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Leibniz-Handschriften zur Mathematik LH 35, 13, 3, fol. 61v

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: 0.89.

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. 60r); this page is its left half.

The machine reads it as

  1. (2)
  2. nempe M + bZ + PP+ 43 +Y yX 55 etc aequ X
  3. +vy + wyy tey n
  4. quem valorem ipsius X substituendo in aequ. 1. habebitur
  5. aequ. 3. in qua solum supererunt literae y et Z. quae
  6. aequatio 3 comparari potentcum data, aliqua 4. ubi
  7. in aquoue necessario7 ad eosdem Tradus assurgit, ad quos X in
  8. aequ. 1. assurgit, sed y admalto plures, sciliet ad
  9. tot dimensiones quot fiunt ex ductu summae dimensionis
  10. ipsius X in aequ. 1, in summam dimensionem ipsius y in
  11. aequ. 2.
  12. quodsi comparatio nondum procedat, prius
  13. equationem datam 4 transformabimus in aliam
  14. aequ. 5 per mechodum differentialium. Posset etiam
  15. praeter aqu. 1. alia assumi ab mitio, eisimilis, ins
  16. quod ponatur co pro X. et in aequ. 2. loco X ponetur
  17. X + d co sed sed tunc alte nimis assurgetur
  18. Videndum aq liceat aequationemdatam 4 attollere multipli
  19. caudo ut ipsi 3 fiat comparabilis
  20. Est et alia methodus conjungendo curvam cum rationali et alia
  21. C1)
  22. incidit et haec: sit axx + bx aequ c + dy + egys +fy erc.
  23. quadus inferioris.
  24. quaeritur X dus per solas X ax et dy. Est autem aliunde:
  25. 2axax + b dx aequ d dus + hey dus +3f yy dy et.
  26. + bXdus cay +ay sus reyyly er
  27. aequationis2
  28. ex XX dus subsituatur ipsius dus valor per aequ. 2
  29. plures alias hujus modi aequationes quaeram
  30. in
  31. ut
  32. a XX y + bx y aequ 9+ dyy + cy t et unde fiet:
  33. 15)
  34. fiet aequ. 4.
  35. a xxdy +2 axy x +b xay + b ydx aequ Cdys + 2dydy t3ey tye
  36. et ax + bxX aequ Cx + dyx + Cyyx+ erc.
  37. unde fiet: 3aX dx + 2bxdx aequ c dx + dy ax + dxdus teyyax
  38. fe x y dy erc.
  39. Datur a)fxxdy + bsxdus per aequ 1 vel 3.)
  40. sednihil
  41. datur et 2 afXy x + b Fydx per aequ. 2.
  42. axx + bx aequ Z.
  43. X equlZ+ mv. XX + bx aequ C
  44. seu X, A X+b aequ y. y+c seu Xaqu
  45. sed nihul hinc. satique hoc modo.
  46. hin.
  47. V. VtC
  48. X + b
  49. Quantilas dey + fecyy + ge + hh et y quanda
  50. quadato, ab ly theeyus c quod est: llyu +
  51. 2l hec y3+ (Chh c2 y), aequ dey +feeyytCy hhc
  52. sublatis tollendis et divisis omnibus per y. fit: a
  53. +9 e3 yy + fee y + de aequ. 0: et fiat ge- 2lhec aequ. 0.
  54. 2thec... . 11
  55. seu fiat: e aequ 21h
  56. Ergo y aequ. de. Et x seu yaequ
  57. 1- fee
  58. sei ita ye erit 2dtih, aequ X ac proinde X fit
  59. gg-4fhh
  60. quantitas determinata contra scopum
  61. idlh d 2dingus
  62. U fauhhus
  63. qu
  64. per dicta ad
  65. paginae 2 sub
  66. ine

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 3, fol. 61v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068200:0124?run=74