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Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 307v

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: 0.75.

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The machine reads it as

  1. 11 410
  2. 120.
  3. 20dl1)
  4. 21d20
  5. + 10 209e
  6. =100. 20. 20(+110. 10. 20) +1011 20d,0 20 = 002n + 101. 10. 11p, : 101. 1) p = 1( 120:100
  7. 10d2 100s. ApP + 12ON I = 0On, Sed ita sit 12OHH H
  8. 2. d120. 10. 11
  9. 120. 1010
  10. =120. 11.H- + 120. 1L. 4 = 00n, seu evastescit 11. Erg
  11. non licet tollere di0. in aeg. 3. si absit 110, et retineamus dio, nec tollams
  12. neque adeo explicemus. P, fint 11. = 00 s(00n:, 100 pe +126)
  13. proenietur secundum 10 ad aequationem non minus data difficilem
  14. sit s hZ X = G
  15. XY a dy: dx = x =F y: 4X = Z
  16. sit ddg: dx - adx dy dx = Xdxq X191
  17. Elo
  18. (ax + dy ( dx) + ydx.
  19. E
  20. et
  21. en ddya = ddX Z = 1 dp dy: x + ZdX. x dx
  22. s
  23. u
  24. ddu A - Y u tX =. dx dy +Zd- di
  25. Z= + + X dd
  26. et 7= de
  27. (2)
  28. XZ = y +X
  29. n
  30. und
  31. es F
  32. XdZe + Z dx = dytap
  33. Xdy + 7dx = dy+ du una differentralis
  34. essi
  35. L
  36. alia disperentia
  37. du dr tu dyXt Axx = ydx-xax x
  38. seu X de = dy X - y dx
  39. Ex 2 fit y = XZ- X ex 5 sit yx dy. dx
  40. ex.
  41. Xdz. dx excsibXZ X dz. dx
  42. quae dude6 et7 aequando fat
  43. = X = XZ- X az: dx
  44. ose
  45. seu
  46. du lx: X seu Z= BL = fax: X = ytX: p
  47. porla
  48. nam dx: X = dyX = ydX, : X
  49. seu dxX = dyx = ydx, seu dix Lydx = Xd
  50. via X 49d. Z-1
  51. eud:Z-
  52. sit AC o 5M gy: p- 1 = y dy. Z. - y dx
  53. seu y2 Z- 1 dy: dZ - Z. 2 dp: dZ
  54. rursi ob 3 fit ydZ. 2-1 + 2x dy + dx se
  55. 19
  56. seu X+G, : X = dy: dx ut desiderabatu
  57. ed sollendam literam X
  58. seu du alsa
  59. dy + dx = Z dx 21: dZ
  60. aequandto valores 18, 19. destinitur dy narus (22)
  61. aequadem
  62. iee adsedeattad utcus
  63. Hinc discimus Caronem generalem, si sit aequac
  64. quae cunguium literarum (ut Z q) ejusque quaeruntur
  65. duae differentiales 3 et 8 et har ope harum ac vg. 2. follantu
  66. mempe az et habotu n hec soctam ax. d
  67. X
  68. potanda in de varis modit nabus diffentat
  69. et difficentio disterentralis cn combinabiles. posum
  70. ersi opt mescheda m s 1 21 sept 1b90
  71. 4x dx 105 dy 4.7
  72. y ex
  73. a
  74. 1y dy 20
  75. hX + a dx + b ay + cxdy + e HaY = C
  76. addex + lddy X c X ady + sexd e_ ddx F e dx dy = c
  77. seu empendio +addx + +b ddy + e de dy = 0
  78. et sidmando teg.
  79. +Cx
  80. compandio u sit et E h. fiet dux + _ ddtus + haxdus =
  81. et b + cX = Y it a+ exL v
  82. et ex ag. 1. fiet a d 1 eg ex v. dx + ydy 20
  83. tolli pe v adeoque y, ope aeg. 7 et 4 et fiet
  84. 1)
  85. =Zay ddx + Zdx ddy +hax du =0, uti abest n vel y
  86. quaeratur ad huc, alia ubi similiter absit, ex nempe
  87. ex aeg. 7 fiat v = a dx. -Z dy. ax fiet
  88. edy ax + Yex y F dx ddy L Cd X dy 4 - Zdy ddx
  89. C0K
  90. sed coincidunt agg. 10 et 8. explicando hper c+ e. itaque
  91. non et tolli nisi uina, ut y, vel ex ex his qua aod
  92. y, X, dy de oordinetur aeg. 8. secuma y
  93. 52
  94. fiet +h dx dy + Z dxddque B seu
  95. a Z ddx
  96. tag: y = +dx: q dex xt. Unde ddx
  97. pro inbibrio explicundu per X et ax habetur
  98. to relato du t. ex, per quadraturas
  99. si tollatur ay ex aequatiae 2. dasitur acys dex
  100. per de fiet alx addus: dxe ta dx in R. y + Xda
  101. at
  102. addy = ex in X, 1 + ed addx in X, yarationem
  103. et quia hes lantor homogeneae, datur ddy: dax per
  104. ax dddx, interventa rationum duanum copo dat
  105. t inventam compotitam ex nga
  106. si y sit sublata restabunt q homogener nempe ax, du) anty ait
  107. et dabitur days: dixper dx: adex et du: adde, interventur
  108. rationum li
  109. a
  110. Cale
  111. no quislum s alu adusolis
  112. a ida
  113. s. manat dduo
  114. indeterminalae a. Ponatur
  115. recolreduti si ponatur dax= ep, habsetur aadginetus
  116. addus: et et d ber
  117. si faciamus days Z0 habetur di non sy per dx ada
  118. luiu lequentu x seu paret iltdum dX
  119. si faviaumm ddus= sponatus ddX ax prsiabit relasio para
  120. inter adx, du ildys et tiet e d
  121. aut - t
  122. xddy: ay per ardax. u interventa e sed nihil horum irem abso
  123. A
  124. lite
  125. Einptur
  126. seu aditus :dus re du: aD) et Ox: a seu t per + et X

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 307v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068196:0610?run=74