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Leibniz-Handschriften zur Mathematik LH 35, 12, 1, fol. 328v

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.

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

One image of two folio pages side by side, registered by the library under both labels (also fol. 329r); this page is its left half.

The machine reads it as

  1. Solvere hoc problema a me diu
  2. quaesitum inveniendi summam proscessio
  3. nis (Zeometricae seu reassumtae, idem
  4. est quod invenire progressionem Har
  5. monicam datis ejus differentiis, diffe
  6. rentiarum qu rationibus:
  7. Xc. at
  8. e = a +
  9. =ea +2b,
  10. GBe: 4
  11. 4
  12. 1
  13. Xa 1
  14. a13+b
  15. a= R +a a+b, +b
  16. = a+b4b
  17. D+1((2)
  18. Brevius ita concipet: quadratum differentiae diffe-
  19. vertiarum dividatur, per differentiam minorem
  20. producto a; quotienti addatur differentia diffe
  21. rentiarum. d triplicata et differentia minor
  22. triplicata. Summa est Terminus Major
  23. au +9a + 12b.
  24. proportionis Harmo.
  25. nica
  26. a dissra pna ada. Ratio earum a
  27. terminus primus qu progcessionis hannonicae
  28. quaesitus 2. Ergo tertius est Za. Ergo
  29. secundus est za
  30. Ergo Ergo segindus erit 2Z- a. et
  31. tertius Z- a + b. at idem tertius est
  32. Za. Ergo Pa = Z- a - b.
  33. quaerendum est aliquid aequale ipsi Z.
  34. 2B = 2 4 +. Ergo
  35. a. - 2 - ab - bb
  36. arta a
  37. 2b = 24- e- ba
  38. 22+ a 2b+ da + ba = Za.
  39. aa + ba = ea - Zb.
  40. Dividantur omnia per a. fiet
  41. A + b = X
  42. jam Zb e = Z. a - b perpra
  43. Ergo.
  44. a+ b = Z 7 2. acb, seu
  45. 2absi a + b = 2+ a+ b-7. En aequa.
  46. imnia Exergo inventam havem.
  47. datis differentis invenire
  48. ei terminos progrestionis par-
  49. tionem nugatoriam, et
  50. a + ba = 2a - Z b. i
  51. Poidantur aa +ba. in duas partes
  52. t
  53. 2- a + b, + b, = 7 b e (Erraveram
  54. ante, quod non expresa +B in aequatione
  55. ratimm attram differentiam praecedento
  56. sequente majorem) multiplicenti omnia per atb
  57. monicae proportionis num qu ati. fet Atb, + bg a + b = 2b. Et
  58. n minon diph addatur differentia ejus
  59. a majore. Summa multiplicetur per ratioem
  60. quolitam unitatem auctum quotiente
  61. dio
  62. producto ex divisione differentiae interdisse
  63. rentias per differentiam minorem, productum
  64. terminus quae sitae profressionim maximus
  65. quo dato racipui duo facile inveniunt
  66. 2 atibatibm a + b b =
  67. 2
  68. La+1. =2
  69. a2-- 42 4a + a,, + 27 a + b, + b = Z+Z
  70. 2- a +brC + 4 1att a 1 a+b+C. - X
  71. 2 termins g.
  72. B, 1b, =

Cite

Leibniz-Handschriften zur Mathematik LH 35, 12, 1, fol. 328v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068194:0658?run=74