Leibniz Legible

Machine transcription of the Leibniz Nachlass

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LBr. 56 · Bernoulli, Jac., fol. 64v

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: 0.81.

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. 65r); this page is its left half.

The machine reads it as

  1. C
  2. sed ut rei fontem quaeramus, inveniamusque quousque se extendat
  3. considerandum est si Cel XG X + Z X +G _ Tormino termino simplice
  4. quaesiti terminum cum suis differentiis et differentio differentiis esse progres
  5. sionis Geometricae, sed hinc non statim sequitur formulam ex his duobus terminis composita
  6. etiam cum suis differentus esse progresionis Geometriae.. Ex. gr. sit sint
  7. duo a et b et a, aa a a etc, progressionis Geometricae,
  8. noncdeo erit a et b, bb, b3 at erc propes itidem
  9. non ideo sequitur etiam anb, aarbi, a +b etc progressionis Geometria esse
  10. nisi illo casu pro proguessio utraque est eadem, si a, aa a etc. sint progressionis
  11. duplae, et b bb b, etc. sint etiam progressionis duplae. Id vero
  12. huc loce contragit, nam differentiae, d d, d,’etc de d’X d’y sunt
  13. quasi grogressionis duplae, procedunt enim per numeros 14, 1+2+19 1+ 3+3 +1, etc.
  14. et differentiae de d’xdt y sunt etium quasi progressionis duplae.
  15. et
  16. Iu
  17. Et rem a differentias traducamus ad potentias. Et scribamus si placet
  18. N + p y cuu potentio P, p X+ 2 pex ply + p y
  19. m
  20. nx pt y + pr X p y cujus potentio p, p, etc sunt prospessionis Geom
  21. p X paxy + priX pr cujus p potatir p, pd etc sunt ititem progr. Geom
  22. et quidem si X et V accipias pro unitatibus, ambo sunt progressionis geometricae duplae
  23. ergo et compositum ex potentuis erit ejusdem progressionis. Geometricae duplae
  24. immo, etsi maneant X et y diversae, item tamen verum est; nam illud dividendo per pxp
  25. fiet y + X, et hoc dividendo per pex pu prodit itidem y+X. Ergo
  26. fit 3 +X, pX p X p y + p X pr y
  27. taque d, d X d’y + d’X d’ylf e, d’+ d 9, d’X d y, quasi in,
  28. aequ. d dXy + dF y, C quasi productrae ex d X d’y + d’xdy in dxdy+ dXd y
  29. t quia per C est ( d X dury + dat x dy quasi product. ex d x d
  30. 1D
  31. etd, de X demy + d X d’ y) . . . . . . . . . dXdme y, xdmy, in dexdir dxdy
  32. d. duX d’y + d’x d y
  33. d, xd’y + d xdy
  34. Er d. d’xry + d’xdy
  35. adeoque tandem
  36. (4
  37. pt ix d y Et hoc= d Xdyrd yd
  38. d. dXd y + d xdy m = d X d y + d Xd + d Xd y + d
  39. Nempe
  40. Ergo de a Xdr y + d d y + d’xd y + d t d’y, seu d
  41. seu per D.
  42. Rer
  43. dexdu q
  44. seu
  45. quasi in dxdyraxus
  46. Ergu d. L Xd y ta xdm
  47. Kdytd xdmus
  48. dadyranaus
  49. dXd G + de x d y quasi in dxdy didus quasi in dxdyrddy
  50. dXd’y + axdy quasi in quasi quadrat y d’x d’yt d Xd y
  51. d,d’Xd y + d x dmy
  52. aequ.
  53. d’neglali l qul quis tetendiynd idys (e quosi (et der ey dpsiu
  54. d, d xdy + d Xdmy, sues pro gustionis quasi-
  55. geometricae ut
  56. quasi ( Ialyrdaty
  57. +PXonu, in . p X
  58. proponebatur
  59. rigius
  60. pexpu rpip
  61. et in universum a differenr de, duX d’y + d X d y = qude y t dex d g quadn, q, dx
  62. etiam
  63. Oequi
  64. =d xd y + xdy + dxd yd xd y, quasi in dxdy rdxdy
  65. pe
  66. Ubi noto on licuisse dicere d, d X d’ y 4 d Xd 9 = quot d X d y + d Xd 9, quadi duct. in quasi potentiam de ipo, dex dys rd ud
  67. generaliter
  68. un laira cere 1e, de x Ny + d XH 7 = d X d y + d X A G, quari dust in d. d X d’9. quo quam il sucedil i uni casa, except. e
  69. un e itaque rectias utemur traductione a potentiis

Cite

LBr. 56 · Bernoulli, Jac., fol. 64v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 159). https://leibnizlegible.com/page/DE-611-HS-958800:0128?run=159