| Refs | {'start': {'reference': '23', 'human_reference': 'Chapter 23'}} |
|---|---|
| Ancestors | [] |
| Children | [] |
| p | 1 | w | 1 |
| 260 | 1 | w | 5 |
| κγ | 1 | w | 7 |
| Τὸ | 1 | w | 10 |
| δοθὲν | 1 | w | 15 |
| χωρίον | 1 | w | 21 |
| μετρῆσαι | 1 | w | 29 |
| διὰ | 1 | w | 32 |
| διόπτρας | 1 | w | 40 |
| ἔστω | 1 | w | 45 |
| τὸ | 1 | w | 47 |
| δοθὲν | 2 | w | 52 |
| χωρίον | 2 | w | 58 |
| περιεχόμενον | 1 | w | 70 |
| ὑπὸ | 1 | w | 73 |
| γραμμῆς | 1 | w | 80 |
| ἀτάκτου | 1 | w | 87 |
| τῆς | 1 | w | 90 |
| ΑΒΓ | 1 | w | 93 |
| ΕΖΗΘ | 1 | w | 97 |
| ἐπεὶ | 1 | w | 102 |
| οὖν | 1 | w | 105 |
| ἐμάθομεν | 1 | w | 113 |
| διὰ | 2 | w | 116 |
| τῆς | 2 | w | 119 |
| κατασκευασθείσης | 1 | w | 135 |
| διόπτρας | 2 | w | 143 |
| διάγειν | 1 | w | 150 |
| πάσῃ | 1 | w | 154 |
| τῇ | 1 | w | 156 |
| δοθείσῃ | 1 | w | 163 |
| εὐθείᾳ | 1 | w | 169 |
| ἑτέραν | 1 | w | 175 |
| πρὸς | 1 | w | 179 |
| ὀρθάς | 1 | w | 184 |
| ἔλαβόν | 1 | w | 191 |
| τι | 1 | w | 193 |
| σημεῖον | 1 | w | 200 |
| ἐπὶ | 1 | w | 203 |
| τῆς | 3 | w | 206 |
| περιεχούσης | 1 | w | 217 |
| τὸ | 2 | w | 219 |
| χωρίον | 3 | w | 225 |
| γραμμῆς | 2 | w | 232 |
| τὸ | 3 | w | 234 |
| Β | 2 | w | 235 |
| καὶ | 1 | w | 239 |
| ἤγαγον | 1 | w | 245 |
| εὐθεῖαν | 1 | w | 252 |
| τυχοῦσαν | 1 | w | 260 |
| διὰ | 3 | w | 263 |
| τῆς | 4 | w | 266 |
| διόπτρας | 3 | w | 274 |
| τὴν | 1 | w | 277 |
| ΒΗ | 1 | w | 279 |
| καὶ | 2 | w | 283 |
| ταύτῃ | 1 | w | 288 |
| πρὸς | 2 | w | 292 |
| ὀρθὰς | 1 | w | 297 |
| τὴν | 2 | w | 300 |
| ΒΓ | 2 | w | 302 |
| καὶ | 3 | w | 306 |
| ταύτῃ | 2 | w | 311 |
| ἑτέραν | 2 | w | 317 |
| πρὸς | 3 | w | 321 |
| ὀρθὰς | 2 | w | 326 |
| τὴν | 3 | w | 329 |
| ΓΖ | 1 | w | 331 |
| καὶ | 4 | w | 335 |
| ὁμοίως | 1 | w | 341 |
| τῇ | 2 | w | 343 |
| ΓΖ | 2 | w | 345 |
| πρὸς | 4 | w | 349 |
| ὀρθὰς | 3 | w | 354 |
| τὴν | 4 | w | 357 |
| ΖΘ | 1 | w | 359 |
| καὶ | 5 | w | 363 |
| ἔλαβον | 1 | w | 369 |
| ἐπὶ | 2 | w | 372 |
| τῶν | 1 | w | 375 |
| ἀχθεισῶν | 1 | w | 383 |
| εὐθειῶν | 1 | w | 390 |
| συνεχῆ | 1 | w | 396 |
| σημεῖα | 1 | w | 402 |
| ἐπὶ | 3 | w | 406 |
| μὲν | 1 | w | 409 |
| τῆς | 5 | w | 412 |
| ΒΗ | 2 | w | 414 |
| τὰ | 1 | w | 416 |
| Κ | 1 | w | 417 |
| Λ | 1 | w | 419 |
| 11 | 1 | w | 422 |
| διὰ | 4 | w | 425 |
| τῆς | 6 | w | 428 |
| Β | 6 | w | 429 |
| εὐθείας | 1 | w | 436 |
| τῆ | 7 | w | 438 |
| διόπτρα | 4 | w | 445 |
| corr | 1 | w | 450 |
| Vi | 1 | w | 453 |
| προσεκ- | 1 | w | 460 |
| βεβλήσθω | 1 | w | 468 |
| corr | 2 | w | 473 |
| Vi | 2 | w | 476 |
| 13 | 1 | w | 478 |
| ἔστω | 2 | w | 482 |
| corr | 3 | w | 487 |
| Vi | 3 | w | 490 |
| 16 | 1 | w | 492 |
| τὴν | 5 | w | 495 |
| Γ | 5 | w | 496 |
| corr | 4 | w | 501 |
| Vi | 4 | w | 504 |
| 23 | 1 | w | 506 |
| et | 1 | w | 508 |
| 26 | 2 | w | 510 |
| supplevi | 1 | w | 518 |
| Μ | 1 | w | 519 |
| Ν | 1 | w | 521 |
| Ξ | 1 | w | 523 |
| Ο | 1 | w | 525 |
| ἐπὶ | 4 | w | 529 |
| δὲ | 1 | w | 531 |
| τῆς | 7 | w | 534 |
| ΒΓ | 3 | w | 536 |
| τὰ | 2 | w | 538 |
| Π | 1 | w | 539 |
| Ρ | 1 | w | 541 |
| ἐπὶ | 5 | w | 545 |
| δὲ | 2 | w | 547 |
| τῆς | 8 | w | 550 |
| ΓΖ | 3 | w | 552 |
| τὰ | 3 | w | 554 |
| Σ | 1 | w | 555 |
| Τ | 2 | w | 557 |
| Υ | 1 | w | 559 |
| Φ | 1 | w | 561 |
| Χ | 1 | w | 563 |
| Ψ | 1 | w | 565 |
| Ω | 1 | w | 567 |
| ἐπὶ | 6 | w | 571 |
| δὲ | 3 | w | 573 |
| τῆς | 9 | w | 576 |
| ΖΘ | 2 | w | 578 |
| τὰ | 4 | w | 580 |
| ϛ | 1 | w | 581 |
| 𝔮 | 1 | w | 583 |
| καὶ | 6 | w | 587 |
| ἀπὸ | 1 | w | 590 |
| τῶν | 2 | w | 593 |
| ληφθέντων | 1 | w | 602 |
| σημείων | 1 | w | 609 |
| ταῖς | 1 | w | 613 |
| εὐθείαις | 1 | w | 621 |
| ἐφʼ | 1 | w | 625 |
| ὧν | 1 | w | 627 |
| ἐστὶ | 1 | w | 631 |
| τὰ | 5 | w | 633 |
| σημεῖα | 2 | w | 639 |
| πρὸς | 5 | w | 644 |
| ὀρθὰς | 4 | w | 649 |
| ἤγαγον | 2 | w | 655 |
| τὰς | 1 | w | 658 |
| ΚϠ | 1 | w | 660 |
| ΛΑ | 1 | w | 663 |
| ΜΑ | 1 | w | 666 |
| ΝΒ | 1 | w | 669 |
| ΕΓ | 1 | w | 672 |
| Ο | 2 | w | 674 |
| ΠΕ | 1 | w | 676 |
| Ρϛ | 1 | w | 679 |
| ΣΖ | 1 | w | 681 |
| ΤΗ | 1 | w | 684 |
| ΥΘ | 1 | w | 687 |
| Φ | 2 | w | 689 |
| ΧΜ | 1 | w | 692 |
| ΨΜ | 1 | w | 695 |
| ΩΕ | 1 | w | 698 |
| ϛΜ | 1 | w | 701 |
| p | 4 | w | 703 |
| 262 | 1 | w | 707 |
| 𝔮 | 2 | w | 708 |
| Μ | 6 | w | 711 |
| οὕτως | 1 | w | 716 |
| ὥστε | 1 | w | 720 |
| τὰς | 2 | w | 723 |
| ἐπὶ | 7 | w | 726 |
| τὰ | 8 | w | 728 |
| πέρατα | 1 | w | 734 |
| τῶν | 3 | w | 737 |
| ἀχθεισῶν | 2 | w | 745 |
| πρὸς | 6 | w | 749 |
| ὀρθὰς | 5 | w | 754 |
| ἐπιζευγνυμένας | 1 | w | 768 |
| ἀπολαμβάνειν | 1 | w | 780 |
| γραμμὰς | 1 | w | 787 |
| ἀπὸ | 2 | w | 790 |
| τῆς | 10 | w | 793 |
| περιεχούσης | 2 | w | 804 |
| τὸ | 4 | w | 806 |
| χωρίον | 4 | w | 812 |
| γραμμῆς | 3 | w | 819 |
| σύνεγγυς | 1 | w | 827 |
| εὐθείας | 2 | w | 834 |
| καὶ | 7 | w | 838 |
| τούτων | 1 | w | 844 |
| γενηθέντων | 1 | w | 854 |
| ἔσται | 1 | w | 859 |
| δυνατὸν | 1 | w | 866 |
| τὸ | 6 | w | 868 |
| χωρίον | 5 | w | 874 |
| μετρεῖν | 1 | w | 881 |
| τὸ | 7 | w | 884 |
| μὲν | 2 | w | 887 |
| γὰρ | 1 | w | 890 |
| ΒΓΖΜ | 1 | w | 894 |
| παραλληλόγραμμον | 1 | w | 910 |
| ὀρθογώνιόν | 1 | w | 920 |
| ἐστιν | 1 | w | 925 |
| ἔπειτα | 1 | w | 932 |
| τὰς | 3 | w | 935 |
| πλευρὰς | 1 | w | 942 |
| ἁλύσει | 1 | w | 948 |
| ἢ | 1 | w | 949 |
| σχοινίῳ | 1 | w | 956 |
| βεβασανισμένῳ | 1 | w | 969 |
| τουτέστιν | 1 | w | 979 |
| μήτʼ | 1 | w | 983 |
| ἐκτείνεσθαι | 1 | w | 994 |
| μήτε | 1 | w | 998 |
| συστέλλεσθαι | 1 | w | 1010 |
| δυναμένῳ | 1 | w | 1018 |
| μετρήσαντες | 1 | w | 1030 |
| ἕξομεν | 1 | w | 1036 |
| τὸ | 8 | w | 1038 |
| ἐμβαδὸν | 1 | w | 1045 |
| τοῦ | 1 | w | 1048 |
| παραλληλογράμμου | 1 | w | 1064 |
| τὰ | 10 | w | 1067 |
| δʼ | 1 | w | 1069 |
| ἐκτὸς | 1 | w | 1074 |
| τούτου | 1 | w | 1080 |
| τρίγωνα | 1 | w | 1087 |
| ὀρθογώνια | 1 | w | 1096 |
| καὶ | 8 | w | 1099 |
| τραπέζια | 1 | w | 1107 |
| ὁμοίως | 2 | w | 1113 |
| μετρήσομεν | 1 | w | 1123 |
| ἔχοντες | 1 | w | 1131 |
| τὰς | 4 | w | 1134 |
| πλευρὰς | 2 | w | 1141 |
| αὐτῶν | 1 | w | 1146 |
| ἔσται | 2 | w | 1152 |
| γὰρ | 2 | w | 1155 |
| τρίγωνα | 2 | w | 1162 |
| μὲν | 3 | w | 1165 |
| ὀρθογώνια | 2 | w | 1174 |
| τὰ | 12 | w | 1176 |
| ΒΚϠ | 1 | w | 1179 |
| ΒΠΕ | 1 | w | 1183 |
| ΓΡϛ | 1 | w | 1187 |
| ΓΣΖ | 1 | w | 1191 |
| ΖΩΕ | 1 | w | 1195 |
| ΖϛΜ | 1 | w | 1199 |
| ΘΗΜ | 1 | w | 1203 |
| τὰ | 13 | w | 1206 |
| δὲ | 4 | w | 1208 |
| λοιπὰ | 1 | w | 1213 |
| τραπέζια | 2 | w | 1221 |
| ὀρθογώνια | 3 | w | 1230 |
| τὰ | 14 | w | 1233 |
| μὲν | 4 | w | 1236 |
| οὖν | 2 | w | 1239 |
| τρίγωνα | 3 | w | 1246 |
| μετρεῖται | 1 | w | 1255 |
| τῶν | 5 | w | 1258 |
| περὶ | 1 | w | 1262 |
| τὴν | 6 | w | 1265 |
| ὀρθὴν | 1 | w | 1270 |
| γωνίαν | 1 | w | 1276 |
| πολλαπλασιαζομένων | 1 | w | 1294 |
| ἐπʼ | 1 | w | 1297 |
| ἄλληλα | 1 | w | 1303 |
| καὶ | 9 | w | 1307 |
| τοῦ | 2 | w | 1310 |
| γενομένου | 1 | w | 1319 |
| τὸ | 10 | w | 1321 |
| ἥμισυ | 1 | w | 1326 |
| τὰ | 15 | w | 1329 |
| δὲ | 5 | w | 1331 |
| τραπέζια | 3 | w | 1339 |
| συναμφοτέρων | 1 | w | 1352 |
| τῶν | 6 | w | 1355 |
| παραλλήλων | 1 | w | 1365 |
| τὸ | 11 | w | 1367 |
| ἥμισυ | 2 | w | 1372 |
| ἐπὶ | 8 | w | 1375 |
| τὴν | 7 | w | 1378 |
| ἐπʼ | 2 | w | 1381 |
| αὐτὰς | 1 | w | 1386 |
| κάθετον | 1 | w | 1393 |
| οὖσαν | 1 | w | 1398 |
| οἷον | 1 | w | 1403 |
| τῶν | 7 | w | 1406 |
| ΚϠ | 3 | w | 1408 |
| ΑΛ | 1 | w | 1411 |
| τὸ | 12 | w | 1413 |
| ἥμισυ | 3 | w | 1418 |
| ἐπὶ | 9 | w | 1421 |
| τὴν | 8 | w | 1424 |
| ΚΛ | 1 | w | 1426 |
| καὶ | 10 | w | 1430 |
| τῶν | 8 | w | 1433 |
| λοιπῶν | 1 | w | 1439 |
| δὲ | 6 | w | 1441 |
| ὁμοίως | 3 | w | 1447 |
| ἔσται | 3 | w | 1453 |
| ἄρα | 1 | w | 1456 |
| μεμετρημένον | 1 | w | 1468 |
| ὅλον | 1 | w | 1472 |
| τὸ | 13 | w | 1474 |
| 6 | 5 | w | 1475 |
| supplevit | 1 | w | 1484 |
| Vi | 5 | w | 1486 |
| Φ | 3 | w | 1487 |
| Φ | 4 | w | 1488 |
| ΨΜ | 2 | w | 1490 |
| 7 | 1 | w | 1491 |
| et | 2 | w | 1493 |
| 8 | 1 | w | 1494 |
| corr | 5 | w | 1498 |
| R | 1 | w | 1500 |
| Schoene | 1 | w | 1508 |
| 18 | 1 | w | 1511 |
| τὸ | 14 | w | 1513 |
| ΒΚΤ | 1 | w | 1516 |
| corr | 6 | w | 1521 |
| Vi | 6 | w | 1524 |
| 18 | 2 | w | 1526 |
| 19 | 1 | w | 1529 |
| Ζωε | 1 | w | 1532 |
| Ζϛμ | 1 | w | 1535 |
| ΘΗμ | 1 | w | 1538 |
| 23 | 2 | w | 1540 |
| ἐπʼ | 3 | w | 1543 |
| αὐτῆς | 1 | w | 1548 |
| correx | 1 | w | 1555 |
| 25 | 1 | w | 1557 |
| ἀναμεμετρημένον | 1 | w | 1572 |
| corr | 8 | w | 1577 |
| Vi | 7 | w | 1580 |
| χωρίον | 6 | w | 1586 |
| διά | 2 | w | 1589 |
| τε | 6 | w | 1591 |
| τοῦ | 3 | w | 1594 |
| μέσου | 1 | w | 1599 |
| παραλληλογράμμου | 2 | w | 1615 |
| καὶ | 11 | w | 1618 |
| τῶν | 9 | w | 1621 |
| ἐκτὸς | 2 | w | 1626 |
| αὐτοῦ | 1 | w | 1631 |
| τριγώνων | 1 | w | 1639 |
| καὶ | 12 | w | 1642 |
| τραπεζίων | 1 | w | 1651 |
| ἐὰν | 1 | w | 1655 |
| δὲ | 7 | w | 1657 |
| τύχῃ | 1 | w | 1661 |
| ποτὲ | 1 | w | 1665 |
| μεταξὺ | 1 | w | 1671 |
| αὐτῶν | 2 | w | 1676 |
| τῶν | 11 | w | 1679 |
| ἀχθεισῶν | 3 | w | 1687 |
| πρὸς | 7 | w | 1691 |
| ὀρθὰς | 6 | w | 1696 |
| ταῖς | 2 | w | 1700 |
| τοῦ | 5 | w | 1703 |
| παραλληλογράμμου | 3 | w | 1719 |
| πλευραῖς | 1 | w | 1727 |
| καμπύλη | 1 | w | 1734 |
| γραμμὴ | 1 | w | 1740 |
| μὴ | 2 | w | 1742 |
| συνεγγίζουσα | 1 | w | 1754 |
| εὐθείᾳ | 2 | w | 1760 |
| οἷον | 2 | w | 1765 |
| μεταξὺ | 2 | w | 1771 |
| τῶν | 12 | w | 1774 |
| ΞΓ | 1 | w | 1776 |
| Ο | 3 | w | 1778 |
| γραμμὴ | 2 | w | 1784 |
| ἡ | 1 | w | 1785 |
| Γ | 13 | w | 1786 |
| ἀλλὰ | 1 | w | 1792 |
| περιφερεῖ | 1 | w | 1801 |
| μετρήσομεν | 2 | w | 1812 |
| οὕτως | 2 | w | 1817 |
| ἀγαγόντες | 1 | w | 1827 |
| τῇ | 3 | w | 1829 |
| Ο | 4 | w | 1830 |
| πρὸς | 8 | w | 1834 |
| ὀρθὰς | 7 | w | 1839 |
| τὴν | 9 | w | 1842 |
| Μ | 11 | w | 1843 |
| καὶ | 13 | w | 1847 |
| ἐπʼ | 4 | w | 1850 |
| fol | 1 | w | 1853 |
| 73v | 1 | w | 1857 |
| αὐτῆς | 2 | w | 1862 |
| λαβόντες | 1 | w | 1870 |
| σημεῖα | 3 | w | 1876 |
| συνεχῆ | 2 | w | 1882 |
| τὰ | 17 | w | 1884 |
| Μ | 12 | w | 1885 |
| Μ | 13 | w | 1887 |
| καὶ | 14 | w | 1891 |
| ἀ | 11 | w | 1892 |
| π | 59 | w | 1893 |
| αὐτῶν | 3 | w | 1898 |
| πρὸς | 9 | w | 1902 |
| ὀρθὰς | 8 | w | 1907 |
| ἀγαγόντες | 2 | w | 1916 |
| τῇ | 4 | w | 1918 |
| Μ | 14 | w | 1919 |
| τὰς | 6 | w | 1922 |
| ΜΜ | 1 | w | 1924 |
| ΜΜ | 2 | w | 1927 |
| ὥστε | 2 | w | 1932 |
| τὰς | 7 | w | 1935 |
| μεταξὺ | 3 | w | 1941 |
| τῶν | 14 | w | 1944 |
| ἀχθεισῶν | 4 | w | 1952 |
| σύνεγγυς | 2 | w | 1960 |
| εὐθείας | 3 | w | 1967 |
| εἶναι | 1 | w | 1972 |
| p | 7 | w | 1974 |
| 264 | 1 | w | 1978 |
| πάλιν | 1 | w | 1983 |
| μετρήσομεν | 3 | w | 1993 |
| τό | 1 | w | 1995 |
| τε | 11 | w | 1997 |
| ΜΞΟ | 1 | w | 2000 |
| παραλληλόγραμμον | 2 | w | 2016 |
| καὶ | 15 | w | 2019 |
| τὸ | 16 | w | 2021 |
| ΜΜ | 3 | w | 2023 |
| τρίγωνον | 1 | w | 2031 |
| καὶ | 16 | w | 2035 |
| τὸ | 17 | w | 2037 |
| ΓΜΜΜ | 1 | w | 2041 |
| τραπέζιον | 1 | w | 2050 |
| καὶ | 17 | w | 2054 |
| ἔτι | 1 | w | 2057 |
| τὸ | 18 | w | 2059 |
| ἕτερον | 1 | w | 2065 |
| τραπέζιον | 2 | w | 2074 |
| καὶ | 18 | w | 2078 |
| ἕξομεν | 2 | w | 2084 |
| τὸ | 19 | w | 2086 |
| περιεχόμενον | 2 | w | 2098 |
| χωρίον | 7 | w | 2104 |
| ὑπό | 1 | w | 2107 |
| τε | 13 | w | 2109 |
| τῆς | 13 | w | 2112 |
| ΓΜΜ | 2 | w | 2115 |
| γραμμῆς | 4 | w | 2122 |
| καὶ | 19 | w | 2125 |
| τῶν | 15 | w | 2128 |
| ΓΞ | 1 | w | 2130 |
| ΞΟ | 2 | w | 2132 |
| Ο | 7 | w | 2134 |
| εὐθειῶν | 2 | w | 2141 |
| μεμετρημένον | 3 | w | 2153 |