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Leibniz-Handschriften zur Mathematik LH 35, 13, 2c, fol. 91v

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

One image of two folio pages side by side, registered by the library under both labels (also fol. 90r); this page is its left half.

The machine reads it as

  1. videndum jam an hac ma altius proced possit
  2. ad usue gradum et.
  3. videtur et alia esse via sit dy + mydx =0 utique est tracta
  4. bilis, fiat y = +v + Y et fire tdv + vdb + dr, =0, quae con-
  5. ferri potest datae
  6. +mtaxB +mrax
  7. f de + 9ut h= 0 multiplicatae per Y
  8. et fiet frdv + grve hr, ∞o et fit dr: r = rax- nax
  9. et t = fr. sed ita in medio deest arbitraria. itaque oporleret
  10. fdo + quax +hdx-o multiplicare per KY, et fieret
  11. fkrdo + gVXrdx + hKY dx = 0 et dr: Y = htidx. md
  12. et + = FKY et dt + mtdx = (gKr =) g: ts. sed vereor
  13. O
  14. ut res ita procedat. praestat igitur dia prior
  15. du sit ac dydus +tfdys + agydxx + hydydx + Kyydxdx + aalaxdx o
  16. sit . 100dy + us) ex tuag cy ryex t afx, mult per rsdyribax
  17. ad e
  18. nult per
  19. fiet 10 15 aa dydus + aasaydydx + 1 15 mult per 13ady + 4 Rydx tS adx
  20. 12. 15a dpdx
  21. + 1014aa...
  22. + 11. 1ta yydxlx 112. 14 aa7 dxt
  23. + 10. 15a..... 4u1
  24. + II. 15aa..
  25. Haec aequatio comparetur cum aeq. data O. et fiet
  26. (1m) 12. 15 = al Edosi. 13 = aeti 1 af . (3to) 11. 14 = ak. Habemus ergo 3114
  27. 15, substituenda i aegu. sequ. (4to) 12. 1 + 10. 15 = aF et (560) 1. 13 +10. 17 = ah
  28. et (6to) 1 12. 14 + H. 15- a9. ubi in aeqque 4, 5, 6 substituendo valores ex
  29. agg. 112, 3. fiet ex ahit acio ivalu at, et habetur 1:10
  30. ekaeg. 6 firt 1 ak Ex aeq. 4 fiet (7mo) 122C. 19 + 10a l: 12 = a5, et datur 12 :10
  31. Ex aeq. 6(1Ct (∞00) 12(a K: 2) + Wsal: 1= aB et datur 122M Et denique
  32. Ex aeque fiet (9no) IRB: 10) + WaK: U = at et datur a: 10
  33. Ergo aliqua harum lationum datur bis, seu habetur aequatio inter datas
  34. unde aequatio data prius est praeformanda, ut salisfaciat huic
  35. conditioni, quod videtur fieri posse, cum sit non nisi unica, et duae
  36. abitrariae possint assumi faciendo, 1F tV+Y
  37. cubile vidtur sequi nempe in data
  38. suit solum
  39. C ayay segnaxda L0. videtur sic res reduci posse ad quadratu-
  40. Hinc aliquit snca
  41. m rationalem maltiplicando 10dys + u x 20 per 13 dy +1d nam frt)
  42. co. B dydy + 10. 1dx dy + 11. 17 yaq xd = 0 sit 10. 14 + 1. 13 20
  43. 11. 1
  44. 10. 13 = ea 11. 14 = aF
  45. Hinc tollendo prius BeM4 fiet 132 _0: 10 et 14 = aK: H. quos valore
  46. substituendur fiet: 10 (aK: 11) 1aC : 10 = 0 unde prodit eandem
  47. e i = 1. 102 = R: C. calculus probus, sed reditur accurate ad
  48. Fdy + yd f. = d9 hady e tmyax Fhncx =0 posito dh.h = indx est tormula summabilis unde
  49. priorem difficultatem
  50. se fy+9.
  51. fet fd9 + y d5 = eg + A fody + hfmgyax
  52. e
  53. +g
  54. hengar t9hulx
  55. + Ihmydx
  56. sed si m = 0 posset s manere
  57. indeterminata et nabet.
  58. potest generaliter ex endus toydxt
  59. udy f.dy +. dx F.. ydx
  60. 25ydy + yy df. + dy 2 yaK e +fdy + gdX c0 fit 25y y 1yyd) +Xag .gLX =0
  61. fyu + Ky +
  62. Atfycys tsgyya kb) t Kygdx
  63. e et faciendo b= -2 rodnestat ydy

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 2c, fol. 91v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068199:0182?run=74