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Leibniz-Handschriften zur Mathematik LH 35, 13, 2b, fol. 197r

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: 0.82.

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The machine reads it as

  1. Nit hinc sugulare
  2. certae
  3. sut AB, AB) progressionis Gometricae et rursus AB, A(B) alterius
  4. progressionis Goetira AB vocentur X; et AB vocentur rX quae
  5. int in data ratiore ad X. patet totidem sumendo YX, quod X; per ipsas
  6. PX longius pertingi, et summatis y, secundum ex majus osse patium
  7. quam si summentur secundum X. N secundum X1 sumana sidx facit
  8. AB CA et secundum rX (, Cytdx facit AB_A. sit aren
  9. y = Hrb) S(at b xns: 1aa+ ExX dve (y) = HCaa Hb rr PXX,:, aat crrux)
  10. quaentur fydx 1 fes) rdx = v
  11. aaa
  12. haberi debet
  13. quaeruntur duae zonae BE, FL, quarum differentia sit data
  14. fitt V et= pt flytrdx rsy) ex - x sydx + sir ( (C Ax - f. e) ((y) dx
  15. e
  16. aa
  17. AdEA
  18. ABCA fRHLA = f AFGAt
  19. Videndum an post differentiationem, quodam possint
  20. i sublationemque fractionum et irrationatium quaedam possint
  21. destrui, quo dende nova summatio melius procedat
  22. Res facilior proratione indaganda Ut si fsydx + 4(y) rx + b = 0
  23. fiet fyax + grydx =0
  24. = aa: xx quia
  25. in Hyperbola primaria dy:dx = y: X (y = a aa : X et fiet
  26. d et di aa dx ax et frit aa 2XX ~
  27. et dydus + lxdx = 4 y LX, X = aa Y XX, : XX
  28. Ex dx
  29. a ai
  30. a
  31. a +1
  32. at + 1)
  33. seu L(dydy + dx dX) = dX, 1(
  34. CM sit Sdx ( 1) et CN - Y Sdx Y(_ + 1), debet esse
  35. PF.CM + F CN + b = 0 seu F(dx (a +1) + X sdx 1( 1) + a =d
  36. et differentiando siet dx Y ( 1) + ax (a + + 1) =0 adeoque frot
  37. f
  38. au
  39. a
  40. aa gua + Wr
  41. sit ftaa = a, seu f= aa
  42. aa sed hoc methodus nen procedi
  43. fiet re aa = rr
  44. IY
  45. elib
  46. aq
  47. C C) = X (C) GC + GR CK HC) + HK = (C)K
  48. besc
  49. R eG + GdE FC = HK H(C) = F(C) = GR
  50. Qarit Data curva quaeritur in ea relatio generalis inter c(C), CK, K(C)
  51. fCF = sit AB GC) = AB) - AB + A p - AP)
  52. K = AB- AB + AP - AF
  53. (C) K = ABAB- AB L AX- A(p)
  54. Dantur ad huc tres aliae aequationes inter AB et AP, A(B) et A(P), AB et AF
  55. l
  56. C
  57. literae autem folleu
  58. poqa
  59. ACC+
  60. AP, A(), A(P), AB, AH, itaque ut hae tollantur
  61. setmpatione LR +H(C) L + LK- mux siet
  62. 2 +. LK = ax CF + _ faet CL deL L LK d+K. cC). cIdeL + A
  63. peb
  64. CLk
  65. +resc C
  66. at summa insirplarum sit maxima, sed optimumforet si posset inveniti
  67. determinatio, per quam progressio iuf perimatiorum pot inserplorum
  68. haberetur
  69. m: n = b: L

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 2b, fol. 197r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068198:0393?run=74