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Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 6r

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. 4v); this page is its right half.

The machine reads it as

  1. ubi signo diffirunt duo membra, quae unum habent factore commutm, seu notam
  2. posteriorem eodem loco. Et quodem omnes pro formandis membris adsunt combination
  3. ba tantum lege semata, ut in quovis membro reperiatur quaevis ut quodvis membrum
  4. sit trificum ( seu brium factorum) et in quovis membro quaevis nota tam prior
  5. quam posterior orepeniatur.
  6. porro harum quantitatum numeris fictitiis bi-notalibus designatarum,
  7. quaevis quan multiplicatur per 1 habens notum posteriorem I, multiplicatur per 100
  8. et quia in quovis membro est una habens notam posteriorem 1, ideo omnia membra
  9. explicata dividentur per 100, et 100, quia non nisa semel est in quovis membro
  10. evanescet, eodem modo evanescent hic 290, et 300 sed hoc praevideri
  11. poterat, nam adhibuimus solum 100, 200, 300, ut ipleui ubique eadem esset maltitudo
  12. numerorum fictitiorum ideo eoanescunt cum p, q.V
  13. +10. 2132 = (1 +12
  14. 31232
  15. LV2. 112. 113. 112. 123. 212, 217, 223.323
  16. +112. 1237212, +112. 1231313, 4212. 232123
  17. 312.323
  18. (- 112. 113. 123 212. 22. 22. 213,223, 323
  19. +212. 2237113, +112. 1137323- 7 112. 12. 113133
  20. 9 -31. 323
  21. 212. 213
  22. 112. 223
  23. ) 2312. 313
  24. 10.2231 =
  25. Sed quia is calculus prolixior, et videmur abundare arbitruriis, ptupideo pro contrahenda aequatione 14
  26. 8112. 10∞ p. - 312.380)
  27. 10Or = 1L = 31
  28. 100p 312 113
  29. 123,100p = 323. 3001
  30. 1e0p 33
  31. nam fit
  32. ponatur 113. 123= 313. 323. Et procontiahenda aequatione 16 ponatur 112. 113 = 312. 313. et fiet
  33. 312: 112 = 113:313 =323: 123. Unde ex aequ. 14 fit 300r: 300p = 313. 13 et ex aqu. 18 similiter
  34. fiet 300r: 100p = 31X0113. Itaque hae duae aequatiores 1g et 18 hac duplici suppositu
  35. ad unam. Revera ergo non nis unam hypothesui consumlimus. Superestae quatio 10seri qua pro
  36. 300r substituamus (213: 112) 100p, et pro 312substituamus (13, 313) 112 et pro 323 substituamus (113: 313)123
  37. itaque ex aequ. 20 fiet (multiplicatis omnibues per 113. 315) fiet
  38. +113 33 2t. 232 uL 100p + 1 aIZ 32 2 uE. 100.
  39. -112. H13. H3 123
  40. 1(3N212. 223.3132112 1p
  41. -112. (113 13. 1 23C
  42. Fil2. 223
  43. 1sL. 13. 13, 1
  44. f113. 100p
  45. 13B. 222
  46. tur 127 313313 Z(I ZEt 2009
  47. 113. 113.l13, 123
  48. sed resumamus securioris calculi causa es ex aq. 30 faciamus
  49. + 1. 193. 313 3( 0op = . in n G e 213. 209
  50. seu multiplicatis omnibus per 13. 313. 313
  51. 112. 1232 313,. 313, 313.313.100p FHIX 123. 313. B132 113. 213. 2009
  52. +212. 223. 313.3132113. 113 100p +
  53. 2. 113. 113. 123 yihi Zt
  54. =112. 113. 113. 123. quae aequatio dividi non potest, nisi coefficiens ipsius dividipossit per
  55. ipsum autem ee s coefficiens est, 313. 3e3 (113H,. 212. 223 ta sed hoc video non litidefier
  56. si esset jam H3 H) 2(3. 33. sera divisis opni omnibus per 13. 113. 113. 3 fiere
  57. +2 +AAS oOp =1Z) 2. 209 adeoque 123 = H~. Ergo 312~323
  58. Et quia 13 H3 = 313. 313 fiet etiam H12H2 = 312. 3R et 123. KG= 323.323
  59. ItL 13
  60. H2 123
  61. itaque conjungendo valores ex rgo primum et itium ipsius ak, ex aequationibus V et 12
  62. fiet 100 100 pp - ab 700 g0 rr-ad. et pro 300300rr substituendo valorem
  63. fieret 100, roopp - ab = (313. 313 : 117 1) 10. 10pP = ad, id est 1 roOpp- ab - 100. 10 pp - ac
  64. quod non licet. Ergo non licet contrahere aequationem C faciendo H3. 113 = 313. 313
  65. +212. 223. 113. 113 +112. 123. 113. 113) 100( = (1. (20 +113. 1137112. 113. 123,213,2009
  66. -113. 113
  67. ium aequatiop duccedit ine ieq a nova determinatione,
  68. recimus.
  69. seu aequatio
  70. = 212-223. 113.113
  71. 112. 123. 113. 113
  72. dividi potest per 4 213. 313 = 113 113. Veum non licet facera 313. 313 =113. 113. nam fiere
  73. neque adeo ponendo 113. I13 = 3(3. 313, quicquam proarbitrio
  74. etiam 112 112 = 312. 312, et 113. 123 = 32 3. 323. Unde conferendo duos valores ipsius ak, primum etterti
  75. ex 2gg. 10t Z, fieret 1 100pp - ab = 300. 300rr -ad. sed posito 113113 = 313. 313 fit 100.10pp = 300. 300rY
  76. ergofiecet ab ab quod o non licet. Itaque aequatio O dividenda est per 313.313 - 113. 113, et fiet
  77. EIL ECG. 313.313 (313.313-113. 113) +112. 123 (31373+11313) (313313 113 13
  78. 3100p = 112. 123. 113. 213. 2009 (313.513- 113. 113) actoque aquationem C dividendo per 313. 313- 113. 1
  79. fiet 112. 123 (113. 113 +313. 313)=212. 23. 313.313,: 112. 113, 123. 212 -,2009: 100p
  80. ubisi faceremus 112. 124 = 212 (23 fieret 113. 43 = 2009: 100p. ita revera hactenus duo tantum pro
  81. bitrio assumsimus
  82. 2133(313313- 113. 43)

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 6r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068196:0011?run=74