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Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 159r

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: 0.75.

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The machine reads it as

  1. a22 + 2f = ( prox
  2. fy2) =B. 2Y 10
  3. 2 + AE = 0 13 es y2. (apor. 27 3 f. u)
  4. L. VDE auonon v nos
  5. y: 4n22 + V oE mo a2E+ voE
  6. a22+ 212 =
  7. 311+ vo1 =O
  8. pos
  9. st. D2L = LiE H0 ps BA2E = 22
  10. P = 21
  11. ps vol gnos
  12. JL. (aG22.
  13. +
  14. 2n +62. pra f. ( f1+ b f. 2
  15. v 22
  16. nos f. 1 + E. 2-) =( 102s
  17. = vI
  18. y oses pagna sug ro oceprumero e nnssod sep. n e3e
  19. =
  20. uvisro funs ny ev: 0E. ZE 1 absi vig
  21. y: av22+ yuec nos
  22. y2: ay22. 2 + ∞ 7 f11 = 6 nof a22 + yr: 2 f1 =
  23. a22
  24. Y2+ EfH bxpE. 2) ns
  25. f: 28n + vb oE. 2 nos
  26. 12: f11 = 12
  27. smos
  28. y injnquis
  29. hus orieuis a
  30. f. bor. 2- = 0, groz. 0- d2 75 fib0c. 2 - f. hpar. 2 = 01
  31. bopZ. fn = 12 quo er f. 6112. 2∞4 gun,. 0 -1C prs f. b12.2 - f. 6112. 2 = 11
  32. ay = V(X + ab XX + ac. fiat X = sam + san Erit
  33. XX = am i 2a smn et x= aamm tbaamn + 4aam Vgrin
  34. an
  35. nn
  36. Ergo x + abxX + aC = aamm tbaamn taabm +aec + Aaamqtmn
  37. + 2aa b)
  38. nn
  39. videamus an et quomodo hoc possit identificari quadrato ex apm
  40. ubi p variabilis, sed f constans, fiet 12) (ap + fsma) = aapp +2afp rmn ident
  41. ficando fiet s ob irrationalem partem fp = ram ab superest aequatio ex ratio
  42. in
  43. nali parte aappeffmn = aamm +baa nn + aab im +aec, Haec aequatio multiplicetur
  44. utrinu per ff, fiet aapfpp +ftum = aaff, nm + 6matbm +ac, et pro ffpp substituendo
  45. in
  46. avalorem inventum fiet 4amm +. 4abm + abb + Fm= aa Hum Faassmn t aatsbm +affe
  47. inn -a au B et 4. saut
  48. 4a- aas
  49. vel gaa s) mn +(F +Ba= 6aass) mn + Aaab (4aa - ff) m + a bb
  50. n = affc
  51. 4a . - aaass 12
  52. tmtal + Se. agis (a F rd)
  53. 64F 8a- 2f + 3f -6 ffaa
  54. e
  55. 5 - 16, a + 24 a - 6 aaHf, ff. Jaa, S. t aua P. _ Win
  56. Aa
  57. aamm Figasum tantm Hnaeit-a Csf. apa, st - ica
  58. conpendio gun + h hun + al in + _C aa K A = 0. fit M
  59. posito ll = k, h1290
  60. nn
  61. Debet numerator dexteri lateris fieri extrahibilis, aempe un 4 rahl- 4 agl m + aall- aagk
  62. lin- 499
  63. +
  64. 49
  65. fiet ∞ mn +2q eY ii erit ats alil- 2agl) - aull- 4 nagk
  66. tih- 19)
  67. Nam
  68. hh- 4d
  69. qul tin- 49g
  70. seu qu qus ht - 2gl) H 49H, sib - 4gg sen l ha = H apti, h + 29
  71. hagh- 29 = 4a - s (3a- baa H (8a) haas = f at h + rg = 5 18a buas 19a 8ao H. J. aa ti1
  72. l = a bb (f- ∞aasf + 164) 49t = 16a, au 55, abb - f5C = b a, a bb - s2c - aaffe
  73. ea U-agk = a bof (abb f (+ 16 a bb - 16 a b) E 6ac f + 16 a st C ( 16 a dbs p)
  74. (
  75. Ergo ex aeq. C) fiit a bb ff- 44, s transs = ( a abibsB 1b actf + 16aC
  76. 2444bb
  77. siet bbss + 2abb= 4 a
  78. (Obb, qu H 4aa) (H) Hrraa- A s
  79. auc aal qu
  80. abH
  81. Ergo ex aeg. d fiet
  82. Saat H Agk
  83. seu l = H -Egk
  84. qu lh+29)
  85. ibbff
  86. tit (Uh) = H129 = Uh) + U29 9Kh - 8ggK seu alg- otih + 2991
  87. seu Al = Bgk + hk seu l = k, h+29
  88. l = bb qu (qua - A K = abb. - ffC - b - 5 + 8 a 6au f g - t a - 4aafs
  89. 1ba 1164 -
  90. g = aa fit h+ 29 = 40a - A
  91. h+2g = f + 164 - 14 aa ff
  92. it tit abb = bb- BC, 4aa- ff seu abb = abb - Ac. quod est inconguum fit erim C = 0 cohaspotitu
  93. fiet II = bb K = abbu Hfc h = raa - H
  94. 2aa - f
  95. Haa - st
  96. (sg (m +n) t G) = g+ G. B n
  97. MH
  98. 49
  99. n + hmn+ln + K
  100. en
  101. Datur gum tabma + lm +k =0 quaeritur pim + g, mB Y = pmn + 2poma + 9 m + Yq
  102. + pr
  103. . +Y = um + 2 mn + gip) in Fr9
  104. r
  105. fit h = 29 et K = l1: 4g
  106. un
  107. Datur nn +h mn +lm +k =0 quaeritur P n 49) Dh. fit h- 2 BY = k: 9 et Z + kp =l
  108. n
  109. nn
  110. hini in mistro casu ff- raa = 2aa
  111. seu = aas quid conlicet
  112. seu 99 + Kpp = l p 9 se q9 (p) + t pp = ql p 1
  113. et 9 = =lp + L p SC H - 4K)

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 159r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068196:0315?run=74