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Leibniz-Handschriften zur Mathematik LH 35, 3 A 4, fol. 9v

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. 8r); this page is its left half.

The machine reads it as

  1. Ex hoc calonlo sequi videtur amnem aequationem
  2. quae unat altiorem v.g. gradus X. quae uno
  3. tartum termino differt B X6. X3 X. deprimi
  4. posse, Nameiusmodi aequatio generalis
  5. OX + pX + qX +Y aequ ninilo
  6. 0X3 + 1X + 2X +3
  7. + 3X3 + 3pX 3_GX +3Y
  8. e l + bX +c4 + d aequ. 0.
  9. companni poest, cum excitum ex XCLpX No 2X + rp. +2g + 2rR
  10. +1X +Ip. +19. +ir.
  11. tax +op. +09. +07.
  12. 0
  13. 1.
  14. +r
  15. aequ. nihilo
  16. fiete Tollamus jam terminos X. N X. X. ope 4 arbitrarieru
  17. nempe. 0. 1. 2. 3.
  18. fiet: Op + 1 aequ. nihilo 09 + 1p +2 aequ nihilo.
  19. 2Y + 39 aequ nihilo
  20. 1r +29 +3p aequ. nihilo
  21. eugat aequ. sed hini jam video literam 0. esse inutilem, nam si caeterae
  22. omnes lexplicentur per ipsam, ipsa evarescet. Sumamus ergo
  23. perindeae si non fuisset ascri, ita, sed fuisset unitas et fiene
  24. aequationes: p + 1. aqu. 0. 2Y +39. 6 qu. 0.
  25. 9+ 1p +2 aequ. 0 1Y + 29 + 3 p aequ. 0.
  26. pro qit 1. substituendo - p. fet: in aequ. 3,54 - p + 2 aequ. 0. et in aerqu 2 fer -rpt 29 +3 paquo
  27. e
  28. porri 2aqu. 34 substituatur in aequ. 5. et 6. fiet q- p = 34 etqu.o er - rp- 3 +3p aequ. 0
  29. Ergo e ex aequ. 7 fier: qY P aequ 3. et ex 8 fiet 3 aequ. YP
  30. ergo fiet
  31. sive
  32. -
  33. 1- p pr - 4 aequ grp. sive
  34. pr- qu
  35. p9 -9
  36. (9pr) = 93 - pr + pq) aequ ( qu p) seu fier raequ.
  37. Heud quo casu aquationis cubicae radix erit radix culica ex radice aequa
  38. tionis quadraticae. Nos autem aliunde seimus eo casu fore rationalem
  39. sihil ergo hinc duci potest ad usum nostrum.
  40. Hine autem apparet unam saltem arbitrariam deesse, quo
  41. minus hoc modo solvantur, aquationes
  42. X + B B. X + 2b X 4 b p0.
  43. X3, aequo pX - 4X - 7.
  44. X ago p X + 2pq X + 2pY X
  45. X + b
  46. quid Liaidas ad aequat productam
  47. vides nihil lucrabimur, quia nihil plimusest
  48. ac si pro 3. scupsissemus 3 +(1) seu multiplican
  49. tem flcissemus: 0x34 1xt + 2X + 2 jam 3+1)
  50. una literm exarimi posset vig 4. ergo eodem reditet
  51. ot 1 aequ. 0. 0q + ip + 2. aequ. 0. imo etsi quadrents hinc X. philile pX - qX - Y
  52. atque inde faciamus novam aequationem, sclicet
  53. sextus gradus ut attollatur ad 30. opus 3 4 aibitrariis Jam _ 30
  54. prX 2pqu escLaqui0. eamque
  55. addamue pricriproductae, nihil lucrabimur, quia hoc aequatao tiam per illam
  56. N+ pX + qX +Y. est divisibitis, ero quotiente exeiente formula rationali
  57. 24
  58. quae ab imsio addita multiplicanti generali, no on ad unam mulsiplicantem
  59. componendam, utique multiplicante generali non constituet generaliorem: Itaque
  60. haec ceddita nihil novant, vec majorem dant comparani libertatem
  61. X + pX + q
  62. pX +X
  63. N + 4X
  64. ppsam dat

Cite

Leibniz-Handschriften zur Mathematik LH 35, 3 A 4, fol. 9v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068217:0018?run=74