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Leibniz-Handschriften zur Mathematik LH 35, 13, 3, fol. 186r

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: 0.77.

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. 187v); this page is its right half.

The machine reads it as

  1. sive 16d
  2. Expuncto dato minimam ducene ad sectionem
  3. Conicam datam:
  4. Punctum datum esto D, sectio conica dara AY cujus axis AX vert A
  5. distantia puncti dati ab axe, DFd et distantia puncti f a vertie
  6. erit AF. f. centro D radio DV describi debet circulus qui
  7. curvam AY tangat in Z sive qui secet in duobus punctis Y et (Y
  8. distantiae infinite parvae; ponamus punctum D. esse vertice A,
  9. altius, et ipsa curva exterius, ut in figura vides; eut GL, FA+ AX
  10. ved G
  11. D , DF= XY et ponendo AX X et XY
  12. 8, sive p 2aX + aX, fit et DZ, S fiet:
  13. 1 d - 2d Srax + a X + _ax + a X + f + 2fX + X
  14. a
  15. 2
  16. (dax e 2d Praxtax Bd + rax fa X + f + 2fXx + X = s
  17. de+s hatr
  18. L
  19. et ponendo + 1 + a B , et 2aK + 2fX B bX. et d +f-5r, ta
  20. a
  21. et aequatio 2d Srax+ax et qudrundo ( +Y X +bX + ta
  22. 2
  23. 4
  24. 4daX + +d a X ( X tYbX, 2YtX, eb X r abtaK + tat
  25. Ju v
  26. a M
  27. 2
  28. ur
  29. + 2VbX + 27 X + 2bta X + ta pjo
  30. ta
  31. +
  32. 1..
  33. +ada.
  34. -8a
  35. estat una conditio ad determinandam hanc aequationem, quod scilicet
  36. incognita X duas habet radices aequales, quam multiplicando per
  37. u extde
  38. a
  39. Huddeniano invento; habebimus aequationem
  40. Ergo te
  41. qqo t
  42. s
  43. 4V X 16)bX , 2b
  44. a
  45. Foa
  46. n- 4 - 2b a
  47. novam.
  48. 4γt X + 2bta X
  49. 2 b
  50. i +∞ da
  51. = 8d a
  52. ed’a
  53. possuntque diversi indagari
  54. valores ipsius + ut inde
  55. eliciatur simpli cissimus
  56. Sed satius est, opinor, in hoc quidem exemplo, Cartesii methodum sequi, is
  57. umadices aequales habentem
  58. nonotur
  59. Xrex + epjo per aliam aeque arbitrariam multiplicare hubet, ut per X +CX +
  60. qua ducta in X- 2ex te
  61. ex Term. 2. C
  62. ur
  63. a
  64. 4
  65. se
  66. a
  67. 2Vb +2)C.
  68. fiet aequatio factitia similis datae, nempe
  69. 2Ye x3
  70. a
  71. X
  72. +C =2C
  73. peunt n eie
  74. e
  75. + s
  76. E lam. s. tra
  77. + et X + he
  78. -2eh.
  79. Quae si conferatur datae
  80. superiori tunc habebimus
  81. Aequationes collatitias sequentes
  82. vel an 1e
  83. per. 2d ax+ 2acp fX ju ex +a
  84. X+ beaee
  85. dvrax + ax
  86. +(6X)
  87. fiet ergo:
  88. quadrando utrotique
  89. ta ax+ea
  90. So
  91. pta
  92. Hve, que X teg
  93. raxere tre
  94. Hia axAd2X et quadrando.
  95. (
  96. ad
  97. abjectasque rursus
  98. qqae
  99. assugunt, ad et et ordinando.
  100. edap
  101. id
  102. d
  103. a+
  104. X
  105. bet rex 4d..)
  106. a
  107. vere
  108. fat
  109. 764 dea eX + 16d
  110. rbe +abex+aCX
  111. 1
  112. 2AX +2aC

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 3, fol. 186r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068200:0373?run=74