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Leibniz-Handschriften zur Mathematik LH 35, 4, 5, fol. 8v

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: 0.87.

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. 9r); this page is its left half.

The machine reads it as

  1. respective ponendo u, 12, 13, 14 et. (ita ex ipsius et valore
  2. numeratore in valone ipsius 31. fit qui ost 10. 21 + 11. 20. fit 11. 21 4 12. 20.)
  3. Dinique notndum esi quod si a in divisore dato sit 20 =0
  4. ve
  5. (vel 20 et 21, vel 120 et
  6. nt
  7. ux
  8. tantum concipiendum est
  9. ac si faisset divisor+E3X ete (vel - 22X + 23X4 24X et
  10. vel -2H x- 23X + 24X +25X et C. Et ita porro). Deinde q
  11. proveniens idem erit qui supra tantum pro 20, 21, 22, 23, 24 etc
  12. respectioc ponem (vel pro respective ponendo 21, 22, 23, 24, 25 et ab 1 utque ad ab usque ad F
  13. (.vel 22, 23, 24, 25, 26, vel 23, 24, 25, 26, 27, et ita porro) et
  14. +Y totum deinde dividendo per X (vel per X, vel per X
  15. et ita porro). Idque locum habet sive provaloribus ipsorum
  16. superius prius
  17. 231, 32, 33, 34 etc. utamur contractis prius positis, ubi
  18. 31 reperitur ex jam reperto 30, et 32 ex jam repertis 31 et 30
  19. cL3 et et ita porre; su et 3) ex jam repertis
  20. et 33 ex jam repertis 32, 31, 30, et ita porro: si ve valoribus
  21. feorum utamur explicatis, per seu per solas initio datas
  22. quantitates 10, 1, 12, etc, 20121, 22 etc.
  23. Quodsi Ut rei coefficientium etiam presiduia valones explicati
  24. invemantum, ommodum erit redire ad exemplum superius
  25. sit Dividendus +10X LX +IX + BX +14X 415X +16X ArXH18
  26. Divisor -20 X +21X + 22X + 23X +24X +
  27. Quotiens +30X +3IX + 32X +D3
  28. Reriduuis
  29. +HXHSK+36X 13IX +38
  30. Residuus
  31. -2X 12X t22X + 13X+ 24X + 25
  32. Et fient valores coefficientium quotientis, nempe 30, 31, 32,
  33. 33 etc. iidem qui ante eodem modo ut expressi ut ante,
  34. penempe erit. 30 erit 10: 20, et =31 erit 10. 21 + 11. 20, : 20
  35. et ita porro, ut ante proxime in alia licet hypothesi, cum
  36. iidem coefficientes infimis, qui nunc summis potestatibus ascripti
  37. essent. Valores autem defficientium Re in Residuo
  38. et ipsi fient iidem; perinde ac si 34, 35 quoad numeratore
  39. st
  40. ac si
  41. valorum perinde a ter
  42. datorem, perinde ac si essent coefficientes in Residuo, esse t
  43. dcontinuati coefficientes in quotiente; hoc uno tantum excepto
  44. quod ubique pro 20 quod poneretur in Quotiente, ponitur in Residu
  45. 10. 21
  46. 33 = 10.∞8. 29 + 11. 20. 22 + 12. 20121 + 13. 207:207
  47. (2) 10. 20. 21. 22 11. 20. 21
  48. 10, 213
  49. +34∞ 10)24 = 11. 23 f2. 22 + 1 14
  50. Hop. 2123) + (2) 1L 2 22 12(21
  51. +(10. f27
  52. 10. 21. 22
  53. 4
  54. 10.00. 24 +1. D. 2 LMom HoB. uNo
  55. (2)10. 00. 2123 (2)11 00. 21. 22 12. 0ct 2F
  56. 16, 00,22
  57. (3)10 ∞. 21. 22
  58. vel pro 00 ponendo -1
  59. +34 = 10.24 - 11.23 f 12. 22 - 13. 21 + 14.
  60. H2110. 21. 23 +(2) 11. 2.22 +12. 25
  61. 10.28
  62. =(3) 10. 2132
  63. Et ita porro eadem lege servata explicate habebuntur 35, - 36, -37, -38. vel
  64. ido 00 seud - 1) + 3 7 +35, - 36, +(37, -38
  65. +200, id est - 1. itaque in praesenti exemplo vaoros sic stabunt. et quadrat t a + b +c etc = a + 2ab
  66. 5+ 30 = 10: 20 C - 31 = 10. 21 + 11. 20,:20 90 = 10. 26 + s1
  67. P- 32 = 10. 20. 22 +11. 20. 21 + 12. 207: 20
  68. le
  69. assV
  70. 2
  71. n

Cite

Leibniz-Handschriften zur Mathematik LH 35, 4, 5, fol. 8v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 73). https://leibnizlegible.com/page/00068002:0016?run=73