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Leibniz-Handschriften zur Mathematik LH 35, 3 A 22, fol. 15v

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: 0.86.

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. 16r); this page is its left half.

The machine reads it as

  1. Hinc jam habeatur appropiaquatio. Numalibi ostendi residua
  2. valde remota omitti posse, et haberi alternis appropinquationem nunc
  3. justo majorem, nunc justo minorem. in infinitum vero erit: Et ponendo
  4. residuos utcunque remotos fiet:
  5. aequ ab
  6. 18
  7. abcd:
  8. af.
  9. abc5.
  10. abeF.
  11. adef.
  12. Cdef
  13. abcdet.
  14. a
  15. abEd
  16. abe.
  17. ade.
  18. abcde:
  19. div, per
  20. 1.85
  21. 53
  22. bc d
  23. bc fa
  24. De fg
  25. des
  26. bc def g
  27. et ponendo E. 9. 8. 3 aequales nnhilo atque inter se, utique omitti
  28. poterunt. Volandum tamen residno quo libet omisso ut
  29. etam sequentes quoticites esse omittendos udt f. g. in infinitum
  30. eundo nulli omitti debent
  31. ponendos qu.0.
  32. Puto hac ratione etiam an finitis
  33. posse componi quotientam rationem ex solis quotientibus neglectis residuis
  34. si fumantur residuia
  35. qua sunt o. Eodem modo et potierit quantitas componi exsolis residuis,
  36. sit jam investigandus modus red ucendi rationem compositam ad simplicem
  37. atib
  38. actis qui
  39. ut si X equ. in ponendo aequ 1 + = et B aequ. s+ =
  40. V
  41. m +1
  42. n +
  43. ++L
  44. n+1
  45. veu
  46. qua e 5 aequ a + quaeritur a. b. c. d. Verror ut res sncredat, generaliter
  47. b+
  48. c+-
  49. et
  50. quia etsi constat
  51. nisi multa meditatione. Est tamen determi
  52. nata
  53. His habitis haberemus facile potentiae fractionem replicatam. Similiter investigaas
  54. asset modus addendi plures fractione replicatas in unam: his habitis possemus
  55. data quavis quantitate per fractionem replicatam expressa invenore ancipisa
  56. sit radio alicujus aequationis, et cujusnam. Quod si est transcendens forte
  57. inveniri Tausitus poterit
  58. si mulliplicebur in
  59. m + 7
  60. 1 sine reductione fractionis fiet: l5 + L
  61. m 11
  62. ne
  63. 15
  64. +s
  65. sit 1
  66. + 1∞
  67. L+ etC mt ere mere terc
  68. m+ + Ha) quaeritur summa n, v
  69. +
  70. mn +() tv. (a)
  71. fiet n +v + n(a))+ no vmn +. v (∞)
  72. mn +V + mnssa 4 +B (a () ( y
  73. Ad ista problema solvenda opus solummodo perfici artem calculandi analysice
  74. in integrist.
  75. forte suffecerit, nos posse explicare desideratum saltem per tatum
  76. fractionum replicatarum consunctiones additione mulliplicatione erc. faciendas
  77. imo non sufficit, quia duae rameri irrationales additi cesse vel in se
  78. si in integrum sit progressus, vel in minimis terminis, si exhauitur
  79. prou fractio replicata, resolvamus, quemadmodum praescribit in partes
  80. quales praescribit O et Y
  81. invicem ducti possunt facere rationalem. Illud tamen certum irrationalem
  82. rationali additum vel per eum multiplicatum non posse facere rationalem

Cite

Leibniz-Handschriften zur Mathematik LH 35, 3 A 22, fol. 15v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068235:0030?run=74