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Leibniz-Handschriften zur Mathematik LH 35, 13, 2a, 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: 0.79.

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. 70r); this page is its left half.

The machine reads it as

  1. Hbc = qu (b.5) ( aequat sit C = b -c et de K = n ( (b-c), fiet
  2. et ca mb. at c: b = m
  3. p
  4. ate
  5. 4bt 4b b -c (2 qu (b. c) = qu (b. C) ut st acb ML9-
  6. aa
  7. 104
  8. 2
  9. at lebo - b (er p , at 1a)
  10. et 4b m =aa ( C) = bt (b-C) seu Atalm -aab talit: prei - nub nub m
  11. seu 4 ab + 4 ab pie L aaba (= aab m + a abM) = elib a + tb m - l8 0t.
  12. et exa dividendo per ba, fit 4a + +um = da L . seu atrm = Boat nn)
  13. 2aa CF = - 2p + pp fiet la = pp - 2aa ip et a + 2p = + p)
  14. seu m = + + pp + 2aa - 2pp - rap, : 2p, = 4 (f.. 2 p p 4 2a -2ap: 9
  15. nun
  16. fiet b: C = 2a + (41 - E) pp + raa (rap,: rpa = atm,: m
  17. et K = (b -c) = d ac - Wmb = 1db. = pp -raa, b
  18. a m
  19. pat
  20. pp- 2aa, b vel PP- 2aa,b
  21. -pp-2aa,
  22. =3pp + 2aa
  23. at
  24. (2a) + (+1-2) pp 4 raa (2ap)
  25. 4bc = quC b.c), posito b manere
  26. et csieri 2apb., (+1-2) pp 4 2aa, seu C = -
  27. est
  28. vel
  29. = pp- 2aa
  30. rap b
  31. 31+2aa
  32. si p sit negativa eligendum prius, tC diversi signi a b, sxeundum
  33. priorem expressiionem gir p sit affirmativa, et c diversi signispotest
  34. utraque inservire ex pressio.
  35. sit e sit data = Y fiet H 1- 2) pp + raa
  36. 2ap
  37. seu apr = (+1 -2) pp = 2aa, et pp - rpr + rr = rr + 2aa
  38. (+1-2)
  39. 544 154
  40. et pr sen pp - 2rr (+ B rt traa (+1 22) si sit
  41. 5
  42. 4
  43. et p = 2r+ Y(rY + 2a a (+ 1- 2)): + 1 - 2
  44. Hinc si Y: a fit D. C sit
  45. si
  46. F12
  47. alioqui in imaginarias incidimus. Hac mefhodo dum reditur
  48. quaesitum adrationalia, etiam habetur determinatio
  49. sed recta 4bb 4bc = bb - 2bc + cc seu bbo - b. bc + cC =0
  50. b+ bb = 2. 3c b + 9cc = 9cc - cc = 9c, fit b: c = 212:1
  51. Cum vero patio C est minor, quam 1 ad 212, res ex impossibilis.
  52. reditr ad imaginrias et ((4bc qu (b. C)) est imaginaria
  53. dixx + lx tam X + (XX + ab, XXtaC) = AViXX t abi) + V A(XEtaC)
  54. fit A qu (Zax +lx tam) (X + ab xtac)
  55. 2X 2LXx. .) (XX tab, xta C) fir 1
  56. hPXX F Ex tan Y CX + ab XX + 40) = ZtCxC +
  57. e
  58. Rh XXF. . = 2V
  59. sit Au (hxY....) + (XX + ab, extaC)
  60. aqu Z (XxA ab) + WV (Xx +ac)
  61. An sic 62 + 10D = 210 + 1D si 669∞ + 0D F 2621 0D = 22 O F DrS + 2 10D
  62. fil qu =89 et Z= R 28 et v - a
  63. mt
  64. Uibi solum C et D) sunt datae
  65. . et 18640 + 0D = m66o + ac 44
  66. ac
  67. mmY
  68. sunt _ C et quaestae variantes,, M quaesita non varians. 8 et Q dant
  69. quatuor quaesitas non vartantes, et m est quinta, de er quae adhibendae pro
  70. qunque asqrationibus identificatoris
  71. si esset et + si B + D essen simelices foret _ d = a et Z= _ m teil t dG +BD rmnaC + au 9y D
  72. et f ubi non non habet locum successs, sed sidendum an non in retento t
  73. posito B, tD
  74. limas

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 2a, fol. 9v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068197:0018?run=74