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Leibniz-Handschriften zur Mathematik LH 35, 3 A 18, fol. 12r

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: 0.87.

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. 13v); this page is its right half.

The machine reads it as

  1. luppono
  2. De Radicibus Aequationum inveniendis
  3. quod
  4. Certum est in radice aequationis generalis rationale esse potest
  5. id esse terminum secundum, numero radicum divisum ut si sit
  6. tunc
  7. aequatio X + p X + gX + YX + 5x + + = 0 erit pars rationalis
  8. radicis generalis = p: 5. Oportet enim esse X = p + etc. quia
  9. erit
  10. sola litera p ipsi X est homogenea
  11. itaue quod in Xx rationale, est pp- 29 dices divis pers
  12. p= 3p9 + 3Y
  13. divisper
  14. p2- 4p 9+ 4pr +. 299- 45
  15. p. 5P9 + 5pr + 5p qps-59r +S
  16. pono autem sublato termino 2d0 p, esse X = Va + +Yc + Id et ment
  17. = h + l + m + n = sh = RC
  18. constat esse XE - 5yX +5Z
  19. eehh
  20. sit hl = y et hlm = Z et hemn= co
  21. + syH X 5yZ. = _ h
  22. =sld XX - 2y
  23. X3 = 3yX + 3Z
  24. X - 4yx + +ZX L 2yy-400
  25. M
  26. C
  27. Amn
  28. X- 5 yX + 5ZX +syyx - 5yZ
  29. 5CoX
  30. Quoniam autem h seu 1 + P+ m +n seu a + b + C +d sunt rationalis quantitas
  31. ex hypothesi quod sunt radices aequationis quadrato-quadrntriae ravalis:)
  32. Et eren si sintequanttas hinc pateb etiam quod X - syx etc. sit quantitas
  33. Nobis id agendum est ut inveniamus h absolute. Quod utique inveniemus, si
  34. rationalis
  35. sciamus quid sit rationale in X et in 5yX et in 5ZX et in SyyX et in 3coX et
  36. in 57Z. Deinde quaerere etiam debetimus quid sit SCE. His enim rationalibus
  37. in unum alditis debet conflari valor totus, quippe rationalis ipsius h5, et oportet
  38. destrui quid quid irrationale intercurrit.
  39. ex Tabula alibi coepta
  40. Eodem modo quaeremus h l absolute tantur enim aequationes
  41. pro hl (seu y) XC, h. m tim similiter inveniemus hVM
  42. a
  43. 12
  44. et denique s lmn horum autem valoribus habitis, utique habebitur aequatio
  45. quadrato- quadratia pro h vel l vel m vel n.
  46. Verum quia prolixum foret nimis investigare quid sit racale in yxd in Z
  47. altinibe
  48. in yyx in cox in yZ; et ita magis adhuc in aequationibus pro h3l, vel hFm et
  49. Rideo reperi insigne compendium, cujus ope sufficial solum nosse quid sit ravate
  50. co in aeq. pro h,
  51. in X et ejus potestatibus. Nompe tollantur tliterae Y, Z
  52. vel alia; ope equationum paulo ante positarum, et Hh h h vocando O, D, 4
  53. supererunt in valore ipsius h, solae
  54. X, O, D, E et quidem hae nihil continent rarale
  55. sed an nt facta ex ipsis, et estum potentiae

Cite

Leibniz-Handschriften zur Mathematik LH 35, 3 A 18, fol. 12r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068231:0023?run=74