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Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 184v

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: 0.79.

Original at the GWLB · Page image · Annotations (IIIF) · Download text

One image of two folio pages side by side, registered by the library under both labels (also fol. 185r); this page is its left half.

The machine reads it as

  1. XX q. X3. Pationales integne
  2. n aequ. x.
  3. v aqu
  4. v aequ
  5. XX
  6. X3
  7. Y nyo ox
  8. Veniamus ad irrationales simplices integras:
  9. v aequ. TX
  10. SXx
  11. x
  12. Ix
  13. VEx
  14. Ex
  15. YX. eu.
  16. Vxx iu
  17. es
  18. ete
  19. y aequ. 2
  20. 2Y X
  21. fYX
  22. 3 x
  23. dix
  24. X.
  25. XX
  26. V aequ
  27. ti V aequ X Et y aequ. X
  28. XI
  29. esx
  30. X
  31. ye
  32. s
  33. eia
  34. vaqu. B Ix
  35. LYX
  36. XHC
  37. ad
  38. 3 Sx
  39. 2st
  40. X
  41. Yx
  42. ri
  43. Habemus Ergo. Q vadraturas omnium
  44. simplices explicabilium.
  45. Curra Figurarum per aequationes
  46. deniamus ad compositas:
  47. Et quidem incipiamus a rationalibus: sit;
  48. ec Primum manifestum est b
  49. x s
  50. V aequ
  51. 1- X revocari ad
  52. X
  53. a+ bX
  54. ponendo Zaequbx
  55. Equidem manifestium est vel 1 permissum enim est mdicem indeterminatam
  56. tox
  57. A - XX
  58. x argere vel minuere quantitate constante a, itemue
  59. eam multiplicare per constantem, ut b. eadem manente figura quadrabili
  60. 1 -X
  61. manifestum est omnes rationales habentes numeratorem indeterminatum
  62. racta
  63. valores
  64. reduci posse ad eas alios fractos habentes numeratorem constantem,
  65. etoem primi frad
  66. ex. g. sit s
  67. ergo fiet:
  68. x multiplicetur per b fiet a +bk
  69. afbx a+bx
  70. X
  71. a+ bx q seu 1. Ergo
  72. a + bx
  73. seu bx aequ. 1- a
  74. a + bx
  75. de
  76. a + bX
  77. 7b
  78. similiter XX reducetur ad X et per hanc ad
  79. a+b
  80. aequ. 1. seu P x aego adtm
  81. a + bX
  82. Ergo quant redacta est 6X ad _ a, quae habet
  83. a + bX
  84. numeratorem constantem.
  85. a+ bx
  86. a +bx
  87. Nam
  88. X a + bX
  89. bb XX + 2ab X + aa aequ a + bX
  90. a + bx
  91. a + bx
  92. a + bX
  93. a + bX
  94. idem est etsi ad cubum assurgamus. Idem etiam ests
  95. quicunque. Et si sit compositus numerator
  96. etsi nominator sit alius
  97. X X + Cx resolvetur in simplices
  98. ea reduci potert ad proxime inferiorem gadum, faciendo Xaequ q + (R
  99. a + bX + XX
  100. het:
  101. Z+_R equ. Ponendo ae R + b R + a aequ. 0.
  102. + WRZ + RR
  103. b Z + bd
  104. x
  105. a + bx. sed quid sit si sit:
  106. qui singuli separatim resolventur modo dicto.

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 184v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068196:0364?run=74