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Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 48v

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: 0.79.

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. 43r); this page is its left half.

The machine reads it as

  1. Hinc
  2. intendum posset fortisse inveniti solvi problema; differentiale si series
  3. differentiarum primarum secundarum tertiarum et. esset exponentialis
  4. vel alia tractabilis
  5. sit dy = dx N(a + b X 4). 4a seu dydy = a + b: a) X, det
  6. fic 2 dus Rds sit dx constans, fiet 2dy ddy = 4b: a) X dx 2 aa seu ddy = (4: 2) b: a) x du .
  7. rursus dydhy + ddy ddy = 2b: 2. 3. (6: a) X dxt: na sed ddy = a )bb. aa) X dx:
  8. et fiet du d’y + 2bb: aa) X dx = 2. 3. (b: a) xx dx dydy
  9. seu eret:
  10. By = 2. 3. (b: a) x (a + b: 4) X2) - 2 1bb: aa) X, dx:, a 1b. a) , atb X
  11. seu d’y - 2.3 (b: a) a . + (2. 3 - 2) bb: aa) X, dx; a + (b: a) X, 1(a + b: a) X2)
  12. in dy dhy = 2. 3 b: a) a Xx + (2. 3 - 2) (bb: 4a) X, dx
  13. 3d ydy ady) + dy) dy = 2.3 (b: a) a X + (2. 3 - 2. 3) (bb: aa) X dx
  14. et fiel
  15. A. a)X (a abia X) du et fiet
  16. (2y = 2. 3sb. a) a N+ (2. 3 = 2. 3) bb aa) X - 2. 3 (b: a) da X i a - 1b. a X)
  17. (a + (b: a) X3) (Y (a +b: 4) p)
  18. ax
  19. Et ita pergendo, uidendum an haberi posset lex. quae si esset retro
  20. continuabiis, posset haberi, y. Et si autem hoc in casu nonsit talis, posset ex cogi–
  21. Et quia in potestate est assumere
  22. relationem inter, X, dx, et dax proarbituo, hinc fortasse faciluis tates leges
  23. tari casos, in quo continuabilis esset
  24. ex cogitari possent.
  25. sit aliqua langentiam inversa, seu differentialis primi gradis aequatio
  26. veluli adue= axs X=+ eax. sumanus X et y ut constantes d et Z, nenoe primas
  27. jam proxima. Erquacdys) = (X + dx + y+ du) (dx) et pro du ponendo valorem, fiet
  28. aldys) = x(dx) + qd Xax) + y A X) + X dx (d X) + y dx (dx)
  29. X+ c
  30. L(dx) +
  31. seu a(dy) = (X + y) (dx) + a + x + Z dx AX) seu (dy) =
  32. a (dy)) = (X + dx + (dy) + y + dy +(dy)) dx (dxD
  33. a+xts
  34. aa
  35. y) = X (dX)) + d x pd X D) + (dX) pdX) + y fdx) + dy (dx) + fau (dy) dX)
  36. illeq
  37. ppste
  38. ) roZ dx (dxI
  39. Xa Z(dx) l + d Ax r X)
  40. dy) = ( p.. X+ 7 puX) = a + X +y (dx (dXD + (d X) (d X) + a + x 19 dx(.tX fl 7
  41. dx = (1X) = (dx ) fint dy=
  42. = (X + Axaclx) tXD Fyrdus adus y) dx) (dy)-
  43. ax ydC +XHLy 1a d, p (d y) =
  44. L. X Y andx + atxFZ dx + xty apdx
  45. 2 a Z dx + ara y
  46. + dx, a
  47. dyIX, a =
  48. +dx, a =
  49. atpay
  50. Unde tundem
  51. dx
  52. dx +
  53. (dy 1
  54. 1 d X dx
  55. dx + 2 dxdx +
  56. a
  57. aa
  58. XLy
  59. X + y ex (d- ( 6B
  60. esc
  61. X + 7 dx +
  62. atx tZ dedx
  63. x +y dx + a+ x+7 dxdx +
  64. aa
  65. at 2 ax
  66. axty
  67. a
  68. (y).y
  69. Sed summa omnium d.y+ dx, a est
  70. a+ x +y
  71. etsumma valorum est
  72. Potuissemus et summare
  73. aa
  74. dx. _ 1+
  75. atxty
  76. 1
  77. a + x+y
  78. 2
  79. dy
  80. as ++
  81. a
  82. x) a (YL fxea
  83. iaest autam numnus 14 dx X: a a + X +
  84. eaaratim cdx. + idyct
  85. et idede rant
  86. 1. dx) in
  87. aal
  88. 1 dx + 3dx dx + 3 dx
  89. vi tatio e)
  90. sihed
  91. in finitus qui
  92. stuctus in infinite parvum, facit constantem
  93. 1 dx + a dxdx + 6. dx + 4 dx F 1d7
  94. Hinc
  95. ac
  96. a +X + Z dxdx
  97. aa
  98. aa
  99. XtZ dx + 3 a +XFy Axdx +
  100. 3
  101. e
  102. cujus valor aliunde haberi potest
  103. Ubi notandum si aliter valorem iave
  104. niremus pure seu sine (Y) ita ut ipsa
  105. (y) haberetur, et poncietur esse
  106. (d = (1H dx: a) a fore
  107. Si adus . +ysr. idcoquia dato sus = pA ryB ) dx: C = (1 + (dX: a)). X. a seu fore
  108. aa
  109. 1= a log. a videtur negligi posse dx: a et fieri = 1. sed
  110. y ∞W s dx 2. 10 potio B= Sod
  111. ax lt hoc nonlicet, tam inde videretur absurdum nam toret
  112. + a) (AXX: a): pax) atia
  113. C
  114. x me
  115. u intialte pavantordinn aditamm
  116. xligaetat ast etata , a. at prt ex sud
  117. um. Uinc st pncii infinite parvam ordinan additam
  118. dy)
  119. itE
  120. +y
  121. +ax, a -
  122. +x+y
  123. = ((d y)) + dx, a
  124. A + X+ y
  125. 1xx +y
  126. ait quim dx, 1r X.: a

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 48v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068196:0096?run=74