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Leibniz-Handschriften zur Mathematik LH 35, 13, 3, fol. 94v

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: 0.82.

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The machine reads it as

  1. btot. 1707
  2. Quaeritur S dx t Cx + ab XX + c) Lsydx sit x = tal + san
  3. fiet XX = al. + 2atla x = aa l + 2 aa ln + 4 aa l SIn LGy =Cqu (+ fY In)
  4. fiet X tabXX + ac = aal + 6aa ln + aabl + ac + 4aa L2 An = yy = qu (ap + f L lu)
  5. yy
  6. in
  7. = aapp +ffln -
  8. + 2aa b.
  9. + 2a fp sIn ubi s constans
  10. fit BC 2al. + ab = fP et p = r + 2a l + ab
  11. 8
  12. et aapp + Bl = a aa ll + & Ca In + 4 aa b l + aa bl = H + 6 ln + bL + ac
  13. seu (1 4 84g eua seu (44a- f) H + (8aa 6) In + (4 aa - s5) bl ++ aa bb - ac ff = 0
  14. Nn
  15. nn +A aa
  16. Yn
  17. compendo
  18. d + p In + bl + aq.
  19. In + bl + aabb -ac f= 0= nn
  20. seu l + 8aa - 6f1(4
  21. HK
  22. 4aa -ff
  23. 4aa -
  24. Examinavi an l et n possent reddi simplices, ope constantis arbitria
  25. no
  26. hujes nm
  27. l= 10V + H et n = 20V +2+. quod F sed res non procissit, quod etiam praevideri poterat, quia
  28. non procedit, si l’exponas per 30n +31, cum tamen prior hypothesis ad hanc simpliciorem utique reduci
  29. poffit Efficiendum necups ut l, et n sunt simplices integrot ex eadem variabili. Itaque nec
  30. speranda aequationis depressio aut radicis extractio.
  31. Cogitavi eanda an non fingi possit
  32. aliquod imaginarium. Notav scilicet aequationem hujusmodi biliteram abmptotam posse
  33. prodninem homoeoptotam, produci posse ex ravice non homeveoptota
  34. fX.9X +ah ducatur in-gx + fy + ah, popuodit - fg(xx + f+ Xy + atis 25+
  35. rgy
  36. seu Xx - 5t +9g xy + abg - abif ( C - natih = 0
  37. g
  38. quae aequatio comparetur propositae simili ex +mxy +n GE + ap =
  39. y
  40. Ad
  41. ponames h= a, nam nihil prodest; porn 5 +d = - f E
  42. n
  43. 12
  44. a
  45. =ahig 52)
  46. 5
  47. e
  48. -+
  49. a
  50. taahh
  51. Ex ret aeg. 1 et 3 fint B + gg = aam: B. Ergo ex 4 et 3 firt f+g9 + 2fg = aa(m: p) -2(a. p)
  52. Ergo f +g = (: p) s(mp - ap) similiter ex 4 et 3 fit H+99 - 259 = aa (m: p) + (a: p) adeoque
  53. f-g = (: Y (mptap). Ergo 2f = (: p), impFap) SEmp ap) ut similiter erit
  54. 29= (. P 3d emp ap) - Emp Fap). Ergo ob aeq. 2 quae nondum usi sumus, seu 25 29 raa fiet
  55. +
  56. mpFa p) + Y(mp hap) Ampiap)- temp dap
  57. n
  58. 2a
  59. p, mp Fap) = emp ap) + semp rap t mp dap)
  60. mp F ap = mp + ap
  61. ubi reducendo ad communem
  62. denominatorem fit
  63. adeoque 2p . (mp vap)
  64. aap
  65. n
  66. 2a
  67. n seu n = a (mp. + rap)
  68. a
  69. Adeoque tandem un = mp + 2ap, quae est determinatio reperienda, in aequatione proposita
  70. ubi p est terminus ultimus, n penultimus, n antepenultimus. Itaque jam pro X et y redeundo
  71. ad priores literas b, n, firt erit pultunus terminus aabb - acss penultimus erit b
  72. +aa - ff,
  73. antepenultumus erit daa -bHE et fiet bb = 8 B, aabb - a C st + 2 (aabb - ac 55) f aa - B)
  74. Ana- H
  75. et
  76. W = ud qu (499 - f5)3
  77. seu (16abb =, e au sob) ans abld) = (8 a bb) BaC s6abb + 6uc 5 8 a bb - 2a bitsp. 8 ses t. d )
  78. dH
  79. Aabb +E = aC s sit
  80. 1n
  81. i eraneseente a bb, potest aequatio feliciter dividi per s et fun multis destructis fiet
  82. (6 C f - 8aaf + 16a = seu f = 4aa 20.
  83. sad eum valorem
  84. ad ribere non licet, nam per eum imogniae indeterminatae in aequ. O Qvanescunt
  85. quis si fariamus l = a fav +214, p0V + 11 1 n = 220a V + aa, :, 10v+ 1)
  86. fiet Aaavb + 2. 21 aav + h1. 21 aa.
  87. 2030aa WV + 2. 20av +a
  88. 20 apWV + 1. 20. 2 apV +21aap
  89. + 1. aaV
  90. 1Ba bvV + 1. 11 ab V
  91. + 1. 10. 21 abV + 11. 21 ab
  92. 10. 20 ab WV + 1. 11. 20abv + H. ab
  93. L
  94. +1. 10alv
  95. ita endu nihilo
  96. minus procede
  97. reductio qua
  98. diaturae
  99. 10V + 11
  100. av +21a
  101. 10a vv + 11 aV
  102. + c0. 21 av + 11. 21 a
  103. 10v + 1
  104. 2oav + aa
  105. 10. 10 aquV +2. 10. 1 agu + H1. Haq
  106. 10.20 avv + n. 21
  107. 110ag0.
  108. Ex primo termino habebitur 20 ex ultimo 21,
  109. controhendi causa fiat divellatur terminus prinus
  110. et
  111. et
  112. ex medio, 10
  113. a + 20. 20a + 20 p = 0
  114. ab + 20ab+ joaque = 0. quanquam nec
  115. et fiat
  116. it opus, possumus enm 10 dissimulare e
  117. cerminum primum ut
  118. solum 20 quaerere, Ex
  119. Cujus valorem subssituendo in . termino ultimo habemus 1
  120. 30 aV + 31 et quae rere solum 21, et
  121. caeterae se at 20 et 31 proderunt harm dutae obserrandae utiliad vitandes cactum
  122. e
  123. errores.
  124. prostat taare
  125. n= 30 a + g: Av+2
  126. ime proftatfmece
  127. = 10 a B + H1,: V + 21
  128. nnod. 2o ess fprturm f. F

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 3, fol. 94v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068200:0190?run=74