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Leibniz-Handschriften zur Mathematik LH 35, 13, 3, fol. 114v

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: 0.83.

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. 115r); this page is its left half.

The machine reads it as

  1. Z aeqpu. X
  2. dZ aequ 1 V d.
  3. Q aequ y.
  4. Raegu.
  5. dx ae qu 1 Z dy + 2y AZ per aequ. 3.
  6. de agt
  7. Zaequ vx. vaequ. yZ. per oqu.
  8. vaequ. 7
  9. Xaqu. Zy
  10. per aaequ. 1.
  11. y aego vr
  12. per aequ. 2
  13. dy aequ. 2 vdx + 4X do per aequ. 4
  14. + Jay
  15. aip. = FXdy
  16. =4) y
  17. ubi notandum numeros 1.2. 3. 4. in aequationibus differentialibus 5 et 6 significare nn numeros, sed signa
  18. variantia, seu unitatem signo affectam.
  19. Ex aequ. 4 et 5 erit: dx aequ. 1Z dy + 1 2V X dZ
  20. Ergo X aequ. dX - 1Z d7 per aequ. 7.
  21. DX aequ. dy - 30dx per aequ. 6
  22. Aequando valores 8 et g. fiet: 4 dx dv + 2. 3. V dxdZ
  23. 20 dZ + 1. 4Zd
  24. aequi dy.
  25. Hunc valorem ipsius dus substituendo in aequ. 9. fiet: X aequ. 4 dxt 2. 3. V pA q- 2. 3 vdpar 34BE
  26. 2. 4v +odZ + 1. +4 Z dudo
  27. seu sublatis tollendis. XC et quia vZ aqu. 1. fiet X aequ. dx - 1. 3. de
  28. am v pequ. . et se
  29. quicquam. E Dubito
  30. 2V 1Z + 1. 4Z d0
  31. vZ aqu. 1. et Zd0 + Ddque aequ.o EEgo tolluntur omnia, nec proinde habetur
  32. uit
  33. Nac lirefsetiam sic procedere: dZ dx. + dZ 48) aequ dy 1
  34. ut inde fiat datum
  35. du aegr. a +bx + cyelry e
  36. 5+grahyt kxus erc Namoypun t dx _ii d7
  37. Nam ge aequ. X et 96
  38. aequ. X
  39. . Ergo Z aequ. X (6) X
  40. 61
  41. et fiet: Ax L + X dy -ydx ) yes
  42. V6)
  43. +(5)(3)
  44. et de aequ Xdy -ydx
  45. 216+ B) aequ dus y. et reducendo fier:
  46. rgy X () (10)
  47. y (4) 10) 6) (6)
  48. Hac methods ob multitudi nem arbitrariarum putem prottema
  49. quo explicata quantitas
  50. pro arbitrio conferenda
  51. esset cum data. Sed hon minuis
  52. (2)
  53. semper rebuai posse adi quadratures dx at dX N + dy Y + dx L.
  54. a dxax
  55. Ax X + dy y + dr Y + dy X , dxX
  56. soelsus)
  57. et du aequ X dy + y dx sit jam formau : X
  58. degu X 7
  59. 20417
  60. cujus differentialis gentratus
  61. d24. 25
  62. ey + X
  63. dx + y dy fula
  64. + y34 935 qu0
  65. 24 25
  66. 136537
  67. xle q
  68. C (eot () + ad
  69. ponendo Zaego XY. hoc formula generatis supra (t e 2.H
  70. X + y
  71. Xau ax
  72. du ()
  73. + d ib - 17 dx + ∞ 269 du7qu 4 y 36t 217 49 16 dt cqu0
  74. videndum, an tali formula ad date adbita vel et tas
  75. Is posse fieri, niti jamtum
  76. u
  77. (14) 9 (5) 4 dy X
  78. (613 (17)
  79. aqu. cujus differentialis generalis
  80. ius.
  81. ∞diz
  82. 10t (1)
  83. X significat
  84. X aliquam
  85. seu utcunque quo
  86. sitam ex
  87. abfracta vriatur semilis ipsi 4. sed hoc video non
  88. merrimu et plan admirabilis compendium aequa–
  89. tiones aequationibus conferendi, si quia hoc modo etiam maxima for–
  90. mala ad paucissimos terminos reducitur; et si aequatio aequationi et
  91. comparabilis, etiam in hujus modi terminis sibi comparabiles erurit. Ita
  92. in aqu. 4. explicetur dz. per aequo 2. quod gueniet comparetur cum au
  93. fiat. X
  94. iqtqsx + Sed hoc ut fieri possit reti video omnia sic
  95. x instituenda ut formulae generalis ex X com-
  96. posita non scribatur hoc modo X, sed +X X ubi notandum X22
  97. esse formulam aliquam generalem ex X compositum et per X divisibilem.
  98. vel etiam scribendo
  99. X. intelligatu dX Z aequ. X
  100. 22 verum in calculo differentiati pluliaris oritur difficultas
  101. Nam da5
  102. E explicando dque per aequ. 2. in et comparar possint qu.
  103. X du + 5ydx. ubi posito x esse multiplicatilem
  104. per X divisibilem idem crit Xq det y dx quod X dus xyex seu qarique dx nam si x
  105. non est divisibilis per X tunc Xay E5 habet partem referendam ad .
  106. a + 2 + 3 + 4 + 24. 42 + 34. 34 aequ.o. he diffentialis de ax + de du + 42 dra de, + 24 d a2 ady + 43d 34 ly 1 frgo in aequ. 5. explicando differentias et subintelligendo eos quibus exc ascriptm est sub eorum primo fiet
  107. L13d34. +34d43XC d. +22d42y + 42d24 634d43y
  108. no- drodu vy 6+67.76458.85 5+57.75468. 86. fet
  109. 1ago 0+

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 3, fol. 114v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068200:0230?run=74