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Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 310v

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

The same scan as fol. 309r (00068196:0613), where its text is given.

The machine reads it as

  1. 2XXY = aaX
  2. videamus an licent toble
  3. a ponendo X = Y bZ + CY et y . WV+
  4. un
  5. 1Z+ mv
  6. 200 E bbZ2 F + 2bcZP + CCVY = aa 1677
  7. fiet 2bc2
  8. sed Jam video non posse tolli aax samm nisi
  9. su hoc explicaive, insi simul si al X
  10. 1
  11. quod te non debes
  12. C
  13. Et
  14. angisur
  15. qideo interdum erem ne po
  16. 3
  17. quidem ese idque cinterdr posse rraevideri
  18. ba ulcum sit vel non
  19. na
  20. erbi
  21. palia in ment aua quarcunque
  22. et suppositio delet sillilxyl.
  23. casus e 1X
  24. 2)
  25. 2XX y . aaX,; 3aay = 2Xyy = dy : dy).. 9. y
  26. ubi ad lolendam aa, debet ficiri 2x9- aa =0
  27. et 3aa 2Xy = 6. quae dummen tolli aa tam
  28. ex 2Xy -aa quiam ex B 2 Xy - aa
  29. quae duo simu feri non possunt. Si tuisset
  30. 2xx Quoni Auia via abhiceri et reductao
  31. aequationum inerementatium ascolatum in puras
  32. seu adquadraturat, si implicatarrum ad explicalas
  33. si efflei possit ut eeat. dux nuo ex hansforcmando
  34. ut cna exliteris novis ut habunt sit hogogenea cum a
  35. assera vliircum posito T. y dx; dy. sit
  36. Eugo ponamus in casin maesentia rushc ovo
  37. et rursus 2B, Hy aa 2 2abZ. 8. Et tabst scores
  38. sudstitamus in hobemus tires aequatio res fundamentales,
  39. i pervabuat, in ribus d
  40. et
  41. osvali
  42. fucel
  43. inibude
  44. quaelibet inter se seval legus homogeneolum jam si
  45. hinc tolli debent X et y. quod et succedit, sed cum toteo praeterea
  46. debene dx et dy. Hinc opus est ex aeq. 2 duci differentialem, ut
  47. quaeramus velem ipsius a, ex 5q. 3, qui sit 2XXy a axy =
  48. EXX 3aa
  49. X =
  50. Nihil ex hac scheta quod non cima
  51. e-
  52. posita ed consta
  53. C. X dx: sit dx = CX
  54. siet ce SXe=
  55. xb
  56. X
  57. y - q
  58. bdx + cdus
  59. Taxa mlus
  60. A2 1 +
  61. X = 8bZ+ cv +C y = 1Z+ mv + n B
  62. Ergo
  63. si sit 2xyy a a Xy: 34a Exg,:: dx: di
  64. Haec hypothesis si servit Tollendis constan
  65. tibus, solutm est problema, nam
  66. circa dx: dus nil mutatur in summa
  67. nam du dxe = ddZ + cd∞
  68. et dy = Cdz + mdv.
  69. ergo
  70. ex 50v = 1dg+ ndo dp.
  71. sit ab una parte
  72. eL
  73. bdy +CB dz
  74. jams. ldZ + m LD, : b dZ+ cdV = O (seu Z: D)
  75. fiet. laque amdo = bZ bOdZ+ cOdv. Ergo
  76. av = ( - b0. seu dv = = bg. v , ubi let,
  77. Z
  78. CO= M duz
  79. et z: V significat
  80. cy: M constante
  81. omnem terminim
  82. utcunque Cpinatum ex ratione Z: Y, quo casu
  83. ostendium rem semper reducta ad quadraturas
  84. c
  85. Imo res etiam reducitur ad quadraturos
  86. si cilli possint constantes ponendo ee
  87. X = Z+ b7Z+ CZV + eYV +f
  88. et y = 1Z2 m Zv +. n vv + p. se
  89. sed video nihil gos has Et ita porro modo
  90. scicet _ Z et V servent inter sa homogercitatem
  91. ex cepta litera F et P, quae in axidus evanescunt
  92. idem est in alturibu.
  93. verte

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 310v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068196:0616?run=74