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Leibniz-Handschriften zur Mathematik LH 35, 14, 1, fol. 105v

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: 0.80.

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. 106r); this page is its left half.

The machine reads it as

  1. ah. X
  2. X +alX + al per N +am X iaf X + a cX + a d Bo
  3. X + a hX + a l
  4. X8 X am X +af N + aC X + a d X
  5. ah aham, aha f. ahacX aha) X
  6. ral
  7. a lan aelaf a lac ael
  8. X X ab X ac X at X anx apX aq X ar
  9. esaena Ubi videndum an tibus ullimis terminis p q. r. aequationis quadia
  10. to quadraticae proposite an producta aequatio comparari possit cum alia quadrato quadratica in
  11. qua tres ultimae literae p. 4. r. pro arbitrio sumantur, fiet: Quod fiet si ope quatuor
  12. arbitrariarum m. f. c. d. quatuor primae aequationes, collatitiae possint absolvi aequatro plane.
  13. nempe m ob at b - h.
  14. fM c- l.
  15. Cpi ab tm ap =sb +ti
  16. et d B an = hF - lm an = het hl - 11(F hD
  17. Omnis ergo aequatio Tubica attolli potest ad quadrato quadraticam aequationem ectavi
  18. quodus, ju aequationi alteri gradus octavi gradus omnes tres ultimos ter minos arbitrarius
  19. alteri
  20. habenti, comparabilem
  21. Ergo comparabilem resolubili, Ergo aequatione per Geonetiam
  22. planam. Ergo pse quoque rresolubilis est per Geometriam planam. Nam omnis aequatio
  23. octavi gadus tres ultimos habens arbitrarias terminos habens arbitiarios, plana est.
  24. Vugae alibo res intelligatur: aesqatio hi producta E. comparetur aequationi pagimae praecedentis
  25. bsi ubi. salis apparret remalse assurgere
  26. resumatur aequatio D. conprundo cu s: me Rb + a lb = 3 p ah 34 l
  27. P7 a l.
  28. s tab + C = Cub B ab tab + 3abc + 3er ab + C3.. H
  29. 15 ac tab c 1I
  30. Si quaedum radio Cubica cndam aggregito planarum quontatatum aequari potest
  31. .
  32. p3+ a2C
  33. calico pura
  34. X +ael. B0. fat: X F + m X + ae l X + a lm p0. Multiplicando per At m quae
  35. redumetur ad aliam cubicam: _t in y 4 Am Y + 4m t p0. cujus toltendo secundum terminum, fie D.
  36. ponnde g_ X +m fai X +sm X + 3 m X + 9. X - (m V - , l o
  37. nem X - m
  38. 27
  39. + (m1). 4 pa
  40. cujus rdi secundum terminum facere affirmativum vel negativum in nostro arbitrio est: Unde radice extrahendo:
  41. Yf y
  42. sive
  43. Se) inila + fs 1M B Bna a a ( ( m) ) fli f 1a
  44. JH 10 1ne t 1a + ln + la
  45. 2a
  46. a
  47. + 16
  48. pone + p+. fer = p. et yB mO + l’a
  49. Im F la + lm = Eae
  50. rique X (+)7X = LY. Ergo per ea quae habet Huddenius reg. 20. pag. 495.
  51. X + A p - aet. sie X LA- a s =
  52. fier: X =EM ut +ga + S. m p L msi nerga + ii Ee yast iga tgn. al
  53. 4
  54. nemrua
  55. H LV + nom -cal . adeoque X1] qn 4 B s n +ga. + se 4m s nrga ( n ga ( ya +ynaniar
  56. (7m ya
  57. YS n aga Jum X alinde pu a s a l. Unde aequatio inter duas quantitales cognitat, in qua in pro
  58. arbitrio assumi potest (ed satis intelligo nihil inde posse duci facite. ablatis enim irationalibus quadiaticis rest abit
  59. enon nisi una cubicam vel simplex vel quadrata) vel 13) 1
  60. X+ X+ anp
  61. sive
  62. unde X, dX + Ap s api
  63. FAH m + S+ m +a
  64. Bph - gat 3a

Cite

Leibniz-Handschriften zur Mathematik LH 35, 14, 1, fol. 105v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068201:0210?run=74