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Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 313v

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: 0.77.

Original at the GWLB · Page image · Annotations (IIIF) · Download text

The same scan is also registered as fol. 311r, fol. 314r; its text is given once, here.

The machine reads it as

  1. Hic ir
  2. Q toriG per X; a y in diffecentioli non post
  3. potest simul tolli X, et a, nilis sit Z= mX + na + 51Z squi
  4. mxa na = valori per Y, Z
  5. videamus an possit inveniri slere er Exemplum, ubi Z- valori
  6. ubi Z= vatori per H, X, a et quaerendo differentialem, ac
  7. Ope ejus tollendo X simul connescat a. Nempe
  8. Z= valori per y14 a Ergo X: a = valori per Hoc rgitur
  9. fieri potest, si ponatur cX: a = y: Z ita erom ex = a
  10. ex idque dxia = d ytque
  11. aaaxxtyy- dy
  12. A yax
  13. sit a G dgrus x dy: yax = _ valori per y, X, a
  14. Sumatur GB om aequatio inter X, B, y, X, a, Z, tatis
  15. ut tram x et a servans leges homogeneorum, in qua etiam y et a
  16. solae inter se servent legem homogeneorum. Siet y: a= valori per z: X
  17. ergo dy: a = valori per de: dx , Z. X. Ergo dy: y = valori p 1 x es Z.
  18. sit aqu. apty A y
  19. ayloy
  20. ae qupropo ita
  21. y si ergo sat gaxedys=
  22. i Gxa X: 4 sutatur ydx: dis = 8
  23. Et absit 8 y: a=
  24. le
  25. A
  26. K
  27. ex simsre tivn via d vatrip ee L.
  28. dlela
  29. pinprementalem
  30. val. per P. X = valori per v: X jam per differentialem
  31. aquationis 3, fit dy: a = valori per dv: dx, v: x Ergo
  32. (5) alter
  33. er ae 1. 3 et 5 sit dy: y = valori per dx: dx, v: X
  34. per
  35. 6 et
  36. jam per 4q.1. et C dy. y = dx: P ergo fil x div. fper vab, e do: C
  37. Aor (St
  38. fit = dx divis per alteram valorem ex de, dv: dx, 8: X; jam ope
  39. 0g. 4 et 8 collatur , et fiter valor et fiet scu ho- AX. 2
  40. valorper v: X ((g. 3) nl pl. in X = dx diuis. per alterum val. ex d v: dx, v: X
  41. id est fit ex du: _X = val. per vex sine interventu ipsius a, seu constantis
  42. ergo solubilis aequatio per quadraturis. Gentemus in exempeo, sit
  43. 3:a + d. x=1 seu yx +Pa = ax seu jamas au A
  44. jam sy =EIxy seu c ay: dys. Erguer 213 fit yxty ) adxi exdu
  45. seundaus seu dy: 2x ya: aX Xy, quae aequalo redmetur ad quodraturas
  46. essuratur a B:x siet v: X1- D. jam perdif. 44. 6. fit dy: a= vdX XB, ZX
  47. rio ayin ieu uX dx: . Ger aq. Eseu _ Rs: p.X) - v xin XX, sebit
  48. a0 qu vex aercndiatis e
  49. ingens compendium pro
  50. neraliibus
  51. ae quationibuad Mechobum ianque
  52. tiam javerscem. Mhullucianu
  53. sit dy: ex = v ( sit jam aolat no
  54. aequatul) inter v. y. X
  55. Moto hacter
  56. me excogitato sumitur aequatio generalis inter X et y
  57. et hujus differentialis dat Y X. Y: X. y avum sabstatua
  58. G
  59. . ita habetur v ratreabiter qui vul cujus valor
  60. substitutus in aeq. 2. reddere debet aeque, 3
  61. quid si sic Aequationis rpperatu
  62. 16 rebi dationisd smplicum
  63. differentialis erit ey (4). Sumatur alia
  64. differentialis AB
  65. D = X. y: X.. y arbitaria; cujus ope dabur
  66. 8) ~
  67. e
  68. iteram de purempliter, duas to aequando
  69. similles
  70. nos valores do aequando et dabitur aeg. 19
  71. ia
  72. X Y. V dy: ex ubi follendo ly. Ex
  73. per 1 sit eq. (10 dm qua solum p y. v. quae
  74. et ita es llud
  75. dbet coincidere cum eg. 5.
  76. est egnerium quod arbitariae assumta
  77. ad oullas polentias littollunta
  78. V = G a + by+ cy erc. posito a ex b, c, danco
  79. fit dv= ada + b ly + y db + 2c y ly+ y de erc seu
  80. do= da + ydb Ly Ac + eu G 1 1bv + 2C70+ 3Cy v
  81. essumatur v l+ mu +n s etc py eu fiet
  82. v2 1l= yamy du et alvtmBL cu Et
  83. equando aos oatore do ex eg. 2et 5 fiet
  84. e
  85. tua
  86. a + db + 5dc etc. ch it a 24) e + 3y p C_ V abus quam
  87. e
  88. e 08 aqy eu
  89. ab ab de
  90. ibetq
  91. a
  92. n
  93. a
  94. ul oer

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 313v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068196:0622?run=74