Leibniz Legible

Machine transcription of the Leibniz Nachlass

Search the Nachlass

Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 17r

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: 0.78.

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

The machine reads it as

  1. solatio aequationis differentialis aadque + Bydx + at dx =0 a medudum
  2. reperta est ex principio comparum terminctam eo jungendi compares terminos qui se javicem habere
  3. possunt, ut sum differentia eabuesa et ferminu e difeentiatum. Hi termini enm hoc loco sunt y et dy
  4. multiplicetur aequatio per h. fiet aahdus +hBydx + abhdx = 0 debet esse daah) = hBdx b
  5. ut aahdus +tByax possit summari sin facere aahus et fiet aadh = hBdx seu dh: h = (Bdx: aa
  6. Sit aequateo aad raaβ dY + B sWVdx +a) pax + aa D ax = 0 fiat
  7. d
  8. (
  9. V = py: a et do = ody + rdp, a et vdo = ppydy + pyyap: aa
  10. unde interpretendo et multipplicando per h
  11. Appydy +ha p dy p gu ap +haβydp thaaddx 0
  12. s
  13. RAppyy axiaa +h) py dx
  14. unde inter pretando fit
  15. et mu
  16. dchpp hp dp thappdx: aa seu 2) aa hpap + ac ppdh = (aa hp ap) + k. A Ahpp dX, et
  17. Ex primo compare yy et ydy
  18. fiet. aa h dp + na pdh = A hp ax. seu aa lous hp = fAdx. Ergo datur EP. quod
  19. si esset X =0 foret hp = ab constanti.
  20. lix primo compare yy et rydys, fiet d (hpp) = hp dp + AAppdx: na, adcoque fiet
  21. aa hpdp, + =Aapp dh = Caa hp ap + AhppdX, et filt logu h = 2(Adx: aa quod si
  22. Li
  23. up
  24. quod si abesset A. foret h constans, seu dh =0
  25. Ex secundo compare y et dy fit d (a Bh0) = a βh dp + ) hpdx
  26. sed eu
  27. sen a ap dCBh) F aBh dp = (a (hap, + Vhpax sed ita evanescit et p) adeoque non
  28. et n= pay+ ydp + dr
  29. et vdo= Oppysdy + 7ypap + 8prdy +ypdr +yrap + rar. Uade interprendo aequationea set
  30. s
  31. adsunt ert B apsbitrariae sufficientes.
  32. G
  33. inde haappudus thaapuyap thaaprdy thaaydx rdr
  34. p hic homogenea est mero)
  35. t, quasi esset pia +hst ppyy ex
  36. 1a
  37. haar ydp
  38. haaBpdus haa By ap iha a βr
  39. 2D pryex rrax
  40. ha py dx tha) Ydx
  41. et multiplicando per h.
  42. Ex primo compare yy et 2ydy, fiet ut ante d sta apBx: 2) = a apdp + hst ep dx,
  43. masong
  44. +tiaaB ex
  45. 2 a aip dp) aappdh = (2 aa hpdp, + 2 A h pp dx
  46. seu
  47. seu dh: n = 2 5 dH seu logh = 2 (Adx: aa
  48. Ex secundo compare y et du, fis act d h pdret h, apss Bdp t EA hpX+ ah) pdx (adhpY +h BP)
  49. quod si abesset A foret dh constranu =0 seu h constans
  50. A
  51. acc prah+ aa Bpato aarhap + aar Bah ( aa Bhapi+ aa B pati nansab+ aanp ds3
  52. la
  53. sumus
  54. aanparet aahrdp + aah βdp + 2) hlpr dx = aa d (lip. r+ C) =
  55. seu
  56. Epraaati
  57. itaque datur 2. omnino.
  58. e
  59. ea
  60. dx faared. het aa Bhaptaa β pantapa apaβ
  61. e
  62. sed
  63. ande fit, BdhataB = ∞ son βh = ab
  64. et a piet que jum habear

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 17r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068196:0033?run=74