς | 4 | w | 1786 |
| σημεῖον | 3 | w | 1793 |
| ἔχειν | 2 | w | 1798 |
| φασί | 1 | w | 1802 |
| καὶ | 8 | w | 1806 |
| πᾶν | 3 | w | 1809 |
| σημεῖον | 4 | w | 1816 |
| στρεφόμενον | 2 | w | 1827 |
| κυκλογραφεῖν | 1 | w | 1839 |