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Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 215r

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: 0.78.

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. 214v); this page is its right half.

The machine reads it as

  1. depressive.
  2. id agitur ut bXX+CX+ d, xte, reddatur spbiitr extrahibilis per explicatione
  3. ipsius X, fiat ergo X = lyy + mnus + n,: ( y+p
  4. fip a = bl s + 2blmmys + 2blnyy
  5. + b m.. + 2bmmny +
  6. CCPX = Ca + CEmm. + CC n..
  7. + 2cc lp.. + 2cemmp.. + 2CCB p ..
  8. + celpp .. + cemmpp. + cer pp
  9. = d. + 4d p.. +6d pp. + 4d p3.. + d pt
  10. d
  11. aqqus + 2a grry + 2agt yy
  12. tart. trarrey + at
  13. sit Y =0. et sit n3 = ppY.
  14. Et ex aeq 2)
  15. Ex H Ilfil Exaeq. companato identificatrice i sit g = sbl + ccl + d: a p(t = pp rbWBCBa
  16. Et ex aeq. 3, fit - mmip = 2ccl + 4d3:, 2bl + cC q unde (4bcc lD+ 8bd v + 2C2 cd) (ab celvusbdltumaud
  17. Et ex aeq. 4 mmip = 2ccB + 4d3:, 2bv + cc) seu 4b 8bd L. v = 2c4 L- v = 0
  18. seu firt bd - et l - B = 0. sed non licet facere 468 =c = 0. ergo fit l = v
  19. superest aeg. 5. unde sit m: pp C + Eemm: p + 2bI +, cC l + 6d aequ + 2bll + rcl + 203
  20. Ergo si F + ∞ + fiet bm: pp + rcemm: p + 4d =0 seu fiet
  21. bb m : pp + 2CC b mm: p + C = c+ - 4 bd. seu b mm: p = e + cc B Sct - 4bd3 l
  22. faccendo W0 =mmip et fit: Ecc l +4d3 :, 2bl + Cc. = c ccob - (ct -4bd: b -H
  23. et fiet Eccl + 4d3 = 2blW + ccW fit l = ccW = 4d,: 2cc - 2bW ergo per valorem t
  24. sit t= cc + 4d3 1y l = ceW - 4d:, 2sc - 4bd = v q- F: pp = Aurcl+ d: a
  25. W seu - mm: p = cc: b - Sc- 4bd: b et
  26. et fiet X
  27. tam ceto -4d3=
  28. et
  29. 2 Y1- 4bd3
  30. sit
  31. X=
  32. cco- qd yy - pV y + ccl- +d
  33. 2 Set- 4b0
  34. yyt 2py + pp
  35. 2YcF- 4683
  36. pr
  37. cSc abd - C + 4bccd NL pH e abd = sC
  38. 2b, c - 4bd3
  39. (e Se abd - C + abccd) yy
  40. C
  41. 1- 4bd
  42. et pl 2b, ct- 4bd = - 2 ccp. + 2psC. 4ld
  43. ( - abd - Bcc) (1. 16d) py)
  44. (C C - 1bd - c + 4bccd3) yy. + (C - 4b93 - CC) C - 4bd 2py + (C Set - 4b8 - C + 4bucd3) pp
  45. 2b, c - 4bd31 + p
  46. vel compendio X = lyy = pa y + lpP, :, y + p, posito (= curv - 4d et W = cc - sc - 4bd
  47. 2 Sci a 4bd
  48. ubi si esset =HyD 1, + Upp et IpW = ellp sin W = 2l, esset etiam x extrahbies, quod tamen hic
  49. non licet licebi pou pro xte, ut fiat extrahibilis poddibit +lgy - ploy + lpP: yp
  50. +rep. + epp
  51. ubi si fat -pco +rep,: lte = 2p sieiet rursus aliquid non est in potestate
  52. quia evanescit p. Itaque hac methorto obtiaere non licet ut tres
  53. formulae Cubicae radices una vice fiant extrahibiles obsine bitui tamen per
  54. gradus quod suficit
  55. l = c - c Sct - 4bd - 4bd Sc - 4bd - Cc -W
  56. 2b Set - 4bd
  57. lyy +mmy+ n3
  58. gy+ 2py + pp
  59. = lppgus t mmppy n pp
  60. +dp1) F2map. F 21 p.
  61. Lly. Fmn. 7 13.
  62. a gyyerrytt
  63. Oyip
  64. vis
  65. s 2
  66. e

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 215r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068196:0425?run=74