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Leibniz-Handschriften zur Mathematik LH 35, 13, 2a, fol. 14r

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: 0.83.

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The machine reads it as

  1. Saltem quoad variabiles)
  2. vel Hgy + bG +aC)
  3. Possumus rationaliter exhibere 1(gy + ab). Csed difficultatem reperio
  4. ranonalitatem ipsius CLZram) CNQ + ap)
  5. naliter lC vy t ab
  6. nta Z+ aapt) + (ZZ + fZ+ ag
  7. d
  8. yy + ac)
  9. vel quod eodem redit ad iapi) + Hea
  10. hoc modo
  11. cl Z+ am) + Y (n A + ap)
  12. et dge compendio y = fact + 1 a D. fiet gy - a0 + 2 a tOV, et gyt ab ducend
  13. in gy + ac, fiet d + 4 aa 83 1 (3.
  14. aa D
  15. + 2aa 3D
  16. aa 8fC
  17. + aa bC
  18. + 2aa b7)
  19. videamus an hoc possit coincidentiar
  20. quadrato a Ba Z +OD, qu ubi e est variam
  21. quod est taa 8 + 2a9810)
  22. +9937
  23. coincidentiando irrationale membrum irrationali fiet raa (O+ D) + 2aa lbtC) = 2a94 se
  24. fiet 8 Ca () = 2a (O+ D) + a Cb+C). Ergo hunc valorem substituendo in coinciden
  25. membrorum rationalium, fieti
  26. O + DD + 20∞ + (b+C) (O + D) + bc = 4 aa qu (0+ D) + 4ca (b+C) (C) +) + aa qu (b +C) + 99C
  27. effitiamus ut g D + at qu Cb+c) bc, dividi possit per O+ D, seu sit (3+ D) 6. ita tota aequatio
  28. SY dividi poterit per (3 + D sit O = 10D + ua et S = 20D tsra, et per aq. +. fiet
  29. 2) 10 D) + 44 1a D + aa (b+ C3 - bc ~ 10. 20 DD + 10 2 4D + p. 2 aa + 20DD + 21 aD, hinc
  30. C) inveniatur rationaliter
  31. + H. 20 a D
  32. prodeunt tres quae aequatio ita praestanda est, ut
  33. integre per D, quod ut habeatur ponatur 10C) + 2D + ita, in 300 +20d + 44a
  34. quae aequatio ita prestabitur ad scopum, si fiet () = 10s + na, et ex aq 7 fiet
  35. (+ 18 +3) + 2. 18. H a D + H. Ht aa
  36. (++a) +00. 00 37 +7.
  37. 00
  38. la
  39. +2. 0. 10 DDY, + 1. 00. dD + v0 1br)a
  40. + 1. 00. 10 (b1C)
  41. + 92 00 10 DD + 4, 00. 11 a
  42. aa
  43. Ex termino medio seu Y e 0D, fit
  44. + 10 =
  45. 1+44
  46. Eex 03 fit 10. 10 + 2 00.
  47. equatio
  48. 400 00 bc
  49. f
  50. id est singuli ter
  51. + (6V a 44:
  52. ODD + 0D + 0D
  53. id est singuli termini aequandi
  54. 10 = 1, (99. a0) 00. a + (4aa - 1) (00. 07b+ cH +
  55. + ae qus H.)
  56. +44 00. 1a + Aga (+2. 00. 11a)
  57. aa
  58. nihito
  59. 400. 001b +C))
  60. .
  61. 2. 11a + 00(b + C)
  62. 200
  63. 110. + 00. 00 = 0 sex 10- - 00 + 99. ca , f. u(t 19 2
  64. 2. 8
  65. -8aa + 2 - 00.
  66. 1+ 4 aa
  67. 10. = b. 10 + ac
  68. 10.10 + b. 10 1 bb = ac F = b1
  69. 10 = - = b + +(ac + = bb
  70. habemu duos valores ipsius 10 quos aequando habebitur 1
  71. sed mlasus habetur i ex termino ultiaro, seu oD
  72. vedetue compendiosias procedemus hoc modo: loco aequationis + per compendium cribamus
  73. 12 9B + C 1230D + 1245 + nona CD =0 fiat 0 = 10D + ua,
  74. fiet 122 10. 10D8 + 2. 122. 10. 11 a D + 122. 11. 11aa (
  75. 122. 00. 00 V B BgCC_1
  76. 123. 00. 10DD + 1. 123, 09. 11 a)
  77. ~01 +01+0d
  78. Ex termino priuo DD est 10too
  79. te
  80. + 1. 121 00 10aD + 121: 00. 11Ma
  81. ns et H1 = 123, 00 + 2. 12210 (u 3. 1Z =
  82. seu 10 = + =3 00 Bo (9 m2. 122
  83. diesC..
  84. Aursus xquos duos valores ut aequemus fiet 12+ 00. 0 ~190.
  85. redio
  86. 00.00 L 121, 00. 1
  87. C . ob e4 123. 00. 11 4 12100.003:, 2. 122 H 1 1121 00 Ex primo 10 10 +. 23 00 10 t B 00. 00
  88. + 1, 121. 00. 00 a D + 120.00500 aa
  89. - 121. 00.00 1. 121. 00. 00 123 (B121. 50. 00 1) (25. 4 11) 173. 00 122. 00
  90. 2. 122
  91. 400
  92. SV
  93. ( L∞. 16. +00. Lu io
  94. 4. R
  95. 3. 1
  96. qui duo vulores ipsius et sunt aequandi, ubi utrobius evanestit 00, quod adhisumius solum ut homogener
  97. (123.00 Es22) n300) (2. 122109 Y(3 - q 2)
  98. tas melins appareret jam restat una adhuc in cognita 4 vel 49, ubi compendio pro q4
  99. trbamus tar. Latet autem que in ipsis 1, 120, 12, 122, 123
  100. 120 = aa (bb + 2bC + CC) - bc et 121 - (4aa - 1) 1b + C) et 122 = (4aa - 1)
  101. et 123 = 94 + (84a - 2)
  102. a
  103. ad
  104. nam est
  105. et 123 - (d ag- 2)
  106. ubi b et c, sunt datae q est quaesita, et quia ubique
  107. comparando duas valores ipsius 1. fiet
  108. -2121. 122 + 121. 123 (121. 121 - 4. 120. 121) ubi ilud comm
  109. est q, ideo pro 44e possumus ponere ar
  110. si bene calculavimus fiet
  111. ((15 - 4. 125)
  112. ubi lud commode evenit, ut unaquadratione
  113. llatur irrationalitas; et fit
  114. ubi pro 120, 121, 122, 12
  115. t blg dev et fit, 7. 120. 1233 = 120. 132 123 4 121. 121. 122. 123 = 2. 121. 121. 122. 122 =0
  116. substituendo valores, in quibus latet qqe vel ar, habebitur aequatio pro que vel r, quae vvidetur pro r assupere
  117. ad sextum gradum, credibile tamen est, si res obtineri potest calculum esse depressionis capacem; si non in
  118. universum, certe in casibus notabilibus; et licet q non sit quantitas rationalis, nihil tamen refert,
  119. a seopam nostrum, modo sublata sit irrationalitas ex variantibus

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 2a, fol. 14r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068197:0027?run=74