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Leibniz-Handschriften zur Mathematik LH 35, 13, 2a, fol. 20r

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. 21v); this page is its right half.

The machine reads it as

  1. (99 +9b dy (yy + by + ac)
  2. y9) F by + ac = (y + v) =(9y)t 2yv + vr
  3. y = aC - vV, :, 2v - b
  4. y tab gu + ac) = (yy +av). (yst abgy+ ac (9)t 2avyy + aavo
  5. gy = aa vV - aeC,: ab - 2 aV
  6. (∞ + AWB +aC V H aa C).
  7. V +
  8. yy = aavv - ac, aa vv c ab - 2aV
  9. (yy + by + ac)
  10. b + Y (yy + by +ac)
  11. a +by + cyy + dy2. +C7
  12. f+ gy + Ryy + K y
  13. VV = ab, n = WW - ac, m
  14. n vv = abn = m WW = aCm
  15. vn Wu = nvv + ac m = abn,: m
  16. qu (ab = 2av)
  17. Y(y + b) + Yby + C) = Z
  18. (my + ab) = V my + ab = vn
  19. Y = vn - ab,: m
  20. ny + ac) = W nytac = WW
  21. y = WW = ae,: n
  22. n
  23. WH W = S(mnov L ac mm = abmn).
  24. entemus auliceat (yytab, gytac) seu ACy + ab vy + aabe) reducere ad HC. XX+. X+.)
  25. sit y=
  26. x S(L X + am) + (M X + ap). = (per compend) 1aO + 1ad
  27. fiet ys = ad + a D + 2a VOD, ergo si gy + ab, multiplicetur per rytac prodibit:
  28. + _3D + (b+0) (O+ D) aa
  29. + D
  30. + 4 aa (O+ D NO3 = y + ab vy + aabc
  31. + 2 aa (b + C).
  32. quod ut fiat aequale quadrato, ponatur ejus latus esse a + qYOD, ubi Q est variabilis simplex:. Xt.
  33. 164C)D + B bc d
  34. sed q est constans, etsi adhuc incognita, et fiet
  35. +aa 7
  36. +49 0
  37. 2a98+37
  38. ac
  39. sunt coincidentiandi
  40. inter se
  41. fiet fiet terminum irrationalem irrationali coincidentiando
  42. 92 = 2a (C +D) + a (brC), seu ∞ = 2a (0+D) + a (b+C)
  43. et terminum rationalem coincidentiando rationali pro e substituendo valorem
  44. fiet OO + DD + 6OD + (b+ e)O + D) + bc = EQ + 940D et pro DE substituendo valorem, et ordinando
  45. fiet (1 - +aa) (09 + 3D + 20DB + brc) (0+1) CD + (2 - 12)OD + bc - aa (bb + 2bC + CC) = 0
  46. Hinc si b et c non essent plane data, sed arbitrarii alicuius capacia, res procederet, faciendo enim
  47. 2 - 44 = 0 seu q = aa s2 et b6 - aa (bb + 2bc +c9) =0 fieret 2bc - bb - 2b1 - cc = 0, seu
  48. fieret b = ced c = b f-1 et ita exaeq. 5 fie et= (O + D) + (b+C) =0 seu O = b (1+ -1) - D
  49. 4qdividendo
  50. Sed talis epsus ubi in datis sit C = bs. 1. meeonunquam offeretur. Itaque videndum an liceat obtinere aliquid
  51. generalius, per compendium sit 2. dt = β et
  52. possit dividi per D1D fiat O= sD + g2 tar
  53. bc - aa (bb 2bc + cc) = Da videanus an B()D +Zaa
  54. ttee
  55. ensiteri in jate
  56. G1 +g) aa
  57. et O+D = (5+ 1)D +94 +at, quod mulsiplicetur per YD
  58. (F,) N fiat d = ft + gr4 tah et D
  59. A +Ce jh +K 2 + A, es e
  60. et (30 + Jaa = BfikB +gK Z 2 H(HK L7 Ha fAF, aBX Y tbaahX
  61. +Bgi 12 Ha hi G HatR 2 + a
  62. 01 fh1 47 + at in vie e Hende 5 tusot 13 ve
  63. X. + aA l 1et) p 2Z HtunZ F ariset,
  64. in (at + X4 + a dabib)t
  65. B astr HaF +at+ (i 2
  66. exagu sint fftik rggi rfait
  67. Bor+7aa
  68. quae concidentrando fit i-B etA
  69. h+N a
  70. restant 19 hes aegus, H+ Kt ti si
  71. aa Lthi fiiht+ efi
  72. q) V
  73. gathit 2) get. X L gk 20 Fonstrg
  74. Fagtum pro Kponendo K, et prog ponendo h, et fit SA- hc -0
  75. Fst fk - gi -b
  76. Ex altera aequatione prodit idem
  77. extertia aquatione nt protit idem qued exprdinen tiles ua ia tiitat bun i te i

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 2a, fol. 20r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068197:0039?run=74