Leibniz Legible

Machine transcription of the Leibniz Nachlass

Search the Nachlass

[Traite Du Triangle Arithmetique, Avec Quelques Autres Petits Traitez Sur La mesme Matiere] Traité Dv Triangle Arithmetiqve, Avec Qvelqves Avtres Petits Traitez Svr La mesme Matiere, fol. 36

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: 0.93.

Original at the GWLB · Page image · Annotations (IIIF) · Download text

The machine reads it as

  1. 36
  2. POTESTATVM NVMERLOARNM
  3. Deinde, ex iplo nuero, 3 qui est differentia radicum consticuro in
  4. propolico quarto oradu, numerus enim absolutus 8t est quartus sra-
  5. dus radicis 3. Elinc igieur elicierur Canon iste.
  6. Duarum similium porestarum differentia, aequatur, difte-
  7. rentix radicum consticuea in eodem oradu in quo lunE
  8. porestares propolicae; Plus minori radice consticuta in
  9. Singulis gradibus propolio sradui inferioribus ac in v.
  10. noquoque mulciplicara per coefficientes quos A lorti-
  11. recur in similibusoradibus, si binomium cuius primum
  12. nomen esset A, alterum vero esser differentia radicum,
  13. constiruererur in eadem porestare propolica.
  14. Sic ergo differenria inter 14 _ 2F, erie 12, 2V, F 54, ZL, F 108, II,
  15. 8T.
  16. Differentia enim radicum est 3.
  17. Ec SIC de careris.
  18. ad summam Potestarum cujustibet progressionis inve-
  19. niendam unica ac generalis methodus.
  20. arithimetica
  21. Acis quorcunque numeris, in qualiber progressione
  22. a quouis numero inchoance, invenire quarumuis
  23. porestatum eorum summa.
  24. Quilibet numerus, 5, sit initium procressionis quae per
  25. incrementum cujusuis numeri verbi graria ternarii pro-
  26. cedat, ex in ea progressione dati sint quorlibet numeri
  27. verbi oratia isti, 5, 8; 1F, 24, qui omnes in quacunque
  28. porestate constituantur et in tertio gradu seu cubo. Opor-
  29. tet invenire summam horum cuborum, nempe, 5, 7 8,
  30. 11. F 143
  31. Cubi illi Tune 125 F 512 + 1331 f 27 443 guorum
  32. Cumma CR 47 12 qua quaeritur e Tic invenitur.
  33. Exponatur binomium A Y 3 cuius primum nomen sit
  34. A, alterum vero sit numerus 3 qui est differentia pro-
  35. rressionis.
  36. Consticuatur binomium Boc A Y 3 in gradu QuartO

Cite

[Traite Du Triangle Arithmetique, Avec Quelques Autres Petits Traitez Sur La mesme Matiere] Traité Dv Triangle Arithmetiqve, Avec Qvelqves Avtres Petits Traitez Svr La mesme Matiere, fol. 36. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/1023099829:0086?run=74