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Leibniz-Handschriften zur Mathematik LH 35, 14, 1, fol. 190v

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: 0.85.

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. 191r); this page is its left half.

The machine reads it as

  1. porro d
  2. et quidem primitivus
  3. quod est quantitas rationalis, quia e est primitions major linario, adeoue
  4. im (alioqui extractio praeparatoria fieri posset secundum radicem exo
  5. denominatam a divisore ipsius e) ergo e est pax impar ac proinde
  6. p-1 est par ergo e - 1: 2 est integer, adeoque e-1. 2
  7. 3,5, 1, 11, 3 19 ete, eritr e-1: 21
  8. hinc si e sit 35i,
  9. 3 36234 etc itaque
  10. = d, d
  11. et radix extyahemd
  12. in exemplo binomii 22+ S98b cum d sit 2, debet binomium mulbiplicari
  13. per 2 et radix extrarenda sit (ubica, seu e sit 3, debet
  14. binomium multiplicari per 2, ut fiat 44 + 1944, hoc binomium
  15. si extrahile est, habet quod habebit differentiaque quadgalorum partium
  16. 8, adeoque ejus radicem cubicam 2.
  17. Hic jam ostendendum
  18. est. si A si radix est extra hibilis ex binomio, et differentia quada
  19. torum a partibus seu nominibus habet partam unam rationalem, tunc
  20. differentiam quadratorum partium esse ex trahibolem per eandem radicem
  21. Ah Nempe binomium est a + Nb, quadratorum partium differen
  22. tia est aetaa b, differut cam nos
  23. sit, radix
  24. binomii quaesitaliux fy ejus quadratum X +g + 2X Hy
  25. cabus ux +3x9 + y+ 3X tus siquadntum ta16Xyg 14X aryly
  26. Generaliter I+m = et (tm = l + C l. m + C. C =1 je- 2 2
  27. 1e-1
  28. e
  29. M + C. P- 1. (- 2 jC3
  30. 102. 3
  31. M et
  32. ubi posito n esse irrationalem et edigerendo fient duae partes producti, una rationalis +f. 15
  33. altera irrationalis Rationalis l+ C. C2 1C. 2 M + _. C- p. C2 2. C. 3 je4
  34. 1. 2. 3.4
  35. Irrationalis ( M, C. C. 1. e (Z M, C. x.1. C. 21P. 3.C4 je
  36. Del irrationalis
  37. 2.3
  38. Y. 2.5. 4. 5.
  39. 5
  40. M
  41. M=6- ad. - f.1. = 14
  42. etc = D = 1b
  43. + Ce1 e2. et 4 Ct (=D - rb
  44. L12
  45. M.
  46. 2
  47. e
  48. -2. Z. 4
  49. Jam bstendendum est O- d quantitatem rationalem dividi posse
  50. aertum
  51. per U l- mm: Quod patet, ex . nam si forimula compendo
  52. loco coefficientium atrobius coincidentium scribantur numeri, fiet
  53. m +14 1C + m + 16je
  54. 1
  55. ) = l + id 1e -2,
  56. D = m + 12 m: V + 14 M - (N + iC RCS 16 et
  57. 1
  58. horum quadrata si a se invicem subtrahantur, habebium terminos tales
  59. C. m +.. lm P2- md, nec alipodu nec
  60. e
  61. alii termini oceurrent, horum autem quilibet dividi potest per I=M
  62. itaque O2 = y, vel a -b necessario dividi potest per. 1- m
  63. demonstratdum est posse radicem e extrahi ex
  64. 2 Quod sic consit potest radix labica e extrahi ex
  65. O + D ex constructione,
  66. sed eadem potest extrahi ex O-
  67. nihil enim interest, quam quod ex +M sit- m. Ergo etiam
  68. potest extruci radix ex jam ex O+ D in C - D fit O-
  69. Ergo extrahi potest cabica radix e ex O- D
  70. et cum
  71. 32 - et sit rationalis, etiam e eo- erit rationalis.
  72. Et idem facile patet, etsi ad serem generali serie non expressissene
  73. et 3
  74. jam

Cite

Leibniz-Handschriften zur Mathematik LH 35, 14, 1, fol. 190v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068201:0380?run=74