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Leibniz-Handschriften zur Mathematik LH 35, 6, 4, fol. 65r

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.

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The machine reads it as

  1. fomula V + CC VV + f4 cit
  2. fiet
  3. a et
  4. ee
  5. ec
  6. aequandos quadrato quod sit a vv + CV + fF +VC
  7. 2)a
  8. geDHFD + 2CV3(F CBVD + 2HCo V (+ fD. et Doisi i et sublatis
  9. se
  10. de
  11. +2C p2AVB 42fe v
  12. t2eco 1s5+C + e. fiit P( e= f12)
  13. +
  14. +
  15. 4 2 ec vV
  16. + cocovv
  17. tollendis ac divisis omnibus per 2072c0
  18. fet vv +
  19. BCo trecot2V + f20
  20. 2Cd+2V
  21. ccote
  22. Tantum ergo opus est efficere nt cocotrecoerss sit divisibilus pe
  23. Hoc enim obtento radix quadratica extrahenda erit a formula quam non ingreditur nis altior
  24. gradus ipsius ed quam ocd. sed video nihil obtineri, quia ut sucecedit divisio oportet esse
  25. f4=
  26. e quo posito formula 1. non opus habet aequali quadrato, sed ei jum est aequata. Quod
  27. si ergo relinquamus aequaliores, 3 qualis est, fiet v ocotr futreo+
  28. e coconeo 5+ Sicotaecut affcoco
  29. qecoco escoet ous
  30. L decos. ge
  31. 4cd+ge
  32. ay S,d imusyt =O sit
  33. e
  34. co -3
  35. o
  36. bffccto
  37. a2e0
  38. ec
  39. ces
  40. 1bees
  41. v-
  42. 23
  43. (coraecoriscto
  44. +
  45. 4c0 +40
  46. que essot)
  47. Sed extractionem ideo non obtinomus
  48. yt = ex + f. et dy = edx: 2 (ex+ et fiet
  49. M eX +mm D: extff. Superest jam tentari alterutrum, pro depressiono
  50. O e (x SeCXX + 2eHX + +4
  51. +n4
  52. pro extrahibilitate Numeratoris debet fieri
  53. C
  54. utrum scilicet numerator sit possit reddi extrahibilis, an
  55. aut si mavis, divisibilis per nominatorem, explicatione
  56. arbitrariarum et F
  57. 4eC. f+mmff+ n= (2) reff+mme, Nam si _ a + b() = aa + 2 ab + bb etga a bb = (2) 2ab
  58. Ergo aeCf + Ammeess + antec 4 eef+ ammeess + mmee. sed ita fit nm ann
  59. Et evanescunt omnes arbitrariae, adeoque nabura sese opponit successui nec succedit quaesitum
  60. tte
  61. nisi in certo datorum casu. Qui intercta notandus time mus
  62. litatem numeratoris per nominatorem
  63. sed ita ut divisio succedat, deberet fieri
  64. n = 0. a contra Hypothesin. itaque sese
  65. iterum opponit natura
  66. =WYXX
  67. LVC
  68. ecXX + res X +
  69. Si faciamus yy XX+I3,: x + 21 fat (27: 8
  70. mne
  71. +s
  72. doiit
  73. ns
  74. Cx + B
  75. centemus jam divisibi
  76. Zex +mm
  77. syy= Lmmo 2oi A X + 13
  78. R 20X + 213. 11. 4V
  79. 4(8
  80. aneemnm se pr
  81. sit +mmyus +n=DD + nm DO +n
  82. +mn13. 2
  83. 2
  84. a
  85. se 122XX + 2, 12. 13X + 132 + nn 1 2XX + nm 12. 21X + nim 13∞Y (F KCX + 2n 2I X + n 21,: I sexr
  86. 2 (113
  87. et Aydy = 2dD - Dd8: F, = d CX (12. 20X) +12. 21 (= 12. 20X) = 13. 208: 20X +2O. 2IX +21
  88. (12)
  89. e)
  90. a
  91. 12. 21= 13.20
  92. Et denique fiet C = s= dx L
  93. p o
  94. 2oX +2I
  95. 2OX +21
  96. 12X +B
  97. (12 XX F2. 12. 13X8+ 132
  98. mXX + mm. 12B, X + nm. 13.2)
  99. AnEo XX +mm. 1Z. 1OX + n. 212
  100. +24 20.2 X
  101. Hic exitus reperiretur, si formula 12XX etc. vinculo radiciali inclusa reddi posset extrahibilis,
  102. vel divisibilis per (20F 12X+ 13. pro extrahibilitate procuranda e debet es
  103. 4. 12+ m. 12. 20 + nt. 20. 13+mm 132) + n 21
  104. 4 le
  105. (21, 2. 12. 13 + mm12. 21 + mm. 13. 28 + 2n. 20. 21 MH
  106. t
  107. 4. (2. 13)+ (4. 12 mn 13. 2D + 4. 12 nF 21 + g m. 12. 20. 133)n. 12. 20. mo 13. 2144m. 12. 20. n217 an 2013897 20 n 13 2000n
  108. 2
  109. e
  110. 20 +4n
  111. d
  112. 202157 8 12. 13.20. 27 2m 12. 21. 13. 2044. 12.Bmm. 12. 2+ (4. 12. 13um 1320)
  113. +4 n 20. 21 mmiz. 2D 4 4 nt 2021 mm 13.20) Et destructis destruendis, atque ordinalis secundum 21, 13, fit
  114. A+MF. 207. 13. 13 + M+ 122, 21. 21.
  115. 4n 20..
  116. =ap
  117. + (D. + 8 nJ. 12. 20. 13, 21
  118. = 2H4. 12, 20. 13. 21
  119. =0 quae aequatio dividi potest
  120. per m- 4n que 6
  121. mirum est, cum ita datae plane evanescant et fit 20. 13 +12. 21 - 2. 20. 12. 13.21 28
  122. (11
  123. et fit 20. 13= 12. 2). Sed ita foret yi = 20. 13X + 21. 13,:, 20. 20X + 20. 21
  124. et res siledit sed praeter intentur
  125. absurdum evanescit enim indeterminata X, et fieret, yuQ 13.2 e ad huc unum brevi
  126. ita et de divisibilitate formulae 12XX ete per 12X +. 13 obtinenda male ominor
  127. ut A in formula 12XK et dectruaatur duo temigi primi, et fit 124 nd 12.20+ n 2020 et 11 ∞0 sci et 20
  128. et
  129. 3. 13. + nm 20
  130. suarado pro rata fil. 12 ae et 1t aA et 2 . 13
  131. ue rornr
  132. nm 20+ 26Y m An (+ mm 20
  133. 2130- mZ0 + haom n 47
  134. 16fftoto 3 2fl0- 1618

Cite

Leibniz-Handschriften zur Mathematik LH 35, 6, 4, fol. 65r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 73). https://leibnizlegible.com/page/00068049:0129?run=73