Leibniz Legible

Machine transcription of the Leibniz Nachlass

Search the Nachlass

Leibniz-Handschriften zur Mathematik LH 35, 12, 1, fol. 188r

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: 0.89.

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. 189v); this page is its right half.

The machine reads it as

  1. NNan hoc modo facilius apparet quae possint innicem conjuns
  2. gi et abbreviari multiplcatio etiam et divisie facilius fiet:
  3. exempli causa scribumus
  4. 5ab f + af b - 2 abfb - b+ egb + e
  5. ordinando secundum b. fiet
  6. b X +5 afb + afb +c
  7. -2af + eg.
  8. sive - b X + 3afb + afb +8
  9. + etg
  10. Nota: qualitates quae gradum sive potentiam ipsius b multi
  11. plicant, snempe quadrato quadratum b cubum b quadratum b
  12. simplicem dignitatem b) appellari solere voefficienites, ita in
  13. termino primo-s
  14. b per - 1 dat - b2) et +3af est coefficiens in termino 3afb et
  15. tota quantitas composita af t eg est coefficiens in termino +a
  16. fb. et solet interdum compendu causa pro integra ejus mo
  17. dis quantitate poni una literi ut pro af + eg poncinclo
  18. (sire supponendo k aequ. a f + eg) tunc pro ab seu pro uf b
  19. + egb. fiet: Sib
  20. c
  21. Jam ut explicemus multiplicationem divisionem et extractionem
  22. Sciendum est illa fieri posse eluobus modis scilicet tum pet sim,
  23. plicem indicationem tum per actualem operationem per simplis
  24. cem indicationem sic siet multiplicatio, ponamus olebere
  25. a + b maltiplicari per c + d, scribemus: a +b c+ d perinde enim
  26. est acsi pro aib per compendium ponendo e et pro et d ponen,
  27. dof, scripsissemus ef. Si vero ita scriptemus. a + b + cd sens
  28. sas soret ad a debere addi b +c et seu prodluctum ex multiplica
  29. tione ipsius b+C in d et proc ponendo g tunc loco a+ b+ cd
  30. fiet a +gd.
  31. Nonnulli alii a +b debere multiplicari per c+ d ita signifiare
  32. selent: a +b X C + d item sic: a + b, c+d.
  33. Actu ipso autem multiplicatio fiet hoc modo.
  34. a + b
  35. C + d.
  36. tad + bd
  37. +ac + bc
  38. a + b
  39. a
  40. UbOD
  41. + aa + ab
  42. summa tac tad + bd + aa X - bb
  43. et bc
  44. quod af b

Cite

Leibniz-Handschriften zur Mathematik LH 35, 12, 1, fol. 188r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068194:0375?run=74