Refs | {'start': {'reference': '11', 'human_reference': 'Paragraph 11'}, 'end': {'reference': '15', 'human_reference': 'Paragraph 15'}} |
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Ancestors | [] |
Children | [] |
Φανερὸν | 1 | w | 7 |
ὅτι | 1 | w | 10 |
μοῖρα | 1 | w | 15 |
ἤτοι | 1 | w | 19 |
μοῖραι | 1 | w | 25 |
ἐπὶ | 1 | w | 28 |
λεπτὸν | 1 | w | 34 |
ἢ | 1 | w | 35 |
καὶ | 1 | w | 38 |
λεπτὰ | 1 | w | 43 |
πρῶτα | 1 | w | 48 |
πρῶτα | 2 | w | 54 |
λεπτὰ | 2 | w | 59 |
ποιεῖ | 1 | w | 64 |
ἀλλὰ | 1 | w | 69 |
δὴ | 1 | w | 71 |
πάλιν | 1 | w | 76 |
τὸ | 2 | w | 78 |
πρῶτον | 1 | w | 84 |
ξον | 1 | w | 87 |
τὸ | 3 | w | 90 |
ΑΞ | 1 | w | 92 |
διῃρήσθω | 1 | w | 101 |
εἰς | 1 | w | 104 |
ξ | 2 | w | 105 |
καὶ | 2 | w | 108 |
ὁμοίως | 1 | w | 114 |
αἱ | 1 | w | 116 |
παράλληλοι | 1 | w | 126 |
ἐπινοείσθωσαν | 1 | w | 139 |
διὰ | 1 | w | 142 |
τῶν | 1 | w | 145 |
Π | 1 | w | 146 |
Η | 1 | w | 148 |
ἔσται | 1 | w | 154 |
ἄρα | 1 | w | 157 |
τὸ | 4 | w | 159 |
ὑπὸ | 1 | w | 162 |
τῶν | 2 | w | 165 |
ΑΠ | 1 | w | 167 |
ὑπό | 1 | w | 170 |
τε | 1 | w | 172 |
μοίρας | 1 | w | 178 |
καὶ | 3 | w | 181 |
λεπτοῦ | 1 | w | 187 |
δευτέρου | 1 | w | 195 |
ἑνός | 1 | w | 199 |
καὶ | 4 | w | 203 |
γίνεται | 1 | w | 210 |
διὰ | 2 | w | 213 |
τὰ | 3 | w | 215 |
αὐτὰ | 1 | w | 219 |
μοῖρα | 3 | w | 224 |
ἐπὶ | 2 | w | 227 |
δεύτερον | 1 | w | 235 |
λεπτὸν | 2 | w | 241 |
ἔν | 1 | w | 243 |
δεύτερον | 2 | w | 252 |
λεπτὸν | 3 | w | 258 |
ἕν | 1 | w | 260 |
καὶ | 5 | w | 264 |
ὁμοίως | 2 | w | 270 |
ἐπὶ | 3 | w | 273 |
δύο | 1 | w | 276 |
δεύτερα | 1 | w | 283 |
δεύτερα | 2 | w | 291 |
δύο | 2 | w | 294 |
διαιρεθέντος | 1 | w | 307 |
δὲ | 1 | w | 309 |
τοῦ | 2 | w | 312 |
πρώτου | 1 | w | 318 |
ξ | 3 | w | 319 |
τῶν | 3 | w | 322 |
δευτέρων | 1 | w | 330 |
ἔξ | 1 | w | 332 |
τοῦ | 3 | w | 335 |
ΑΠ | 2 | w | 337 |
εἰς | 2 | w | 340 |
ξ | 5 | w | 341 |
τὰ | 5 | w | 344 |
αὐτὰ | 2 | w | 348 |
φήσομεν | 1 | w | 355 |
καὶ | 6 | w | 358 |
τοῦτο | 1 | w | 363 |
ἀεί | 1 | w | 366 |
ὥστε | 1 | w | 371 |
μοῖρα | 4 | w | 376 |
ἢ | 2 | w | 377 |
καὶ | 7 | w | 380 |
μοῖραι | 2 | w | 386 |
ἐφʼ | 1 | w | 389 |
ἄν | 1 | w | 391 |
εἶδος | 1 | w | 396 |
πολλαπλασιασθῶσι | 1 | w | 412 |
ποιήσουσι | 1 | w | 421 |
τὸ | 7 | w | 423 |
αὐτὸ | 1 | w | 427 |
ἐξ | 1 | w | 429 |
ἀνάγκης | 1 | w | 436 |
εἶδος | 2 | w | 441 |
Πάλιν | 1 | w | 447 |
δὴ | 2 | w | 449 |
ἔστω | 1 | w | 453 |
ἡ | 1 | w | 454 |
Α | 4 | w | 455 |
διῃρημένη | 1 | w | 464 |
εἰς | 3 | w | 467 |
ξ | 7 | w | 468 |
ὧν | 1 | w | 471 |
δύο | 3 | w | 474 |
ἔστω | 2 | w | 478 |
τὰ | 7 | w | 480 |
ΑΣ | 1 | w | 482 |
ΣΥ | 1 | w | 485 |
ξξ | 1 | w | 487 |
πρῶτα | 3 | w | 492 |
ἐὰν | 1 | w | 496 |
δὴ | 3 | w | 498 |
πολλαπλασιάσω | 1 | w | 511 |
τὸ | 9 | w | 513 |
πρῶτον | 2 | w | 519 |
ξ | 10 | w | 520 |
τὸ | 10 | w | 522 |
ΑΞ | 2 | w | 524 |
ἐπὶ | 4 | w | 527 |
τὸ | 11 | w | 529 |
πρῶτον | 3 | w | 535 |
τὸ | 12 | w | 537 |
ΑΣ | 2 | w | 539 |
ἔσται | 2 | w | 545 |
τὸ | 13 | w | 547 |
γενόμενον | 1 | w | 556 |
τὸ | 14 | w | 558 |
ΑΧ | 1 | w | 560 |
δεύτερον | 3 | w | 568 |
γενόμενον | 2 | w | 577 |
γίνεται | 2 | w | 585 |
γὰρ | 1 | w | 588 |
τοῦ | 5 | w | 591 |
ΑΒ | 1 | w | 593 |
γχ | 1 | w | 595 |
μέρος | 1 | w | 600 |
ὁμοίως | 3 | w | 607 |
κἂν | 1 | w | 610 |
δύο | 4 | w | 613 |
πρῶτα | 4 | w | 618 |
λεπτὰ | 3 | w | 623 |
τὰ | 9 | w | 625 |
Υ | 2 | w | 626 |
ἐπὶ | 5 | w | 629 |
δύο | 5 | w | 632 |
ὁμοίως | 4 | w | 638 |
πρῶτα | 5 | w | 643 |
τὰ | 10 | w | 645 |
Α | 10 | w | 646 |
πολλαπλασιάζοις | 1 | w | 661 |
ἕξεις | 1 | w | 667 |
χωορίον | 1 | w | 674 |
γινόμενον | 1 | w | 683 |
τὸ | 15 | w | 685 |
ΑΦ | 1 | w | 687 |
τοιούτων | 1 | w | 696 |
γὰρ | 2 | w | 699 |
ὂν | 1 | w | 701 |
τεσσάρων | 1 | w | 709 |
οἵων | 1 | w | 713 |
τὸ | 16 | w | 715 |
ΑΒ | 2 | w | 717 |
γχ | 2 | w | 719 |
ὥστε | 2 | w | 724 |
τὰ | 11 | w | 726 |
γινόμενα | 1 | w | 734 |
ἔσται | 3 | w | 739 |
δεύτερα | 3 | w | 746 |
καὶ | 8 | w | 749 |
τοῦτο | 2 | w | 754 |
ἑξῆς | 1 | w | 758 |
ὥστε | 3 | w | 763 |
πρῶτα | 6 | w | 768 |
ἐπὶ | 6 | w | 771 |
πρῶτα | 7 | w | 776 |
ποιεῖ | 2 | w | 781 |
δεύτερα | 4 | w | 788 |
1 | 1 | w | 790 |
εἰς | 4 | w | 793 |
delevi | 1 | w | 799 |
2 | 1 | w | 801 |
δὴ | 4 | w | 803 |
δὲ | 2 | w | 806 |
AB | 1 | w | 808 |
2 | 2 | w | 809 |
3 | 1 | w | 811 |
τὸ | 17 | w | 813 |
ΑΟ | 1 | w | 815 |
τῆς | 1 | w | 819 |
αο | 1 | w | 821 |
A | 2 | w | 822 |
6 | 1 | w | 824 |
ἓν | 1 | w | 826 |
ἢ | 3 | w | 827 |
addidi | 1 | w | 833 |
19 | 1 | w | 835 |
ΑΣ | 3 | w | 837 |
ΣΥ | 2 | w | 839 |
ασυ | 1 | w | 843 |
AB | 2 | w | 845 |
23 | 1 | w | 848 |
πολλαπλασίας | 1 | w | 860 |
A | 4 | w | 861 |
πολλαπλασίαζ | 1 | w | 874 |
B | 3 | w | 875 |
cum | 1 | w | 879 |
marginali | 1 | w | 888 |
coniectura | 1 | w | 898 |
πολλαπλασιάζοις | 2 | w | 913 |
24 | 1 | w | 916 |
τοιοῦτον | 1 | w | 924 |
AB | 3 | w | 926 |
26 | 1 | w | 929 |
πρῶτον | 4 | w | 935 |
ἐπὶ | 7 | w | 938 |
πρῶτον | 5 | w | 944 |
AB | 4 | w | 946 |
Πάλιν | 2 | w | 952 |
δὴ | 5 | w | 954 |
ἔστω | 3 | w | 958 |
τοῦ | 7 | w | 962 |
ΑΣ | 4 | w | 964 |
διαιρεθέντος | 2 | w | 976 |
πρώτου | 2 | w | 982 |
ξου | 1 | w | 985 |
εἰς | 5 | w | 988 |
δεύτερα | 5 | w | 995 |
ξξα | 1 | w | 998 |
ὧν | 2 | w | 1001 |
δύο | 6 | w | 1004 |
τὰ | 12 | w | 1006 |
ΑΡ | 1 | w | 1008 |
ΡΨ | 1 | w | 1010 |
ἐὰν | 2 | w | 1014 |
μὲν | 1 | w | 1017 |
πρῶτα | 8 | w | 1022 |
ἐπὶ | 8 | w | 1025 |
δεύτερα | 6 | w | 1032 |
οἷον | 1 | w | 1037 |
τὸ | 18 | w | 1039 |
ΞΑ | 1 | w | 1041 |
ἐπὶ | 9 | w | 1044 |
τὴν | 1 | w | 1047 |
ΨΑ | 1 | w | 1049 |
τουτέστι | 1 | w | 1057 |
πρῶτον | 6 | w | 1063 |
λεπτὸν | 4 | w | 1069 |
ἓν | 2 | w | 1071 |
ἐπὶ | 10 | w | 1074 |
δεύτερα | 7 | w | 1081 |
δύο | 7 | w | 1084 |
γίνονται | 1 | w | 1093 |
τρίτα | 1 | w | 1098 |
λεπτὰ | 4 | w | 1103 |
δύο | 8 | w | 1106 |
τὰ | 14 | w | 1109 |
δὲ | 3 | w | 1111 |
τρίτα | 2 | w | 1116 |
λεπτὰ | 5 | w | 1121 |
δύο | 9 | w | 1124 |
γίνεται | 3 | w | 1131 |
δευτέρου | 2 | w | 1139 |
ἑξηκοστὰ | 1 | w | 1147 |
δύο | 10 | w | 1150 |
ὅπερ | 1 | w | 1155 |
δὴ | 6 | w | 1157 |
καὶ | 9 | w | 1160 |
ὁρᾶται | 1 | w | 1166 |
ἔστι | 1 | w | 1171 |
γὰρ | 3 | w | 1174 |
τοῦ | 8 | w | 1177 |
Α | 19 | w | 1178 |
ὄντος | 1 | w | 1183 |
δευτέρου | 3 | w | 1191 |
ξ | 17 | w | 1193 |
γχου | 1 | w | 1197 |
δύο | 11 | w | 1200 |
ἑξηκοστά | 1 | w | 1208 |
ἀλλὰ | 2 | w | 1213 |
δὴ | 7 | w | 1215 |
κἂν | 2 | w | 1218 |
δύο | 12 | w | 1221 |
πρῶτα | 9 | w | 1226 |
ἐπὶ | 11 | w | 1229 |
δύο | 13 | w | 1232 |
δεύτερα | 8 | w | 1239 |
πολλαπλασιάζοις | 3 | w | 1254 |
ἑξῆς | 2 | w | 1258 |
γίνεται | 4 | w | 1266 |
τρίτα | 3 | w | 1271 |
διὰ | 3 | w | 1274 |
τὰ | 17 | w | 1276 |
εἰρημένα | 1 | w | 1284 |
εἰ | 7 | w | 1287 |
δὲ | 4 | w | 1289 |
δεύτερα | 9 | w | 1296 |
ἐπὶ | 12 | w | 1299 |
δεύτερα | 10 | w | 1306 |
τέταρτα | 1 | w | 1314 |
ἐὰν | 3 | w | 1318 |
γὰρ | 4 | w | 1321 |
τὰ | 18 | w | 1323 |
ΑΡ | 2 | w | 1325 |
ΡΨ | 2 | w | 1327 |
δεύτερα | 11 | w | 1334 |
δύο | 14 | w | 1337 |
ἐπὶ | 13 | w | 1340 |
τὰ | 19 | w | 1342 |
ΑΠ | 3 | w | 1344 |
ΠΗ | 1 | w | 1347 |
ὁμοίως | 5 | w | 1353 |
δύο | 15 | w | 1356 |
δεύτερα | 12 | w | 1363 |
ποιῶν | 1 | w | 1368 |
πολλαπλασιάσῃς | 1 | w | 1382 |
ἓξεις | 1 | w | 1388 |
τὸ | 20 | w | 1390 |
Α | 22 | w | 1391 |
χωρίον | 1 | w | 1397 |
γινόμενον | 2 | w | 1406 |
λεπτῶν | 1 | w | 1412 |
δ | 55 | w | 1413 |
τετάρτων | 1 | w | 1421 |
γίνεται | 5 | w | 1429 |
γὰρ | 5 | w | 1432 |
ὁμοίως | 6 | w | 1438 |
τοιούτων | 2 | w | 1446 |
τὸ | 21 | w | 1448 |
ΑΤ | 1 | w | 1450 |
τεσσάρων | 2 | w | 1458 |
οἵων | 2 | w | 1462 |
τὸ | 22 | w | 1464 |
ΑΧ | 2 | w | 1466 |
γχ | 4 | w | 1468 |
Σαφηνισθέντωον | 1 | w | 1483 |
δὴ | 8 | w | 1485 |
τῶν | 5 | w | 1488 |
πολλαπλασιασμῶν | 1 | w | 1503 |
δεικτέον | 1 | w | 1512 |
ἑξῆς | 3 | w | 1516 |
πῶς | 1 | w | 1519 |
τε | 23 | w | 1521 |
δεῖ | 1 | w | 1524 |
πολλαπλασιάζειν | 1 | w | 1539 |
καὶ | 10 | w | 1542 |
ἔτι | 1 | w | 1545 |
πῶς | 2 | w | 1548 |
μερίζειν | 1 | w | 1556 |
πρῶτον | 7 | w | 1563 |
ὁρισαμένους | 1 | w | 1574 |
τί | 1 | w | 1576 |
ἐστι | 1 | w | 1580 |
μερισμός | 1 | w | 1588 |
μερισμὸς | 1 | w | 1597 |
γάρ | 1 | w | 1600 |
ἐστιν | 1 | w | 1605 |
ἀριθμοῦ | 1 | w | 1612 |
τινος | 1 | w | 1617 |
κατὰ | 1 | w | 1621 |
ἕτερον | 1 | w | 1627 |
ἀριθμὸν | 1 | w | 1634 |
διαίρεσις | 1 | w | 1643 |
εἰς | 6 | w | 1646 |
ἴσα | 1 | w | 1649 |
τε | 25 | w | 1651 |
καὶ | 11 | w | 1654 |
ἰσοπληθῆ | 1 | w | 1662 |
ταῖς | 1 | w | 1666 |
τοῦ | 9 | w | 1669 |
ἀριθμοῦ | 2 | w | 1676 |
μονάσι | 1 | w | 1682 |
διαιρουμένου | 1 | w | 1694 |
εἴτε | 1 | w | 1699 |
μονάδας | 1 | w | 1706 |
ἐπὶ | 14 | w | 1709 |
μονάδας | 2 | w | 1716 |
μερίζειν | 2 | w | 1724 |
δέοι | 1 | w | 1728 |
εἴτε | 2 | w | 1733 |
λεπτὰ | 6 | w | 1738 |
ἐπὶ | 15 | w | 1741 |
λεπτά | 1 | w | 1746 |
εἴτε | 3 | w | 1751 |
λεπτὰ | 7 | w | 1756 |
καὶ | 12 | w | 1759 |
μονάδας | 3 | w | 1766 |
ἐπὶ | 16 | w | 1769 |
λεπτὰ | 8 | w | 1774 |
καὶ | 13 | w | 1777 |
μονάδας | 4 | w | 1784 |
Λέγεται | 1 | w | 1792 |
δὲ | 5 | w | 1794 |
καὶ | 14 | w | 1797 |
ἄλλως | 1 | w | 1802 |
μερίζεσθαι | 1 | w | 1812 |
ἀριθμός | 1 | w | 1819 |
ὁπόταν | 1 | w | 1826 |
διαιρῆται | 1 | w | 1835 |
εἰς | 7 | w | 1838 |
ἄνισα | 1 | w | 1843 |
ὁποσαοῦν | 1 | w | 1851 |
ἀπλῶς | 1 | w | 1857 |
γὰρ | 6 | w | 1860 |
παρὰ | 1 | w | 1864 |
τὸ | 23 | w | 1866 |
διαμερίζεσθαι | 1 | w | 1879 |
τὴν | 2 | w | 1882 |
τοῦ | 10 | w | 1885 |
ἀριθμοῦ | 3 | w | 1892 |
σύνθεσιν | 1 | w | 1900 |
ἀλλʼ | 1 | w | 1905 |
ἐπιστῆσαί | 1 | w | 1914 |
ἐστιν | 2 | w | 1919 |
ὅτι | 2 | w | 1922 |
ἄλλο | 1 | w | 1926 |
τι | 10 | w | 1928 |
ποιεῖ | 3 | w | 1933 |
ὁ | 11 | w | 1934 |
μερισμὸς | 2 | w | 1942 |
οὗτος | 1 | w | 1947 |
διὸ | 1 | w | 1951 |
καὶ | 15 | w | 1954 |
οἱ | 1 | w | 1956 |
πολλοὶ | 1 | w | 1962 |
μᾶλλον | 1 | w | 1968 |
τὸ | 24 | w | 1970 |
τοιοῦτο | 2 | w | 1977 |
διαίρεσιν | 1 | w | 1986 |
ἀριθμοῦ | 4 | w | 1993 |
καλοῦσιν | 1 | w | 2001 |
οὐκέτι | 1 | w | 2008 |
δὲ | 6 | w | 2010 |
μερισμόν | 1 | w | 2018 |
ὁ | 12 | w | 2020 |
γὰρ | 7 | w | 2023 |
κυρίως | 1 | w | 2029 |
μερισμὸς | 3 | w | 2037 |
τεταγμένος | 1 | w | 2047 |
ἐστί | 1 | w | 2051 |
κατὰ | 2 | w | 2056 |
γὰρ | 8 | w | 2059 |
τὴν | 3 | w | 2062 |
αὐτὴν | 1 | w | 2067 |
τάξιν | 1 | w | 2072 |
τῷ | 1 | w | 2074 |
πολλαπλασιασμῷ | 1 | w | 2088 |
7 | 1 | w | 2089 |
γχ | 5 | w | 2091 |
glossam | 1 | w | 2098 |
delevi | 2 | w | 2104 |
9 | 2 | w | 2106 |
δεύτερα | 13 | w | 2113 |
alt | 1 | w | 2116 |
β | 1 | w | 2119 |
β | 2 | w | 2120 |
B | 6 | w | 2121 |
β | 3 | w | 2123 |
β | 4 | w | 2124 |
δύο | 16 | w | 2127 |
A | 7 | w | 2128 |
11 | 1 | w | 2131 |
ΑΤ | 2 | w | 2133 |
α | 128 | w | 2135 |
AB | 5 | w | 2139 |
13 | 1 | w | 2142 |
τοιούτων | 3 | w | 2150 |
τὸ | 25 | w | 2152 |
τοῖς | 1 | w | 2157 |
AB | 6 | w | 2159 |
οἵων | 3 | w | 2164 |
ὁμοίων | 1 | w | 2171 |
AB | 7 | w | 2173 |
23 | 2 | w | 2176 |
διαιρεῖται | 1 | w | 2186 |
AB | 8 | w | 2188 |
25 | 1 | w | 2191 |
ὅτι | 3 | w | 2194 |
ὅταν | 1 | w | 2199 |
B | 11 | w | 2200 |
τέτακται | 1 | w | 2209 |
κἂν | 3 | w | 2213 |
δοκῇ | 1 | w | 2217 |
ἐναντίως | 1 | w | 2225 |
αὐτῷ | 1 | w | 2229 |
ἔχειν | 1 | w | 2234 |
ὅτι | 4 | w | 2238 |
ὁ | 14 | w | 2239 |
μὲν | 2 | w | 2242 |
σύνθεσις | 1 | w | 2250 |
οὗτος | 2 | w | 2256 |
δὲ | 7 | w | 2258 |
διαίρεσίς | 1 | w | 2267 |
ἐστι | 4 | w | 2271 |
τάξιν | 2 | w | 2277 |
δὲ | 8 | w | 2279 |
ὁμοίαν | 1 | w | 2285 |
ἔχουσιν | 1 | w | 2292 |
ὅτι | 5 | w | 2295 |
ὥσπερ | 1 | w | 2301 |
ἐκεῖνος | 1 | w | 2308 |
ἰσάκις | 1 | w | 2314 |
συνετέθη | 1 | w | 2322 |
οὕτως | 1 | w | 2328 |
καὶ | 16 | w | 2331 |
οὗτος | 3 | w | 2336 |
ἰσάκις | 2 | w | 2342 |
μερίζεται | 1 | w | 2351 |
ὁ | 16 | w | 2353 |
γὰρ | 9 | w | 2356 |
μερίζων | 1 | w | 2363 |
κατὰ | 3 | w | 2367 |
ἕτερον | 2 | w | 2373 |
ἀριθμὸν | 2 | w | 2380 |
μερίζει | 3 | w | 2387 |
δοθέντα | 1 | w | 2394 |
τοῦτο | 3 | w | 2400 |
γὰρ | 10 | w | 2403 |
τέλος | 1 | w | 2408 |
τοῦ | 12 | w | 2411 |
μερισμοῦ | 1 | w | 2419 |
τὸ | 26 | w | 2422 |
εὑρεῖν | 1 | w | 2428 |
ἀριθμόν | 1 | w | 2435 |
τινα | 1 | w | 2439 |
ὃς | 1 | w | 2441 |
πολλαπλασιαζόμενος | 1 | w | 2459 |
ἤτοι | 2 | w | 2463 |
συντιθέμενος | 1 | w | 2475 |
ἐπὶ | 17 | w | 2478 |
τὸν | 5 | w | 2481 |
παρʼ | 1 | w | 2485 |
ὃν | 1 | w | 2487 |
γίνεται | 6 | w | 2494 |
ὁ | 17 | w | 2495 |
μερισμός | 2 | w | 2503 |
ποιήσει | 1 | w | 2511 |
τὸ | 28 | w | 2513 |
τοῦ | 13 | w | 2516 |
μεριζομένου | 1 | w | 2527 |
πλῆθος | 1 | w | 2533 |