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Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 314r

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: 0.78.

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

The same scan as fol. 313v (00068196:0622), where its text is given.

The machine reads it as

  1. HHic vera
  2. Z tt G ber X, a y in differentioli non post
  3. potest simul tolli X, et a, nilis sit Z= mX + na + 51Z squi
  4. Mxa na = valori per B 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 X: a = y: Q ita erom ex = a
  10. ex idque dxia = d ytque
  11. aaaxxtyy- dy
  12. X7 Ydx
  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. aa Fy A ay
  19. ayloy
  20. ae qupropo ita
  21. y si ergo sat gaxedys=
  22. i G X: sutatur ydx: dis = 9
  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 seu yx +Pa = ax seu jamas- A 45
  44. a jam 1y9 =LXy seu a y: dy Ergues 2 13 fit yxty + adxY extus
  45. seumus seu dy: ex Fya: aX Xy, quae aequalo reduretur 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. veraliibus
  51. ae quationibuad Mechobum ianque
  52. tium javerscem Mhullucianum
  53. sit dy: ex = v sit jam aalat o
  54. aequatul) inter v. y. X
  55. Moto hacter
  56. me excogitato sumitur aequatio generalis inter X et y
  57. Et hujus differentialis dat X X. V: X. 4 quum substitua
  58. . ita habetur v ratreabiter qui vul cujus valor
  59. substitutus in aeq. 2. reddere debet aeque, 3
  60. quid si sic Aequationis rpperatu
  61. 5 reb dationis sao simplica
  62. differentialis erit eg. (4). Sumatur alia
  63. differentialis AB
  64. D = X. .y: X.. y arbitaria; ujus ope dab
  65. B) ~ 1
  66. e
  67. iterum do purcimplinter, duas do aequando
  68. similles
  69. nos valores do aequando et dabitur aeg. 19
  70. ea
  71. X y. V dy: ee ubi pollendo ly. Ex
  72. per V hil eq. (10tm qua solum p y. v. quae
  73. et ita es illud
  74. dbet coincidere cum eg. 5.
  75. est egnerium quod arbitariae assumta
  76. ad oullas polentias littollunta
  77. _ V = G a +by+ Cy etc. posito a ex b, c, daneo
  78. fit dv= ada + b ly + y db + 2c y ly+ y de erc seu
  79. do= da + ydb Ly Ac + eu G 1 1bv + 2C70+ 3Cy v
  80. essumatur v l+ mu +n s etc py eu fiet
  81. v2 1l= yamy du et alvtmBL cu Et
  82. equando aos oatore do ex eg. 2et 5 fiet
  83. e
  84. tua
  85. a + db + 5dc etc. c it a 24) e + 3y p C_ V abus quam
  86. e
  87. a 05 a4y eu
  88. ibet
  89. at ab de 1 2
  90. n
  91. a
  92. ul oer

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 314r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068196:0623?run=74