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Leibniz-Handschriften zur Mathematik LH 35, 12, 2, fol. 194r

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: 0.80.

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The machine reads it as

  1. Hacaccuralius vestiganda
  2. cujus terminus,
  3. Sit Fractionum summandarum senies (
  4. e
  5. exyy + myt nn
  6. sit seriei summatricis terminus . et sit dy = d. itaque differentiando
  7. ey+,
  8. fiet: + + -
  9. eys eyred seu ted
  10. ceyy + eed 9 + effd
  11. 1eff.
  12. 54
  13. = D, set
  14. porro () multiplicetur per e D seu per ed. et sit 1)d = d. et fiet
  15. ed
  16. cegy+ eedy + efd
  17. cegus + cemus +eenn
  18. = 4
  19. +2cf0 4 f4
  20. unde comparando siet ed + 21+ = em, seu f = L em = L ed et f+ = e, m - 2md q
  21. rursus etsd +s = eenn. Ergo edm = 1 ed + m- md +. est dd = et nn
  22. in datu
  23. ita evanescit e, et sit L mm - Ldd = nn seu mm = 4 nn + dd seu dd - nn tu
  24. unde patet etiam datis in et n, qualo
  25. tebe
  26. jacu sniapta na quarr seu sit
  27. Retque
  28. sit jam GV+ q+ rr et fiat v = y + p.
  29. yy + 2p y + pp et debet esse ( Ep+q = 4 nn + dd = 4 ppt aqpu + arr + dd
  30. seu (a pp 4 p4) + 4q = () pD + (4 q p + 4 rr + dd ita nil b
  31. + 9 y + qp
  32. + YI
  33. a=
  34. lucramur
  35. ergodu d
  36. it ergo L WD + qu +rra siat hY + p = V (et do - hdu = d
  37. misus
  38. ita variatur ipsa diffe
  39. et fiet: hhyu + 2hpy+ pp quodividatur per hh et fiet yy + 2Py +(AP
  40. +9h y+ qp
  41. 11
  42. hy 79p
  43. rebet esse: B ip + q = 4 xp tqp 1Nr taudd ethi
  44. hh
  45. ergo 4hupp + 4 pghh + hb q = 4 pp + +qp + 4rr + dd sit
  46. tk
  47. th
  48. h = 2 fiet 1pp + 12p9 + 499 = 4 1r. + dd. se 3 prt 3pa t4q = rr + 4dd
  49. quae cerras impossibilis
  50. pt h= firt (16p B + 16p 9 + 49q = 2pp (3) pp + Cd qp + 32rY + do
  51. 1 16
  52. 16
  53. seu pp + p9 + 449 = 449- 5 99 - Le
  54. fit app +4gP + sit p 16 p p + 169p + +q = 4 ps ZL 32rr - dd
  55. a
  56. seu 4p + 24 = app 1899 - 32rr - dd. seu p = 894- 3rrr- dd-
  57. sit ergo v = 2y + 899 - 22 rr - dd + 4
  58. videtur his successum aliquempondere
  59. nuncericarum
  60. nisi sit error intcal culo, ut liceat serierum
  61. timmas eec nmeri investigare
  62. sit 1. rn . fiat v = hy + p de = 1 fiet dy = 1: h - porro
  63. Ergo ex ve fit: th gy + 2hp y 4 pp dividatur per ha, fiet gu + 2p. h y = pB. h
  64. ebet esse nim = 4 un 4 du seu mai = + un + 1: th hoc loco, ideo gy + my + nn
  65. fiet 4 pp: th = 4 pp: hh + 1: tih. sed ita _ 1: s foret infinite parva, quod
  66. absurdum sit. 1: v0 +1 et v - hy+ p. ub ante fiet yy + 2p. h y = ppitihi
  67. my
  68. un
  69. sit app: hG = 4 psi: hh + 4 a + 1: hh seu a = = 1. 4hh seu h = it-a
  70. Hembrevus resumta formula eegu + eodus + eff fiat ey= tiv her
  71. 12 T2 eff y +f4
  72. et fet rrcico +eribco + d b
  73. + ed Y co + ed
  74. +2 ff Y co +254
  75. ner P. edt is
  76. cd + 4
  77. st formula data in qua deo = 1 = ed: Y
  78. haec famula Coco + hed + KK. multipl cetur per
  79. fet rrcoco + retco + rrkK, fiet
  80. 494
  81. 2it + ed + 2f = rh et 4 + ed 4 2H V = YYKK
  82. seum FS s = 17 = 4 bi + B5 + 4sL,: th rh+1 = P + 2
  83. hal. n
  84. seu 4. k LV Y a 92 EXsi + fAL = hh H +ohtit( 4 A atous Ed ilta
  85. e
  86. v

Cite

Leibniz-Handschriften zur Mathematik LH 35, 12, 2, fol. 194r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068195:0387?run=74