Leibniz Legible

Machine transcription of the Leibniz Nachlass

Search the Nachlass

Leibniz-Handschriften zur Mathematik LH 35, 8, 30, fol. 19r

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: 0.86.

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. 20v); this page is its right half.

The machine reads it as

  1. Analysis Fractio
  2. Omnis summatio qualis
  3. nferio
  4. dividendos
  5. 6S
  6. ex aquae est summabilis
  7. re-t
  8. 1 reducit ad propime
  9. hanc
  10. e-1
  11. saltem)
  12. F dx tandem reducitur ad
  13. X+b
  14. dx
  15. S.x +b
  16. x +b
  17. idanest sed et eodem modo sX, Odx reducitur ad proxime inferiorem
  18. X+
  19. o et ponendo dein b= c = d ex sed speciali tamen ratione idem consequi Bnam si addat si summanda sit X multiplicata per C quamcunque
  20. se
  21. ax reducitur ad proxime inferiorem, nam si addas X
  22. 21b
  23. ponatur x+b = XrC seu b = c, ita enim in valore ipsius (ax haud dubie evanesqe itaque omnis ut
  24. reducetur res eodem modo
  25. e
  26. eodem modo reducetur ad
  27. curentibus
  28. cum
  29. turam
  30. IX Dax
  31. 4d
  32. Hinc
  33. X+b
  34. si quaeratur
  35. xtt
  36. dx seu
  37. db
  38. Odx, res
  39. Sed suppositis tamen ipsis fractione
  40. 3dx et et reliquis, usque ad s0dx
  41. X+b
  42. Hinc et si O sit ipsa
  43. X
  44. . XX
  45. +b
  46. reduci posse ad s
  47. X+b, Xtb
  48. patet hanc quadra
  49. dx
  50. Xe +b, Xt b
  51. et praeterea
  52. a dx. quanquam potuissems
  53. ad nominatoris simplicioris summationes, ut (X
  54. etiam uti methodo articuli
  55. C+b
  56. Et cum hae rursus reduci possunt per artic.2. He hunc patet posse
  57. ta b
  58. x (Xe ax
  59. dx
  60. xtb, x +b
  61. sXe dx
  62. X +b
  63. habeatur absolute hinc sequitur
  64. saltem.
  65. posse demum reducilad
  66. X + b, X + b
  67. Et eodem modo pro cedetur in
  68. ebt seu p = (d- b) n 3: c-d7 quib substitute inde fieri
  69. dx
  70. O
  71. C, posito C esse
  72. per artic. 3 reducitur ad (ax
  73. Xtb
  74. ax
  75. X+b
  76. re dx
  77. X+
  78. .Nam potest
  79. XtbXb nam per quia redu
  80. , seu ad ax quae datur absolute
  81. X+
  82. intervenientibus X Oax et similibus, seu intervenientibus
  83. C-1
  84. quas artic 5 jam reduximus ad sax
  85. x+ b
  86. Ergo
  87. CXdx
  88. e- 1
  89. (X. dx
  90. x+b, xtb
  91. X+F3 reducitur ad (dx
  92. Xtb
  93. tunc methodo opus. Et puto supra dictam sucvessuram. artic. 15. quanquam et res aliunde (7) Et pari jure ac methodo unusquisque nominatoris gradus per inferio ree
  94. sit) Xax reducetur tandem ope cognitarum
  95. X+b
  96. reducetur adeoque
  97. saltem ad quadraturam hyper bolae seu
  98. (dx
  99. X+b
  100. saltem inquam, nam interdum fieri potest, ut haec evanescat, et quaesitum
  101. habeatur absolute, ut cum e = 0.
  102. fiet

Cite

Leibniz-Handschriften zur Mathematik LH 35, 8, 30, fol. 19r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 73). https://leibnizlegible.com/page/00068124:0037?run=73