Leibniz Legible

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. 374

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: 0.84.

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The machine reads it as

  1. ARLT HMP FIC A.
  2. PFOP. XXI.
  3. Puca (E cerminus pot 0 primus pongcue 2, et ulcimi lacus 1,) F L p . P
  4. Vel (potico numero seu mulcimdine cerminorum m, d ulimi lacere 1,) P
  5. 6m
  6. Cum autem crelcente numero terminorum, excestus ille supra suberiplum ita
  7. continuo minuatur, uc tandem quolibet assignabili minor cradat, (UE Patet;) A
  8. in intinicum procedatur, prortus craniturus cst. Adeoque -
  9. PR OP. XXT.
  10. Theorema.
  11. CY PrOPOnatuE Serres infinita Ouanciratum in duplicata ratione A-
  12. richimetice proportionalium, (sive juxta seriem numerorum qua-
  13. draticorum,) continue crescentium, a puncto seu o inchoatarum; erit
  14. illa ad seriem toridem maximae eegualium, ut F ad 3.
  15. 11
  16. Patet ex praeced.
  17. 10i
  18. PKOP XXII.
  19. rss) M1SSHOGOI.
  20. Seritiee
  21. Sis Bes) Seueiei Corollarium. e S CeisCES SsIS Se
  22. le
  23. s
  24. Deoque conus vel Peyramis ad Cylindrum vel Prisma (super cadem vel
  25. aequali base aeque altum) est et L ad 3.
  26. Constare enim supponimus tam Conum quam Ppramidem ex intinicis planis
  27. similibus e parallelis, in duplicata racione Arichimetice proportionalium constitu.
  28. tis, quorum minimum supponitur Punctum, maximum rero balIS; (per ea quae
  29. diximus ad Prop. 6. Con. Sect.) Cylindrus aurem vel Prisma, ex toridem, maxi.
  30. mo aequalibus (uc patet:) Racio nicur At uC L all 3, per pruced.
  31. PR OP. ZXTTI. ∞
  32. Corollarium.
  33. Lem complementum Semi parabola, (intellige fieuram AOF quae cum
  34. ipsa semi parabola comput Paralleloerammum,) est ad Paralleloeram-
  35. mum LD (super eadens sel aequali base aeque- altum) ut F ad 3. (Ft con-
  36. sequenter, ibsa sent abola est ad idem P aralleloerammum, ut 2 ad 3.)
  37. Fsto enim FIOVE AO F vertex A, diameter A F, batis FO, eique perallelae
  38. quorlibet (balem inter de rerricem) YO, FO, Sc. Ouoniam LUINE (per PrOP. 2F.
  39. Con. Sect.) recta DO, DO, etc. in Tubduplicata
  40. ratione rectarum AD, AD, _C. FFUNE C COnTra
  41. ipta AD, AD, ecc. hoc cAt TO, FO, etc. in ra
  42. tione duplicata ipsarum DO, DO, dec. hoc cAt A Y
  43. AT, Ec. FOra iBItuT fGUITa AOT (constans ex
  44. intinitis numero rectis TO, FO, ec. in duplicata ra-
  45. tionc rectarum AY, AF, ec. Arichmetice prOpOr-
  46. cionalium) erie ad Parallelosrammum aeque alcum
  47. TD (constans ex cocidem rcclis ipsi TO maximae
  48. aequalibuS) ut F ad 3. per PTOP. 2F. (Ouod crat
  49. Oltendendum.) Ec consequenter, semiparabola AOD
  50. (parallelosrammi residuum) ad idem P’arallelorram.
  51. mum, ut 2 a c 3.
  52. PAtEE ex PPOP. praecec.
  53. PROL.

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. 374. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/851387705:0394?run=74