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Machine transcription of the Leibniz Nachlass

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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. 602

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: 0.85.

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The machine reads it as

  1. les:) Delcentuuu Ascenluue Alricydines, aequales erunt. Quod erac ulcimo
  2. probandum.
  3. Idem rirtous as motricibus Faeile accommodabicur.
  4. Cap. TI.
  5. De Cravium Descensib
  6. PL O P.
  7. 2
  8. Crarium, Rectac sue ad Horirontem inclinatas, Descensus, in
  9. Ca FatBBC Dollent, quae Componitur ex rationibus et ponderum, et
  10. Longicudinam ementalum, et. Reciproca Consitudinum aeque. al
  11. Idemquemoris ab allà Vi morrice Faeile accommoctabitur.
  12. 7 AlenE enim (per 5 hujus) in ratione ex Ponderum ee Altiruidinum rationi.
  13. e
  14. bus compotira: Hloc elt, (per praecedentem,) ex rationibus Ponderum, e
  15. Congicudinum, ementarum, et Rectprioca Lonxicudinum aeque alcarum. Ouod
  16. erat probandum.
  17. e ROP. XIV.
  18. Rectarum Decliritas Lonsicudine aequalium, est Alcicudinibus pronr
  19. tionalis.
  20. Rectarum Decliritas AEque altarum s CR Fonsitudinibus Reciproce
  21. proportionalis.
  22. Adeoque; Rectarum quarumvis Déctiricas, et in earaciorie, quae ex ra
  23. tione Alcitudinum et Reciproea Lonsitudinum componitur.
  24. Acque; Si Rectarum Longicudines sint Acitudinibus proporciohales:
  25. carum Decliritas aequalis eAt.
  26. 1i e
  27. Duod et aliis perinde ac prarium im oribus a ccomolabitus.lt
  28. encx
  29. 4 1I_ X R 3111 Sip s. e 121. mscritori
  30. F. 37D D. p
  31. ciuitie it rilut u . l Alastiro Te: Supussis
  32. nt
  33. mb.. 1-. Zp. MA, m F ma m B = 1. Si ir CcjeICI
  34. imin sininiimm L. SIsesit
  35. A Puncto F, dueantur aequales rectae, quoctibet F P, H O, F B,, quae continvatae
  36. occurranc Horizontali Recta (vel Plano Calrem) in punctis P, S, T.
  37. Rectarum P P, FO, F B, longicudine aequalium, Decli-
  38. ricaces, Tunc earum AIcicudinibus, puta, F P, FG, FR, pro-
  39. Portionales. per Det. 17, +8. Cap. F.
  40. Rectarum F P, FOS, FBV F, aeque alrarum Declivita.
  41. tes, Tunc carum Longicudinibus, hoc cAt, ip(IS F P, FS, F Y
  42. Reciproce proporrionales. per caldem Del. 17, 16, Cap. F.
  43. Ouxe erant demonstranda.
  44. Ouas quidem rationes eatdent etté; adeoque seminam
  45. quae hrabetur DeF. 18. Cap. T. Majoris Dectivitatis detini-
  46. tionem tantundem valere, (et Minoris similiter;) hine
  47. constat: Duoniam, Siretumantur rectarum F P, F. OS, porriones longicudine -
  48. quales P P LO, quarum Alicudines (INC F P, FQ; Sive portiones aeque altX F P
  49. FS, quarum lonsitudines reciproCR, TUnE FS, F P, hoc est FS, PO; Ladem vErO.
  50. bique prorenic Declivitacum ratio. Nam, ut FP, ad F.: Sic elt FSad FO:
  51. per 2 Elem. 6. Similiter, in rectis FP, FBT; porcionum aequalium FP, FB
  52. alricudines FP, PR; et porcionum aequealcarum F P, F T, lonsimdines RCCIprOCX
  53. FT, FP, hOC CAF T, FB; proportionales sune: per 2 Flem. 6. Trem; rectarum
  54. FO, FBV, porcionum aequalium FO, F B, alcicudines FO, P R; _ porrionum
  55. aeque altarum PO, PV, longicudines FeCIPTOCK FV, FO, hocCAFV, FB; pro-
  56. portionales sunc: per Z F. temr. 6.)
  57. Ideoque;
  58. tarum. Acque Ascensussimiliter.

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. 602. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/851387705:0622?run=74