 | Size | Height 297 mm, width 204 mm. | | Watermark | Two watermarks. Unicorn with 4 legs, little circle on top of the forehead. Crown with encircled cross. Drake's identification: Watermark type 13. Drake's description: Rhinoceros 75mm (smaller on letter cited?). Date of earliest letter with this watermark is August 1607. | | Comments | The folio is part of a larger sheet of paper combining the folios 86 and 87 . Written by Galileo; contains texts, drawings, calculations. Relation to the Discorsi: statement and elaboration of 3/05-pr-02; work on projectile impetus; draft of 3/05-pr-02-cor. | | References | Wisan 1974 268; Damerow et al. 1992 203-205, 222, 349; Wohlwill 1899 621 |
|
| | | Folio 87 v (final text) | | 1A | Datae parabolae elevationem invenire, ex qua decidens mobile parabolam datam describat. | | 1B | Sit data parabola bf, cuius altitudo bi, amplitudo vero if. Ducta orizontali bl, accipiatur in perpendiculo be aequalis bi, et connectatur elf, quae parabolam tanget in f et orizontalem secabit in l; fiat ut eb ad bl, ita lb ad ba. Dico, ab esse elevationem ex qua decidens mobile, in b conversum, describet parabolam bf. | | 1C | Si enim intelligatur, tempus casus per eb esse ipsum eb, et idem eb esse momentum celeritatis in b, erit bl tempus et momentum in b cadentis ex a: cadens igitur ex a in b, conversum in orizonte, tempore bl transibit duplam ba; ergo in eodem motu, tempore eb, transibit duplam bl: est enim ut tempus eb ad tempus bl, ita dupla bl ad duplam ba. Dupla vero bl est ipsa fi; ergo tempore be a cadenti ex a conficietur orizontalis if: sed eodem tempore eb conficitur perpendicularis bi ex quiete in in b: ergo cadens ex a, conversus in b, eodem tempore conficit orizontalem if et perpendicularem bi ex quiete in b: describet ergo parabolam bf. | | 1D | Constat, dimidiam basim esse mediam proportionalem inter altitudinem parabolae et elevationem supra parabolam, ex qua cadens illam designat. | | 1E | Scritta | | C01 | 116 * 76 = 696 + 812[0] = 8866
sqrt 8866 = 94 | | C02 | 116 * 40 = 4640
sqrt 4640 = 68
116 - 68 = 48 | | C03 | (49 * 94) : 116
49 * 94 = 196 + 441[0] = 4606
sqrt 4606 = 67 | | C04 | (50 * 94) : 116
50 * 94 = 4700
4700 : 116 = 40
4606 : 116 = 39 | | C05 | 116 - = 48 |
|
