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Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 97r

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. 98v); this page is its right half.

The machine reads it as

  1. Sit lata aequatio differentialis 100 +10C + 120 Coco + 10ideo = (1) =0
  2. Assumatur a =() 217 +20,: 317 +30, et explicetur aequ. 1. 7er 2. fiet
  3. +109. 30. 30 +, 100. 30.31 + 100. 31. 31 yy
  4. +110. 20.30 + 110. 20. 3Cy
  5. 116. 2, 30y + 110. 21. 31 yy
  6. +120. 20. 20 +2. 120. 20. 21 y + 120, 21. 21 9y
  7. + 101 d2o. 30 4 101. d+ 30y
  8. +101. d20. 31y + 101 d21. 319y
  9. = 101. 20. d30 -101. 20. d314
  10. E
  11. = 101. 21 d30y = 101. 21 d31 yy
  12. Hic patet non posse tolli terminum absolutum, ubi ab est y et du; nec terminum
  13. qui habet yy. quin incidatur in aequationem a similem datae,
  14. nam _ res reducitur ad 31E 30: 20 quantitatem quaerendam in termino absoluto
  15. et ad 31: 21 quaerendam in Termino qui habet yy. sed nec potestterminus dus
  16. tolli, fiere eni 31: 21 = 30: 20, quo facto co fieret quantitas constans.
  17. D
  18. Unus ergo qui tolli possit est terminus y. Et ad hoc sufficit esse 20 =0 =31
  19. seu esse co = 217: 30, et esse 3 constantem, fiet enim 110. 21. 30 + 101421. 30 =0 seu
  20. fiet d21: 21 = = 110: 101.
  21. Effingamus aequationem differentialem summabilem, et
  22. videamus an huic identificari possit. sit 9 + do = (4) =- et sit
  23. V (5L s dl + ydm + mdy H yydp + 2pyd ( log ((+ my + pry) Ergo
  24. L + my + pyu
  25. explicando aequ. 4 per 5. adifferentiaque aequ. 5, et explicatam 4 ordinando
  26. fiet 1), +gl = gmy +gpyy
  27. l
  28. (d
  29. by Mheyys Hedus +hfydy =0
  30. identificabimus ergo aequ. 7, summabilem, seu ex summabili factam cum aequ generali
  31. multiplicata per h,et
  32. pareseu articulum 9 _ identificationeque
  33. patet secundum du fieri
  34. instituamus. Identificando terminos dis utrobique, fiet m= e se m = (10) = he
  35. secundum ydy fieri p = hf p = (11) = hf: 2. secundum gy fit g = hc - Lhaf - L. fdh, :bs
  36. seu g = (12) = 2hc - hdf - fdk, : hf. Secundum y fit g = (13) = hb - hde- edh,:he
  37. quos duos ipsius g valores aequando, evanescet utrobique dh: h, dividique poterit utraque pars perhi
  38. nam fiet ihc - hdf,: hf (= ah: h) = hb -hde, ihe (-dh: h), adeoque tantepr
  39. prodibit 2cif - df. f = (14) b: e - de: e. t re t exeds atquod si abesset.
  40. b et c, uti sane semper abesse possunt, oporteret esse inf: C ration constan
  41. Ansic B = (5) = (_ + gamt mdy + plt pnyt gllus totmoes
  42. l+ my
  43. ds g + + gl + gmy
  44. set +armus
  45. alatus + matyus+ lfdue + Mtlus
  46. pl +omus
  47. + 9l dy +9m ydy
  48. +mdy
  49. r9 , et fint tritus
  50. ficrta etm g= ltf - ene +fm, :, m. l
  51. n h = tmm -Eml Altf-F me + fm, : (n - 1)f
  52. hat hby s hegy+ hedus +hf ydus
  53. fic a c. f = dt: t +9
  54. poragus
  55. Hic, p, g, h carent differentialibus, ergo ab is incipiatur gy est m = hc: dt = F+ 4 hf:, t 4)
  56. dl + dmys
  57. et fiet et + c9 = fdt, seu q = f dF - Ct; C, godus, firce lt + (fat tet + chI
  58. ob dy sit 1+ + 1f dt = lct + m H hE = dC hC = hC, seu ficet taB. + lfalat lc taC) tech = chedt
  59. habetur F
  60. ubi c ponatur abesse
  61. Exsolute, et m perh
  62. juperest y, et y. sane ar est superfluum, possent etiamq et de se destruere seu poni ar = -g imo et
  63. 9 + dr + p, possunt haberi pro una quantitate X et super sunt ob y, et y duae aequationes
  64. H = - dl: 1 + ha: l = lat: te = (Bde Be -Bdh: C) + hb. de ubi non licet ponere rationem inter
  65. et si constantem, evanesieret enim sit ergo _l = hst, fint dl = hdA +Adh, et aequatro talis prodibit
  66. -T.): 3 AAB. F (dh: H) + 4 :d = A dt: e - de: e (= dh: h) + b: e. sed ita incidimus, in aequationem
  67. datae non cedentem
  68. Ergo ponamus b adesse + abesse C et b, firc at = 0
  69. opeat nn im aleadta eo spreus a 3 btm. (i 1000 dor a an buer 3) d hiaet cas
  70. h = tm + am,: f
  71. + 101. 21.3
  72. -101. 21

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 97r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068196:0191?run=74