| Refs | {'start': {'reference': '7', 'human_reference': 'Paragraph 7'}, 'end': {'reference': '8', 'human_reference': 'Paragraph 8'}} |
|---|---|
| Ancestors | [] |
| Children | [] |
| Λέγεται | 1 | w | 7 |
| μὲν | 1 | w | 10 |
| καὶ | 1 | w | 13 |
| ἄλλῃ | 1 | w | 17 |
| σύνθεσις | 1 | w | 25 |
| ἀλλʼ | 1 | w | 30 |
| οὐ | 1 | w | 32 |
| πολλαπλασιασμός | 1 | w | 47 |
| καὶ | 2 | w | 51 |
| γὰρ | 1 | w | 54 |
| ὁ | 1 | w | 55 |
| ἐκ | 1 | w | 57 |
| τῶν | 1 | w | 60 |
| δοθέντων | 1 | w | 68 |
| εἴτε | 1 | w | 72 |
| ἴσων | 1 | w | 76 |
| εἴτε | 2 | w | 80 |
| ἀνίσων | 1 | w | 86 |
| ἀριθμῶν | 1 | w | 93 |
| καὶ | 3 | w | 96 |
| εἴτε | 3 | w | 100 |
| δύο | 1 | w | 103 |
| ἢ | 1 | w | 104 |
| τριῶν | 1 | w | 109 |
| ἢ | 2 | w | 110 |
| καὶ | 4 | w | 113 |
| πλειόνων | 1 | w | 121 |
| συντεθείς | 1 | w | 130 |
| ἀπλῶς | 1 | w | 136 |
| λέγεται | 1 | w | 143 |
| συγκεῖσθαι | 1 | w | 153 |
| οὐ | 2 | w | 156 |
| μέντοι | 1 | w | 162 |
| πολλαπλασίων | 1 | w | 174 |
| πολλαπλασιάζομεν | 1 | w | 191 |
| δὲ | 1 | w | 193 |
| ἢ | 3 | w | 194 |
| μοῖραν | 1 | w | 200 |
| ἐπὶ | 1 | w | 203 |
| μοῖραν | 2 | w | 209 |
| ἢ | 4 | w | 210 |
| μοίρας | 1 | w | 216 |
| ἐπὶ | 2 | w | 219 |
| μοίρας | 2 | w | 225 |
| καὶ | 5 | w | 229 |
| πάλιν | 1 | w | 234 |
| ἢ | 5 | w | 235 |
| λεπτὸν | 1 | w | 241 |
| ἐπὶ | 3 | w | 244 |
| λεπτὸν | 2 | w | 250 |
| ἢ | 6 | w | 251 |
| λεπτὰ | 1 | w | 256 |
| ἐπὶ | 4 | w | 259 |
| λεπτά | 1 | w | 264 |
| καὶ | 6 | w | 268 |
| ἀνάμιξ | 1 | w | 274 |
| μοῖραν | 3 | w | 280 |
| ἐπὶ | 5 | w | 283 |
| λεπτὸν | 3 | w | 289 |
| καὶ | 7 | w | 292 |
| λεπτά | 2 | w | 297 |
| ἀλλʼ | 2 | w | 302 |
| ἡ | 1 | w | 303 |
| μὲν | 2 | w | 306 |
| μοῖρα | 4 | w | 311 |
| ἐφʼ | 1 | w | 314 |
| ὃ | 1 | w | 315 |
| ἂν | 1 | w | 317 |
| εἶδος | 1 | w | 322 |
| πολλαπλασιασθῇ | 1 | w | 336 |
| τὸ | 4 | w | 339 |
| αὐτὸ | 1 | w | 343 |
| εἶδος | 2 | w | 348 |
| ποιεῖ | 1 | w | 353 |
| ἐπὶ | 6 | w | 357 |
| γὰρ | 2 | w | 360 |
| πρῶτα | 1 | w | 365 |
| λεπτὰ | 2 | w | 370 |
| πολυπλασιαζομένη | 1 | w | 386 |
| ἡ | 2 | w | 387 |
| μοῖρα | 5 | w | 392 |
| ἢ | 7 | w | 393 |
| μοῖραι | 1 | w | 399 |
| πρῶτα | 2 | w | 404 |
| λεπτὰ | 3 | w | 409 |
| ποιοῦσιν | 1 | w | 417 |
| καὶ | 8 | w | 421 |
| ἀνάπαλιν | 1 | w | 429 |
| λεπτὰ | 4 | w | 434 |
| πρῶτα | 3 | w | 439 |
| ἐπὶ | 7 | w | 442 |
| μοῖραν | 4 | w | 448 |
| ἢ | 8 | w | 449 |
| μοίρας | 3 | w | 455 |
| ποιεῖ | 2 | w | 460 |
| πρῶτα | 4 | w | 465 |
| λεπτά | 3 | w | 470 |
| καὶ | 9 | w | 474 |
| ἐξῆς | 1 | w | 478 |
| ὁμοίως | 1 | w | 484 |
| μοῖρα | 8 | w | 491 |
| ἐπὶ | 8 | w | 494 |
| δεύτερα | 1 | w | 501 |
| δεύτερα | 2 | w | 509 |
| ποιεῖ | 3 | w | 514 |
| καὶ | 10 | w | 517 |
| ἐπὶ | 9 | w | 520 |
| τρίτα | 1 | w | 525 |
| τρίτα | 2 | w | 531 |
| καὶ | 11 | w | 534 |
| ἑξῆς | 1 | w | 538 |
| πρῶτα | 5 | w | 544 |
| δὲ | 2 | w | 546 |
| ἐπὶ | 10 | w | 549 |
| πρῶτα | 6 | w | 554 |
| ποιεῖ | 4 | w | 559 |
| δεύτερα | 3 | w | 566 |
| ἅπερ | 1 | w | 571 |
| ἐστὶν | 1 | w | 576 |
| ἐλάσσονα | 1 | w | 584 |
| τῶν | 2 | w | 587 |
| πρώτων | 1 | w | 593 |
| τῶν | 3 | w | 597 |
| μὲν | 3 | w | 600 |
| γὰρ | 3 | w | 603 |
| πρώτων | 2 | w | 609 |
| τὸ | 6 | w | 611 |
| ἕν | 1 | w | 613 |
| λεπτὸν | 4 | w | 619 |
| ξ | 4 | w | 620 |
| ἐστι | 1 | w | 624 |
| τῆς | 1 | w | 627 |
| μοίρας | 4 | w | 633 |
| τῶν | 4 | w | 637 |
| δὲ | 3 | w | 639 |
| δευτέρων | 1 | w | 647 |
| γχον | 1 | w | 652 |
| ὅπερ | 1 | w | 658 |
| 7 | 1 | w | 659 |
| κατὰ | 1 | w | 663 |
| A | 1 | w | 664 |
| ἂριθμὸν | 1 | w | 672 |
| compendio | 1 | w | 681 |
| B | 1 | w | 682 |
| καὶ | 12 | w | 686 |
| A | 2 | w | 687 |
| 8 | 1 | w | 689 |
| ἢ | 9 | w | 690 |
| AB | 1 | w | 692 |
| 12 | 1 | w | 695 |
| ἄλλη | 1 | w | 699 |
| AB | 2 | w | 701 |
| 16 | 1 | w | 704 |
| πολλαπλασίων | 2 | w | 716 |
| πολλαπλασ | 6 | w | 726 |
| A | 5 | w | 727 |
| πολλαπλάσιον | 1 | w | 740 |
| B | 4 | w | 741 |
| 19 | 1 | w | 744 |
| μοῖρα | 9 | w | 749 |
| Μ | 1 | w | 751 |
| A | 6 | w | 752 |
| μονὰς | 1 | w | 758 |
| Β | 1 | w | 759 |
| μοῖρα | 10 | w | 765 |
| in | 1 | w | 767 |
| margine | 1 | w | 774 |
| 21 | 1 | w | 777 |
| ἡ | 3 | w | 778 |
| om | 2 | w | 780 |
| B | 5 | w | 782 |
| 22 | 1 | w | 785 |
| ποιοῦσι | 2 | w | 792 |
| B | 6 | w | 793 |
| ἐπὶ | 11 | w | 797 |
| om | 3 | w | 799 |
| A | 7 | w | 801 |
| 27 | 1 | w | 804 |
| ξξ | 1 | w | 806 |
| id | 1 | w | 808 |
| est | 1 | w | 811 |
| ἑξηκοστῶν | 1 | w | 820 |
| AB | 3 | w | 822 |
| ἐναντίον | 1 | w | 831 |
| ἐστὶ | 2 | w | 835 |
| τῷ | 1 | w | 837 |
| πολλαπλασιασμῷ | 1 | w | 851 |
| τῶν | 6 | w | 854 |
| λοιπῶν | 1 | w | 860 |
| ἀριθμῶν | 2 | w | 867 |
| ἐπαυξήσει | 1 | w | 877 |
| γὰρ | 4 | w | 880 |
| πολλαπλασιάζονται | 1 | w | 897 |
| ὡς | 1 | w | 899 |
| ἐὰν | 1 | w | 902 |
| πεντάκις | 1 | w | 910 |
| τὸν | 5 | w | 913 |
| Ϛ | 1 | w | 914 |
| πλάττοντες | 1 | w | 924 |
| συνθῶμεν | 1 | w | 932 |
| καὶ | 13 | w | 935 |
| ποιήσωμεν | 1 | w | 944 |
| τὸν | 6 | w | 947 |
| λ | 57 | w | 948 |
| πρῶτα | 7 | w | 954 |
| δὲ | 4 | w | 956 |
| ε | 46 | w | 957 |
| λεπτὰ | 5 | w | 962 |
| ἐπὶ | 12 | w | 965 |
| πρῶτα | 8 | w | 970 |
| πολλαπλασιάζοντες | 1 | w | 987 |
| λ | 62 | w | 989 |
| δεύτερα | 4 | w | 996 |
| ποιοῦμεν | 1 | w | 1004 |
| ὅπερ | 2 | w | 1009 |
| ἥμισύ | 1 | w | 1014 |
| ἐστιν | 1 | w | 1019 |
| ἑνὸς | 1 | w | 1023 |
| πρώτου | 1 | w | 1029 |
| λεπτοῦ | 1 | w | 1035 |
| τοῦτο | 1 | w | 1041 |
| δὲ | 5 | w | 1043 |
| γίνεται | 1 | w | 1050 |
| διὰ | 1 | w | 1053 |
| τὴν | 1 | w | 1056 |
| τῶν | 7 | w | 1059 |
| μορίων | 1 | w | 1065 |
| πρὸς | 1 | w | 1069 |
| τὴν | 2 | w | 1072 |
| μονάδα | 1 | w | 1078 |
| ἀντιπεπόνθησιν | 1 | w | 1092 |
| ἀεὶ | 1 | w | 1096 |
| γὰρ | 5 | w | 1099 |
| τὰ | 7 | w | 1101 |
| μόρια | 1 | w | 1106 |
| πολλαπλασιαζόμενα | 1 | w | 1123 |
| ἐναντίως | 1 | w | 1131 |
| ταῖς | 1 | w | 1135 |
| μοίραις | 1 | w | 1142 |
| ἐπʼ | 1 | w | 1145 |
| ἔλαττον | 1 | w | 1152 |
| χωρεῖ | 1 | w | 1157 |
| ἐφʼ | 2 | w | 1161 |
| ἑαυτὸ | 1 | w | 1166 |
| γὰρ | 6 | w | 1169 |
| τὸ | 11 | w | 1171 |
| ἥμισυ | 1 | w | 1176 |
| πολλαπλασιαζόμενον | 1 | w | 1194 |
| τέταρτον | 1 | w | 1202 |
| γίνεται | 2 | w | 1209 |
| β | 1 | w | 1211 |
| δὲ | 6 | w | 1213 |
| μονάδες | 1 | w | 1220 |
| ἐπὶ | 13 | w | 1223 |
| β | 2 | w | 1224 |
| δ | 19 | w | 1226 |
| ποιοῦσιν | 2 | w | 1234 |
| ὁμοίως | 2 | w | 1241 |
| καὶ | 14 | w | 1244 |
| τρίτον | 1 | w | 1250 |
| ἐπὶ | 14 | w | 1253 |
| τρίτον | 2 | w | 1259 |
| ἔνναιον | 1 | w | 1267 |
| γίνεται | 3 | w | 1274 |
| γ | 14 | w | 1276 |
| δὲ | 7 | w | 1278 |
| ἐπὶ | 15 | w | 1281 |
| γ | 15 | w | 1282 |
| θ | 11 | w | 1284 |
| ὅπερ | 3 | w | 1289 |
| δοκεῖ | 1 | w | 1294 |
| λῆρον | 1 | w | 1299 |
| τοῦτο | 2 | w | 1305 |
| δὲ | 8 | w | 1307 |
| συμβαίνει | 1 | w | 1316 |
| τοῖς | 1 | w | 1320 |
| μορίοις | 1 | w | 1327 |
| ὅτι | 1 | w | 1330 |
| οὐ | 3 | w | 1332 |
| συντίθενται | 1 | w | 1343 |
| κατὰ | 2 | w | 1347 |
| μονάδα | 2 | w | 1353 |
| ἀλλὰ | 1 | w | 1358 |
| τοὐναντίον | 1 | w | 1368 |
| μερίζονται | 1 | w | 1378 |
| κατὰ | 3 | w | 1382 |
| τὰ | 10 | w | 1384 |
| ὁμώνυμα | 1 | w | 1391 |
| μέρη | 1 | w | 1395 |
| ταῖς | 2 | w | 1399 |
| μονάσιν | 1 | w | 1406 |
| τὸ | 12 | w | 1409 |
| γὰρ | 7 | w | 1412 |
| ἥμισυ | 2 | w | 1417 |
| ἐπὶ | 16 | w | 1420 |
| τὸ | 13 | w | 1422 |
| ἥμισυ | 3 | w | 1427 |
| νῦν | 1 | w | 1430 |
| οὐ | 5 | w | 1432 |
| συνετέθη | 1 | w | 1440 |
| καθʼ | 1 | w | 1444 |
| ὅλον | 1 | w | 1448 |
| ἑαυτό | 1 | w | 1453 |
| ὥσπερ | 1 | w | 1459 |
| τὰ | 11 | w | 1461 |
| β | 4 | w | 1462 |
| ἐπὶ | 17 | w | 1465 |
| τὰ | 12 | w | 1467 |
| β | 5 | w | 1468 |
| ἀλλὰ | 2 | w | 1473 |
| κατὰ | 4 | w | 1477 |
| τὸ | 14 | w | 1479 |
| ἥμισυ | 4 | w | 1484 |
| ἑαυτοῦ | 1 | w | 1490 |
| ὡς | 2 | w | 1493 |
| ἔστιν | 1 | w | 1498 |
| ἰδεῖν | 1 | w | 1503 |
| καὶ | 15 | w | 1506 |
| ἐπὶ | 18 | w | 1509 |
| διαγράμματος | 1 | w | 1521 |
| οὕτως | 1 | w | 1526 |
| Ἔστω | 1 | w | 1531 |
| γὰρ | 8 | w | 1534 |
| μοναδιαῖον | 1 | w | 1544 |
| χωρίον | 1 | w | 1550 |
| τὸ | 15 | w | 1552 |
| ΑΒ | 1 | w | 1554 |
| ἐκ | 2 | w | 1556 |
| πλευρᾶς | 1 | w | 1563 |
| τῆς | 2 | w | 1566 |
| ΑΖ | 1 | w | 1568 |
| τετράγωνον | 1 | w | 1578 |
| δίχα | 1 | w | 1582 |
| διῃρημένης | 1 | w | 1592 |
| κατὰ | 5 | w | 1596 |
| τὸ | 16 | w | 1598 |
| Γ | 1 | w | 1599 |
| καὶ | 16 | w | 1603 |
| ἀπὸ | 1 | w | 1606 |
| τῆς | 3 | w | 1609 |
| ΑΓ | 1 | w | 1611 |
| ἀναγεγράφθω | 1 | w | 1622 |
| χωρίον | 2 | w | 1628 |
| τετράγωνον | 2 | w | 1638 |
| τὸ | 17 | w | 1640 |
| Α | 4 | w | 1641 |
| Ε | 1 | w | 1642 |
| τοῦτο | 3 | w | 1647 |
| δὴ | 1 | w | 1649 |
| τέταρτον | 2 | w | 1657 |
| μέρος | 1 | w | 1662 |
| ἐστὶ | 3 | w | 1666 |
| τοῦ | 6 | w | 1669 |
| ΑΒ | 2 | w | 1671 |
| μοναδιαίου | 1 | w | 1681 |
| χωρίου | 1 | w | 1687 |
| καὶ | 17 | w | 1691 |
| ἔστιν | 2 | w | 1696 |
| ἥμισυ | 5 | w | 1701 |
| ἐπὶ | 19 | w | 1704 |
| ἥμισυ | 6 | w | 1709 |
| ἡ | 4 | w | 1711 |
| ΑΓ | 2 | w | 1713 |
| γὰρ | 9 | w | 1716 |
| ἐπὶ | 20 | w | 1719 |
| τὴν | 3 | w | 1722 |
| Α | 7 | w | 1723 |
| γέγονεν | 1 | w | 1730 |
| ὁμοίως | 3 | w | 1737 |
| οὖν | 1 | w | 1740 |
| δείξεις | 1 | w | 1747 |
| ὅτι | 2 | w | 1750 |
| καὶ | 18 | w | 1753 |
| γʹ | 1 | w | 1755 |
| ἐπὶ | 21 | w | 1758 |
| γʹ | 2 | w | 1760 |
| θʹ | 1 | w | 1763 |
| γίνεται | 4 | w | 1770 |
| καὶ | 19 | w | 1774 |
| δʹ | 1 | w | 1776 |
| ἐπὶ | 22 | w | 1779 |
| δʹ | 2 | w | 1781 |
| ιϛʹ | 1 | w | 1785 |
| οὕτως | 2 | w | 1791 |
| οὖν | 2 | w | 1794 |
| δεῖ | 2 | w | 1797 |
| νοεῖν | 1 | w | 1802 |
| καὶ | 20 | w | 1805 |
| ἐπὶ | 23 | w | 1808 |
| τῶν | 8 | w | 1811 |
| λεπτῶν | 1 | w | 1817 |
| μορίων | 2 | w | 1823 |
| ὄντων | 1 | w | 1828 |