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Leibniz-Handschriften zur Mathematik LH 35, 6, 24, fol. 2v

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: 0.85.

Original at the GWLB · Page image · Annotations (IIIF) · Download text

The machine reads it as

  1. pag. L.
  2. L + Px + X + = A
  3. X + EXX + C. X +
  4. quondam coefficiens nominatoris, ex. gr.
  5. c - b, dab, e-b; semper est productum
  6. ex multiplcatis invicem residuis,
  7. rediens valorem ita
  8. ntre
  9. c
  10. da b,
  11. a qualibet caeterarum
  12. reliqua
  13. jster
  14. entium
  15. il
  16. in numeratore
  17. epistents,
  18. se b i constan
  19. qu
  20. Fractione prosion
  21. cabi
  22. vel aciam altiorem
  23. denominatoris nempe
  24. nunc formulam (HX + EXX + aX + A multiptrcando se
  25. dividendo per FG reducemus ad X + E XX + _ X. +
  26. si opus, faciemus.
  27. Huius divisores ponamus esse Xtb, X+C, X+d, us compludium
  28. eosque per compendium vocemus l, m, n exc.
  29. divello
  30. sita fractio resoli poterit in sequentes
  31. L. I +
  32. itaque propo–
  33. 3X. H + V xxY, d X: N
  34. Imn Ium lum imn.
  35. Ajo quamvis harum reduci posse ad talem qualis est prima
  36. L. N. igitur primum hanc resolvemus, deinde quomodo caeterae
  37. ad hanc revocentur ostendemus.
  38. Neglecto igitur numeratore constante qui
  39. inn
  40. nihil in summationibus mutat turbat, aggrediamur
  41. De
  42. resolutionem fractio num
  43. resolutionem fractionis
  44. vel generalius lmnpq...
  45. Imn
  46. ete
  47. Imup
  48. posito, ut dixi esse l = Xtb; m= xFC;
  49. q= X + f; et ita porro. His positis
  50. reperi, quod quidque experiando, de monstrare poterit ne opus
  51. n = x +d; p = X+C;
  52. semes reper jan facile
  53. sit i demonstrationibus non necessariis tempus terere
  54. BL
  55. Im c- b, l
  56. b-c, M
  57. Imn cab. d. b, l b- c, duc, M b- d, c- d, n
  58. Imnp cub, da b, e. b. l b. C, d. 5, C C, bad, cd. C. d. W b.l, cre, d.C, p
  59. nam ex aspecta patet
  60. et ita porro, patet enim progressus
  61. t
  62. Aalocaipin
  63. ut autem aliquis si velit veritatem experiundo comprobare
  64. in infiur qivoet
  65. acile posse
  66. cissimus, quia ita facile appare, nec in reliquis diff ceteris
  67. possit dabo
  68. oniam ib
  69. differt nisi prolixitate.
  70. bm-cm + el - b. jam pro
  71. c - b, l b -c, m 2bc = bb = cC, LM
  72. L +
  73. ipsis l, m, substituendo valores X+b, X+0 fiet
  74. bm - cm + et - bl = bx + bc - cx - cc + cx + bc - bx - bb
  75. =(eon destructis nembris inquibus est indeterminata X) 2bC - bb - cc
  76. ergo erit
  77. 2bc - bb -cc
  78. bn-cm + cl - bl
  79. 2bc - bb - cC, M 2bc - bb - cc, lm
  80. prout desiderabatur asserebatur
  81. XX
  82. Jam omnes fractiones mn. Imn. imn..
  83. etc
  84. Quarum numerator non est constans, reducemus ad frac
  85. numeratoris constantis qualis est. Reperi igitur esse
  86. Imn..
  87. rursus quae sequuntur:
  88. n
  89. reu
  90. pude
  91. Im
  92. Regulae universales

Cite

Leibniz-Handschriften zur Mathematik LH 35, 6, 24, fol. 2v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 73). https://leibnizlegible.com/page/00068069:0004?run=73