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Leibniz-Handschriften zur Mathematik LH 35, 5, 20, fol. 1v

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: 0.82.

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. 2r); this page is its left half.

The machine reads it as

  1. Haec methodus etiam serviet si non ad summandas series omnino, saltem
  2. ut summandae reducantur ad alias summandas simpliciores Ut s
  3. E sit summanda series cujus terminus X aequy. fiet: y. Xta aequ Z
  4. xtatax
  5. Xta. X + a + dx
  6. ex y. X+a + aequ =. _ y. X+ a + dY = y. X+ a aequ y dx
  7. xta
  8. aequ
  9. X dx
  10. X+a. X +a+ dx
  11. se Generaliter ergo dispiciendum an series quaelibet altio reduci
  12. possit ad prexime inferiores. Ita enim aliae quadraburae
  13. reduci possent ad Quadraturam Circuli et Hyperbolae.
  14. L
  15. sunt ter Est Terminus seriei progres sionis Harmonicae, item
  16. reducatur ad priorem nam
  17. item B
  18. xta
  19. xta
  20. X+a F a aequ 1. Ergo X aequ 1 - a
  21. xta
  22. X,
  23. X+a
  24. x ta
  25. X reducetur ad priorem. addendo a xa + aa, (quae jam dantur quia datu 2Xa et aa
  26. X + a
  27. X +a
  28. ex supposita pr summa progressionis harmonicae) fiet
  29. xta
  30. ergo L aequ x+a L
  31. X+a
  32. X
  33. rrataa aequ x - exa
  34. x+a
  35. xta
  36. X+2xataq Xta, X+a
  37. Xta
  38. Eodem modo habebitur
  39. aequ 2+a
  40. et X. Et ita porro. Ergo habentur
  41. et compositae ex potentiis xta numeralorem ingredientibus
  42. Sergamus jam ad secundum denominatoris gradum, e
  43. h + m unde fiet:
  44. X+n +x+m si hx + uhi xeaxib
  45. 1
  46. X + LX + In V
  47. .
  48. X+I X+n
  49. X + Ex + In
  50. Oblata jam serie quaecunque, cujus numerator sit constans, nominator vero
  51. formula secundi, gradus, quaratur divisor ut . comparetur
  52. X + bx +c
  53. X +bX FC cum X + 1X + In vel quod idem est quaerantur divisores vel
  54. radices formulae X CbX +C consideratae instar aequationis, nempe X. si x+bxte
  55. erit X+ bx + b aequ. b- c. seu X + aego Yb - c. seu X + b = -c aequ.
  56. vel X+ b + st -C aequ. 0. ergo divisores ert formulae: XX + bX + C
  57. erunt: X + b + Yb -C et X + b - L -C. Ubi cpjo. fient X + b et X
  58. Sumto jam uno divisores ut x+b inde formetur novus terminus hujusmodi:
  59. qui ductus in alterum X + b Y -c dabit: P X + pb - p b C
  60. X+ L + (b-C
  61. aequ. P
  62. -c
  63. Et fiet.
  64. X + bx +C
  65. 1 + pX + pb + p Nb-c
  66. aegu + Y
  67. XX + b X +C
  68. EXtXtC X+B+ NF-C
  69. Ergo conferatur D cum C. fiet paego 1+ B. et 1+ PB + PAb c aequ naml.
  70. X + b +
  71. fiet: l aequ. b + sb = c et n aego = - 1b∞c. et p aequ h+ m. et
  72. denique: 1+ Pb + plb -c aequ ( b) + (m Yc+ h 6) - h N-c
  73. d restabit 1 aequ = 2h st - c. seu h aequ. 2
  74. seu 1 aequ m autem assumi potest qualiscunque ut 1.
  75. seu
  76. Ergo si sit: fiet aequ. +
  77. aequ
  78. XX+bX +C
  79. XX + bx +C
  80. + +
  81. b- 4c
  82. 1-+ 51
  83. X+ L - s.c 2 C. Xt hr C
  84. X+ L- BC Xb+
  85. ite t
  86. utu

Cite

Leibniz-Handschriften zur Mathematik LH 35, 5, 20, fol. 1v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 73). https://leibnizlegible.com/page/00068038:0002?run=73