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. 365

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. TIMD
  2. C A l2CL L.
  3. S I V F
  4. NOrA AELHODOS IHOBTREHOI
  5. in Currilineorum Ouadraturam, aliaque
  6. Difficiliora Matheseos P roblemata.
  7. PRO P. I.
  8. Lemma.
  9. Y proponatur series Ouantitatum Prithmetice proporcionalium (sire
  10. juxta naturalem numerorum consecutionem) continue crescen-
  11. tium, a puncto vel o (ciptra, seu nihilo) inchoatarum, (puta
  12. UE O, 2, 2, 3, 4, _C.) Proposicum sic inguirere, quam habeat ra-
  13. tionem earum omnium axxresatum, ad axeregatum tocidem maxima
  14. aequalium.
  15. Simpliciltimus investisandi modus, in hoc et seguentibus aliquot Problematis,
  16. est, rem iplam aliquousque praestare, de rationes prodeunces oblerrare atque invi-
  17. cem comparare; ut inductione tandem univertalis proposicio innotescat.
  18. Es isitur, exempli gracia,
  19. 0 = 2+ 2 + 3=6
  20. 3 + 3
  21. = +2
  22. 0+ c + 2 +3 +4 +5 = 75
  23. + 5 +5 +
  24. +
  25. +
  26. 10
  27. 0 = T
  28. 0 + r + 2 =
  29. 1 2 + 2 =
  30. O = F + 2. + 3 + 4 = 20
  31. 4 + 4. + 4 + 4 + 4. = 20
  32. 0 = 5 + 2 +3 + 4+5 +.6 = 27
  33. 6+6+6 +6+6. + 6 +6 = 42
  34. Et pari modo, quancumlibet progrediamur, prodibit semper ratio subdupla. A-
  35. deoque-
  36. PROP. II.
  37. Theorema.
  38. U7 sumatur series quantitatum Arichmetice proportionalium (sive
  39. juxta naturalem numerorum consecurionem) contimue crescenti-
  40. um, a puncto relo inclioatarum, et numero quidem rel tinitarum rel
  41. intinitarum (nulla enim discriminis causa erit,) erit illa ad seriem cori-
  42. dem maximae aequalium, ut 2dd 2.
  43. Nempe, Si primus terminus (LO, secundus 2, (nam si secus, moderatio achi.
  44. vencta erit) e ultimus l, exie summa-, = Y (erit enim, eo Casu, RUETIS LT.
  45. minorum I. + L.) Vel, (polico numero cerminorum m, quancuscunque sic terminus
  46. Sccundus) Zm
  47. PROF.

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. 365. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/851387705:0385?run=74