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Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 309r

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 is also registered as fol. 310v; its text is given once, here.

The machine reads it as

  1. 2XXy = aaX
  2. videamus an licent loble
  3. a ponendo X = Y bZ + CY et y . WV+
  4. un
  5. 2.
  6. fiet 2bc2
  7. 1Z+ mv
  8. sed Jam video non posse tolli aax samm nisi
  9. sm hac expliceve, insi simul si al X _C
  10. 1
  11. quod te non debes
  12. C
  13. uryde adg
  14. Et
  15. anisur
  16. video interdum, etem ne pos
  17. 3
  18. quidem ese idque cinterdr posse rraevideri
  19. ba ulcum sit vel non
  20. na
  21. berbi
  22. palia in ee ausa qacunus
  23. re suppositio detet sillilxyl.
  24. casus e 1X
  25. 2)
  26. 2XX y . aaX,; 3aay = 2Xyy = dy : dy).. 9. y
  27. ubi ad lolendam aa, debet ficiri 2x9- aa =0
  28. et 3aa 2Xy = 6. quae dummen tolli aa tam
  29. ex 2Xy -aa quiam ex B 2 Xy - aa
  30. quae duo simul feri non possunt. Si tuisset
  31. 2xx Quoni Auia via abhiceri et reductao
  32. aequationum inerementatium ascolatum in puras
  33. seu adquadraturat, si implicatarrum ad explicalas
  34. si efflei possit ut eeat dux nuo ex hans forcmando
  35. ut cna exliteris novis ut habunt sit hogogenea cum a
  36. assera vliircum posito T. y dx; dy. sit
  37. e ove
  38. Eugo ponamus in easin mesenti nha
  39. et rursus 283 ry aa n 2abZ. 8. Et tabores
  40. sudstitamus in habemus fires aequatio rec fundamenta les
  41. uhit pervabuet, in cibus d
  42. et
  43. osvalo
  44. que
  45. d
  46. quaelibet inter se seval legus homogeneolum jam si
  47. hinc tolli debent X et y. quod et succedit, sed cum toteo praeterea
  48. debene dx et dy. Hinc opus est ex aeq. 2 duci differentialem, ut
  49. quaeramus velem ipsius a, ex 5q. 3, qui sit 2XXy a axy =
  50. EXX 3aa
  51. X =
  52. Nihil ex hac scheta quod non cimn
  53. e-
  54. posita ed consta
  55. C. X dx: sit dx = CX
  56. siet ce SXe=
  57. b
  58. X
  59. y q.
  60. bdx + cdus
  61. Taxa mlus
  62. A2 1 +
  63. X = 8bZ+ cv +C y = 1Z+ mv + n B
  64. Ergo
  65. si sit 2xyy a a Xy: 34a Exg,:: dx: di
  66. Haec hypothesis si servit Tollendis constan
  67. tibus, solutm est problema, nam
  68. circa dx: dus nil mutatur in summa
  69. nam
  70. dx bdZ + cd D
  71. et dy = ld7 + mdv.
  72. ergo
  73. x yix = 1dget ndo dp.
  74. sit ab una prorte
  75. eL
  76. bdy +CB dz
  77. jam s ldZ + m dD, : bdZ+ cdY = O (seu Z. D
  78. fiet. laque amdo = bZ bOdZ+ cOdv. Ergo
  79. av = ( - b0. seu dv = = bg. v , ubi let,
  80. Z
  81. CO= M duz
  82. et z: V significat
  83. cy: M constante
  84. omnem terminim
  85. utcunque Cpinatum ex ratione Z: Y, quo casu
  86. ostendium rem semper reducta ad quadraturas
  87. c
  88. Imo res etiam reducitur ad quadraturvis
  89. si cilli possint constantes ponendo ee
  90. X = 2+ b7Z+ CZV + eVV +f
  91. et y = 1ZZ+ mzr + n vv + p. se
  92. sed video nihil gos has Et ita porro modo
  93. scicet _ Z et V servent inter sa homogercitatem
  94. ex cepta litera + et P, quae in axidu evanescunt
  95. idem est in alturiau.
  96. verte

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 309r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068196:0613?run=74