Leibniz Legible

Machine transcription of the Leibniz Nachlass

Search the Nachlass

Leibniz-Handschriften zur Mathematik LH 35, 13, 2c, fol. 198r

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 machine reads it as

  1. C
  2. ractavi alicubi de differentiis inter eodem modo denominatas, tam Arthmeticas
  3. quam fluxionalibus seu Geomebricis. Ooservavi autem ifiliter fortasse hine aliquid duci posse
  4. ingendneris, n pita eorum s aggregata aut alia ab iis formata. Exega. et
  5. 1
  6. s
  7. tos Et sane intendum fit ut quadratura aliqua redecatur ad aliam smiliter formatam. Exempls
  8. gretia log summ loc sex log +b) et (dx CogX pendent ex se invicem Nam ( lo loq Xlloq X+s
  9. s
  10. diferentati gedabit dx logX+6) + de logX. Ergo log. X. loq (X+b) = (ax logk + b) + (at logX. quaeramus
  11. x+b
  12. A+b
  13. Ex logse +b)) = y et ((aX log X) = v, fiet d dy: do = (xt b log (Xt b): XlogX
  14. X1b
  15. sin dy ad dv ut lognt logX logk+ B ad logX logx+B M+b
  16. p
  17. aliam inter haec relationem, sit
  18. 1
  19. seu talia sunt reciproce ut sua XlogX
  20. ay: do = : dy + dx = dl Ergo du = dl- dy = mdy: a
  21. tognt Xeb, log +b)
  22. a ceris, e itemque ipsas ay et deu esse hetervienems quantitates sed
  23. s d y +. v = 1
  24. non esse
  25. logX
  26. at.s
  27. cicet pit
  28. et v- (X logX + b) b93
  29. logX. log(+b
  30. dit hogotentus quantitates tuli modo hnam y. (ax ex lo0x
  31. Notandum
  32. pti X +b, log (xb
  33. nat tamen otest neque enim ut unius nominator ita et numerator ex altero formatur
  34. lonoee
  35. sed sintetemem differentiae tamen seu dus et do sunt inter se ut homogenea quantitates ejusdem
  36. tamb
  37. e
  38. foruet, sunt enim ut 1: XlbgX ad 1: (X+b, log(X+ b),
  39. x ita secari in partes, ut ex logX log(+ b) forent quantitates
  40. constantes, quod utique in potestate est, foreut sa y ut ad v, reci proce ut
  41. summle X logx ad d summ. X+b, log( +b). sed tales summalum exscressiones quibus
  42. si poneretur
  43. ds
  44. enes homogeneorum violantur juvare non solent
  45. e
  46. (X+b) =y. sit X loq Y log(X +b) = log y
  47. = y. Ergo V logZ = logy. Ergo vaz. Z + ZB logque dv = dy: y. sit
  48. b + X+
  49. am v aa: Z+b sit jam
  50. Aliter
  51. qu l0gX. (X
  52. ( Glogxa
  53. 19
  54. et D = caBe (ee aa 10G +b)
  55. fiet vv 9udzue. Z +1log2 dv = dus = d
  56. C
  57. s
  58. Vd + 08
  59. 1
  60. Vv-
  61. ado du
  62. xidque + ~ logdze dv
  63. logx d =y fit dy = dxlogx AdeslogXdx . Ergo A hujus summatatur. M, datur summa)
  64. D = y
  65. sot si foret gd. L
  66. XyR(Lu t) dx = y Xy- P5 Coqxib et Xdu +ydX-
  67. G
  68. G
  69. b
  70. N+b S
  71. logx ax mg axu)
  72. y - logX dX C Xt
  73. A+b
  74. logx ex
  75. g
  76. (1
  77. a dx. lo1 + dx
  78. Ergo du: dx = log. X i Xtb
  79. datur e summa C
  80. afxib, 9) xib dy ydx logx ax

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 2c, fol. 198r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068199:0395?run=74