Leibniz Legible

Machine transcription of the Leibniz Nachlass

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LBr. 57, 1 · Bernoulli, Joh., fol. 9r

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: 0.91.

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. 10v); this page is its right half.

The machine reads it as

  1. a compusime et (eleberrimme
  2. fautor Honoratissime
  3. um ante ociduum à rure (uti per aliquot mentes comoratu aqnarum
  4. Fabariensium gratia mihi potandarum) in Urbem reverterer, portremae
  5. Tuae gratissime mihi denum tradebantur; quod caura est ut ob in
  6. gruentes nundinas Liptienres ad quas Kortrates jam jam abituriunt
  7. Je lui petiti omnino compotem reddere nequeam. Breviter tamen
  8. quantum per temporis angustiam licit ad Tuas respondebo.
  9. Gaudeo Tibi quoque esse consideratas curvas illa quas vocas esponen
  10. tialiter transcendentes ejo autem percurrentes; quid peculiare in illis
  11. observarin paucis exponan: Aequatio percurrons contat quantitati
  12. bus percurreatibus, quae sunt vel primi, secundi, tertii vel ulterioris gene
  13. ris; quantilas percurrens pritur generis ed, uin ejus esponens eit numerus
  14. vel quantitas simpliciter indeterminata ut ; secundi vero generi
  15. (
  16. cum ejus exponens et quantilas percurrens purimmi generis ut ; et ita
  17. de aliis. Siguidem autem esponentes dimensionum sunt numeri, hic vero
  18. per literas indelermnatas qua litreas denotant exprimuntur, assunitur
  19. quadam linee condans b prounitate, per quam si linea indetriminata
  20. dividuntur provehiuat numeri, sii itaque = y, pariter si aequationis
  21. percurrentis membra non ubique aequatem numerum dimensionum habeant, mul
  22. Liplicata intelliguntur per b ad sufficientem dimensionem elevatam ita ut nu
  23. merui dimensionum compleatur, sic si proponatur aequatio f - y, intel–
  24. ligitur y multiplicata per b, et sic aequatio x = bF y, utrolique aeguules
  25. dimensiones habebit. His praeliminatis sit ABb curva logarithmica en quaa
  26. g applicata AC = b = 1, subtangens = a, et BD ordinata varians vel
  27. indeterminata = X, appello CD, Ex ad eit logarithmum iprius
  28. X: Si BD = y, m, n X erit pariter CD = ly, lm, la y: sit bd
  29. elementaliter diitans, erit, BD exirtente X, y, m, n p, bg = dx,
  30. des, dm, du : Dd = alx, aly, dlm, ila x id est = differential:
  31. ipsim Lx, ly, Im, In y: quoniam autem ex natura logaritho
  32. cae BBX Dd = a xbg, erit Xdlx, ydly, malm, nala ip = adx, ady, adm, adm x:
  33. ideoque alx, aly, alm, dln ∞ = eds adye, adm, adn p. condtat eliam
  34. quod logarithmus quantitatis ex multiplicatione progenitae sit = summa
  35. logarithmorum partium multiplicanlium, ut lxy2 = ly + ly +CZ, et contra
  36. logarithmus quarti lalis diisae = differentiae Logarithmorur dividenda et
  37. dividentis, ut l = lx - by, CF = 1x + ly -lZ, 1F = lx - 12 - ly, item logarith
  38. y
  39. mus quantitatis percurrendis = exponenti duito in logarithonum radicis:
  40. Sic l= mlx, Lyen
  41. =m Ly, Cy=mlx+ ulis, l = ulx-ulus
  42. Ortendendum num quo parto quantitatum percuvientium differentialia
  43. sumenda scnt, sit quanitas percalrens sei to generis neiu quaa ponatar = d, ergo

Cite

LBr. 57, 1 · Bernoulli, Joh., fol. 9r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/DE-611-HS-958803:0017?run=74