| Refs | {'start': {'reference': '21', 'human_reference': 'Section 21'}, 'end': {'reference': '25', 'human_reference': 'Section 25'}} |
|---|---|
| Ancestors | [] |
| Children | [] |
| τήν | 1 | w | 3 |
| τε | 1 | w | 5 |
| ἀριθμητικήν | 1 | w | 16 |
| ἣ | 1 | w | 18 |
| τῷ | 1 | w | 20 |
| ἰσαρίθμῳ | 1 | w | 28 |
| ὑπερέχει | 1 | w | 36 |
| καὶ | 1 | w | 39 |
| ὑπερέχεται | 1 | w | 49 |
| οἷον | 1 | w | 54 |
| ἐπὶ | 1 | w | 57 |
| τοῦ | 1 | w | 60 |
| ἓν | 1 | w | 62 |
| καὶ | 2 | w | 65 |
| δύο | 1 | w | 68 |
| καὶ | 3 | w | 71 |
| τρία | 1 | w | 75 |
| καὶ | 4 | w | 79 |
| τὴν | 1 | w | 82 |
| γεωμετρικήν | 1 | w | 93 |
| καθ | 1 | w | 97 |
| ἣν | 1 | w | 100 |
| οἷος | 1 | w | 104 |
| ὁ | 1 | w | 105 |
| λόγος | 1 | w | 110 |
| πρὸς | 1 | w | 114 |
| τὸν | 1 | w | 117 |
| πρῶτον | 1 | w | 123 |
| τοῦ | 2 | w | 126 |
| δευτέρου | 1 | w | 134 |
| τοιοῦτος | 1 | w | 143 |
| καὶ | 5 | w | 146 |
| ὁ | 2 | w | 147 |
| πρὸς | 2 | w | 151 |
| τὸν | 2 | w | 154 |
| δεύτερον | 1 | w | 162 |
| τοῦ | 3 | w | 165 |
| τρίτου | 1 | w | 171 |
| ὡς | 1 | w | 174 |
| ἔχει | 1 | w | 178 |
| ἐπὶ | 2 | w | 181 |
| τοῦ | 4 | w | 184 |
| ἓν | 2 | w | 186 |
| καὶ | 6 | w | 189 |
| δύο | 2 | w | 192 |
| καὶ | 7 | w | 195 |
| τέσσαρα | 1 | w | 202 |
| ἔν | 1 | w | 205 |
| τε | 3 | w | 207 |
| διπλασίοις | 1 | w | 217 |
| καὶ | 8 | w | 220 |
| τριπλασίοις | 1 | w | 231 |
| καὶ | 9 | w | 234 |
| συνόλως | 1 | w | 241 |
| πολυπλασίοις | 1 | w | 253 |
| καὶ | 10 | w | 256 |
| πάλιν | 1 | w | 261 |
| ἐν | 1 | w | 263 |
| ἡμιολίοις | 1 | w | 272 |
| καὶ | 11 | w | 275 |
| ἐπιτρίτοις | 1 | w | 285 |
| καὶ | 12 | w | 288 |
| τοῖς | 1 | w | 292 |
| παραπλησίοις | 1 | w | 304 |
| ἔτι | 1 | w | 308 |
| μέντοι | 1 | w | 314 |
| καὶ | 13 | w | 317 |
| τὴν | 2 | w | 320 |
| ἁρμονικήν | 1 | w | 329 |
| καθ | 2 | w | 333 |
| ἣν | 2 | w | 336 |
| ὁ | 3 | w | 337 |
| μέσος | 1 | w | 342 |
| τῶν | 1 | w | 345 |
| ἄκρων | 1 | w | 350 |
| τῷ | 2 | w | 352 |
| ἴσῳ | 1 | w | 355 |
| μορίῳ | 1 | w | 360 |
| ὑπερέχει | 2 | w | 368 |
| τε | 4 | w | 370 |
| καὶ | 14 | w | 373 |
| ὑπερέχεται | 2 | w | 383 |
| ὡς | 2 | w | 386 |
| ἔχει | 2 | w | 390 |
| ἐπὶ | 3 | w | 393 |
| τοῦ | 5 | w | 396 |
| τρίτου | 2 | w | 402 |
| καὶ | 15 | w | 405 |
| τετάρτου | 1 | w | 413 |
| καὶ | 16 | w | 416 |
| ἕκτου | 1 | w | 421 |
| περιέχει | 1 | w | 430 |
| δὲ | 1 | w | 432 |
| ἡ | 2 | w | 433 |
| δεκὰς | 1 | w | 438 |
| καὶ | 17 | w | 441 |
| τὰς | 1 | w | 444 |
| τῶν | 2 | w | 447 |
| τριγώνων | 1 | w | 455 |
| καὶ | 18 | w | 458 |
| τετραγώνων | 1 | w | 468 |
| καὶ | 19 | w | 471 |
| τῶν | 3 | w | 474 |
| ἄλλων | 1 | w | 479 |
| πολυγώνων | 1 | w | 488 |
| ἐμφαινομένας | 1 | w | 500 |
| ἰδιότητας | 1 | w | 509 |
| καὶ | 20 | w | 512 |
| τὰς | 2 | w | 515 |
| τῶν | 4 | w | 518 |
| συμφωνιῶν | 1 | w | 527 |
| τήν | 2 | w | 531 |
| τε | 7 | w | 533 |
| διὰ | 1 | w | 536 |
| τεσσάρων | 1 | w | 544 |
| ἐν | 2 | w | 546 |
| ἐπιτρίτῳ | 1 | w | 554 |
| λόγῳ | 1 | w | 558 |
| τῷ | 3 | w | 561 |
| τέσσαρα | 2 | w | 568 |
| πρὸς | 3 | w | 572 |
| τρία | 2 | w | 576 |
| καὶ | 21 | w | 580 |
| τὴν | 3 | w | 583 |
| διὰ | 2 | w | 586 |
| πέντε | 1 | w | 591 |
| ἐν | 3 | w | 593 |
| ἡμιολίῳ | 1 | w | 600 |
| τῷ | 4 | w | 603 |
| τρία | 3 | w | 607 |
| πρὸς | 4 | w | 611 |
| δύο | 3 | w | 614 |
| καὶ | 22 | w | 618 |
| τὴν | 4 | w | 621 |
| διὰ | 3 | w | 624 |
| πασῶν | 1 | w | 629 |
| ἐν | 4 | w | 631 |
| διπλασίῳ | 1 | w | 639 |
| τῷ | 5 | w | 642 |
| δύο | 4 | w | 645 |
| πρὸς | 5 | w | 649 |
| ἕν | 1 | w | 651 |
| καὶ | 23 | w | 655 |
| τὴν | 5 | w | 658 |
| δὶς | 1 | w | 661 |
| διὰ | 4 | w | 664 |
| πασῶν | 2 | w | 669 |
| ἐν | 5 | w | 671 |
| τετραπλασίῳ | 1 | w | 682 |
| τῷ | 6 | w | 685 |
| ὀκτὼ | 1 | w | 689 |
| πρὸς | 6 | w | 693 |
| δύο | 5 | w | 696 |
| παρό | 1 | w | 701 |
| μοι | 1 | w | 704 |
| δοκοῦσι | 1 | w | 711 |
| καὶ | 24 | w | 714 |
| οἱ | 1 | w | 716 |
| πρῶτοι | 1 | w | 722 |
| τὰ | 3 | w | 724 |
| ὀνόματα | 1 | w | 731 |
| τοῖς | 2 | w | 735 |
| πράγμασι | 1 | w | 743 |
| θέμενοι | 1 | w | 750 |
| σοφοὶ | 1 | w | 756 |
| γὰρ | 1 | w | 759 |
| ἦσαν | 1 | w | 763 |
| εἰκότως | 1 | w | 771 |
| αὐτὴν | 1 | w | 776 |
| προσαγορεῦσαι | 1 | w | 789 |
| δεκάδα | 1 | w | 795 |
| ὡσανεὶ | 1 | w | 802 |
| δεχάδα | 1 | w | 808 |
| οὖσαν | 1 | w | 813 |
| παρὰ | 1 | w | 818 |
| τὸ | 3 | w | 820 |
| δέχεσθαι | 1 | w | 828 |
| καὶ | 25 | w | 831 |
| κεχωρηκέναι | 1 | w | 842 |
| τὰ | 4 | w | 844 |
| γένη | 1 | w | 848 |
| πάντα | 1 | w | 853 |
| τῶν | 5 | w | 856 |
| ἀριθμῶν | 1 | w | 863 |
| καὶ | 26 | w | 866 |
| λόγων | 1 | w | 871 |
| τῶν | 6 | w | 874 |
| κατ | 1 | w | 877 |
| ἀριθμὸν | 1 | w | 885 |
| 1 | 1 | w | 886 |
| εὐθὺς | 1 | w | 891 |
| M | 1 | w | 892 |
| 1 | 2 | w | 893 |
| 2 | 1 | w | 895 |
| περατουμένων | 1 | w | 907 |
| codd | 1 | w | 911 |
| περαιουμένων | 1 | w | 925 |
| Turn | 1 | w | 929 |
| περανουμένων | 1 | w | 943 |
| Mang | 1 | w | 947 |
| 2 | 2 | w | 949 |
| ἣ | 4 | w | 950 |
| εἰ | 2 | w | 953 |
| M | 3 | w | 954 |
| ἀριθμῶν | 2 | w | 961 |
| ἀριθμουμένων | 1 | w | 974 |
| AP | 1 | w | 976 |
| διαφορὰς | 1 | w | 984 |
| ἀρτίων | 1 | w | 990 |
| ἀριθμῶν | 3 | w | 997 |
| transp | 1 | w | 1003 |
| G | 1 | w | 1005 |
| 2 | 3 | w | 1006 |
| 3 | 1 | w | 1008 |
| καὶ | 27 | w | 1011 |
| ἀρτιοπερίττων | 1 | w | 1024 |
| om | 1 | w | 1026 |
| L | 1 | w | 1028 |
| Turn | 2 | w | 1033 |
| 3 | 2 | w | 1036 |
| δυοῖν | 1 | w | 1041 |
| ex | 1 | w | 1043 |
| δυεῖν | 1 | w | 1048 |
| corr | 1 | w | 1052 |
| Η | 1 | w | 1054 |
| δυεῖν | 2 | w | 1060 |
| FG | 1 | w | 1062 |
| 4 | 1 | w | 1063 |
| 5 | 1 | w | 1065 |
| ὑποεπιμερῶν | 1 | w | 1076 |
| M | 4 | w | 1077 |
| ἐπιμορίων | 1 | w | 1087 |
| ceteri | 1 | w | 1093 |
| v | 1 | w | 1095 |
| 5 | 2 | w | 1097 |
| δὲ | 2 | w | 1099 |
| M | 5 | w | 1100 |
| om | 2 | w | 1103 |
| Arm | 1 | w | 1107 |
| ἡ | 4 | w | 1108 |
| τῷ | 7 | w | 1110 |
| τῷ | 8 | w | 1113 |
| γὰρ | 2 | w | 1116 |
| Arm | 2 | w | 1119 |
| 5 | 3 | w | 1120 |
| 6 | 1 | w | 1122 |
| τῶν | 7 | w | 1125 |
| ἰσαρίθμων | 1 | w | 1134 |
| AP | 2 | w | 1136 |
| τῶ | 8 | w | 1139 |
| ἴσω | 1 | w | 1142 |
| ἀριθμῶ | 4 | w | 1148 |
| M | 6 | w | 1149 |
| 6 | 2 | w | 1150 |
| ἐπὶ | 4 | w | 1153 |
| τὸ | 4 | w | 1155 |
| α | 76 | w | 1156 |
| καὶ | 28 | w | 1160 |
| β | 1 | w | 1161 |
| καὶ | 29 | w | 1165 |
| γ | 13 | w | 1166 |
| M | 7 | w | 1168 |
| 7 | 1 | w | 1169 |
| 8 | 1 | w | 1171 |
| πρὸς | 7 | w | 1175 |
| τὸν | 3 | w | 1178 |
| πρῶτον | 2 | w | 1184 |
| τοῦ | 6 | w | 1187 |
| δευτέρου | 2 | w | 1195 |
| τοῦ | 7 | w | 1199 |
| α | 79 | w | 1200 |
| πρὸς | 8 | w | 1205 |
| τὸν | 4 | w | 1208 |
| τοῦ | 8 | w | 1211 |
| β | 2 | w | 1212 |
| M | 8 | w | 1214 |
| 8 | 2 | w | 1215 |
| τοιοῦτος | 2 | w | 1223 |
| om | 3 | w | 1225 |
| AP1 | 1 | w | 1229 |
| ὁ | 4 | w | 1230 |
| MH | 1 | w | 1232 |
| om | 4 | w | 1235 |
| ceteri | 2 | w | 1242 |
| πρὸς | 9 | w | 1246 |
| τὸν | 5 | w | 1249 |
| δεύτερον | 2 | w | 1257 |
| τοῦ | 9 | w | 1260 |
| τρίτου | 3 | w | 1266 |
| τοῦ | 10 | w | 1270 |
| β | 3 | w | 1271 |
| πρὸς | 10 | w | 1276 |
| τὸν | 6 | w | 1279 |
| γ | 14 | w | 1280 |
| M | 10 | w | 1282 |
| 9 | 1 | w | 1283 |
| τοῦ | 11 | w | 1286 |
| τὸ | 9 | w | 1289 |
| F | 2 | w | 1290 |
| om | 5 | w | 1293 |
| M | 11 | w | 1295 |
| ἓν | 3 | w | 1297 |
| καὶ | 30 | w | 1300 |
| ἓν | 4 | w | 1302 |
| ὁ | 5 | w | 1303 |
| εῖς | 1 | w | 1306 |
| καὶ | 31 | w | 1309 |
| δύο | 6 | w | 1312 |
| καὶ | 32 | w | 1315 |
| τρεῖς | 1 | w | 1320 |
| καὶ | 33 | w | 1323 |
| τριάκοντα | 1 | w | 1332 |
| τέσσαρες | 1 | w | 1340 |
| M | 12 | w | 1341 |
| τέτταρα | 1 | w | 1348 |
| AP | 4 | w | 1350 |
| 9 | 2 | w | 1351 |
| 10 | 1 | w | 1354 |
| καὶ | 34 | w | 1357 |
| συνόλως | 2 | w | 1364 |
| πολυπλασίοις | 2 | w | 1376 |
| MF | 1 | w | 1378 |
| Arm | 3 | w | 1381 |
| om | 6 | w | 1384 |
| ceteri | 3 | w | 1391 |
| 12 | 1 | w | 1393 |
| post | 1 | w | 1397 |
| μορίῳ | 2 | w | 1402 |
| add | 1 | w | 1405 |
| καὶ | 35 | w | 1409 |
| Η | 2 | w | 1410 |
| v | 2 | w | 1412 |
| ὑπερέχει | 3 | w | 1421 |
| τε | 12 | w | 1423 |
| καὶ | 36 | w | 1426 |
| ὑπερέχεται | 3 | w | 1436 |
| MF | 2 | w | 1438 |
| ὑπερέχεται | 4 | w | 1449 |
| καὶ | 37 | w | 1452 |
| ὑπερέχει | 4 | w | 1460 |
| ceteri | 4 | w | 1466 |
| v | 3 | w | 1468 |
| τρίτου | 4 | w | 1475 |
| α | 95 | w | 1477 |
| MG | 1 | w | 1480 |
| δευτέρου | 3 | w | 1489 |
| coni | 1 | w | 1493 |
| Christophorson | 1 | w | 1508 |
| Mang | 2 | w | 1513 |
| sed | 1 | w | 1519 |
| cf | 1 | w | 1521 |
| de | 1 | w | 1524 |
| opif | 1 | w | 1528 |
| mundi | 1 | w | 1534 |
| 110 | 1 | w | 1538 |
| τετάρτου | 2 | w | 1546 |
| δ | 33 | w | 1548 |
| M | 17 | w | 1550 |
| τέσσαρα | 3 | w | 1558 |
| G | 4 | w | 1559 |
| 13 | 1 | w | 1561 |
| ἕκτου | 2 | w | 1566 |
| ς | 41 | w | 1568 |
| M | 18 | w | 1570 |
| ἐς | 1 | w | 1573 |
| G | 5 | w | 1574 |
| ἕκτου | 3 | w | 1579 |
| καὶ | 38 | w | 1582 |
| τετάρτου | 3 | w | 1590 |
| καὶ | 39 | w | 1593 |
| τρίτου | 5 | w | 1599 |
| transp | 2 | w | 1605 |
| Arm | 4 | w | 1609 |
| τῶν | 8 | w | 1612 |
| H | 2 | w | 1613 |
| om | 7 | w | 1616 |
| ceteri | 5 | w | 1623 |
| 15 | 1 | w | 1625 |
| τεττάρων | 1 | w | 1633 |
| FH | 1 | w | 1635 |
| ἐν | 6 | w | 1637 |
| om | 8 | w | 1639 |
| APF | 1 | w | 1643 |
| τῷ | 9 | w | 1645 |
| τοῦ | 12 | w | 1649 |
| G | 6 | w | 1650 |
| δ | 34 | w | 1651 |
| M | 19 | w | 1653 |
| 15 | 2 | w | 1655 |
| 16 | 1 | w | 1658 |
| πρὸς | 11 | w | 1662 |
| τὸν | 7 | w | 1665 |
| τρία | 4 | w | 1669 |
| G | 7 | w | 1670 |
| 16 | 2 | w | 1672 |
| γ | 15 | w | 1673 |
| M | 20 | w | 1675 |
| γ | 16 | w | 1676 |
| M | 21 | w | 1678 |
| β | 4 | w | 1679 |
| M | 22 | w | 1681 |
| 17 | 1 | w | 1683 |
| β | 5 | w | 1684 |
| M | 23 | w | 1686 |
| α | 101 | w | 1687 |
| M | 24 | w | 1689 |
| δὶς | 2 | w | 1692 |
| καὶ | 40 | w | 1695 |
| διὰ | 5 | w | 1698 |
| Η | 3 | w | 1699 |
| 18 | 1 | w | 1701 |
| τῶ | 10 | w | 1703 |
| τὰ | 5 | w | 1706 |
| Η | 4 | w | 1707 |
| η | 6 | w | 1708 |
| M | 25 | w | 1710 |
| β | 6 | w | 1711 |
| M | 26 | w | 1712 |
| 20 | 1 | w | 1714 |
| ὡσανεὶ | 2 | w | 1720 |
| οἱονεὶ | 1 | w | 1727 |
| Ἀρ | 1 | w | 1729 |
| 21 | 1 | w | 1732 |
| συγκεχωρηκέναι | 1 | w | 1746 |
| Turn | 3 | w | 1750 |
| τὰ | 6 | w | 1753 |
| γένη | 2 | w | 1757 |
| τῶν | 9 | w | 1760 |
| ἀριθμῶν | 4 | w | 1767 |
| πάντα | 2 | w | 1772 |
| καὶ | 41 | w | 1775 |
| κεχωρηκέναι | 3 | w | 1786 |
| transp | 3 | w | 1792 |
| M | 27 | w | 1794 |
| πάντα | 3 | w | 1799 |
| τὰ | 7 | w | 1801 |
| γένη | 3 | w | 1805 |
| transp | 4 | w | 1811 |
| AP | 6 | w | 1814 |
| λόγους | 1 | w | 1820 |
| M | 28 | w | 1821 |
| ἀριθμῶν | 5 | w | 1828 |
| corr | 2 | w | 1832 |
| in | 1 | w | 1835 |
| ἀριθμὸν | 2 | w | 1842 |
| AFH | 1 | w | 1845 |
| καὶ | 42 | w | 1848 |
| ἀναλογιῶν | 1 | w | 1857 |
| ἁρμονιῶν | 1 | w | 1865 |
| τε | 16 | w | 1867 |
| αὖ | 1 | w | 1869 |
| καὶ | 43 | w | 1872 |
| συμφωνιῶν | 2 | w | 1881 |
| τὴν | 7 | w | 1885 |
| μέντοι | 2 | w | 1891 |
| δεκάδα | 2 | w | 1897 |
| πρὸς | 12 | w | 1901 |
| τοῖς | 3 | w | 1905 |
| εἰρημένοις | 1 | w | 1915 |
| καὶ | 44 | w | 1918 |
| διὰ | 6 | w | 1921 |
| ταῦτα | 1 | w | 1926 |
| εἰκότως | 2 | w | 1933 |
| ἄν | 1 | w | 1935 |
| τις | 1 | w | 1938 |
| θαυμάσειε | 1 | w | 1947 |
| περιέχουσαν | 1 | w | 1958 |
| τήν | 3 | w | 1961 |
| τε | 17 | w | 1963 |
| ἀδιάστατον | 1 | w | 1973 |
| φύσιν | 1 | w | 1978 |
| καὶ | 45 | w | 1981 |
| τὴν | 8 | w | 1984 |
| διαστηματικήν | 1 | w | 1997 |
| ἡ | 5 | w | 1999 |
| μὲν | 1 | w | 2002 |
| οὖν | 1 | w | 2005 |
| ἀδιάστατος | 1 | w | 2015 |
| τάττεται | 1 | w | 2023 |
| κατὰ | 1 | w | 2027 |
| σημεῖον | 1 | w | 2034 |
| μόνον | 1 | w | 2039 |
| ἡ | 6 | w | 2041 |
| δὲ | 3 | w | 2043 |
| διαστηματικὴ | 1 | w | 2055 |
| κατὰ | 2 | w | 2059 |
| τρεῖς | 2 | w | 2064 |
| ἰδέας | 1 | w | 2069 |
| γραμμῆς | 1 | w | 2076 |
| καὶ | 46 | w | 2079 |
| ἐπιφανείας | 1 | w | 2089 |
| καὶ | 47 | w | 2092 |
| στερεοῦ | 1 | w | 2099 |
| τὸ | 11 | w | 2102 |
| μὲν | 2 | w | 2105 |
| γὰρ | 3 | w | 2108 |
| δυσὶ | 1 | w | 2112 |
| σημείοις | 1 | w | 2120 |
| περατούμενόν | 1 | w | 2132 |
| ἐστι | 1 | w | 2136 |
| γραμμή | 1 | w | 2142 |
| τὸ | 12 | w | 2145 |
| δ | 47 | w | 2146 |
| ἐπὶ | 5 | w | 2150 |
| δύο | 7 | w | 2153 |
| διαστατὸν | 1 | w | 2162 |
| ἐπιφάνεια | 1 | w | 2171 |
| ῥυείσης | 1 | w | 2179 |
| ἐπὶ | 6 | w | 2182 |
| πλάτος | 1 | w | 2188 |
| γραμμῆς | 2 | w | 2195 |
| τὸ | 14 | w | 2198 |
| δ | 50 | w | 2199 |
| ἐπὶ | 7 | w | 2203 |
| τρία | 5 | w | 2207 |
| στερεόν | 1 | w | 2214 |
| μήκους | 1 | w | 2221 |
| καὶ | 48 | w | 2224 |
| πλάτους | 1 | w | 2231 |
| βάθος | 1 | w | 2236 |
| προσλαβόντων | 1 | w | 2248 |
| ἐφ | 1 | w | 2251 |
| ὧν | 1 | w | 2254 |
| ἵσταται | 1 | w | 2261 |
| ἡ | 7 | w | 2262 |
| φύσις | 1 | w | 2267 |
| πλείους | 1 | w | 2275 |
| γὰρ | 4 | w | 2278 |
| τριῶν | 1 | w | 2283 |
| διαστάσεις | 1 | w | 2293 |
| οὐκ | 1 | w | 2296 |
| ἐγέννησεν | 1 | w | 2305 |