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. 403

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.

Original at the GWLB · Page image · Annotations (IIIF) · Download text

The machine reads it as

  1. TOD
  2. ENFLNLTORO
  3. ea0L. L42412.
  4. Corollarium.
  5. SImiliter. Si respectiors rectis Trianculi ADB, C3 Semipurao AH F.
  6. sumantur tertia proportionales, prodibit Parallelozrammum B:
  7. respectivis rectis Paralleloerammi BD, C Semiparabolae AD F, prodibit
  8. Frianculum ADB: si respectivis rectis semiparabolae primae AD B, Cs secundae
  9. ADF, prodibit semiparabola tertia AD B: C sic in aliis.
  10. Sequitur ex praecedente. Ouadrata enim rectarum in semiparabola, constituene
  11. Pgramidoeides Parabolieum. Oltendicur, in tis. praeced.
  12. SCHOLYV M.
  13. Et pari modo de aliis Feurarum folidarum ad Planas axplicarionibus respectiris
  14. judicium tiet Sufticie paucas exempli caula indicalse, ad quarum imicarionem fieri
  15. Postunc innumerae aliae.
  16. P R OP. LZXZVIL.
  17. Theorema.
  18. EF PrOxOatur series quaelibet praedictarum per aliam superioris
  19. Gractus seu Potestatis diridenda, nulla jam memoratarum series
  20. prodire poterit, (cum index porestatis superioris ex indice potestatis
  21. interioris, major quipre ex minore, anferri non POL:) Sed aliusmodi
  22. Plane Series, cujus nempe termini sunt reciproce proportionales ho-
  23. molosis terminis alterius seriei, qua indicem habet aequalem excellui
  24. indicis seriei diridentis supra indicem Serici dirila.
  25. Series aurem sic provenientes, Scries Reciproca appellantor, habe.
  26. ancque indices nesatiros.
  27. Fxempli gratia. Si series Secundanorum dividenda sic per Periem Terriano.
  28. rum, vel series Primanorum, per seriem Sccundanotum, vel series Ai qualium per
  29. seriem Primanorum, (uhi leries diridens est uno gradu superior serie dividenda
  30. adeoque index seriei diridentis unitare major quam index seriei divila, puta
  31. 2 =
  32. T - O = F:) Termini serici oriundae crunE RCCIPTOCC PFOPOT.
  33. cionales homoloxisrerminis teriei Primanorum. Puca si respectire dividatur
  34. Peries
  35. Oa2, 2a2, 4a2, 942, 1642, ec.
  36. per leriem 043, 207 84, 27a3, 64a3, ec.
  37. vel series
  38. Oa, Ia , 24,
  39. 34, 44, ec.
  40. Der Periem Oa 2, 2a2, 442, 9a2, 16a2, ec.
  41. vel Peries
  42. 2
  43. ec
  44. per Teriem Oa, 24, 20, 34 3 41 7 C.
  45. Da 2a 24, 3a3d 4a, dc.
  46. cujus teriei cermini sume reviproce proporiionales homoloris cerminis seriei prima.
  47. norum
  48. ubique.
  49. a 3a 4E, c. ut putet. Nemre 2 a 3 a
  50. 3
  51. Eodem modo series primanorum dividenda sic per seriem tercianorum; vel
  52. F. CC 2
  53. (quod
  54. +
  55. E
  56. 22 F He

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. 403. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/851387705:0423?run=74