Refs | {'start': {'reference': '21', 'human_reference': 'Paragraph 21'}, 'end': {'reference': '25', 'human_reference': 'Paragraph 25'}} |
---|---|
Ancestors | [] |
Children | [] |
ἔτι | 1 | w | 3 |
τῶν | 1 | w | 6 |
συνθέτων | 1 | w | 14 |
ἀριθμῶν | 1 | w | 21 |
οἱ | 1 | w | 23 |
μὲν | 1 | w | 26 |
ἰσάκις | 1 | w | 32 |
ἴσοι | 1 | w | 36 |
εἰσὶ | 1 | w | 40 |
καὶ | 1 | w | 43 |
τετράγωνοι | 1 | w | 53 |
καὶ | 2 | w | 56 |
ἐπίπεδοι | 1 | w | 64 |
ἐπειδὰν | 1 | w | 72 |
ἴσος | 1 | w | 76 |
ἐπὶ | 1 | w | 79 |
ἴσον | 1 | w | 83 |
πολλαπλασιασθεὶς | 1 | w | 99 |
γεννήσῃ | 1 | w | 106 |
τινὰ | 1 | w | 110 |
ἀριθμόν | 1 | w | 117 |
ὁ | 1 | w | 120 |
γεννηθεὶς | 1 | w | 129 |
ἰσάκις | 2 | w | 135 |
τε | 2 | w | 137 |
ἴσος | 2 | w | 141 |
καὶ | 3 | w | 144 |
τετράγωνός | 1 | w | 154 |
ἐστιν | 1 | w | 159 |
ὡς | 1 | w | 162 |
ὁ | 2 | w | 163 |
δ | 3 | w | 164 |
ἔστι | 1 | w | 169 |
γὰρ | 1 | w | 172 |
δὶς | 1 | w | 175 |
β | 1 | w | 176 |
καὶ | 4 | w | 180 |
ὁ | 3 | w | 181 |
θ | 6 | w | 182 |
ἔστι | 2 | w | 187 |
γὰρ | 2 | w | 190 |
τρὶς | 1 | w | 194 |
γ | 7 | w | 195 |
οἱ | 2 | w | 198 |
δὲ | 1 | w | 200 |
ἀνισάκις | 1 | w | 208 |
ἄνι- | 1 | w | 212 |
σοι | 2 | w | 215 |
ἐπειδὰν | 2 | w | 223 |
ἄνισοι | 1 | w | 229 |
ἀριθμιοὶ | 1 | w | 237 |
ἐπʼ | 1 | w | 240 |
ἀλλήλους | 1 | w | 248 |
πολλαπλα- | 1 | w | 257 |
σιασθῶσιν | 1 | w | 266 |
ὡς | 2 | w | 269 |
ὁ | 4 | w | 270 |
ϛ | 1 | w | 271 |
ἔστι | 3 | w | 276 |
γὰρ | 3 | w | 279 |
δὶς | 2 | w | 282 |
γ | 9 | w | 283 |
ϛ | 2 | w | 284 |
τούτων | 1 | w | 291 |
δὲ | 2 | w | 293 |
ἑτερομήκεις | 1 | w | 304 |
μέν | 1 | w | 307 |
εἰσιν | 1 | w | 312 |
οἱ | 3 | w | 314 |
τὴν | 1 | w | 317 |
ἑτέραν | 1 | w | 323 |
πλευρὰν | 1 | w | 330 |
τῆς | 1 | w | 333 |
ἑτέρας | 1 | w | 339 |
μονάδι | 1 | w | 345 |
μείζονα | 1 | w | 352 |
ἔχοντες | 1 | w | 359 |
ἔστι | 4 | w | 364 |
δὲ | 3 | w | 366 |
ὁ | 5 | w | 367 |
τοῦ | 1 | w | 370 |
περισσοῦ | 1 | w | 378 |
ἀριθμοῦ | 1 | w | 385 |
μονάδι | 2 | w | 391 |
πλεονάζων | 1 | w | 400 |
καὶ | 5 | w | 403 |
ἄρτιος | 1 | w | 409 |
5 | 1 | w | 411 |
inscr | 1 | w | 416 |
περὶ | 1 | w | 421 |
περισσάκις | 1 | w | 431 |
ἀρτίων | 1 | w | 437 |
Α | 1 | w | 438 |
ια | 3 | w | 441 |
in | 2 | w | 443 |
mg | 1 | w | 445 |
14 | 1 | w | 448 |
inscr | 2 | w | 453 |
περὶ | 2 | w | 458 |
ἰσάκις | 3 | w | 464 |
ἴσων | 1 | w | 468 |
A | 1 | w | 469 |
ιβ | 1 | w | 472 |
in | 4 | w | 474 |
mg | 2 | w | 476 |
15 | 1 | w | 479 |
καὶ | 6 | w | 482 |
ἐπίπεδοι | 2 | w | 490 |
fort | 1 | w | 494 |
del | 1 | w | 498 |
γὰρ | 4 | w | 501 |
post | 1 | w | 505 |
ἐπειδὰν | 3 | w | 512 |
add | 1 | w | 515 |
A | 2 | w | 517 |
16 | 1 | w | 519 |
γεννήση | 1 | w | 526 |
ση | 2 | w | 529 |
corr | 1 | w | 533 |
ex | 1 | w | 536 |
σ | 32 | w | 537 |
A | 3 | w | 540 |
18 | 1 | w | 542 |
inscr | 3 | w | 547 |
περὶ | 3 | w | 552 |
τῶν | 2 | w | 555 |
ἀνισάκις | 2 | w | 563 |
ἀνίσων | 1 | w | 569 |
A | 4 | w | 570 |
ιγ | 1 | w | 572 |
in | 6 | w | 574 |
mg | 3 | w | 576 |
21 | 1 | w | 579 |
sqq | 1 | w | 582 |
cf | 1 | w | 585 |
Cantor | 1 | w | 592 |
mathemat | 1 | w | 600 |
Beitr | 1 | w | 606 |
zum | 1 | w | 610 |
Culturleben | 1 | w | 621 |
der | 1 | w | 624 |
Völker | 1 | w | 630 |
p | 2 | w | 631 |
105 | 1 | w | 635 |
sqq | 2 | w | 638 |
inser | 1 | w | 644 |
περὶ | 4 | w | 649 |
ἑτερομηκῶν | 1 | w | 659 |
corr | 2 | w | 664 |
ex | 2 | w | 667 |
ἑτε- | 1 | w | 671 |
ρομμιήκων | 1 | w | 680 |
A | 5 | w | 682 |
23 | 1 | w | 684 |
τοῦ | 2 | w | 687 |
περισσοῦ | 2 | w | 695 |
ἀριθμοῦ | 2 | w | 702 |
mut | 1 | w | 705 |
in | 8 | w | 708 |
τῶ | 3 | w | 710 |
περισσῷ | 1 | w | 717 |
ἀριθμῶ | 2 | w | 723 |
A | 6 | w | 724 |
διὸ | 1 | w | 728 |
μόνον | 1 | w | 733 |
ἄρτιοι | 1 | w | 739 |
οἱ | 4 | w | 741 |
ἑτερομήκεις | 2 | w | 752 |
ἡ | 1 | w | 754 |
γὰρ | 5 | w | 757 |
ἀρχὴ | 1 | w | 761 |
τῶν | 3 | w | 764 |
ἀριθμῶν | 2 | w | 771 |
τουτέστιν | 1 | w | 781 |
ἡ | 2 | w | 782 |
μονάς | 1 | w | 787 |
περισσὴ | 1 | w | 795 |
οὖσα | 1 | w | 799 |
τὴν | 2 | w | 802 |
ἑτερό- | 1 | w | 808 |
τητα | 1 | w | 812 |
ζητοῦσα | 1 | w | 819 |
τὴν | 3 | w | 822 |
δυάδα | 1 | w | 827 |
ἑτερομήκη | 1 | w | 836 |
τῷ | 1 | w | 838 |
αὐτῆς | 1 | w | 843 |
διπλα- | 1 | w | 849 |
σιασμῷ | 1 | w | 855 |
ἐποίησε | 1 | w | 862 |
καὶ | 7 | w | 866 |
διὰ | 1 | w | 869 |
τοῦτο | 1 | w | 874 |
ἡ | 3 | w | 875 |
δυὰς | 1 | w | 879 |
τῆς | 3 | w | 882 |
μονάδος | 1 | w | 889 |
ἑτερομήκης | 1 | w | 899 |
οὖσα | 2 | w | 903 |
καὶ | 8 | w | 906 |
μονάδι | 3 | w | 912 |
ὑπερέχουσα | 1 | w | 922 |
τοὺς | 1 | w | 926 |
ἀρτίους | 1 | w | 933 |
ἀριθμοὺς | 1 | w | 941 |
τῶν | 4 | w | 944 |
περισσῶν | 1 | w | 952 |
ἑτερομήκεις | 3 | w | 963 |
ποιεῖ | 1 | w | 968 |
μονάδι | 4 | w | 974 |
ὑπερ- | 1 | w | 979 |
ἐχοντας | 1 | w | 986 |
γεννῶνται | 1 | w | 996 |
δὲ | 4 | w | 998 |
διχῶς | 1 | w | 1003 |
ἔκ | 1 | w | 1006 |
τε | 13 | w | 1008 |
πολλαπλασιασμοῦ | 1 | w | 1023 |
καὶ | 9 | w | 1026 |
ἐπισυνθέσεως | 1 | w | 1038 |
ἐκ | 1 | w | 1041 |
μὲν | 2 | w | 1044 |
ἐπισυνθέσεως | 2 | w | 1056 |
οἱ | 5 | w | 1058 |
ἄρτιοι | 2 | w | 1064 |
τοῖς | 1 | w | 1068 |
ἐφεξῆς | 1 | w | 1074 |
ἐπισυντιθέμενοι | 1 | w | 1089 |
τοὺς | 2 | w | 1093 |
ἀπογεννωμένους | 1 | w | 1107 |
ποιοῦσιν | 1 | w | 1115 |
ἑτερομήκεις | 4 | w | 1126 |
οἷον | 1 | w | 1131 |
ἐκκείσθωσαν | 1 | w | 1142 |
ἄρτιοι | 3 | w | 1148 |
κατὰ | 1 | w | 1152 |
τὸ | 1 | w | 1154 |
ἑξῆς | 1 | w | 1158 |
βʹ | 1 | w | 1160 |
δʹ | 1 | w | 1162 |
ςʹ | 1 | w | 1164 |
ηʹ | 1 | w | 1166 |
ι | 81 | w | 1167 |
ιβʹ | 1 | w | 1170 |
ιδʹ | 1 | w | 1173 |
ιςʹ | 1 | w | 1176 |
ιηʹ | 1 | w | 1179 |
γίνονται | 1 | w | 1188 |
δὲ | 5 | w | 1190 |
κατʼ | 1 | w | 1194 |
ἐπισύνθεσιν | 1 | w | 1205 |
βʹ | 3 | w | 1207 |
καὶ | 10 | w | 1210 |
δ | 28 | w | 1211 |
ϛʹ | 1 | w | 1213 |
ϛʹ | 2 | w | 1216 |
καὶ | 11 | w | 1219 |
ϛʹ | 3 | w | 1221 |
ιβ | 3 | w | 1223 |
ιβʹ | 2 | w | 1227 |
καὶ | 12 | w | 1230 |
ηʹκ | 1 | w | 1233 |
κʹ | 1 | w | 1236 |
καὶ | 13 | w | 1239 |
ι | 91 | w | 1240 |
λ | 16 | w | 1241 |
ὥστε | 1 | w | 1246 |
εἶεν | 1 | w | 1250 |
ἂν | 1 | w | 1252 |
οἱ | 6 | w | 1254 |
γεγεννημένοι | 1 | w | 1266 |
ἑτερομήκεις | 5 | w | 1277 |
ϛʹ | 4 | w | 1279 |
ιβʹ | 3 | w | 1282 |
κʹ | 2 | w | 1284 |
λ | 17 | w | 1285 |
ὁ | 6 | w | 1287 |
δὲ | 6 | w | 1289 |
αὐτὸς | 1 | w | 1294 |
λόγος | 1 | w | 1299 |
καὶ | 14 | w | 1302 |
ἐπὶ | 2 | w | 1305 |
τῶν | 5 | w | 1308 |
ἑξῆς | 2 | w | 1312 |
κατὰ | 2 | w | 1317 |
δὲ | 7 | w | 1319 |
πολλαπλασια- | 1 | w | 1331 |
σμὸν | 1 | w | 1335 |
οἱ | 7 | w | 1337 |
αὐτοὶ | 1 | w | 1342 |
ἑτερομήκεις | 6 | w | 1353 |
γεννῶνται | 2 | w | 1362 |
τῶν | 6 | w | 1365 |
ἐφεξῆς | 2 | w | 1371 |
ἀρτίων | 2 | w | 1377 |
τε | 18 | w | 1379 |
καὶ | 15 | w | 1382 |
περιττῶν | 1 | w | 1390 |
τοῦ | 5 | w | 1393 |
πρώτου | 1 | w | 1399 |
ἐπὶ | 3 | w | 1402 |
τὸν | 1 | w | 1405 |
ἑξῆς | 3 | w | 1409 |
πολλαπλασια- | 2 | w | 1421 |
ζομένου | 1 | w | 1428 |
οἷον | 2 | w | 1433 |
αʹ | 1 | w | 1435 |
βʹ | 6 | w | 1437 |
γʹ | 1 | w | 1439 |
δʹ | 3 | w | 1441 |
εʹ | 1 | w | 1443 |
ϛʹ | 5 | w | 1445 |
ζ | 5 | w | 1446 |
ηʹ | 4 | w | 1448 |
θʹ | 1 | w | 1450 |
ιʹ | 1 | w | 1452 |
ἅπαξ | 1 | w | 1456 |
μὲν | 3 | w | 1459 |
γὰρ | 6 | w | 1462 |
βʹ | 7 | w | 1464 |
β | 11 | w | 1465 |
θὶς | 1 | w | 1469 |
δὲ | 8 | w | 1471 |
γʹ | 2 | w | 1473 |
ϛ | 8 | w | 1474 |
τρὶς | 2 | w | 1479 |
δὲ | 9 | w | 1482 |
δʹ | 4 | w | 1485 |
ιβ | 6 | w | 1487 |
τετράκις | 1 | w | 1496 |
δὲ | 10 | w | 1498 |
εʹ | 2 | w | 1500 |
κ | 43 | w | 1501 |
πεντάκις | 1 | w | 1510 |
δὲ | 11 | w | 1512 |
ϛʹ | 6 | w | 1514 |
λ | 25 | w | 1515 |
καὶ | 16 | w | 1519 |
ἐπὶ | 4 | w | 1522 |
τῶν | 8 | w | 1525 |
ἑξῆς | 4 | w | 1529 |
ὁ | 7 | w | 1530 |
αὐτὸς | 2 | w | 1535 |
λόγος | 2 | w | 1540 |
ἑτε- | 2 | w | 1545 |
ρομήκεις | 7 | w | 1553 |
δὲ | 12 | w | 1555 |
οἱ | 8 | w | 1557 |
τοιοῦτοι | 1 | w | 1565 |
κέκληνται | 1 | w | 1574 |
ἐπειδὴ | 1 | w | 1581 |
πρώτην | 1 | w | 1587 |
ἑτε- | 3 | w | 1591 |
ρότητα | 1 | w | 1597 |
τῶν | 9 | w | 1600 |
πλευρῶν | 1 | w | 1607 |
ἡ | 4 | w | 1608 |
προσθήκη | 1 | w | 1616 |
τῇ | 1 | w | 1618 |
ἑτέρᾳ | 1 | w | 1623 |
πλευρᾷ | 1 | w | 1629 |
τῆς | 4 | w | 1632 |
μονάδος | 2 | w | 1639 |
ποιεῖ | 2 | w | 1644 |
παραλληλόγραμμοι | 1 | w | 1661 |
δέ | 1 | w | 1663 |
εἰσιν | 2 | w | 1668 |
ἀριθμοὶ | 1 | w | 1675 |
οἱ | 9 | w | 1677 |
δυάδι | 1 | w | 1682 |
ἢ | 1 | w | 1683 |
καὶ | 17 | w | 1686 |
μείζονι | 1 | w | 1693 |
ἀριθμῷ | 1 | w | 1699 |
τὴν | 4 | w | 1702 |
ἑτέραν | 2 | w | 1708 |
πλευρὰν | 2 | w | 1715 |
τῆς | 5 | w | 1718 |
ἑτέρας | 2 | w | 1724 |
1 | 7 | w | 1725 |
διὸ | 2 | w | 1728 |
corr | 3 | w | 1732 |
ut | 2 | w | 1735 |
vid | 1 | w | 1738 |
ex | 3 | w | 1741 |
δύο | 1 | w | 1744 |
Α | 2 | w | 1745 |
3 | 2 | w | 1746 |
ἑτερομήκη | 3 | w | 1755 |
ο | 105 | w | 1757 |
corr | 4 | w | 1761 |
ex | 4 | w | 1764 |
ω | 15 | w | 1765 |
Α | 3 | w | 1766 |
5 | 4 | w | 1768 |
ἑτερομήκης | 2 | w | 1778 |
ομήκη | 5 | w | 1784 |
in | 9 | w | 1786 |
ras | 1 | w | 1789 |
ερο | 12 | w | 1794 |
corr | 5 | w | 1798 |
ut | 3 | w | 1801 |
vid | 2 | w | 1804 |
ex | 5 | w | 1807 |
έρα | 5 | w | 1810 |
Α | 4 | w | 1811 |
6 | 2 | w | 1813 |
τῶν | 10 | w | 1816 |
περισσῶν | 2 | w | 1824 |
mut | 2 | w | 1827 |
in | 10 | w | 1830 |
τῷ | 2 | w | 1832 |
περισσῷ | 2 | w | 1839 |
Α | 5 | w | 1840 |
9 | 1 | w | 1841 |
ἀπογεννωμένους | 2 | w | 1855 |
ω | 17 | w | 1857 |
corr | 6 | w | 1861 |
ex | 6 | w | 1864 |
ο | 111 | w | 1865 |
Α | 6 | w | 1866 |
11 | 1 | w | 1868 |
ϛ | 10 | w | 1869 |
ιβ | 7 | w | 1871 |
κ | 54 | w | 1872 |
λ | 34 | w | 1873 |
μβ | 1 | w | 1875 |
νς | 1 | w | 1877 |
οβ | 1 | w | 1879 |
supra | 1 | w | 1884 |
numerorum | 1 | w | 1893 |
seriem | 1 | w | 1899 |
add | 2 | w | 1902 |
A | 7 | w | 1904 |
13 | 1 | w | 1907 |
γεγενημένοι | 1 | w | 1918 |
Α | 7 | w | 1919 |
em | 3 | w | 1922 |
Bull | 1 | w | 1927 |
16 | 2 | w | 1930 |
τὸν | 2 | w | 1933 |
apogr | 1 | w | 1938 |
τῶν | 11 | w | 1943 |
Α | 8 | w | 1944 |
18 | 2 | w | 1946 |
δὲ | 13 | w | 1948 |
add | 3 | w | 1951 |
Bull | 2 | w | 1956 |
20 | 1 | w | 1959 |
πρώτην | 2 | w | 1965 |
corr | 7 | w | 1969 |
ex | 7 | w | 1972 |
πρῶτον | 1 | w | 1978 |
Α | 9 | w | 1979 |
23 | 2 | w | 1982 |
inser | 2 | w | 1987 |
περὶ | 5 | w | 1992 |
παραλληλογράμμων | 1 | w | 2008 |
ἁριθμῶν | 1 | w | 2015 |
Α | 10 | w | 2016 |
ιε | 3 | w | 2019 |
in | 12 | w | 2021 |
mg | 4 | w | 2023 |
figuras | 1 | w | 2031 |
inutiles | 1 | w | 2039 |
add | 4 | w | 2042 |
Α | 11 | w | 2045 |
ὑπερέχουσαν | 1 | w | 2056 |
ἔχοντες | 2 | w | 2063 |
ὡς | 3 | w | 2066 |
ὁ | 8 | w | 2067 |
δὶς | 3 | w | 2070 |
δʹ | 5 | w | 2072 |
καὶ | 18 | w | 2075 |
ὁ | 9 | w | 2076 |
τετράκις | 2 | w | 2084 |
ϛʹ | 7 | w | 2086 |
καὶ | 19 | w | 2089 |
ὁ | 10 | w | 2090 |
ἑξάκις | 1 | w | 2096 |
ηʹ | 5 | w | 2098 |
καὶ | 20 | w | 2101 |
ὁ | 11 | w | 2102 |
ὀκτάκις | 1 | w | 2109 |
ι | 126 | w | 2110 |
οἵτινές | 1 | w | 2118 |
εἰσιν | 3 | w | 2123 |
ὁ | 12 | w | 2124 |
ηʹ | 6 | w | 2126 |
κδʹ | 1 | w | 2129 |
μηʹ | 1 | w | 2132 |
π | 66 | w | 2133 |
τετράγωνοί | 1 | w | 2144 |
εἰσιν | 4 | w | 2149 |
οἱ | 10 | w | 2151 |
ἐκ | 3 | w | 2153 |
τῶν | 12 | w | 2156 |
κατὰ | 3 | w | 2160 |
τὸ | 6 | w | 2162 |
ἑξῆς | 5 | w | 2166 |
περισσῶν | 3 | w | 2174 |
ἐπισυντιθεμένων | 1 | w | 2189 |
ἀλλήλοις | 1 | w | 2197 |
γεννώμενοι | 1 | w | 2207 |
οἷον | 3 | w | 2212 |
ἐκκείσθω- | 1 | w | 2221 |
σαν | 3 | w | 2224 |
ἐφεξῆς | 3 | w | 2230 |
περισσοὶ | 1 | w | 2238 |
αʹ | 2 | w | 2240 |
γʹ | 3 | w | 2242 |
εʹ | 3 | w | 2244 |
ζ | 7 | w | 2245 |
θʹ | 2 | w | 2247 |
ια | 8 | w | 2249 |
ἓν | 1 | w | 2251 |
καὶ | 21 | w | 2254 |
γʹ | 4 | w | 2256 |
δʹ | 7 | w | 2258 |
ὅς | 1 | w | 2261 |
ἐστι | 2 | w | 2265 |
τετράγωνος | 1 | w | 2275 |
ἰσάκις | 4 | w | 2282 |
γάρ | 1 | w | 2285 |
ἐστιν | 2 | w | 2290 |
ἴσος | 3 | w | 2294 |
τουτέστι | 2 | w | 2303 |
δὶς | 4 | w | 2306 |
βʹ | 8 | w | 2308 |
δʹ | 8 | w | 2310 |
δʹ | 9 | w | 2312 |
καὶ | 22 | w | 2315 |
εʹ | 4 | w | 2317 |
θʹ | 3 | w | 2319 |
ὸς | 3 | w | 2322 |
καὶ | 23 | w | 2325 |
αὐτὸς | 3 | w | 2330 |
τετράγωνος | 2 | w | 2340 |
ἔστι | 5 | w | 2345 |
γὰρ | 7 | w | 2348 |
τρὶς | 3 | w | 2352 |
γʹ | 5 | w | 2354 |
θʹ | 4 | w | 2356 |
θʹκαὶ | 1 | w | 2362 |
ζ | 8 | w | 2363 |
ιϛ | 1 | w | 2365 |
ὃς | 1 | w | 2368 |
καὶ | 25 | w | 2371 |
αὐτὸς | 4 | w | 2376 |
τετράγωνός | 2 | w | 2386 |
ἐστι | 4 | w | 2390 |
τετράκις | 3 | w | 2399 |
γὰρ | 8 | w | 2402 |
δ | 53 | w | 2403 |
ιςʹ | 2 | w | 2406 |
ιςʹ | 3 | w | 2409 |
καὶ | 26 | w | 2412 |
θʹ | 6 | w | 2414 |
κε | 10 | w | 2416 |
ὃς | 2 | w | 2419 |
καὶ | 27 | w | 2422 |
αὐτὸς | 5 | w | 2427 |
τετράγωνός | 3 | w | 2437 |
ἐστι | 5 | w | 2441 |
καὶ | 28 | w | 2444 |
ἰσάκις | 5 | w | 2450 |
ἴσος | 4 | w | 2454 |
ἔστι | 6 | w | 2459 |
γὰρ | 9 | w | 2462 |
πεντάκις | 2 | w | 2470 |
εʹ | 5 | w | 2472 |
κε | 11 | w | 2474 |
καὶ | 29 | w | 2478 |
μέχρις | 1 | w | 2484 |
ἀπείρου | 1 | w | 2491 |
ὁ | 13 | w | 2492 |
αὐτὸς | 6 | w | 2497 |
λόγος | 3 | w | 2502 |
κατὰ | 4 | w | 2507 |
μὲν | 4 | w | 2510 |
οὖν | 1 | w | 2513 |
ἐπισύνθεσιν | 2 | w | 2524 |
οὕτως | 1 | w | 2529 |
γεννῶν- | 1 | w | 2536 |
ται | 5 | w | 2539 |
οἱ | 11 | w | 2541 |
τετράγωνοι | 2 | w | 2551 |
τῶν | 13 | w | 2555 |
ἐφεξῆς | 4 | w | 2561 |
περισσῶν | 4 | w | 2569 |
τῷ | 3 | w | 2571 |
γεννωμένῳ | 1 | w | 2580 |
ἀπὸ | 1 | w | 2583 |
μονάδος | 3 | w | 2590 |
τετραγώνῳ | 1 | w | 2599 |
προστιθεμένων | 1 | w | 2612 |
κατὰ | 5 | w | 2617 |
πολλαπλα- | 2 | w | 2626 |
σιασμιὸν | 1 | w | 2634 |
δέ | 2 | w | 2636 |
ἐπειδὰν | 4 | w | 2644 |
ὁστισοῦν | 1 | w | 2652 |
ἀριθμὸς | 1 | w | 2659 |
ἐφʼ | 1 | w | 2662 |
ἑαυτὸνπολλα- | 1 | w | 2674 |
πλασιασθῇ | 1 | w | 2683 |
οἷον | 4 | w | 2688 |
δὶς | 5 | w | 2691 |
βʹ | 9 | w | 2693 |
δʹ | 10 | w | 2695 |
τρὶς | 4 | w | 2700 |
γʹ | 6 | w | 2702 |
θʹ | 7 | w | 2704 |
τετράκις | 4 | w | 2713 |
δʹ | 11 | w | 2715 |
ιϛ | 2 | w | 2717 |
οἱ | 12 | w | 2720 |
μὲν | 5 | w | 2723 |
οὖν | 2 | w | 2726 |
τετράγωνοι | 3 | w | 2736 |
πάντες | 1 | w | 2742 |
τοὺς | 3 | w | 2746 |
ἐτερομιήκεις | 1 | w | 2758 |
περιλαμβάνουσι | 1 | w | 2772 |
κατὰ | 6 | w | 2776 |
τὴν | 5 | w | 2779 |
γεωμετρικὴν | 1 | w | 2790 |
ἀναλογίαν | 1 | w | 2799 |
καὶ | 30 | w | 2802 |
μέσους | 1 | w | 2808 |
αὐτοὺς | 1 | w | 2814 |
ποιοῦσι | 2 | w | 2821 |
τουτέστι | 3 | w | 2830 |
τοὺς | 5 | w | 2834 |
μονάδι | 5 | w | 2840 |
μείζονας | 1 | w | 2848 |
τὴν | 6 | w | 2851 |
ἑτέραν | 3 | w | 2857 |
πλευρὰν | 3 | w | 2864 |
τῆς | 6 | w | 2867 |
ἑτέρας | 3 | w | 2873 |
ὑπερέχοντας | 1 | w | 2884 |
οἱ | 13 | w | 2888 |
δὲ | 14 | w | 2890 |
ἑτερομήκεις | 7 | w | 2901 |
οὐκ | 1 | w | 2904 |
ἔτι | 2 | w | 2907 |
τοὺς | 6 | w | 2911 |
τετραγώνους | 1 | w | 2922 |
περιλαμβάνουσιν | 1 | w | 2937 |
ὡς | 4 | w | 2939 |
μέσους | 2 | w | 2945 |
εἶναι | 1 | w | 2950 |
κατὰ | 7 | w | 2954 |
ἀναλογίαν | 2 | w | 2963 |
οἷον | 5 | w | 2968 |
αʹ | 3 | w | 2970 |
βʹ | 10 | w | 2972 |
γʹ | 7 | w | 2974 |
δʹ | 12 | w | 2976 |
εʹ | 6 | w | 2978 |
οὖτοι | 1 | w | 2984 |
τῷ | 4 | w | 2986 |
μὲν | 6 | w | 2989 |
ἰδίῳ | 1 | w | 2993 |
πλήθει | 1 | w | 2999 |
πολλαπλασιαζόμενοι | 1 | w | 3017 |
ποιοῦσι | 3 | w | 3024 |
τετραγώνους | 2 | w | 3035 |
ἅπαξ | 2 | w | 3040 |
τε | 41 | w | 3042 |
γὰρ | 10 | w | 3045 |
αʹ | 4 | w | 3047 |
αʹ | 5 | w | 3049 |
καὶ | 31 | w | 3052 |
δὶς | 6 | w | 3055 |
βʹ | 11 | w | 3057 |
δʹ | 13 | w | 3059 |
καὶ | 32 | w | 3062 |
τρὶς | 5 | w | 3066 |
γʹ | 8 | w | 3068 |
θʹ | 8 | w | 3070 |
καὶ | 33 | w | 3073 |
τετράκις | 5 | w | 3081 |
δʹ | 14 | w | 3083 |
ιϛʹ | 1 | w | 3086 |
καὶ | 34 | w | 3089 |
πεντάκις | 3 | w | 3097 |
εʹ | 7 | w | 3099 |
κε | 14 | w | 3101 |
καὶ | 35 | w | 3105 |
οὐκ | 2 | w | 3108 |
ἐκβαίνουσι | 1 | w | 3118 |
τῶν | 14 | w | 3121 |
ἰδίων | 1 | w | 3126 |
ρων | 1 | w | 3131 |
ἣ | 1 | w | 3133 |
τε | 43 | w | 3135 |
γὰρ | 11 | w | 3138 |
δυὰς | 2 | w | 3142 |
ἑαυτὴν | 1 | w | 3148 |
3 | 5 | w | 3149 |
inscr | 4 | w | 3154 |
περὶ | 6 | w | 3159 |
τετραγώνων | 1 | w | 3169 |
ἀριθμῶν | 3 | w | 3176 |
Α | 12 | w | 3177 |
ις | 33 | w | 3180 |
in | 15 | w | 3182 |
mg | 5 | w | 3184 |
τε- | 4 | w | 3188 |
τράγωνοι | 4 | w | 3196 |
δέ | 3 | w | 3199 |
εἰσιν | 5 | w | 3205 |
5 | 5 | w | 3208 |
δ | 70 | w | 3209 |
θ | 40 | w | 3210 |
ιϛ | 4 | w | 3212 |
κε | 15 | w | 3214 |
λϛ | 1 | w | 3216 |
supra | 2 | w | 3221 |
numerorum | 2 | w | 3230 |
se- | 1 | w | 3233 |
rien | 1 | w | 3237 |
add | 5 | w | 3240 |
Α | 13 | w | 3242 |
ὅς | 2 | w | 3245 |
apogr | 2 | w | 3250 |
ὅ | 3 | w | 3253 |
Α | 14 | w | 3254 |
16 | 3 | w | 3257 |
inscr | 5 | w | 3262 |
ὅτι | 1 | w | 3266 |
οἱ | 14 | w | 3268 |
τετράγω- | 1 | w | 3276 |
νοι | 10 | w | 3279 |
μιέσους | 1 | w | 3286 |
τοὺς | 7 | w | 3290 |
ἑτερομήκεις | 8 | w | 3301 |
λαμβάνουσιν | 2 | w | 3312 |
Α | 15 | w | 3313 |
ιζ | 1 | w | 3316 |
in | 17 | w | 3318 |
mg | 6 | w | 3320 |
18 | 3 | w | 3323 |
μείζονα | 3 | w | 3330 |
Gelder | 1 | w | 3336 |
19 | 1 | w | 3338 |
ὑπερέχοντας | 2 | w | 3349 |
ἔχοντας | 1 | w | 3357 |
apogr | 3 | w | 3362 |
22 | 1 | w | 3365 |
οὗτοι | 1 | w | 3370 |
οὕτως | 2 | w | 3376 |
οἱ | 15 | w | 3378 |
Α | 16 | w | 3379 |
25 | 1 | w | 3381 |
τὸν | 4 | w | 3384 |
ἴθιον | 1 | w | 3389 |
ὅρον | 1 | w | 3393 |
Α | 17 | w | 3394 |
ἐδύασε | 1 | w | 3400 |
καὶ | 36 | w | 3403 |
ἡ | 5 | w | 3404 |
τριὰς | 1 | w | 3409 |
ἑαυτὴν | 2 | w | 3415 |
ἐτρίασεν | 1 | w | 3423 |
ὥστε | 2 | w | 3428 |
εἶεν | 2 | w | 3432 |
ἂν | 2 | w | 3434 |
τε- | 5 | w | 3437 |
τράγωνοι | 5 | w | 3445 |
οἱ | 16 | w | 3447 |
ἑξῆς | 6 | w | 3451 |
αʹ | 6 | w | 3453 |
δʹ | 15 | w | 3455 |
θʹ | 9 | w | 3457 |
ιςʹ | 4 | w | 3460 |
κε | 17 | w | 3462 |
μέσους | 3 | w | 3469 |
δὲ | 15 | w | 3471 |
ἔχουσι | 1 | w | 3477 |
τοὺς | 8 | w | 3481 |
ἑτερομήκεις | 9 | w | 3492 |
οὕτως | 3 | w | 3497 |
τετράγωνοι | 4 | w | 3508 |
δύο | 2 | w | 3511 |
ἐφεξῆς | 5 | w | 3517 |
ὅ | 6 | w | 3518 |
τε | 52 | w | 3520 |
αʹ | 7 | w | 3522 |
καὶ | 37 | w | 3525 |
δʹ | 16 | w | 3527 |
τούτων | 2 | w | 3534 |
μέσος | 1 | w | 3539 |
ἑτερομήκης | 3 | w | 3549 |
ὁ | 15 | w | 3550 |
β | 24 | w | 3551 |
κείσθωσαν | 2 | w | 3561 |
δὴ | 2 | w | 3563 |
αʹ | 8 | w | 3565 |
βʹ | 12 | w | 3567 |
δ | 77 | w | 3568 |
μέσος | 2 | w | 3574 |
γίνεται | 1 | w | 3581 |
ὁ | 16 | w | 3582 |
βʹ | 13 | w | 3584 |
τῷ | 5 | w | 3587 |
αὐτῷ | 1 | w | 3591 |
λόγῳ | 1 | w | 3595 |
τῶν | 15 | w | 3598 |
ἄκρων | 1 | w | 3603 |
τοῦ | 6 | w | 3606 |
μὲν | 7 | w | 3609 |
ὑπερέχων | 1 | w | 3617 |
ὑφʼ | 1 | w | 3621 |
οὐ | 3 | w | 3623 |
δὲ | 16 | w | 3625 |
ὑπερεχόμενος | 1 | w | 3637 |
τοῦ | 7 | w | 3641 |
μὲν | 8 | w | 3644 |
γὰρ | 12 | w | 3647 |
ἑνὸς | 1 | w | 3651 |
τὰ | 8 | w | 3653 |
βʹ | 14 | w | 3655 |
διπλάσια | 1 | w | 3663 |
τῶν | 16 | w | 3667 |
δὲ | 17 | w | 3669 |
βʹ | 15 | w | 3671 |
τὰ | 9 | w | 3673 |
δʹ | 17 | w | 3675 |
πάλιν | 1 | w | 3681 |
τετράγω- | 2 | w | 3689 |
νοι | 13 | w | 3692 |
μὲν | 9 | w | 3695 |
ὁ | 17 | w | 3696 |
δʹ | 18 | w | 3698 |
κἰαὶ | 1 | w | 3702 |
θʹ | 10 | w | 3704 |
μέσος | 3 | w | 3710 |
δὲ | 18 | w | 3712 |
αὐτῶν | 1 | w | 3717 |
ἑτερομήκης | 4 | w | 3727 |
ὁ | 18 | w | 3728 |
ϛʹ | 9 | w | 3730 |
κείσθωσαν | 3 | w | 3740 |
δὴ | 3 | w | 3742 |
δʹ | 19 | w | 3744 |
ϛʹ | 10 | w | 3746 |
θʹ | 11 | w | 3748 |
μέσος | 4 | w | 3754 |
ὁ | 19 | w | 3755 |
ϛʹ | 11 | w | 3757 |
τῷ | 7 | w | 3760 |
αὐτῷ | 2 | w | 3764 |
λόγῳ | 2 | w | 3768 |
τῶν | 18 | w | 3771 |
ἄκρων | 2 | w | 3776 |
τοῦ | 8 | w | 3779 |
μὲν | 10 | w | 3782 |
γὰρ | 13 | w | 3786 |
ὑπερέχων | 2 | w | 3795 |
ὑφʼ | 2 | w | 3799 |
οὗ | 2 | w | 3801 |
δὲ | 19 | w | 3803 |
ὑπερεχόμε- | 1 | w | 3813 |
νος | 4 | w | 3816 |
τῶν | 19 | w | 3820 |
μὲν | 11 | w | 3823 |
γὰρ | 14 | w | 3826 |
δʹ | 20 | w | 3828 |
τὰ | 10 | w | 3830 |
ϛʹ | 12 | w | 3832 |
ἡμιόλια | 1 | w | 3839 |
τῶν | 20 | w | 3843 |
δὲ | 20 | w | 3845 |
ϛʹ | 13 | w | 3847 |
τὰ | 11 | w | 3849 |
θ | 47 | w | 3850 |
ὁ | 20 | w | 3852 |
δὲ | 21 | w | 3854 |
αὐτὸς | 7 | w | 3859 |
λόγος | 4 | w | 3864 |
καὶ | 38 | w | 3867 |
ἐπὶ | 5 | w | 3870 |
τῶν | 21 | w | 3873 |
ἑξῆς | 7 | w | 3877 |
οἱ | 17 | w | 3880 |
δὲ | 22 | w | 3882 |
ἑτερομήκεις | 10 | w | 3893 |
ὑπὸ | 1 | w | 3897 |
τῶν | 22 | w | 3900 |
τ | 256 | w | 3901 |
μονάδι | 6 | w | 3907 |
ὑπερεχόντων | 1 | w | 3918 |
πολλαπλασιαζόμενοι | 2 | w | 3936 |
οὔτε | 1 | w | 3941 |
μένουσιν | 1 | w | 3949 |
ἐν | 1 | w | 3951 |
τοῖς | 2 | w | 3955 |
ἰδίοις | 1 | w | 3961 |
ὅροις | 1 | w | 3966 |
οὔτε | 2 | w | 3970 |
περιέχουσι | 1 | w | 3980 |
τοὺς | 9 | w | 3984 |
τετραγώνους | 3 | w | 3995 |
οἷον | 6 | w | 4000 |
τὰ | 12 | w | 4002 |
δὶς | 7 | w | 4005 |
γʹ | 9 | w | 4007 |
γεννᾷ | 1 | w | 4012 |
τὸν | 5 | w | 4015 |
ϛʹ | 14 | w | 4017 |
καὶ | 39 | w | 4020 |
τὰ | 13 | w | 4022 |
τρὶς | 6 | w | 4026 |
δʼ | 1 | w | 4028 |
γεννᾷ | 2 | w | 4033 |
τὸν | 6 | w | 4036 |
ιβʹ | 4 | w | 4039 |
καὶ | 40 | w | 4042 |
τὰ | 14 | w | 4044 |
τετράκις | 6 | w | 4052 |
εʹ | 8 | w | 4054 |
γεννᾷ | 3 | w | 4059 |
τὸν | 7 | w | 4062 |
κ | 120 | w | 4063 |
καὶ | 41 | w | 4067 |
οὐδεὶς | 1 | w | 4073 |
αὐτῶν | 2 | w | 4078 |
μένει | 1 | w | 4083 |
ἐν | 2 | w | 4085 |
τῷ | 9 | w | 4087 |
ἑαυτοῦ | 1 | w | 4093 |
ὅρῳ | 1 | w | 4096 |
ἀλλὰ | 1 | w | 4101 |
μεταπίπτει | 1 | w | 4111 |
ἐν | 3 | w | 4113 |
τῷ | 10 | w | 4115 |
πολλαπλασιασμῷ | 1 | w | 4129 |
οἷον | 7 | w | 4134 |
δυὰς | 3 | w | 4138 |
ἐπὶ | 6 | w | 4141 |
τριάδα | 1 | w | 4147 |
καὶ | 42 | w | 4150 |
τριὰς | 2 | w | 4155 |
ἐπὶ | 7 | w | 4158 |
τετράδα | 1 | w | 4165 |
καὶ | 43 | w | 4168 |
τετρὰς | 1 | w | 4174 |
ἐπὶ | 8 | w | 4177 |
πεντάδα | 1 | w | 4184 |
οἵ | 2 | w | 4187 |
τε | 64 | w | 4189 |
γεννώμενοι | 2 | w | 4199 |
ὑπὸ | 2 | w | 4202 |
τῶν | 24 | w | 4205 |
ἑτερομηκῶν | 2 | w | 4215 |
οὐ | 5 | w | 4217 |
περιλαμβάνουσι | 3 | w | 4231 |
τοὺς | 10 | w | 4235 |
τετραγώ- | 1 | w | 4243 |
νους | 6 | w | 4247 |
ἀριθμούς | 1 | w | 4255 |
οἷον | 8 | w | 4260 |
ἐφεξῆς | 6 | w | 4266 |
ἑτερομήκεις | 11 | w | 4277 |
βʹ | 17 | w | 4279 |
ϛʹ | 15 | w | 4281 |
μεταξὺ | 1 | w | 4288 |
δὲ | 23 | w | 4290 |
αὐτῶν | 3 | w | 4295 |
ἐστι | 6 | w | 4299 |
τῇ | 2 | w | 4301 |
τάξει | 1 | w | 4306 |
τετράγωνος | 3 | w | 4316 |
ὁ | 21 | w | 4317 |
δʹ | 21 | w | 4319 |
ἀλλὰ | 2 | w | 4324 |
κατʼ | 2 | w | 4328 |
οὐδεμίαν | 1 | w | 4336 |
ἀναλογίαν | 3 | w | 4345 |
περιλαμβάνεται | 1 | w | 4359 |
ὑπʼ | 1 | w | 4362 |
αὐτῶν | 4 | w | 4367 |
ὥστε | 3 | w | 4371 |
ἐν | 4 | w | 4373 |
τῷ | 11 | w | 4375 |
αὐτῷ | 3 | w | 4379 |
λόγῳ | 3 | w | 4383 |
πρὸς | 1 | w | 4387 |
τὰ | 15 | w | 4389 |
ἄκρα | 1 | w | 4393 |
εἶναι | 2 | w | 4398 |
ἐκκείσθω | 3 | w | 4407 |
γὰρ | 15 | w | 4410 |
βʹ | 18 | w | 4412 |
δʹ | 22 | w | 4414 |
ϛʹ | 16 | w | 4416 |
ἡ | 7 | w | 4418 |
τετρὰς | 2 | w | 4424 |
ἐν | 5 | w | 4426 |
διαφόροις | 1 | w | 4435 |
λόγοις | 1 | w | 4441 |
πρὸς | 2 | w | 4445 |
τὰ | 16 | w | 4447 |
ἄκρα | 2 | w | 4451 |
γενήσεται | 1 | w | 4460 |
τῶν | 27 | w | 4464 |
μὲν | 12 | w | 4467 |
γὰρ | 16 | w | 4470 |
βʹ | 19 | w | 4472 |
τὰ | 17 | w | 4474 |
δʹ | 23 | w | 4476 |
διπλάσια | 2 | w | 4484 |
τῶν | 28 | w | 4488 |
δὲ | 24 | w | 4490 |
δ | 108 | w | 4491 |
9 | 3 | w | 4492 |
μέσος | 5 | w | 4497 |
ὁ | 22 | w | 4498 |
μέσα | 1 | w | 4503 |
τὰ | 18 | w | 4505 |
Α | 18 | w | 4506 |
10 | 2 | w | 4509 |
γὰρ | 17 | w | 4512 |
om | 1 | w | 4514 |
apogr | 4 | w | 4520 |
20 | 2 | w | 4523 |
ὑπὸ | 3 | w | 4526 |
τῶν | 29 | w | 4529 |
ἑτερομήκῶν | 1 | w | 4539 |
del | 2 | w | 4542 |
vid | 3 | w | 4546 |
23 | 3 | w | 4549 |
οὐδὲ | 1 | w | 4553 |
μίαν | 2 | w | 4557 |
Α | 19 | w | 4558 |
em | 4 | w | 4561 |
apogr | 5 | w | 4567 |
24 | 1 | w | 4570 |
αὐτῶ | 5 | w | 4574 |
supra | 3 | w | 4579 |
vs | 1 | w | 4581 |
add | 6 | w | 4585 |
Α | 20 | w | 4587 |
ἐκκείσθω | 4 | w | 4595 |
γὰρ | 18 | w | 4598 |
ἐκκείσθωσαν | 2 | w | 4610 |
apogr | 6 | w | 4615 |
26 | 1 | w | 4618 |
τὰ | 19 | w | 4620 |
δ | 110 | w | 4621 |
πλάσια | 3 | w | 4627 |
Α | 21 | w | 4628 |
em | 5 | w | 4631 |
apogr | 7 | w | 4637 |
τὰ | 20 | w | 4640 |
ϛʹ | 17 | w | 4642 |
ἡμιόλια | 2 | w | 4649 |
ἵνα | 1 | w | 4653 |
δὲ | 26 | w | 4655 |
ἀναλόγως | 1 | w | 4663 |
μέσον | 1 | w | 4668 |
ᾖ | 1 | w | 4669 |
δεῖ | 1 | w | 4673 |
αὐτ | 19 | w | 4676 |
οὕτως | 4 | w | 4683 |
μέσον | 2 | w | 4688 |
εἶναι | 3 | w | 4693 |
ὥστε | 4 | w | 4698 |
ὃν | 1 | w | 4700 |
ἔχει | 1 | w | 4704 |
λόγον | 1 | w | 4709 |
τὸ | 17 | w | 4711 |
πρῶτον | 2 | w | 4717 |
πρὸς | 3 | w | 4721 |
τὸ | 18 | w | 4723 |
μέσον | 3 | w | 4728 |
τοῦτον | 1 | w | 4735 |
τὸ | 19 | w | 4737 |
μέσον | 4 | w | 4742 |
πρὸς | 4 | w | 4746 |
τὸ | 20 | w | 4748 |
τρίτον | 1 | w | 4754 |
πάλιν | 2 | w | 4760 |
τῶν | 30 | w | 4763 |
ϛʹ | 18 | w | 4765 |
καὶ | 44 | w | 4768 |
ιβʹ | 5 | w | 4771 |
ἑτερομηκων | 1 | w | 4781 |
μέσος | 6 | w | 4786 |
τῇ | 3 | w | 4788 |
τάξει | 2 | w | 4793 |
τετράγωνος | 4 | w | 4803 |
θʹ | 12 | w | 4807 |
ἀλλʼ | 1 | w | 4812 |
οὐχ | 1 | w | 4815 |
εὑρεθήσεται | 1 | w | 4826 |
ἐν | 6 | w | 4828 |
τῷ | 13 | w | 4830 |
αὐτῷ | 4 | w | 4834 |
λόγῳ | 4 | w | 4838 |
πρὸς | 5 | w | 4842 |
τὰ | 21 | w | 4844 |
ἄκρα | 3 | w | 4848 |
ϛʹ | 19 | w | 4851 |
θʹ | 13 | w | 4853 |
ιβʹ | 6 | w | 4856 |
τῶν | 31 | w | 4861 |
μὲν | 13 | w | 4864 |
γὰρ | 19 | w | 4867 |
ϛʹ | 20 | w | 4869 |
τὰ | 22 | w | 4871 |
θʹ | 14 | w | 4873 |
ἡμιόλια | 3 | w | 4880 |
τῶν | 32 | w | 4884 |
δὲ | 27 | w | 4886 |
θʹ | 15 | w | 4888 |
τὰ | 23 | w | 4890 |
ιβʹ | 7 | w | 4893 |
ἐπίτριτα | 1 | w | 4901 |
ὁ | 23 | w | 4903 |
δὲ | 28 | w | 4905 |
αὐτὸς | 8 | w | 4910 |
καὶ | 45 | w | 4913 |
ἐπὶ | 9 | w | 4916 |
τῶν | 33 | w | 4919 |
ἑξῆς | 8 | w | 4923 |
λόγος | 5 | w | 4928 |