| Refs | {'start': {'reference': '6', 'human_reference': 'Paragraph 6'}, 'end': {'reference': '10', 'human_reference': 'Paragraph 10'}} |
|---|---|
| Ancestors | [] |
| Children | [] |
| Πολλαπλασιασμός | 1 | w | 15 |
| ἐστι | 1 | w | 19 |
| σύνθεσις | 1 | w | 27 |
| ἀριθμοῦ | 1 | w | 34 |
| τινος | 1 | w | 39 |
| δοθέντος | 1 | w | 47 |
| καθʼ | 1 | w | 51 |
| ἕτερον | 1 | w | 57 |
| ἀριθμὸν | 1 | w | 64 |
| δοθέντα | 1 | w | 71 |
| οἱονεὶ | 1 | w | 78 |
| ὅταν | 1 | w | 82 |
| ὁ | 1 | w | 83 |
| ἕτερος | 1 | w | 89 |
| τοσαυτάκις | 1 | w | 99 |
| συντιθέμενος | 1 | w | 111 |
| ὁπόσος | 1 | w | 117 |
| ἐστὶν | 1 | w | 122 |
| ὁ | 3 | w | 123 |
| ἕτερος | 2 | w | 129 |
| ἐν | 1 | w | 131 |
| τῷ | 1 | w | 133 |
| πλήθει | 1 | w | 139 |
| τῶν | 1 | w | 142 |
| μονάδων | 1 | w | 149 |
| καὶ | 1 | w | 152 |
| ποιῇ | 1 | w | 156 |
| τινα | 1 | w | 160 |
| κατὰ | 1 | w | 164 |
| τὸ | 1 | w | 166 |
| πλῆθος | 1 | w | 172 |
| τῆς | 1 | w | 175 |
| συνθέσεως | 1 | w | 184 |
| ὁ | 4 | w | 186 |
| γενόμενος | 1 | w | 195 |
| λέγεται | 1 | w | 202 |
| πολλαπλασιασμὸς | 1 | w | 217 |
| τοῦ | 1 | w | 220 |
| ἑτέρου | 1 | w | 226 |
| κατὰ | 2 | w | 230 |
| τὸν | 1 | w | 233 |
| ἕτερον | 2 | w | 239 |
| Λέγεται | 1 | w | 247 |
| μὲν | 1 | w | 250 |
| καὶ | 2 | w | 253 |
| ἄλλῃ | 1 | w | 257 |
| σύνθεσις | 2 | w | 265 |
| ἀλλʼ | 1 | w | 270 |
| οὐ | 1 | w | 272 |
| πολλαπλασιασμός | 1 | w | 287 |
| καὶ | 3 | w | 291 |
| γὰρ | 1 | w | 294 |
| ὁ | 5 | w | 295 |
| ἐκ | 1 | w | 297 |
| τῶν | 2 | w | 300 |
| δοθέντων | 1 | w | 308 |
| εἴτε | 1 | w | 312 |
| ἴσων | 1 | w | 316 |
| εἴτε | 2 | w | 320 |
| ἀνίσων | 1 | w | 326 |
| ἀριθμῶν | 1 | w | 333 |
| καὶ | 4 | w | 336 |
| εἴτε | 3 | w | 340 |
| δύο | 1 | w | 343 |
| ἢ | 1 | w | 344 |
| τριῶν | 1 | w | 349 |
| ἢ | 2 | w | 350 |
| καὶ | 5 | w | 353 |
| πλειόνων | 1 | w | 361 |
| συντεθείς | 1 | w | 370 |
| ἀπλῶς | 1 | w | 376 |
| λέγεται | 2 | w | 383 |
| συγκεῖσθαι | 1 | w | 393 |
| οὐ | 2 | w | 396 |
| μέντοι | 1 | w | 402 |
| πολλαπλασίων | 1 | w | 414 |
| πολλαπλασιάζομεν | 1 | w | 431 |
| δὲ | 1 | w | 433 |
| ἢ | 3 | w | 434 |
| μοῖραν | 1 | w | 440 |
| ἐπὶ | 1 | w | 443 |
| μοῖραν | 2 | w | 449 |
| ἢ | 4 | w | 450 |
| μοίρας | 1 | w | 456 |
| ἐπὶ | 2 | w | 459 |
| μοίρας | 2 | w | 465 |
| καὶ | 6 | w | 469 |
| πάλιν | 1 | w | 474 |
| ἢ | 5 | w | 475 |
| λεπτὸν | 1 | w | 481 |
| ἐπὶ | 3 | w | 484 |
| λεπτὸν | 2 | w | 490 |
| ἢ | 6 | w | 491 |
| λεπτὰ | 1 | w | 496 |
| ἐπὶ | 4 | w | 499 |
| λεπτά | 1 | w | 504 |
| καὶ | 7 | w | 508 |
| ἀνάμιξ | 1 | w | 514 |
| μοῖραν | 3 | w | 520 |
| ἐπὶ | 5 | w | 523 |
| λεπτὸν | 3 | w | 529 |
| καὶ | 8 | w | 532 |
| λεπτά | 2 | w | 537 |
| ἀλλʼ | 2 | w | 542 |
| ἡ | 1 | w | 543 |
| μὲν | 2 | w | 546 |
| μοῖρα | 4 | w | 551 |
| ἐφʼ | 1 | w | 554 |
| ὃ | 1 | w | 555 |
| ἂν | 1 | w | 557 |
| εἶδος | 1 | w | 562 |
| πολλαπλασιασθῇ | 1 | w | 576 |
| τὸ | 6 | w | 579 |
| αὐτὸ | 1 | w | 583 |
| εἶδος | 2 | w | 588 |
| ποιεῖ | 1 | w | 593 |
| ἐπὶ | 6 | w | 597 |
| γὰρ | 2 | w | 600 |
| πρῶτα | 1 | w | 605 |
| λεπτὰ | 2 | w | 610 |
| πολυπλασιαζομένη | 1 | w | 626 |
| ἡ | 2 | w | 627 |
| μοῖρα | 5 | w | 632 |
| ἢ | 7 | w | 633 |
| μοῖραι | 1 | w | 639 |
| πρῶτα | 2 | w | 644 |
| λεπτὰ | 3 | w | 649 |
| ποιοῦσιν | 1 | w | 657 |
| καὶ | 9 | w | 661 |
| ἀνάπαλιν | 1 | w | 669 |
| λεπτὰ | 4 | w | 674 |
| πρῶτα | 3 | w | 679 |
| ἐπὶ | 7 | w | 682 |
| μοῖραν | 4 | w | 688 |
| ἢ | 8 | w | 689 |
| μοίρας | 3 | w | 695 |
| ποιεῖ | 2 | w | 700 |
| πρῶτα | 4 | w | 705 |
| λεπτά | 3 | w | 710 |
| καὶ | 10 | w | 714 |
| ἐξῆς | 1 | w | 718 |
| ὁμοίως | 1 | w | 724 |
| μοῖρα | 8 | w | 731 |
| ἐπὶ | 8 | w | 734 |
| δεύτερα | 1 | w | 741 |
| δεύτερα | 2 | w | 749 |
| ποιεῖ | 3 | w | 754 |
| καὶ | 11 | w | 757 |
| ἐπὶ | 9 | w | 760 |
| τρίτα | 1 | w | 765 |
| τρίτα | 2 | w | 771 |
| καὶ | 12 | w | 774 |
| ἑξῆς | 1 | w | 778 |
| πρῶτα | 5 | w | 784 |
| δὲ | 2 | w | 786 |
| ἐπὶ | 10 | w | 789 |
| πρῶτα | 6 | w | 794 |
| ποιεῖ | 4 | w | 799 |
| δεύτερα | 3 | w | 806 |
| ἅπερ | 1 | w | 811 |
| ἐστὶν | 2 | w | 816 |
| ἐλάσσονα | 1 | w | 824 |
| τῶν | 3 | w | 827 |
| πρώτων | 1 | w | 833 |
| τῶν | 4 | w | 837 |
| μὲν | 3 | w | 840 |
| γὰρ | 3 | w | 843 |
| πρώτων | 2 | w | 849 |
| τὸ | 8 | w | 851 |
| ἕν | 1 | w | 853 |
| λεπτὸν | 4 | w | 859 |
| ξ | 4 | w | 860 |
| ἐστι | 2 | w | 864 |
| τῆς | 2 | w | 867 |
| μοίρας | 4 | w | 873 |
| τῶν | 5 | w | 877 |
| δὲ | 3 | w | 879 |
| δευτέρων | 1 | w | 887 |
| γχον | 1 | w | 892 |
| ὅπερ | 1 | w | 898 |
| 7 | 1 | w | 899 |
| κατὰ | 3 | w | 903 |
| A | 1 | w | 904 |
| ἂριθμὸν | 1 | w | 912 |
| compendio | 1 | w | 921 |
| B | 1 | w | 922 |
| καὶ | 13 | w | 926 |
| A | 2 | w | 927 |
| 8 | 1 | w | 929 |
| ἢ | 9 | w | 930 |
| AB | 1 | w | 932 |
| 12 | 1 | w | 935 |
| ἄλλη | 1 | w | 939 |
| AB | 2 | w | 941 |
| 16 | 1 | w | 944 |
| πολλαπλασίων | 2 | w | 956 |
| πολλαπλασ | 7 | w | 966 |
| A | 5 | w | 967 |
| πολλαπλάσιον | 1 | w | 980 |
| B | 4 | w | 981 |
| 19 | 1 | w | 984 |
| μοῖρα | 9 | w | 989 |
| Μ | 1 | w | 991 |
| A | 6 | w | 992 |
| μονὰς | 1 | w | 998 |
| Β | 1 | w | 999 |
| μοῖρα | 10 | w | 1005 |
| in | 1 | w | 1007 |
| margine | 1 | w | 1014 |
| 21 | 1 | w | 1017 |
| ἡ | 3 | w | 1018 |
| om | 2 | w | 1020 |
| B | 5 | w | 1022 |
| 22 | 1 | w | 1025 |
| ποιοῦσι | 2 | w | 1032 |
| B | 6 | w | 1033 |
| ἐπὶ | 11 | w | 1037 |
| om | 3 | w | 1039 |
| A | 7 | w | 1041 |
| 27 | 1 | w | 1044 |
| ξξ | 1 | w | 1046 |
| id | 1 | w | 1048 |
| est | 1 | w | 1051 |
| ἑξηκοστῶν | 1 | w | 1060 |
| AB | 3 | w | 1062 |
| ἐναντίον | 1 | w | 1071 |
| ἐστὶ | 3 | w | 1075 |
| τῷ | 2 | w | 1077 |
| πολλαπλασιασμῷ | 1 | w | 1091 |
| τῶν | 7 | w | 1094 |
| λοιπῶν | 1 | w | 1100 |
| ἀριθμῶν | 2 | w | 1107 |
| ἐπαυξήσει | 1 | w | 1117 |
| γὰρ | 4 | w | 1120 |
| πολλαπλασιάζονται | 1 | w | 1137 |
| ὡς | 1 | w | 1139 |
| ἐὰν | 1 | w | 1142 |
| πεντάκις | 1 | w | 1150 |
| τὸν | 6 | w | 1153 |
| Ϛ | 1 | w | 1154 |
| πλάττοντες | 1 | w | 1164 |
| συνθῶμεν | 1 | w | 1172 |
| καὶ | 14 | w | 1175 |
| ποιήσωμεν | 1 | w | 1184 |
| τὸν | 7 | w | 1187 |
| λ | 66 | w | 1188 |
| πρῶτα | 7 | w | 1194 |
| δὲ | 4 | w | 1196 |
| ε | 58 | w | 1197 |
| λεπτὰ | 5 | w | 1202 |
| ἐπὶ | 12 | w | 1205 |
| πρῶτα | 8 | w | 1210 |
| πολλαπλασιάζοντες | 1 | w | 1227 |
| λ | 71 | w | 1229 |
| δεύτερα | 4 | w | 1236 |
| ποιοῦμεν | 1 | w | 1244 |
| ὅπερ | 2 | w | 1249 |
| ἥμισύ | 1 | w | 1254 |
| ἐστιν | 1 | w | 1259 |
| ἑνὸς | 1 | w | 1263 |
| πρώτου | 1 | w | 1269 |
| λεπτοῦ | 1 | w | 1275 |
| τοῦτο | 1 | w | 1281 |
| δὲ | 5 | w | 1283 |
| γίνεται | 1 | w | 1290 |
| διὰ | 1 | w | 1293 |
| τὴν | 1 | w | 1296 |
| τῶν | 8 | w | 1299 |
| μορίων | 1 | w | 1305 |
| πρὸς | 1 | w | 1309 |
| τὴν | 2 | w | 1312 |
| μονάδα | 1 | w | 1318 |
| ἀντιπεπόνθησιν | 1 | w | 1332 |
| ἀεὶ | 1 | w | 1336 |
| γὰρ | 5 | w | 1339 |
| τὰ | 9 | w | 1341 |
| μόρια | 1 | w | 1346 |
| πολλαπλασιαζόμενα | 1 | w | 1363 |
| ἐναντίως | 1 | w | 1371 |
| ταῖς | 1 | w | 1375 |
| μοίραις | 1 | w | 1382 |
| ἐπʼ | 1 | w | 1385 |
| ἔλαττον | 1 | w | 1392 |
| χωρεῖ | 1 | w | 1397 |
| ἐφʼ | 2 | w | 1401 |
| ἑαυτὸ | 1 | w | 1406 |
| γὰρ | 6 | w | 1409 |
| τὸ | 13 | w | 1411 |
| ἥμισυ | 1 | w | 1416 |
| πολλαπλασιαζόμενον | 1 | w | 1434 |
| τέταρτον | 1 | w | 1442 |
| γίνεται | 2 | w | 1449 |
| β | 1 | w | 1451 |
| δὲ | 6 | w | 1453 |
| μονάδες | 1 | w | 1460 |
| ἐπὶ | 13 | w | 1463 |
| β | 2 | w | 1464 |
| δ | 22 | w | 1466 |
| ποιοῦσιν | 2 | w | 1474 |
| ὁμοίως | 2 | w | 1481 |
| καὶ | 15 | w | 1484 |
| τρίτον | 1 | w | 1490 |
| ἐπὶ | 14 | w | 1493 |
| τρίτον | 2 | w | 1499 |
| ἔνναιον | 1 | w | 1507 |
| γίνεται | 3 | w | 1514 |
| γ | 16 | w | 1516 |
| δὲ | 7 | w | 1518 |
| ἐπὶ | 15 | w | 1521 |
| γ | 17 | w | 1522 |
| θ | 21 | w | 1524 |
| ὅπερ | 3 | w | 1529 |
| δοκεῖ | 1 | w | 1534 |
| λῆρον | 1 | w | 1539 |
| τοῦτο | 2 | w | 1545 |
| δὲ | 8 | w | 1547 |
| συμβαίνει | 1 | w | 1556 |
| τοῖς | 1 | w | 1560 |
| μορίοις | 1 | w | 1567 |
| ὅτι | 1 | w | 1570 |
| οὐ | 3 | w | 1572 |
| συντίθενται | 1 | w | 1583 |
| κατὰ | 4 | w | 1587 |
| μονάδα | 2 | w | 1593 |
| ἀλλὰ | 1 | w | 1598 |
| τοὐναντίον | 1 | w | 1608 |
| μερίζονται | 1 | w | 1618 |
| κατὰ | 5 | w | 1622 |
| τὰ | 12 | w | 1624 |
| ὁμώνυμα | 1 | w | 1631 |
| μέρη | 1 | w | 1635 |
| ταῖς | 2 | w | 1639 |
| μονάσιν | 1 | w | 1646 |
| τὸ | 14 | w | 1649 |
| γὰρ | 7 | w | 1652 |
| ἥμισυ | 2 | w | 1657 |
| ἐπὶ | 16 | w | 1660 |
| τὸ | 15 | w | 1662 |
| ἥμισυ | 3 | w | 1667 |
| νῦν | 1 | w | 1670 |
| οὐ | 5 | w | 1672 |
| συνετέθη | 1 | w | 1680 |
| καθʼ | 2 | w | 1684 |
| ὅλον | 1 | w | 1688 |
| ἑαυτό | 1 | w | 1693 |
| ὥσπερ | 1 | w | 1699 |
| τὰ | 13 | w | 1701 |
| β | 4 | w | 1702 |
| ἐπὶ | 17 | w | 1705 |
| τὰ | 14 | w | 1707 |
| β | 5 | w | 1708 |
| ἀλλὰ | 2 | w | 1713 |
| κατὰ | 6 | w | 1717 |
| τὸ | 16 | w | 1719 |
| ἥμισυ | 4 | w | 1724 |
| ἑαυτοῦ | 1 | w | 1730 |
| ὡς | 2 | w | 1733 |
| ἔστιν | 1 | w | 1738 |
| ἰδεῖν | 1 | w | 1743 |
| καὶ | 16 | w | 1746 |
| ἐπὶ | 18 | w | 1749 |
| διαγράμματος | 1 | w | 1761 |
| οὕτως | 1 | w | 1766 |
| Ἔστω | 1 | w | 1771 |
| γὰρ | 8 | w | 1774 |
| μοναδιαῖον | 1 | w | 1784 |
| χωρίον | 1 | w | 1790 |
| τὸ | 17 | w | 1792 |
| ΑΒ | 1 | w | 1794 |
| ἐκ | 2 | w | 1796 |
| πλευρᾶς | 1 | w | 1803 |
| τῆς | 3 | w | 1806 |
| ΑΖ | 1 | w | 1808 |
| τετράγωνον | 1 | w | 1818 |
| δίχα | 1 | w | 1822 |
| διῃρημένης | 1 | w | 1832 |
| κατὰ | 7 | w | 1836 |
| τὸ | 18 | w | 1838 |
| Γ | 1 | w | 1839 |
| καὶ | 17 | w | 1843 |
| ἀπὸ | 1 | w | 1846 |
| τῆς | 4 | w | 1849 |
| ΑΓ | 1 | w | 1851 |
| ἀναγεγράφθω | 1 | w | 1862 |
| χωρίον | 2 | w | 1868 |
| τετράγωνον | 2 | w | 1878 |
| τὸ | 19 | w | 1880 |
| Α | 4 | w | 1881 |
| Ε | 1 | w | 1882 |
| τοῦτο | 3 | w | 1887 |
| δὴ | 1 | w | 1889 |
| τέταρτον | 2 | w | 1897 |
| μέρος | 1 | w | 1902 |
| ἐστὶ | 4 | w | 1906 |
| τοῦ | 7 | w | 1909 |
| ΑΒ | 2 | w | 1911 |
| μοναδιαίου | 1 | w | 1921 |
| χωρίου | 1 | w | 1927 |
| καὶ | 18 | w | 1931 |
| ἔστιν | 2 | w | 1936 |
| ἥμισυ | 5 | w | 1941 |
| ἐπὶ | 19 | w | 1944 |
| ἥμισυ | 6 | w | 1949 |
| ἡ | 4 | w | 1951 |
| ΑΓ | 2 | w | 1953 |
| γὰρ | 9 | w | 1956 |
| ἐπὶ | 20 | w | 1959 |
| τὴν | 3 | w | 1962 |
| Α | 7 | w | 1963 |
| γέγονεν | 1 | w | 1970 |
| ὁμοίως | 3 | w | 1977 |
| οὖν | 1 | w | 1980 |
| δείξεις | 1 | w | 1987 |
| ὅτι | 2 | w | 1990 |
| καὶ | 19 | w | 1993 |
| γʹ | 1 | w | 1995 |
| ἐπὶ | 21 | w | 1998 |
| γʹ | 2 | w | 2000 |
| θʹ | 1 | w | 2003 |
| γίνεται | 4 | w | 2010 |
| καὶ | 20 | w | 2014 |
| δʹ | 1 | w | 2016 |
| ἐπὶ | 22 | w | 2019 |
| δʹ | 2 | w | 2021 |
| ιϛʹ | 1 | w | 2025 |
| οὕτως | 2 | w | 2031 |
| οὖν | 2 | w | 2034 |
| δεῖ | 2 | w | 2037 |
| νοεῖν | 1 | w | 2042 |
| καὶ | 21 | w | 2045 |
| ἐπὶ | 23 | w | 2048 |
| τῶν | 9 | w | 2051 |
| λεπτῶν | 1 | w | 2057 |
| μορίων | 2 | w | 2063 |
| ὄντων | 1 | w | 2068 |
| Ὁμοίως | 1 | w | 2075 |
| δὲ | 9 | w | 2077 |
| καὶ | 22 | w | 2080 |
| πρῶτα | 9 | w | 2085 |
| ἐπὶ | 24 | w | 2088 |
| δεύτερα | 5 | w | 2095 |
| τρίτα | 3 | w | 2101 |
| ποιεῖ | 5 | w | 2106 |
| καὶ | 23 | w | 2110 |
| 4 | 1 | w | 2111 |
| ε | 97 | w | 2112 |
| addidi | 1 | w | 2118 |
| Ϛ | 2 | w | 2120 |
| β | 6 | w | 2122 |
| A | 9 | w | 2123 |
| 5 | 1 | w | 2125 |
| πρώτου | 2 | w | 2131 |
| om | 4 | w | 2133 |
| A | 10 | w | 2135 |
| 14 | 1 | w | 2138 |
| μονάσι | 2 | w | 2144 |
| B | 8 | w | 2145 |
| 21 | 2 | w | 2148 |
| 22 | 2 | w | 2151 |
| δίχα | 2 | w | 2155 |
| τετράγωνον | 3 | w | 2168 |
| om | 5 | w | 2170 |
| A | 11 | w | 2171 |
| 24 | 1 | w | 2174 |
| ἐπὶ | 25 | w | 2177 |
| ἥμισυ | 7 | w | 2182 |
| om | 6 | w | 2184 |
| A | 12 | w | 2186 |
| 26 | 1 | w | 2189 |
| καὶ | 24 | w | 2192 |
| δ | 41 | w | 2193 |
| νοεῖν | 2 | w | 2201 |
| om | 7 | w | 2203 |
| A | 13 | w | 2205 |
| πλασιάζωμεν | 1 | w | 2217 |
| εἰς | 1 | w | 2220 |
| τὴν | 4 | w | 2223 |
| Α | 8 | w | 2224 |
| οὖσαν | 1 | w | 2229 |
| μοῖραν | 5 | w | 2235 |
| α | 151 | w | 2236 |
| ἐπὶ | 26 | w | 2240 |
| τὸ | 20 | w | 2242 |
| ἓν | 1 | w | 2244 |
| ξον | 1 | w | 2247 |
| λέγω | 1 | w | 2252 |
| δὴ | 2 | w | 2254 |
| τὴν | 5 | w | 2257 |
| ΑΞ | 1 | w | 2259 |
| ἔσται | 1 | w | 2265 |
| τὸ | 21 | w | 2267 |
| πρῶτον | 1 | w | 2273 |
| χωρίον | 3 | w | 2279 |
| τὸ | 22 | w | 2281 |
| ΑΟ | 1 | w | 2283 |
| ξ | 11 | w | 2284 |
| ἑνός | 1 | w | 2288 |
| εἰ | 2 | w | 2291 |
| δὲ | 10 | w | 2293 |
| ἐπὶ | 27 | w | 2296 |
| τὰ | 17 | w | 2298 |
| β | 7 | w | 2299 |
| λεπτὰ | 6 | w | 2304 |
| τὰ | 19 | w | 2306 |
| ΑΞ | 2 | w | 2308 |
| ΞΖ | 1 | w | 2311 |
| ἔσται | 2 | w | 2317 |
| λεπτὰ | 7 | w | 2322 |
| ἤτοι | 1 | w | 2326 |
| ξξ | 2 | w | 2328 |
| β | 8 | w | 2329 |
| καὶ | 25 | w | 2332 |
| τὰ | 21 | w | 2334 |
| ἑξῆς | 2 | w | 2338 |
| ὁμοίως | 4 | w | 2345 |
| οὖν | 3 | w | 2348 |
| καὶ | 26 | w | 2351 |
| μοῖρα | 12 | w | 2356 |
| ἐπὶ | 28 | w | 2359 |
| ἓν | 2 | w | 2361 |
| πρῶτον | 2 | w | 2367 |
| λεπτὸν | 5 | w | 2373 |
| ἢ | 10 | w | 2374 |
| δύο | 2 | w | 2377 |
| ποιοῦσι | 4 | w | 2385 |
| πρῶτα | 10 | w | 2390 |
| τῆς | 5 | w | 2394 |
| Α | 12 | w | 2395 |
| ὑποτεθείσης | 1 | w | 2406 |
| μοίρας | 5 | w | 2412 |
| ἓν | 3 | w | 2415 |
| ἢ | 11 | w | 2416 |
| δύο | 3 | w | 2419 |
| καὶ | 27 | w | 2422 |
| ἑξῆς | 3 | w | 2426 |