Leibniz Legible

Machine transcription of the Leibniz Nachlass

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[Ps. 1], fol. 289

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: 0.81.

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

The machine reads it as

  1. elecun
  2. signande
  3. l5. 851
  4. 6 le
  5. des
  6. Nant
  7. imparet
  8. COMMEHTARET IN LIDERMIIL 289
  9. narium ipsi addirum.) Nocandum hic est, quod, dum, ausendo
  10. cernario veram radicem aequationis propolicae x =L A X3 = 19
  11. _ X 106X = 120 ∞0, in aequationem incidimus, tres tantum
  12. dimentiones habentem, cujus ideo non nisitres luneradices, nu
  13. merus 3, quo rera radix ae quationis propolita est aucta, (IE se qua-
  14. Jis alicui ex talsis radicibus, ut liquet ex iis, qua ab AuCOrC P. 72
  15. Paulo post explicantur. Ita, quoniam, diminuendo ternario veras
  16. radices aequatiOnIS x = -- 4 X 3- - F9N X - f- 106X - - 12030, in -
  17. cidimus in aequationem p + - L 8 y3 - - + yy - 8 y X ∞ 0, vel
  18. 73. 87y - + - 8∞O, innorescit, unam ex veris radicibus
  19. esse z. Et Sic de aliis.
  20. Nimirum, diminuendo veras radices, quantitate coenitâ se- C
  21. cundi termini divisa per numerum dimensionum primi, si unus
  22. ex hisce duobus terminis notatus fuerit sieno es alter sie
  23. no -. Vel etiam hoc modo: Nimirum, diminuendo quanti-
  24. tatem coenitam secundi termini divisam per numerum dimen-
  25. sionum primi, unaquaque verarum radicum; si unus ex hisce
  26. duobus terminis notatus fuerit sieno. 1 es alter signo -. IIc ad
  27. tollendum secundum terminum Equationis X + = = a X 3 + 2 a a
  28. X X = = a 3 X. f a = ∞0, divido 2 a per 4, & provenit ; a: unde
  29. Faciendo = a = x ∞ Z, hoc est, : a - Z ∞ x, Scribendum eAt
  30. 1s a 43Z = a a k
  31. d ==44 + = a3Z- 3aa
  32. et a+ 2 a3Z 2aa
  33. Z
  34. Z
  35. de aaC L aCCZ- c6Z2
  36. et a+ + 43Z
  37. CUM. a+
  38. F 164= a3Z.
  39. +aaCC aCC c6
  40. 2 a
  41. 2 aZ
  42. 3.
  43. PrO
  44. X
  45. PrOnm2_ X3
  46. PFO. aaX X
  47. PrOm 66 X X
  48. DTO = A3 X
  49. e exlurget
  50. DO, aquacio,
  51. Secundo carens termino, et ab illa Rutoris difterens tantum in
  52. quartotermino, qui hic per L denotatur, e illic per -. IInde
  53. fic, ut per ea, quae pas. 70 lune ostensa, aequationes ha in eotan-
  54. cum inter se differant, quod Fal(a illius aequales sint veris hujus, da
  55. Contra, atque ita radicum mutua sic reciprocatio. Duod in aliis
  56. Quoque erenire reperietur.
  57. Ubi porro opera pretium est considerare, quod, collendo se-
  58. cundum

Cite

[Ps. 1], fol. 289. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/175905688X:0311?run=74