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Leibniz-Handschriften zur Mathematik LH 35, 3 B 5, fol. 35r

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: 0.79.

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. 36v); this page is its right half.

The machine reads it as

  1. Ut additio dyprithmica generabis a me constituta est, ta
  2. et subtractio etsi non similigener alitate, sed per gradus constitui
  3. potest Nam ab ipso a non potest subtrahi b, quia dubium est
  4. an a non sit 0. sed nec ab ex a bsa, aut ab cIbsa, aut apipliori
  5. etiam dyarithmico, generaliter potest detrahi n, quia si omnes ista notae
  6. possunt esse o. ile ept detruhi itaque per gradus est eundum,
  7. ab 1 potest detrahi h, idem ab ipso isa, item ab ipso isbsa, aut
  8. ab ipso 1scIbsa, et ila porro.
  9. Et quidem si ex a1 subtruhas h, fit 1-h, seu
  10. k
  11. si ex isa subtrahere opertent A, ese ponamus esse
  12. Ita, quaeritur tam X quany si a sita o et h sit o fit X = 0 et y = 1
  13. Si a sit 1 et h sit 0 fit X = 4 et y = 1
  14. )IX
  15. si a sit 0 et h sit 1 fit X = 1 et y =0
  16. si a sit 1, et h sit 1 fit X = 0 et y = 1
  17. Hinc generaliter valores notarum X et y omni generales omnibus istis casibus
  18. convenientes sic inveniemus. sit X = M + na t ph + gat, ponamus
  19. esse a = 0 et h =0 fit X = C = m. Ergo generaliter
  20. evanescere oportet m, et fit X = na + ph + gah. ponamus porro a = 1
  21. et h = 0 fit X = 1 = n. Ergo gens raliter X = a + ph + gah. si s
  22. a = 0 et h = 1 fiet X = q P = 1. Et generaliter X = a + h + ga h denique
  23. sit a = 1 et h = 1 fiet X = (0 = 1+ 1 + q. Ergo q = - 2. Itaque
  24. tandem generaliter X = a + h = 2 ah
  25. similiter sit y = m + na + ph + gah ponamuse esse a = 0 = h fit y = 1 = m
  26. Ergo generaliter y = 1 + na + ph + gah sin a = 1 et h = 0 fit y = 1+ n = 1. Ergo
  27. generaliter est 1+ ph + gah sit a = 0 et h = 1 sit y = 1+ p B = Ergo p = - 1
  28. seu (y = 1 - h + gah sit denique a = h = 1 fiet y = 1 - 1 + 4 = 1 Ergo 4 = 1
  29. et fiet generaliter y = 1 - h + ah.
  30. Itaque fiet
  31. +∞ (Fa ubi notandum quod i jam in additione notavimus
  32. F
  33. 1
  34. ta
  35. A
  36. as
  37. hah
  38. esse liceqaque identicitatem sub columnis
  39. larvatam, nam sublatis sdibus, sedum
  40. discriminibus, multiplicando per 2, quod est in
  41. columna 2da B patet assuisse 2 + a = h
  42. atque inde factum esse 2- (2)h ( 2 ah, + a (+h (= rat), id est manere
  43. B 2 + a = h
  44. F
  45. Veniamus jam ad
  46. iIbsa manet autem X = a+h- 2ah
  47. A
  48. itaquein a secunda cotumma si eb ad b, addetur - h + at, quod per regulam additionis
  49. est ibh+ b quid debet addi ad I et per Hom abl et pro tertia columna
  50. V
  51. nabh tat
  52. ta
  53. (+gabh
  54. ida tandem
  55. a
  56. +bsC
  57. pus est regata addendo quia non
  58. be mal 2ba + d nbh 1 bh + abt
  59. na in siuadtam comprobatio
  60. na
  61. +) b ta a 4bh qabh + rb htrah
  62. de
  63. b1
  64. s=lat
  65. +abs tabh scalotu
  66. -pbh + gabh
  67. +Bbh
  68. Sed hoc omuntur perplexitates, nam videtur
  69. nihil debet esse in quarta columna quod possit esse
  70. 1. praestat ergo procedere in hoc gradu
  71. ut in praecedente.
  72. Ilc
  73. rat
  74. Ep
  75. ab
  76. trabeti

Cite

Leibniz-Handschriften zur Mathematik LH 35, 3 B 5, fol. 35r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068255:0069?run=74