Leibniz Legible

Machine transcription of the Leibniz Nachlass

Search the Nachlass

Leibniz-Handschriften zur Mathematik LH 35, 13, 2c, fol. 193r

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: 0.89.

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. 194v); this page is its right half.

The machine reads it as

  1. dy: dx = xx + gy,: aa Assumatur g 34y + 33y3 + 32yy + 31y + 30 =0
  2. fiet -dy = d30 + d3iyt d3ryy + d33y + d34y: 317 2. 31943. 339y + 4. 34y = Xx + gy,: aa
  3. 1.31 XX + 2.3F pyy + 3. 33 Xx yy + 4. 34 Xx y3
  4. + 1. 31 yy +2. 32 y + 3. 33y + 4. 34y = 0 ~ 30 m + 31 my + 32 myy + 34 + 34 mys
  5. 3ony + 31 nyy1 317 131 1y t 31 py
  6. = d30 - d31y - d32 yy - d33 y = d34y e Fiet n = 4. ex summo
  7. 2 sit m supersunt aequationes 5, et incognitae 5, nempe 34, 33, 32, 31,30, cum constrnte
  8. arbitiaria (3= hom + d30 fit 3. 33 +30m + 1g0 d31= 32m t 3. 30m + 9d30
  9. 3(33 = = 434 - 3 34m. Hinc 31 et 33 tollendo in y7, fiet
  10. -3de rx 1 3. 3+M X + 30m + d30 - d32 = 32m H X = a35 1 4 L.5C
  11. - 3 d34 pp - 3. 34mXX - d32 = 32m + 30m + d30
  12. supersunt y et y
  13. in y fit 2. 32 = d31 + 31m + 4. 30
  14. it 4. (34 - 30) = a (31 + 33) m + d (31 +33)
  15. Er
  16. Ey y fit 4. 34 = d33+ 33m
  17. + d31 + 31m + 4. 30
  18. sed nihil ex his, nisi prius investigemus modum ex divensis literis simpli aequationibus
  19. differentialibus simplicitus inve compositis investigandi pluriliteris, in vestigandi uniliter
  20. sit aequatu sint binae aequationes dta differentiales simplices biliterae
  21. datae, iIt y + 112dy + 121Z + 122d7 + 100 = 0 et 211y +212dy + 2218 + 222d7 + 200
  22. c(
  23. Ossumantur binae tale, 32Z + 322 dZ + 300 =0 et 4uy+ 412 dy + 421Z+ 422 dz +400 =0
  24. quaesitae.
  25. videatur an ex his duabus componi possint priores duae. Ope a44. daturum
  26. Follatur dzue siet + 111. 2229+ 1h2. 222 dy + 121. 222 Z (t 122 222 d7) + 100. 222-8 = 0
  27. = 172. 211 y - 122. 212 dy - 122. 2417( Frr. 222 d,3 - 122. 200)
  28. Espari modo ex duabus posterioribus tollatur aZ, fiet t
  29. + 321, 472Z + 392. 422 dy + 300. 4227
  30. - 922. 411y - 312. 412dy 322. 42178322. 422 d3 - 322.400)
  31. 6 = 0
  32. Et aequationes 5 et b coincidentiandofiet 4+= 1m 222+ 122. 2H: 32.
  33. 400 = - 100. 222 F122. 200 4 300. 422,
  34. et 411 = - 118. 222 + 122. 214,: 322
  35. 41Z = - 112. 222 + 122. 211,: 322
  36. 421 = - 121. 222 + 122. 221 4 321, 4227: 322
  37. dollatur jam q iterum bis, et fiet:
  38. et ex cognitis fet + 11. 22y f 12. 22) d9s 121. 221Z) + 122. 211 dZ + 100. 2217
  39. quaesitis seu
  40. ilemque ex incognitis
  41. = 141. 2ug - 121. 212 dy R. 121. 2417- 121. 222 clZ - 121. 200)
  42. (+ 321. 421 3(+ 322. 421 dz +300. 121 2 - 9-0
  43. 32. 411Y - 321.912 dy = 311. 421 7-321. 422 dz - 321. 400)
  44. Et aequationes _7 et 8 coincidentiando fiet
  45. 400 = = 100. 221 + 141. 200 7 300. 421, : 321
  46. 41 = - 111. 2217 121. 211, : 321
  47. 412 = - 112. 2U F 121. 212, : 321
  48. 421 = + 122. 221 - 121. 222 4 321. 4227: 322
  49. ope quatuor aequationum, 1, 2, 3, + pestunt bis haberi aequatio, in qua absit Z et d3
  50. adsuntque y, dy et y, quae reddentur, identicae, faciendo ut y, du, et y evanescant, quod siet
  51. ope aaquationum sex, cum tamen habeamus arbitrarias 8
  52. per aeq. 3 tollatur dZ ex aeq. 1.
  53. et et ex orq. 2, habebuntur binae aeo binae aequationes se in quibus supererit Z, quarum
  54. ope tollendo Z, fiet aequatio in qua extant y, dy, et y
  55. Eodem modo per aequ. 1,2,4
  56. habebitur talis aequatio, harum aequationum quaevis tollatur reddatur identica, et habebitur
  57. si tres dentur aequationes assumentur aliae tres, literarum arbitrarium
  58. tilitorae
  59. una quaevis 7 sunt literae 21; et brua literurum arbitrnriarum septem poterunt reduci
  60. videndum annoue earum unius gliterae affectione, ita res ilut redacta ad casum priorem
  61. desideratum.
  62. in nostro casu 131-d30= 3om 2. 32 - d31 = 31m tn 4. 30 et 3. 33 +1. 31 - d32 = 32m + 4. 31 ubi patat
  63. Et non posse omnino tolli d31, quia occunit semel tantum sed solamus 31, fit 31 = jom + dec = 4 92 - = a32 = = 32M
  64. sed Assumantur binae biliterae, (quippe jam solute), et una tulitera, habemus arbitr literas 10+12 = 22
  65. um meritum eo aem quca ateru sett pu pert eisur ite

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 2c, fol. 193r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068199:0385?run=74