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[Johannis Wallis S. T. D. Geometriae Professoris Saviliani, in Celeberrima Academia Oxoniensi; Opera Mathematica] Johannis Wallis S. T. D. Geometriæ Professoris Saviliani, in Celeberrima Academia Oxoniensi; Opera Mathematica, fol. 601

Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German. Mean line confidence on this page: 0.86.

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The machine reads it as

  1. ti
  2. C
  3. a
  4. l
  5. i alLodc CeCibabe
  6. FO. FL:: FP. FD.
  7. TE DO, Forizontalis recta; FP ad FTorizontem pet
  8. pendicularis; FO, inclinara recta, per quam vel
  9. Descendit vel Ascendit Crare; Ec rectae PO, parallel
  10. DE, (trianguli crura sccans proportionaliter, per 2
  11. Elem. 6.) ErgO: uE FO, ad P L, Longitudo ad Lon
  12. gicudinem; lic FP, ad FD: HIOC CHt, (per 3 _ TOhu
  13. jus,) Descentus ad Descentum (s Deortum,) vel (A
  14. TurCum mOveatuT) ACcentus ad Ascensum. Ouod CraL
  15. Propolicum.
  16. Idem, mutatis mucandis, de moris ab alia Viquaris, similiter octendetur.
  17. SCHOF TV M.
  18. vmie haec Demonstratio: Forironcalis rectae PO, puncta omnia, uE P, C
  19. aeque alta: adeoque PO rectam, quasi in superticie Sphaerica, Perrae concen-
  20. trica, jacere. Sin arerBcs loquamur, pro rectis PO, DL, Substiendi funt arcus
  21. circulares, Perra ce fentrici; (ee quidem pro singulis in FO punctis, mucabitur
  22. Perpendiculi rolicio, ec inclinacio decliris rectae:) Sed rancillum a Rectis differunt
  23. Arcus illi, ut pro Rectis ruro usurpari soleane, ob causas ad DeF. 15. Cap. L. emOrataS.
  24. P R OP. X
  25. Reais, lire ad orizontem perpendicularibus, sire utcunque inclina-
  26. tis; Si per AEquales Longitudines feratur Crare: Descensuum AF
  27. centuumre Alcicudinco, sunc Consicudinibus portionum aque alta
  28. rum reciproce proportionales.
  29. Su per Inaequales Longitudines ferantur: Descensuum Ascensuumre
  30. Alticudines, sunt in ea ratione qua componitur ex ratione Longi
  31. tudinum pex quaS HIcmOtuS, _ reciproca Congirudinum portionum
  32. aeque altarum.
  33. Adeogue; Si emensa Fongitudines, sint Consitudinibus aque altis
  34. proportionales: Descensus Alcentutre sunt aquales.
  35. Idem intellige, mutatis mutandis, de alia Vi motrice.
  36. FO. FP:: FL. = F P. FD: F K. FM.
  37. mL. L:: H = D. = D:: nM. = D.
  38. TTE PP, ad Forirontem recta; FO, inclinata: Per PP, descendat P Crare:
  39. in F O, grave L; per Longicudinem P L, recta PP aequalem. Jungatur PO
  40. Florizontalis recta, (abscindens porciones PP, FO, aque altas:) ec, huic D2
  41. rallela, L. D. Descenlus itaque graris P, tantus est quanta recta F P; pravis L
  42. quanta est recta FD; (per LO hujus.) Eltque (per 2 Elem.: 6.) uc FO (Jonei
  43. cudo porrionis obliguae,) ad F L, vel huic aqualem F P, (longitudinem perpen-
  44. diculi aeque alti:) Sic, rice rerla, F P (alcitudo Delcentus, in perpendiculo de
  45. Ccendentis, P,) ad F D (altidinem descensus, oblique descendentis L, per lon-
  46. picudinem aequalem.) Idemque de ascendenrium per ealdem L. F, PF, Ascen
  47. libus, similicer ostendetur. Ouod crat probandum
  48. Adeoque; Si per Tnaequales Lonsitudines terantur; (puta, per PD; _ FR =
  49. EF P;) erunt Descensus Ascentulre, in ratione quX ex illa, dt longicudinum per
  50. quas feruntur, compolica; (nempe F M = E LD.) Dec praeced. OuOd POTEOPEO.
  51. baltcuim ctal.
  52. Fis. 4
  53. altarum, ee directa longicudinum emenlarum,) Cint inricem reciprocx; IIOc et
  54. ( lonsicudines emensa, sint consitdinibus aque altis proportionales; (PUta, F L
  55. FD, longicudines ementae, iplis F O, F P, lonsicudimitis aque altis, proporciona
  56. +88E
  57. Ldeoque; (per 6 Cap. 7. ) Si TaLIOHILS La, (MLMMDC, RCCIPFOCA PONLOMII aGUC

Cite

[Johannis Wallis S. T. D. Geometriae Professoris Saviliani, in Celeberrima Academia Oxoniensi; Opera Mathematica] Johannis Wallis S. T. D. Geometriæ Professoris Saviliani, in Celeberrima Academia Oxoniensi; Opera Mathematica, fol. 601. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/851387705:0621?run=74