Overview Level of Folio 087 v


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


Overview Level of Folio 087 v