Leibniz Legible

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. 31

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: 0.90.

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

The machine reads it as

  1. C,OM BIALL = LOHL S.
  2. Prop. 9
  3. Summa omnium combinarionum qua heri possunt in quo-
  4. uis numerornitare minura, dupla est lumma combina-
  5. tionum qua feri porsune in numero proximéminori.
  6. aec cum praecedente omnino convenit.
  7. Sine duo numeri proximi 4, 5, Dico summam omnium combinario-
  8. num qua heri pollune in 5, nempe 3E, rnirare minuram nempe 30, esle
  9. duplam omnium combinarionum qua heri postune in 4 nempe 15.
  10. Frenim ex praeced. Cumma combinar. quae Rune in s rnitare aucta,
  11. dupla est lumma combinationum quae hune in a vnicare auctae, (I ergo
  12. ex minori LAII a AUFCTATUErnITaS, _ ex aupla Cumma aUFeTaNEUE duX
  13. vnicares, reliquum Cummae duplae nempe summa combinationum quae
  14. funt in s unitare minuta, remanebie dupla relidui alterius (UMIMa
  15. nempe summa combinationum quae fiunt in 4.
  16. Prop. 10.
  17. Summa omnium combinacionum qua hieri possune inquo-
  18. libet numero minura iplometnumero, aequatur lumnia
  19. omnium comibinacionum qua hieri poltune in singulis
  20. numeris proxosico minoribus.
  21. HLaec cum 8 consect. Er. arith. concurrit quae sie habet, balis quaeli-
  22. beernicare minuca, aequatur summae omnium peaecedentium. Sic au
  23. tem ostendo.
  24. Sic numerus quiliber 5. Dico summam omnium combinacionum
  25. quae possune Reri in s nempe zt ipsos minutam nempe 26, aequari
  26. lummae omnium combinacionum quae polluncheri in 4 nempers; Plus
  27. Cumma omnium quae possuncheri in 3 nempe 7; Plus lumma omnium
  28. qua pollune heri in 2 nempe 3; Plus ea qua porest heri in Lnemper,
  29. quaru aggregacus eA 26.
  30. Ecenim, Proprium numerorum huius progrectionis duplae illud est,
  31. ve quilibet ex ip(S V. 8. PexeuS 3E, exponence luo minurus nempe 6,
  32. id est 26, aequecur lummae inferiorum numerorum huius progrectionis,
  33. nempe 16 78 Y 4 f 2 = 2 vnicare minurorum nempe, 15 + 7 + 3+ 170
  34. nempe, 26. Vndetacilis est demonstrario huius propolirionis.
  35. Proble .
  36. Daco quooto ee ulha co
  37. macionum qua I a. atB.

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. 31. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/1023099829:0081?run=74