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Machine transcription of the Leibniz Nachlass

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[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. 35

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: 0.92.

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

The machine reads it as

  1. S V M MI A.
  2. ve quod vlcimum cA, à numero qui non sit eius pro-
  3. gressionis, et isti 5, 8, IF, T4, quorum prorressio per ter-
  4. narii differentiam procedit, es a numero 5, ipsiproorel
  5. sioni exrranco, exordium sumit. Et quod lane taeli-
  6. cicer inventum est, tam mulci differentes casus, vni-
  7. ca ac generalissima resoluit methodus; adeo lim-
  8. plex, et absque litcerarum auxilio, quibus difficiliores
  9. esent enuntiationes, paucis lineis contineatur. Ve ad A.
  10. nem problematis sequentis parebit.
  11. Definitio.
  12. Si binomium, cuius alcerum nomen sIC A, alcerUM verO nUMCTUS
  13. quilibee re3, nempe A F 3, ad quamliber constiruarur porestatem re
  14. ad quarrum gradum, cujus haec lc exposirio,
  15. A+ Y 12, A F 54, A Y 208, A F 81.
  16. IpSE numeri, 12, 54, 208, per quos ipse A mulciplicarur in singulis
  17. gxadibus, quique parrim ex numeris hguraris, parrim ex numerO 3, qui
  18. binomii est lecundum nomen, formantur, rocabuneur Coefficientes
  19. ipsus A.
  20. Erie ergo in hoc exemplo, 12 coefficiens A cubi, de 54 coefficiens A
  21. quadrari, e 108 coefficiens A radicis.
  22. NumerUS verO St numerus absolutus dicerUE.
  23. Temma.
  24. Sic radix quaeliber, 24; alcera vero sic binomium 14 F 3 cuius pri
  25. nam nomen (ic r4, alcerum vero alius quiliber numerus z, ica ve ha-
  26. rum radicum, r4, X T4 F 3, differencia (Ic 3. Consticuaneur ip (xe in quo-
  27. liberoradu rein quarro, erso quarrus gradus radicis 14. est 14 . Ouar-
  28. cus veco gradus binomii, 14 Y 3, eAt,
  29. 24 7 12, 24 F 54, 24 Y 108, r4 Y 81
  30. Cujus quidem binomi primum nomen 14, eosdem coefficientes sertitur
  31. in sinculis eradibus, quos A sortitus est in similibus gradibus in expo-
  32. sitione ciusdem gradus binomii A + 3, quod rarioni consentaneum est,
  33. harum vero porestacum, nempe huius r4 X huius 14 7 12, 243754
  34. 24 Y 108, 24 F 81, differencia eA, 12, 14 7 54, 14 F 208, 14 + SI
  35. qua quidem constar Primo, ex radice r4 consticura in singulis gradibus
  36. Propoliro gradui guarco interioribus, nempe in tertio in secundo et in
  37. primo, et in ruoquoque mulciplicarâ per coefEcientes quos A CorrieuT
  38. in similibus gradibus, in exposirione eiuldem gradus binomii A Y 3.

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. 35. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/1023099829:0085?run=74