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Leibniz-Handschriften zur Mathematik LH 35, 15, 4, fol. 11v

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.

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

The same scan as fol. 12r (00068206:0023), where its text is given.

The machine reads it as

  1. X xqX +r
  2. XX ∞ qXa.
  3. aX+btg3X
  4. 2
  5. 2
  6. X X H qX +r
  7. ax tozue 17X Ab
  8. 14X +r
  9. axt
  10. ax +ZX
  11. yg
  12. b
  13. axut bX + yX ∞ 4X + Y
  14. ax + b Fy + bX + yx ∞ 9X +Y
  15. ax - gX +
  16. er axtoty
  17. + bty
  18. axpbx2
  19. X3 x axp 467
  20. XXX
  21. yy x X9 ta
  22. bX cy+ d Z tC
  23. xxgetr
  24. yx ∞ +r - Z
  25. +
  26. a
  27. ra-Y
  28. =Y7a) +r79 - rz
  29. 1aq (+raz
  30. XA
  31. Z
  32. a - 9+ 7
  33. a +9+Z- 2ag + 2a7-29
  34. Sonse a atia a ra r
  35. a-4+
  36. =.
  37. Y+C.
  38. c t
  39. 2YZ
  40. erzue
  41. Ya -YZ a - 9tZ
  42. +Z, a -9t
  43. ra= raq +Z4 - rZ +Zat 39 +2
  44. =2Za9 + 24 7 -
  45. 12
  46. t
  47. XXL
  48. a - r
  49. X x
  50. Xx a +B
  51. X x a-
  52. a
  53. b
  54. +6+c
  55. e
  56. c
  57. a -6 -c
  58. aa
  59. tem
  60. a- F.b- 1
  61. xa
  62. X
  63. 1 qX + Y
  64. X X
  65. aX + Z
  66. ax (+ ZX
  67. axtaZe +ZX 1 qX + Y
  68. s
  69. Nit hinc
  70. demonstratia quod non detud formili radicus
  71. Cubicae imnginarias habentis, sine imaginaris
  72. sit aliqua a +F- b + Y a - (- b p c. posito
  73. Cesteatiam expressionem sine imaginariis, fiet.
  74. Yar lb 1 C - 3 a - f- b B C - v
  75. Ergo
  76. Ergo 2a p, C - 2CV F 3CY. seu v - CD + C7 22
  77. X H qX+ raysut XH bX + CX + dX + C
  78. X
  79. bxrxen dure
  80. XX c
  81. bx +CXFx ex H qX X sxt
  82. b XAbXrbdxabe qbX qcX qdxtqC
  83. XH qX + rx + SX + t
  84. bx Bx
  85. bXab B ex+ )
  86. at L. 6), C 2C J a- Lib + 3e a -b- 2ar. b ( (+ fb) atr. b
  87. seu 2a 7 c - 3C + 3C V
  88. a (t s- b) 1 C - 3ev + 3cv2 - v
  89. = a(t s. 6)
  90. X’H
  91. X H bX + CX + dXFe
  92. H bX + B.
  93. X a - bB - x) X (seu X H
  94. X p aX rx+ st
  95. 6+ c-9
  96. X bX + CX + dx+ e
  97. X5 bX + cx + dx +CX
  98. X+p X q X + YX + fX + t p
  99. - d C
  100. B 6X Ap X L Bdx + p C
  101. X - qX + r p d
  102. CnX aH =
  103. possibil.
  104. seu v2- cB + C p E - C + 2a p = C + 2a. Ergo + v +C Y S-C + 3a (Ego si 34 pE erit, v quantitas impossibilis aequalis ipsi 4C, - e42a
  105. BC
  106. 12 3C
  107. quod est absardim imo generalius adhuc ipsa C- 3CV + 3CV 2a cum requirat ipsam V solam ad constructionem eut possibilis C. determinuta per po 2C
  108. di imporsibilem Adhuc talilius forre. ponatur a DC. fiet C - 3CV + 3V EB. Ergo C- ct GV 1 9V - 3V +2C B v + 2C. Ergo C - 2Vp S. 2132G
  109. sed omnium optine sic. quia jam =V + E V. C +2 a et v est imaginam, e
  110. Nilcil est
  111. pt = CP+ CBH ZaV Madirembubicae affectae non posse exprimi sine imaginariis melius ita demonstratur, sit radius cubica non imarinarie expossa c. ejusvalor,
  112. a - f- b
  113. 3C per Imaginarias Ya + (b + _ aequ. C. ubi una eademque imaginaria. compendio ea vocetur v. fiet: V +Y aequc. et Vv + Yaequ cV. e virvu
  114. Sai. b
  115. seu a, +S- b q + YV aequ CVY, pro vo valor ex aego 4. fiet a + 1 - b f YB aeqo ccp = cr. Ergo
  116. grecdinset tu pr cotatias qoen se nas ri ps s sumtitasi n flliaribu
  117. +
  118. h = (bs- aequ pa +9S b, seu n. - 3bH
  119. qu
  120. q- 3Ch + b
  121. eqt
  122. ZH
  123. sem an qx, SY
  124. concludendum quo
  125. gaper
  126. quoritar an seuan Y
  127. seu an X HAY. seu an qX. 19 4r
  128. possibili. quod est as absurdum
  129. X B aX +Z

Cite

Leibniz-Handschriften zur Mathematik LH 35, 15, 4, fol. 11v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068206:0022?run=74