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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. 30

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.

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The machine reads it as

  1. COM BENA PTOHES.
  2. numet 2 Ia 3 sac Ccta 3, balI6 5, nempe C, Ccu 6. Mulcieu
  3. do quoque combinarionum numeri z in 4, aequacur cellula q, balis
  4. 5. nempe P, Peu 4. Mulcieudo denique combinationum numeri + in 4.
  5. aeguatur cellulae 5, basis 5, nempe II, Ceu r. Igitur Cumma cellularum
  6. balis quintae dempra exrrem a sen vnitare, aequarur lummx omnium
  7. combinarionum quae pollune heri in 4.
  8. Prop. 7
  9. Summa omus combnationum quae fieri porsune innu.
  10. mero quolibeernitare aucta, estnumerus progressionis
  11. dupla qua abruitace lumie exordium, quippeille cu-
  12. ius exponens est numerus proxime major quam dacus.
  13. Sic numerus quilibet r. 8. 4. Dico summam omnium combinario-
  14. num quae Reri poltune in 4 nempe is rnicare auctam nempe 16, clle
  15. numerum quintum (nempeproxime majorem quam quartum) pro-
  16. srestionis duplae quae ab rnirare Cumie exordium.
  17. Hoc nihil aliud est quam 7 consect. trians. arith. sic uno verbo
  18. demonstrari posset, omnis enim balis estnumerus progressionis dupla,
  19. sic tamen demonstro.
  20. Summa enim combinationum omnium quae feri possune in q unica-
  21. ce aucta, aequarur, ex lem. 6. Tumma cellularum balis quintae, ipla ve.
  22. obalis est guintus numerus progresionis duplxe quae ab rnirare lumie
  23. exordium, ex 7. consect. crians. arich.
  24. Prop. 8
  25. Summa osu cobinationum guxe Reri possune in nu-
  26. mero quolibeernicare aucta, dupla est lumma omnium
  27. combinationum quae fieri possune in numero proxime
  28. minori vnicare auctx.
  29. HLoc convenit cum b consect. triang. arith. nempe omnis ba(is du-
  30. pla est praecedentis, sic autem ostendemus.
  31. Sinc duo numeri proximi 4, 5, dico summam combinarionum quae
  32. fieri polluneins nempe z vnicare auctam nempe 32, esse duplam Cum-
  33. mae combinarionum quae heri poltune in 4 nempe is rnitare aucta
  34. nempe 16.
  35. Summa enim combinarionum quae heri possune in srnitare aucta,
  36. aGUaTUT, ex PraecCd. eato numero progressionis duplae. Summa vero
  37. combinarionum quae heri possune in 4 vnicare aucta, X quaTUC, ex ca.
  38. dem, quinto numero progrectionis dupIX. SC.NTIS AUTEM HUWCTUS PTO-
  39. prestionis duplx, duplus est proxime praecedenris nempe quinti.

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. 30. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/1023099829:0080?run=74