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. 382

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. ARITHMETICA LIODLECLETA.
  2. juneatur quxe proxime erat insecutura, (quod cantundem est atque pro figura ex
  3. Sectoribus inseripca, circumseriptam lubsticuere,) atque tandem addlatur a; habe.
  4. bitur ex omnibus ageregata recta qua vera spirali major erir; sed quae ad justam
  5. eo propius accedet quo plures supponantur Sectores ad (eribI.
  6. PR DT. RL LL
  7. Lemma.
  8. I Proponatur series quantitatum in Triplicata ratione Arichmerice
  9. proxortionalium, (sire juxta seriem numerorum Cubicorum,) con-
  10. tinue crescentium, a puncto vel o inchontarum, (pNt2 UL 0, 2, 8, 277
  11. 64 eC.) proposicum lic inguirere quam habeat illa rationem dd seri
  12. em cocidem maximae aequalium:
  13. Piac inveltigatio per modum inductionis (urin prop. F. XC 19.) Fxicque
  14. 1 =
  15. 0 F 1= 6+2, = 36
  16. 0
  17. +8 = c
  18. 8 +. 8 + 8 == 2.6
  19. 27+27 +27 +27 =108 a t 12.
  20. 0 F F + 8. f2
  21. 20c
  22. 64. +64 +64 + 64 +64 = 320
  23. F F + 8 + 27 + 64 7 125 ==225
  24. +25 F 125 F 125 F125 + 125 + 1252 750=
  25. 0
  26. +8 + 27+ 64 + 125 +216 = 44
  27. 216 = 216 +216 f 216 f216f216 +216 =2512 21a l 34
  28. Et sic deinceps.
  29. Ratio proveniens est ubique major quam Subquacruplas sen I. FxceNus autem
  30. perpetuo decrescit prOUE nUMCTUS terminOrum ausCTIIE, Puta 2, 3, 13, 163 303 27
  31. Ec. aucto nimirum tractionis denominatore, sire consequente rationis, in singulis
  32. locis, nummero quaternario, (uE Patet;) uc sit racionis provenientis excectus supra
  33. Tubquadruplam, ea quam haber unitas ad quadruplum numeri terminorum polt 0.
  34. AdCBquC-
  35. PROP. XI
  36. Theorema.
  37. EF proponatur series quanticatum in Triplicata ratione Rrictime.
  38. rice proportionalium (sire juxta seriem numerorum cubicorum)
  39. continue crescentium, a puncto relo inchoatarum; ratio, quam ha-
  40. bec illa ad seriem cotidem maximae aequalium, subquadruplam suPCxa
  41. bIL; exitque exCeNTuS, ea ratio quam habet unitas ad quacruplum nu-
  42. meri terminorum posto; sire, quam habet radix cubica termini pri-
  43. mi Dost o, ad quadruplum radieis cubica termini maximI.
  44. euca F B +F ) p vet 1 + P = = mt +: mV.
  45. Patet ex praecedente.
  46. Cum autem, crescente numero terminorum, exceltus ille supra rationem subqua-
  47. druplam ita concinuo minuatue, ue tandem quolibet altignabili minor eradat, (ut
  48. Pacet;) si in intinicum procedatur, prortus eranicurus est. Adeoque -
  49. L R O P. XLI.
  50. Theorema.
  51. 1l10.
  52. L proxonatur leries intinita quantitatum in Lriplicata ratione Aritli-
  53. metice proportionalium (hire juxta leciem numerorum cubicorum)
  54. continue

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. 382. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/851387705:0402?run=74