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Leibniz-Handschriften zur Mathematik LH 35, 12, 1, fol. 302v

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: 0.77.

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. 301r); this page is its left half.

The machine reads it as

  1. 3
  2. +
  3. eE
  4. )
  5. et nt
  6. s
  7. Hoc jam artificiam saine pulcherrimum, et generalisuum
  8. et totam Methodum diosanteam mire illustraturum
  9. applicemus ad formulam datam X, etc. et
  10. sit H formula haac: X X +CCX + bcC Traisformanda
  11. depossite ex traubilem, seu cujus factor sit extrahibilis, quantum satis est
  12. fiat X =h, Vy + ly +mm,: yy+ 2ny+ nn, ubi facio denom natore
  13. extrahibilem, quia. trasfer in formulis non negligendus
  14. est nominator, e si in aequationibus negligatur
  15. S.
  16. pro X sonendo b, fiet b = h, gytlyt mm,:, yy+ 2ny+ nn,
  17. in th gy + hl y + hmm = , quae ut habect
  18. -b..
  19. =2bn = b nn
  20. yy + hC - 2bn + hmm -bun - 0. et de
  21. s
  22. b
  23. p - b
  24. seu
  25. debet esse
  26. 2ftmm -bun = hl - 2bn, seut himmabui hab = hblli quibu ab
  27. dtium quia hoc modo, pro una sola roidice ipsius X res efficeretur, seu solum
  28. itm unum detur par radicum aequalium pro y, deo praestat assumere
  29. et divellendis
  30. fiet.
  31. e
  32. nonsst
  33. XX + bx + CC = 0 fiet XX + bX + 4bb = Zbb cc et X = - 2 b + Y bb -cC
  34. uod in aeq. D substituamus pro b, et fiet:
  35. ani - Lbun D + nn F Abb cc, h - L b + Si bb -cc = hl. + nb - p sibb
  36. pot tum = Zbbn. h- 2b + nn 4bb- cc = ht hl - nb +un bb - cc
  37. idem
  38. hum - Lbnn + R. h - =6 un = - hL + nb, 4n ut evanescat irratinall,
  39. brevius fieri sit n = 0 et fiit hum, et h b = + fiit utique
  40. M = 2 et h: h b = 1 4 seu 4h h. b seu h ab seu b -
  41. fnimbun faret 4m
  42. t fintmm, h. 2b = sll, et hmni- 0 sed hoc absurdum, ergo
  43. et pro 2 1.
  44. si volumus sollere n, retinenda irrationatis, et fiet.
  45. l
  46. 4 b S bb- cc h+ 4 bribb -cc
  47. 2 Fhae ei Em 1.
  48. det
  49. seu fiet
  50. m.H h + 2b_S= bb -cC = hhHl. sit iet mn = A Hl
  51. 11
  52. 4n + 2b-2Y. tec
  53. sit Et idem est ac si voluissemus Xx +bX + cc facere exhahibilem
  54. assumendo X = h, yjs + ly + mm: yy, fieret utiqre h
  55. A GAhh l 3 chhrin gu +
  56. + hh U. + 2hhlmmys + hhm: t
  57. +b t +hlb B. Fhamb yy
  58. Ubi numerator
  59. potest reddi extrahibilis, es
  60. debel repercti tem succe dere modo
  61. fiat nim = hll 2, 4h. + 2b - 2 vbb- tc
  62. patet etiam hinc egregrum sane compendium quod etiam ab cartu
  63. noolim debuisset in measem venire. Nam si velimus extrahibile
  64. eddere factum ex X frmulam Nm EEE. de quae fH ex
  65. XF XX + bX + ce ducta in X + sufficit reddi extrahibile
  66. XX +bx + CC ope X =hgh, yyt ly +mm, :gy ita enim
  67. X. + x +f fiit +hyu +hly + hmm,: yy, et Yx 1S fuit Asgus Agatum
  68. et X+5 fiit =L Y 1+ Fyy + ly+ mm
  69. si mn = ut dxinus. fiet _ X h, 3 + lytl
  70. X = siht 2bh - rh Sb. ac gy 4+ ly. + htill 8E t
  71. +h + 2b - 2b166 -4cc, yy
  72. ubi l, et h manenti arbilrarict
  73. et video si faciamus
  74. l: (L +( fih) = 2M: ( (l.: ( s. 2
  75. eti seu (=amml: C1(. h))
  76. in
  77. (a +h LH: (41 + 2b - 2V 66. 4cc)
  78. aequ. l+ (f: h), etiam stfyu tluem
  79. tuii
  80. ei b
  81. X A bXXH CX
  82. AX+ bX+CC
  83. = bxx) abbX +bet
  84. eet
  85. + 1
  86. 3
  87. e
  88. Ea
  89. =_c et

Cite

Leibniz-Handschriften zur Mathematik LH 35, 12, 1, fol. 302v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068194:0604?run=74