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Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 200r

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: 0.87.

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. 199v); this page is its right half.

The machine reads it as

  1. Eisso per 7 15 116 fit deo - Gt, glogys. ylogr
  2. seu cut
  3. d
  4. seu erit do =) (olog - y log D + xlogy - Xlog X + X (= vlog d F ylog - q ixy seu siet
  5. dv = (16) Xlogy - X logX + X - y, :, X - y.
  6. 7
  7. lonc
  8. Ex 7 est deo . df logdv: log.lz.
  9. Sed video
  10. Erqu per 15, 16 fiet = xlogis - xlogX + X - y, :, y logy - y log X + X- 7
  11. jam ips = Y: a. unde sequeretur V: a seu valorem datum ipsius d dy: dx ex x ety
  12. demum sub finem ingredi in calculum atque ita omnia exempla eodem modo tractari
  13. per regressum generaliter
  14. snon sivce
  15. quod parum credibile: Et vel hinc demonstratur quod
  16. res non pottest demonstrari, ique enio aequ. 17 differantpando rediret dy: dx = Y: a
  17. redeundo ad aequ. g. et sres
  18. oportat igitur ut relinquamue. E du
  19. dque logdque dque + haco d lon dv d. jam deo = Glogd f log dv: logd Z. Ergo
  20. Hinc explicando
  21. jam datur
  22. (10)
  23. ex aeq. 9 fiet dZ logdz - dZ + h logdv: logdz = de logdo - de
  24. des per dZ et du ex datis, habetu t dv: dZ per logdz et log dv
  25. do: dZ= X y: X (per 2 et 3 Ergo log de logdzue + log(x: y) Hinc ex aequ. 11 tollendo
  26. seu de = dZy.
  27. durdx de et log du: dz et logdo, habebitur aequ. (14) in qua datur logdz per
  28. superest aequatio una ex duabrs
  29. X et y, vel a, et log. log (X: y) et X: y
  30. 2 et 3. nam ambas jam conjaux imus in aequ. 12. sumamus ergo
  31. aequ. 3 X: a = dZ: deo jam seu ex 7, X: a = dz logdz: stogdv seu
  32. F: a = Z logdZ; de (logd Z + log (X. y)) ubi to obt dz: d, tollitur az, ut restet solum
  33. log d+. in aeq. 16) quam conjungendo cum aequ. 14 a tolletur az et habebilus
  34. aequ quaesita qu(7) in qua solum X. y X, y, et log. (X: y)
  35. dy. de 1) X Xy: aa H: a = (2) du: du
  36. satis simplex
  37. et Xa = dq:deo. fiat dy. de (4) = dav: ddZ. Et hos tres valores substituendo
  38. Sumamus exemplum pli
  39. In aequ. data, 1. fiet ddv: ddz= (5) dudz dcodu. definienda jam est valor
  40. ipsia so, seu afsumenda progressio fandamentalis, st ergo dvaz: dcodio = (6) sa seu logez: logtr
  41. unde fiet ex 5 et 6 fiet ddv: ddz = (7) logau: logdo. adeoque dar logdo = ddlogaz
  42. teodu- dv
  43. et X: a = (3) dz: , et fiet
  44. et quaerando dZ logdzue - dZ + hdco = 18)
  45. dy: ex L X: a sit g: a = video
  46. et hos valores substituendo in aequationedita)
  47. fiet: dav: ddze = C5) dZ: deo definendus jam est valor ipsius deo
  48. seu deo= log dz. loglv: logd2
  49. dd dy: dx = ddV: ddze
  50. et fiat dz: ded = (6) logo du: log dv
  51. Ergo ex 5 et 6, fit dav: ddZ = logdze: Cg. dv. seu ddv logdo = ddzue logdz.
  52. quan aequationem quadando fit dZ logdZ - dqe + hdco D = dv logdo- dv
  53. ubi primum ponendo r=0. fit dv: dz = logdd - 1: logdo - 1
  54. 12
  55. pono
  56. ex 2 et 2 patet esse bo: dZ =H: Y adeoque log dv = log dz + log ( s: Y
  57. y: X
  58. Ergo ex aequ. 10 fit et 12 fit y. X Ee = log dZ- 1,:, logdze + log)-1 et fiet
  59. porro ex (7 et 11 lit ded = du H. (log(. x: logtZ). quem valorem
  60. seu fiet.
  61. logulu
  62. substituendo in aequ. 3. fiet a: X = , + (log(H: x): log dZ)
  63. log dque X. log (B: x),: a - x quem vatorem a quando priori aequee
  64. fit ( (Xy) logZ + a - x X logsY. 2), sed qua aquatio ab omni
  65. diferentialitate liberata est. Jam aliunde scrimus esse per
  66. 247 = x seu = ya y: X = X: na. Ergo ex 6qu. 18
  67. et loque y: X = log. X = log. 2a. Unde ex aequ. 18 fit
  68. (a - X) X_log X = log. 24) + 2a a = x) = 2 X log X = 2a x log. 2a
  69. (ax 2og X = ax log2a) - exlogX + V logna 2aa = 2 ax = (D ax log K = (Dax log. 2a
  70. quae aequatio
  71. est
  72. seu 2a 2a (a - x),: ax + xX (= loque (X: 2a), petento
  73. qu
  74. esse identica, quod non est. Ergo redeamus ad
  75. log: )
  76. 2 et d est dv: dz itemque e logao- loga
  77. +hM flogty. X): bagdque) =(y. 4) + (Y: X Hlog y. X): logdque y: X) Bilog ilts si h = 1
  78. X logdz - x + hX log dv: logdq = y log dv = Y
  79. et eil botic
  80. deberet
  81. arete h
  82. ea:d yix. et
  83. silio
  84. an
  85. sec logehtesti binte. toria loguin

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 200r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068196:0395?run=74