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Leibniz-Handschriften zur Mathematik LH 35, 4, 3, fol. 7r

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: 0.73.

Original at the GWLB · Page image · Annotations (IIIF) · Download text

The machine reads it as

  1. nx
  2. XxIMX. aequari debet quadrato, et XX- etiam aequani d debet quadrato
  3. a XX +ax = XXyy fit aax ta Xyy et aa = Xyy- aax et x = aari, gy -aa
  4. aa
  5. aanx
  6. Aursus aaxX ga = XX vY sit aaX. ~ = xvo et a aa X - X WV et X = aapi, aa - vV
  7. sit ha-Wv = yy ga seu yyrvo = 2aa sit ay az -aa et av = tz- aa
  8. et
  9. fiet ergu ob pagy + a 1vv = 2a fiet auZZ 2a7+ ) + (t 2 2adtZ (F a) = (2a +)
  10. aaZ= 2a +. HZ. = 2aat - 0 seu aaZ F HZ = 20 + 2aat fit Z = 2aa, att,: at H
  11. 1 5
  12. ut y = a pEaat (a- aH;, a aq + H = a, rat + na - H,:, aa t H- y
  13. etrm,
  14. seumaC: et v lZ : a =a, seu v- Gat + (aH = a F att), :, eaa + H
  15. epuunct ut
  16. aa, gaa+ 4uet4a B a 2uat + V 1 aa - 4a rat ra (rai B 13
  17. seu v = a, Eat= aa + H, : aa + H A a L+
  18. gy+ 00 = m
  19. a t eL qu (aa + H)
  20. 6
  21. s
  22. are
  23. fiet gy+ vo = 2aava + t + 2 auH,: qu (aa +H) = 2aa
  24. c
  25. n = a B gma y A V
  26. mvaq
  27. Requla quaer antur duo numeri, quorum quadrata in unum addita faciant 2.
  28. n nome
  29. e in
  30. x et
  31. nete
  32. eitque x jam guaa Canin: quaeruntur duo Numeri, quorum summa
  33. in num addita faci quorum quadrati in unum additi faciant quadatum 2aa
  34. nea
  35. Fiat y = a, 2at + aa -, et v - a, 2a t - aa +H
  36. aa t
  37. aatu
  38. ata
  39. Hinc jam _ aa m:, gg. ap ana ffina vu pa =
  40. H
  41. +
  42. Hinc ry-aa = (4aD 4at- 4at a2ataat a (2a aa,: qu (aa TH)
  43. s
  44. seu gy.aa = 2 Aat, a- eat,: qu (na +H). Et X (am, qu (aat ) at (aa - H - at)
  45. Et X = aa m qu (aa +H): q aut 4at (aa = H)
  46. et X+ m = m n qu (aat H) + Aamt I4atm,: 4at (a a -H)
  47. _ = Xgy = maa qu (2at taa - H), : 4at (ag - H)
  48. 4
  49. a+ 2aat + t f qut )4 aB = qufeat taa (H)H, qu (Adt Faa L H)
  50. Ergo x, X4m) qu (aat H). qu (+at faa + H), : 16aat (aa - H)
  51. n
  52. 23
  53. Itaque Itaque quaeritur ut sit XX + mX = quadrato, et XX = mx = quadrato
  54. (autB
  55. sit X = in quadrat (aa +H) m + 2a met +mt = M qu (aa + H) ingulam te)
  56. v
  57. 4at - 4 at
  58. 4at (aa - H) tad (D. ad
  59. SietxX + nx aequale quadrato a m aatH, in tat f pa- H vet a X 1 4
  60. (7XX -MX aequale quatrato ac
  61. qua +4)
  62. seu X = m
  63. +at Gutua - H)
  64. 4at= 4a t3
  65. aatH, in, 2at aa tH
  66. 4a+ = 4 a +3
  67. Catm. aF
  68. Aaati qu (aa r H)
  69. fiet X =
  70. 625 + 3 2
  71. 8 64 X
  72. si aaaH + qu(aa -) 41 c. ∞.g (2a+. + (aa +t))
  73. in qu 2ab - (aa -t
  74. Ergu XX +IaX, in YX-mX =liquadinto
  75. p
  76. Aequ. qu ( 4 a a (= qu lo ne lt) u qu (aa + H)
  77. ab. (aa Lt), Caa + H),: 4 a t - 4a +3
  78. 1.
  79. 600
  80. et a = 1
  81. 1D- aa = 3
  82. Obraa = 5
  83. 4ab
  84. sit sit m = 3, e1- 2
  85. 25+2. 25
  86. 54
  87. 625 +600
  88. 1225, 23
  89. _ 7.25
  90. 5d

Cite

Leibniz-Handschriften zur Mathematik LH 35, 4, 3, fol. 7r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 73). https://leibnizlegible.com/page/00068000:0013?run=73