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Leibniz-Handschriften zur Mathematik LH 35, 3 A 2, fol. 34r

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: 0.81.

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The machine reads it as

  1. aquationi
  2. 14
  3. addatur aequatio multiplicata per arbitrariam h
  4. et fiet K + l K + mK. +n
  5. + h K + hcK + hd
  6. = hy
  7. equatione 18. K - e K2 - fk = 9
  8. = co
  9. 0
  10. 17d
  11. quae comparari potest cum
  12. aequatione 18
  13. Rursus aequationem 12 multiplicemus per quanticatem K + fier
  14. K3 + lK + mk+ n
  15. K + G
  16. K3 +(BL +mRK + n A (22)
  17. l
  18. +K + lK3 +mK +n K
  19. 10
  20. K + SK + +K + VK +W p0
  21. igitur ut reapse comparemus aeg9. 21. et 18. ac 22. et 17.
  22. in equ.
  23. ita procedi debet quaeratur _ co per y ita ut contra se invicem
  24. et datae
  25. pollantur, de reliquo s. t. v. W. sunt cognitae et reliquae omnes
  26. assumtitiae. Comparando aequ. 27 et 17. per quatuor collatitias habebuntur
  27. literae quatuor l.. 9. l. m. n.
  28. comparando vero aequationes
  29. 21 et 18. primum ponemus co p, hy. ut literae co et y. destruantu
  30. deinde ope reliquarum einde reliquas c. d. quaeremus per c. f. g. h
  31. ex quibus tres sunt super numerariae itaque compendii causa, ponendo
  32. (22)
  33. (24)
  34. 1) 10. et eri 0
  35. (29)
  36. cdI - ly.
  37. 8
  38. 30)
  39. 3
  40. S-l mpi + - Is + P
  41. WH + Sv + s+l - 2521V +5 13 - 14
  42. t + st. - + +2s
  43. =W - v. -
  44. +s+.
  45. (26)
  46. 62)
  47. (2
  48. Cri m
  49. nei v -s+ +15 -
  50. +tl -512 + l
  51. 2
  52. + + -53. +s
  53. + v + U
  54. sed inde patet, et facle praevideri poterat calculum istum esse
  55. inutilem, seu non deberi comparari aequationes 22 et 17.
  56. equ.
  57. 7
  58. quae comparati potest cum
  59. X si adtt ox + cX + d
  60. + P X + 9 p
  61. paX + pbx + pcX + pd
  62. +py
  63. +bX + CX + dX
  64. + yX
  65. aN + abx + aCX + a
  66. +ay
  67. X + pb X + pCX + pd
  68. C
  69. + d
  70. pat b +a + ac + ay
  71. + 9y + iy
  72. a X + b X + CX + d
  73. - e-a
  74. - f X
  75. =0 - a
  76. e x2 = fX = h
  77. 1, - lX
  78. = n X
  79. = myX q = βy
  80. V+ dy V+Sy
  81. + py
  82. + ab + y h+ ad
  83. per compendium X + e X + f X + h X f o
  84. X
  85. X
  86. =
  87. 70
  88. pa+b+a patbta
  89. +7
  90. +9y X + h + iy X + d+
  91. eoa
  92. e
  93. fier: X + B _ X + e
  94. +A y. + Ey
  95. 10 + y
  96. rgo 10 sed jam omnino video methodum hanc esse inutilem
  97. novissime enim necesse est fieri vel X1) y + 8 vel X7 3 + gy era
  98. itaque sic poteramus initio supponere
  99. in aequatione X + pX + 9 10. ponamus
  100. Py + N
  101. a y + hy +C
  102. de + fy +g
  103. ayt+ In aequatione data sudst aliqua assumtr
  104. substituamque atrum
  105. (I valorem, ouctuo alia cum incognita altius oscendente, utique prodibit
  106. equatio altior priore, ut si in aequatione X + pX + 9. pro X substituatur y
  107. Ergo X ay + 3ay by +3a stc
  108. faciendo XpaV + by +c.
  109. dyr + ey +f V
  110. seu X, ay + 3a b y5 + 38Cy+ +6 abc y3 + 3ac y
  111. + 3ab
  112. + b3 in +3bC..
  113. +3ay by +6ay bcy + 3ayC
  114. +3bey+C
  115. V +3d Cy +3d fy 46 def y3 +3 d fry +3efy +f
  116. +3de) +5 .. 43ef.
  117. + B3y + 3bVc +3b98+0
  118. et
  119. X
  120. jam
  121. s
  122. Ergo X + lX + n
  123. + m y +β7
  124. a
  125. et
  126. edus

Cite

Leibniz-Handschriften zur Mathematik LH 35, 3 A 2, fol. 34r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068215:0067?run=74