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Leibniz-Handschriften zur Mathematik LH 35, 13, 2a, fol. 118v

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: 0.81.

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. 119r); this page is its left half.

The machine reads it as

  1. plutis aequationibus simplicibus d differentialibus duarum
  2. duabus
  3. literarum d multe habentur silutiones non simplices nujus
  4. sit gtf fZ 1gdZ t.
  5. sit fv +Gdae + hZ+ KdZ _ =0, et lV+ mdv + n Z + pdz =0
  6. literae.
  7. fiat Z= e B= Z = b et v = y . unde ex aequationibus propositis
  8. fiet fiy +AX gd ref y tagdus tak dx tah =0 et aly tamdy tapax + n =0
  9. Oxy
  10. Mdxy
  11. fiet - dx = fy + gdy + h.,:, gy + R = ly +mdy +n,:, mytap, quas duos
  12. pg
  13. Valores ats aequando, fit + fmgus (F om ydus + ah mys tagpaus + actep
  14. +at py +agpdus + achp
  15. -gl yy( gmydu leagnus
  16. aKly = atmdy -aa tin
  17. 2 quae aequatio identificanda est datae; possunt autem poni
  18. aequales a, quia sunt arbitrariae superfluae imo licet etiam h et n
  19. facere quales libet. Possent esse f - a et h =0 et 1 =0 et n - a
  20. fieret av + gdv F KdZe = 0 et Mdo + az + pdZ = 0
  21. et fiet amgu + Lapu + popdus + qar = 0 sit data aequatio du = xxryuse
  22. + gogy- ftmdy
  23. K = +XX: a
  24. fiet m = a knt XX v XX. K
  25. ax
  26. aa
  27. seu agu a dy +axX = 0
  28. P=9 et ggAXx = aa
  29. seu g9 = aa - xX et fit av + (aa - Xx) dv + XX dX = 0 et adv taZ = 1 (a - ) dz -0
  30. sed prostat conscrvare generalilitem, fiet sm. gl= aa hm+ fp-gn - Kl =0
  31. qu - Km = = aa hp - K n = XX quaerantur f, ny K, m. g, , In, p
  32. += ta gl,: m a l tgn hnc: p f g - sm- aa = tm = aa, : p rCLAtm Sp, : n
  33. na limu honp taan,, nin + pl =K
  34. K= Hta- aap4 aat, . lm s em
  35. etm _ = Ap. K P = Km: g fot a~ AB(Kg m: g = l. f sege g
  36. sit p = Kl: f et nhl. f p= Kn: h fit l. f = n: h = m: 9
  37. Pok- Lf fit m: 9 = f: l = p: K = hn ita nulla liter opurrit bis
  38. M= gf. 1 = 5g: m h = nm: g p= Km: 9,
  39. superest aequatio hm + fp = gn + Kl in qua substituemus hosualores fiet
  40. num + fkm gn + fgK. m seu C mn + fkmm = ggma + fggH
  41. R = m -ggmn, :, f99 = fnm = - mn: f. Euo p = - mm n + Fg
  42. Habemu ergo l = fg: m h = mni
  43. p= K f :b p. Kur.gHo mo p-mma
  44. abrys + aac dy aad dy 200
  45. datam generalem ats) i aadus + aasibus + a
  46. k = pp. H sumamus D+
  47. n + hp- ag,: t l= fm ac, : g an n hp. af,: K
  48. n= prost
  49. h= . ae +KR i Cgt:, ad t km
  50. p= ad 4Km: 9 undejus ecalores tstomamus in sa
  51. l= fm - ab, : 9
  52. in aeq. hm + fp - gn +KC = ac
  53. fet aem tkemn + adf + KFm - gn + fk ( - ab k = aC
  54. siet aegm tgtema + Ldfp +Ksmp ggpu = fKlp. abtp- acgp
  55. D
  56. ad +Am
  57. et fiet aeggm + ggkmn + ad f qu (ad Hem) = adgg GKmn + K(fl. ab ad akin)
  58. aacd + act
  59. m
  60. d + 2adtem tskmm-adgus = asimo +Ad kfLaabd s H fretlm abtrm
  61. ad f qu (ad 1Kt) -+ (fKC l. abk - ac9) ad T Km) +ggm (ae + Kn), : gg (ad +Km)
  62. a eggm gytemus
  63. fit n=
  64. jaciendo p- 0 = ad +Km et h = o = aetKn fit M = ad. K, e n = - ae: H gm = ac 5f. M- ac: 9
  65. possumus hanc aequationem partia in duas simplicuores
  66. et se l adf- abk igk
  67. en

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 2a, fol. 118v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068197:0236?run=74