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Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 400r

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.

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. 399v); this page is its right half.

The machine reads it as

  1. sed ad simplicius redeamus
  2. (at Exx
  3. y = a v
  4. a+bXX
  5. datur ralionalite
  6. syydx. Ergo et datur (xydus quaeratur X per y et fiet
  7. ayy + bxX yy = a + aa Cxx seu fit X = Y a L a 1Y. Ergo dabitur
  8. . Sydy 1a- a gy
  9. byy -aac
  10. byy - aac.
  11. ita revolvimur ad priora
  12. sed praestat sic generalius y= a sae + alX+ m
  13. a3 + a nX + p XX
  14. datur ry rulco
  15. datur (yyax. Ergo et (xgdy. Ergo quaeratur X per y, fret
  16. agy +angyx + pgyxx = a + a lx faamxx, seu fiet
  17. XX +8) + anyy -a l X + a yy = a = 0
  18. pyy-aam
  19. seu
  20. XX +
  21. sen 5
  22. pyus-aam
  23. angys
  24. an gy- a + 4 pyy -aam
  25. pgy-aam
  26. eanny - 2anaLyy + aell
  27. 4) 2a y tapa yy
  28. aaine
  29. + s)...
  30. + taamayy aam a
  31. Pegus - a
  32. PgG-aam
  33. 1: (2) puu- aam
  34. ubi non licel destruere nec et, nec y aliuqui numerator vel nominas
  35. in valore ipsius yfieret extrahibilis. vdeanus an liceat
  36. farere totum extrahabile
  37. et 2X A.
  38. staannyt - 2atu gy + a
  39. in gy- al + Y -4 pa
  40. pyusnam
  41. sumngari potest
  42. dy
  43. pyy-aam
  44. 4a
  45. +4a m
  46. pyu aam
  47. qam
  48. Stagno st - 2a yy + 46t
  49. V-ap 44a.
  50. um
  51. a
  52. saarx fiet yy = aXX
  53. sit AB, X BC, y et y = a d aa = Xx
  54. aa = XX
  55. in est momentum ipsius ABCH ex AB, syydx, habetur rationali
  56. quadratura. Ergo habetur et Exydus. seu momentum
  57. ipsius HFCH ex AB eritque sxydus = -syu dx 4 moment.
  58. psius FB ex AB, quod est FB, y
  59. et
  60. erit Caxex ilaa
  61. Cyy-aa
  62. =asydy taa
  63. jam si (ydy se
  64. gy +ac
  65. e ryy. ergo
  66. x + aax
  67. aa - XX
  68. a taaxX dx =
  69. aa = XX
  70. per x
  71. rat
  72. ny-aa habebitur valore nal
  73. ejus differentia sagdus yntaa
  74. altem hansendente rationli sed yndu semper habebur valore rationali, si
  75. Ergo sequetetur etiam Y∞y-aq
  76. gy +aa
  77. haben valore rationalis licet transcendente, per X, imo ut jam patet est ria
  78. ju sit ratunalis
  79. tantum ergo opus esset haberi dus valore to rationali per x
  80. et yg, et gdys
  81. -a
  82. nsat
  83. ex Ygy-aB et gy, et codu utcunque formatam, sine interventu
  84. ystga
  85. Et video jam omnem formulam in qua
  86. alicuius radicum extractionis ratinaliter, per x haberi posse
  87. rationaliter perx habeantur
  88. y+aque
  89. et qy, et ydy
  90. tinde patet eliam admitti posse yt, et yddus et tales, quae ex jus, et ydas rursus
  91. gys taa)
  92. quia syu dx datur rationaliler, et adeo datur et sxydus ideo haec per X ex
  93. faa - XX ex Ax +. 2X dx aa x
  94. 1 (an - XX
  95. ornantur sed non licel transire ad dy, y
  96. yedq et
  97. a+x et dy-
  98. y= a l aaux
  99. gydus st dy
  100. sed nec hicquicqua litramur, aeque enim podeunt nisi ax, ndx, et nata
  101. naxp
  102. agAX
  103. quae oia possunt
  104. exressu exprimatur
  105. haber alimaliter per y
  106. Ergo rationaliter raberi pt
  107. -Xxyy + aa yy- a tadr
  108. XX= aayy -a
  109. X a +
  110. +aa

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 400r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068196:0795?run=74