| Refs | {'start': {'reference': '1.2.1', 'human_reference': 'Book 1 Chapter 2 Section 1'}} |
|---|---|
| Ancestors | [{'reference': '1'}, {'reference': '1.2'}] |
| Children | [] |
| ΠΡΟΤΑΣΙΣ | 1 | w | 8 |
| β | 1 | w | 9 |
| ΠΡΟΒΛΗΜΑ | 1 | w | 19 |
| Τῆς | 1 | w | 23 |
| δοθείσης | 1 | w | 31 |
| σφαίρας | 1 | w | 38 |
| τὸ | 1 | w | 40 |
| κέντρον | 1 | w | 47 |
| εὑρεῖν | 1 | w | 53 |
| Ἔστω | 1 | w | 58 |
| δοθεῖσα | 1 | w | 65 |
| σφαῖρα | 1 | w | 71 |
| δεῖ | 1 | w | 75 |
| δὲ | 1 | w | 77 |
| τὸ | 2 | w | 79 |
| αὐτῆς | 1 | w | 84 |
| κέντρον | 2 | w | 91 |
| εὑρεῖν | 2 | w | 97 |
| Τετμήσθω | 1 | w | 106 |
| ἡ | 1 | w | 107 |
| δοθεῖσα | 2 | w | 114 |
| σφαῖρα | 2 | w | 120 |
| ἐπιπέδῳ | 1 | w | 127 |
| τινὶ | 1 | w | 131 |
| ποιήσει | 1 | w | 139 |
| δὲ | 2 | w | 141 |
| τομὴν | 1 | w | 146 |
| κύκλον | 1 | w | 152 |
| Ποιείτω | 1 | w | 160 |
| τὸν | 1 | w | 163 |
| ΑΒΓ | 1 | w | 166 |
| καὶ | 1 | w | 170 |
| εἰλήφθω | 1 | w | 177 |
| αὐτοῦ | 1 | w | 182 |
| τὸ | 4 | w | 184 |
| κέντρον | 3 | w | 191 |
| καὶ | 2 | w | 195 |
| ἔστω | 1 | w | 199 |
| τὸ | 5 | w | 201 |
| Δ | 1 | w | 202 |
| σημεῖον | 1 | w | 209 |
| καὶ | 3 | w | 213 |
| ἀπὸ | 1 | w | 216 |
| τοῦ | 2 | w | 219 |
| Δ | 2 | w | 220 |
| σημείου | 1 | w | 227 |
| τῷ | 1 | w | 229 |
| τοῦ | 3 | w | 232 |
| ΑΒΓ | 2 | w | 235 |
| κύκλου | 1 | w | 241 |
| ἐπιπέδῳ | 2 | w | 248 |
| πρὸς | 1 | w | 252 |
| ὀρθὰς | 1 | w | 257 |
| ἀνεστάτω | 1 | w | 265 |
| ἡ | 2 | w | 266 |
| ΔΕ | 1 | w | 268 |
| καὶ | 4 | w | 272 |
| ἐκβεβλήσθω | 1 | w | 282 |
| καὶ | 5 | w | 285 |
| συμβαλλέτω | 1 | w | 295 |
| τῇ | 1 | w | 297 |
| ἐπιφανείᾳ | 1 | w | 306 |
| τῆς | 2 | w | 309 |
| σφαίρας | 2 | w | 316 |
| κατὰ | 1 | w | 320 |
| τὰ | 2 | w | 322 |
| Ε | 2 | w | 323 |
| Ζ | 1 | w | 325 |
| καὶ | 6 | w | 329 |
| τετμήσθω | 1 | w | 337 |
| ἡ | 3 | w | 338 |
| ΕΖ | 1 | w | 340 |
| δίχα | 1 | w | 344 |
| κατὰ | 2 | w | 348 |
| τὸ | 6 | w | 350 |
| Η | 2 | w | 351 |
| σημείον | 1 | w | 358 |
| λέγω | 1 | w | 363 |
| ὅτι | 1 | w | 367 |
| τὸ | 7 | w | 369 |
| Η | 3 | w | 370 |
| σημεῖον | 2 | w | 377 |
| κέντρον | 4 | w | 384 |
| ἐστὶ | 1 | w | 388 |
| τῆς | 3 | w | 391 |
| σφαίρας | 3 | w | 398 |
| Μὴ | 1 | w | 401 |
| γὰρ | 1 | w | 404 |
| ἀλλ | 1 | w | 408 |
| εἰ | 2 | w | 412 |
| δυνατὸν | 1 | w | 419 |
| ἔστω | 2 | w | 424 |
| τὸ | 9 | w | 426 |
| Θ | 1 | w | 427 |
| καὶ | 7 | w | 431 |
| ἀπὸ | 2 | w | 434 |
| τοῦ | 4 | w | 437 |
| Θ | 2 | w | 438 |
| ἐπὶ | 1 | w | 441 |
| τὸ | 10 | w | 443 |
| τοῦ | 5 | w | 446 |
| ΑΒΓ | 3 | w | 449 |
| κύκλου | 2 | w | 455 |
| ἐπίπεδον | 1 | w | 463 |
| κάθετος | 1 | w | 470 |
| ἤχθω | 1 | w | 474 |
| καὶ | 8 | w | 478 |
| συμβαλλέτω | 2 | w | 488 |
| τῷ | 2 | w | 490 |
| ἐπιπέδῳ | 3 | w | 497 |
| κατὰ | 3 | w | 501 |
| τὸ | 11 | w | 503 |
| Κ | 1 | w | 504 |
| σημεῖον | 3 | w | 511 |
| τὸ | 12 | w | 514 |
| ἄρα | 1 | w | 517 |
| Κ | 2 | w | 518 |
| σημεῖον | 4 | w | 525 |
| κέντρον | 5 | w | 532 |
| ἐστὶ | 2 | w | 536 |
| τοῦ | 6 | w | 539 |
| ΑΒΓ | 4 | w | 542 |
| κύκλου | 3 | w | 548 |
| ἀλλὰ | 1 | w | 553 |
| καὶ | 9 | w | 556 |
| τὸ | 13 | w | 558 |
| Δ | 4 | w | 559 |
| ὅπερ | 1 | w | 564 |
| ἐστὶν | 1 | w | 569 |
| ἀδύνατον | 1 | w | 577 |
| οὐκ | 1 | w | 581 |
| ἄρα | 2 | w | 584 |
| τὸ | 14 | w | 586 |
| Θ | 3 | w | 587 |
| σημεῖον | 5 | w | 594 |
| κέντρον | 6 | w | 601 |
| ἐστὶ | 4 | w | 605 |
| τῆς | 4 | w | 608 |
| σφαίρας | 4 | w | 615 |
| Ὁμοίως | 1 | w | 622 |
| δὴ | 1 | w | 624 |
| δείξομεν | 1 | w | 632 |
| ὅτι | 2 | w | 636 |
| οὐδὲ | 1 | w | 640 |
| ἄλλο | 1 | w | 644 |
| πλὴν | 1 | w | 648 |
| τὸ | 15 | w | 650 |
| Η | 4 | w | 651 |
| Τὸ | 1 | w | 654 |
| Η | 5 | w | 655 |
| ἄρα | 3 | w | 658 |
| σημεῖον | 6 | w | 665 |
| κέντρον | 7 | w | 672 |
| ἐστὶ | 5 | w | 676 |
| τῆς | 5 | w | 679 |
| σφαίρας | 5 | w | 686 |
| Πόρισμα | 1 | w | 694 |
| Ἐκ | 1 | w | 697 |
| δὴ | 2 | w | 699 |
| a | 1 | w | 700 |
| τούτου | 1 | w | 706 |
| φανερὸν | 1 | w | 713 |
| ὅτι | 3 | w | 717 |
| ἐὰν | 1 | w | 720 |
| ᾖ | 1 | w | 721 |
| ἐν | 1 | w | 723 |
| σφαίρᾳ | 1 | w | 729 |
| κύκλος | 1 | w | 735 |
| ἀπὸ | 3 | w | 739 |
| δὲ | 4 | w | 741 |
| τοῦ | 7 | w | 744 |
| κέντρου | 1 | w | 751 |
| αὐτοῦ | 2 | w | 756 |
| τῷ | 3 | w | 758 |
| ἐπιπέδῳ | 4 | w | 765 |
| αὐτοῦ | 3 | w | 770 |
| πρὸς | 2 | w | 774 |
| ὀρθὰς | 2 | w | 779 |
| εὐθεῖα | 1 | w | 785 |
| ἀνασταθῇ | 1 | w | 793 |
| ἐπὶ | 2 | w | 797 |
| τῆς | 6 | w | 800 |
| ἀνασταθείσης | 1 | w | 812 |
| τὸ | 16 | w | 814 |
| κέντρον | 8 | w | 821 |
| ἐστὶ | 6 | w | 825 |
| τῆς | 7 | w | 828 |
| σφαίρας | 6 | w | 835 |