Leibniz Legible

Machine transcription of the Leibniz Nachlass

Search the Nachlass

Leibniz-Handschriften zur Mathematik LH 35, 4, 3, fol. 43v

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: 0.78.

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. 42r); this page is its left half.

The machine reads it as

  1. e
  2. de Xx - yy = 1
  3. XX ZZ = tum
  4. yy -ZZ = nn,
  5. fiat
  6. Xty = fl.a unde n A . ras y-f a. l. raf jum draad lnos = puraa, m. raque
  7. xtque = gm: a unde X =
  8. gm: 209, g = 4g ga, m: 2a9
  9. 9Z = hn: a unde y = hintoam: rati Z- hh -aa, n: 2gh
  10. 1= gytea f m n = gg-aa h et fiat L = htr + aa.
  11. ftaa g
  12. hh- aa a
  13. ff-aa) h
  14. Sf . a, 1: 2a f = hhtaa, n: 2ah
  15. g9- aa, M. 2a9 = hh- aa, n: 2at
  16. = 99 + aa, Bhh -aa (f) Amlicet facere hh = g9
  17. fftaa, 99- aa, (h)
  18. nec ff-qu
  19. siferet s = hsi fiert htrua jau stua = Notua. sed hiff.cula eficietur ut gytua ge. pa sissum hut
  20. 1faa +oguaa
  21. Itaque pdeundum ad aequs , suagu + a = +gina bi fiete C g = D d 9d bb + 2bga a + a,
  22. fiet aug gabb aag = bbus +2aab, seu 9 = 2aab:, aa - bb a9+a = auqu (bg + aa)
  23. c(9. + b = b9 + aa ap bciul (G9 + aa, :, gg -na = b rg b9 taa,: ((9- a) = qu (85taa, ff - aa) et pro ponendo valorem
  24. 2
  25. 3e l
  26. fet C= _qb tgea; Zb- ata - b E
  27. Unde tandened
  28. et agndo daosi valores ipsus 9 fiet perab: 1aa. bb = pa a i c G
  29. Estaa, ffaaa
  30. Z aabb +4:, a ab +B3
  31. C= Ga(aa +bb) f55 -aa): (Sstaa) (2ab - aa - bb) = aa:
  32. unde Cnabe alt = aC aabe) - b
  33. aabo
  34. seu C= aa bb ta, aaBtb.
  35. seu c2 au:
  36. seu b Caardet s5 - aa) = a (st taa) (2ab - a a - bb) (5 - na = B(cit a b -a) e (b- a))
  37. b(ca tl6) ee = sf tna qu Cs5 +aa) Ergo suffecertit
  38. Aliter ex pag. praecedenti, si XX =gy = l et XX - ZZ = nim et gy. ZZ = nn, fi
  39. fiet 2XX = l+ nim -na et 2yy = Hma l - mm + un et 2ZZ= U+ mntnn
  40. Ergo qualibet horum devet aqua summarum debet aequari dimidio quatrato
  41. sit tm bin = (f: a) m et x = poria fiat 2ppmaa = Am) (f: a) on ((- n tnm seu Eppm: aa = ff: a) (l- n) + m
  42. l+m (4: an et y = gn: a fiet 299n: aa = (g: a) ((_n) + N sed culiudo absolito evanesceret, 1, m, n
  43. denique n = (k. a)m et Z = rm:a fiet 2Yrm: aa = (h1 a) (+ 1) + in
  44. Ad piius videtur brevius
  45. Artic hoc: l= ext G +C n = X +Z+f
  46. Alibi 3X - (379 = D (Dmm-(2nn
  47. (1
  48. fint X + y = b in + bn xc
  49. X- y = 4m 1 qn
  50. Utpry = bm + ln
  51. (DXX 7Z-Obm-dnn
  52. X = l + p Z = n 4
  53. Elp+pp Bng79= 0
  54. 2lp +pp = 2nq + 44
  55. Utp y=4 me4 an i q-
  56. (4
  57. y +n +9-
  58. 3yy-
  59. 3 + Z
  60. y-
  61. cl(F am
  62. y - n -9 = al + am
  63. n = y + 2+9
  64. = (3I1-3) mm
  65. =. El A)on
  66. = 2l(B2m
  67. ope harum ua aequationum quinque invenientur rationaliter t, p l, M, n, 9,

Cite

Leibniz-Handschriften zur Mathematik LH 35, 4, 3, fol. 43v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 73). https://leibnizlegible.com/page/00068000:0086?run=73