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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. 27

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.

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The machine reads it as

  1. COM BIHATTONES.
  2. 25 Sic mulcieudo quoque combinarionum numeri a in 6 XquaEur ex
  3. eodem Ceriei quariae crianguli scari, Nempe cellulis D + F + F, seu
  4. cellulae IE; ip (a vero R, est reciproca iplius E, ideoque ipsi aequalis,
  5. quare e mulcirudo combinarionum numeri 2 in 6, aequatur muleiru-
  6. dini combinarionum numeri 4 in 6. 9. F. D.
  7. Coroll.
  8. Ergo omnis numerus cories combinatur in proxime ma-
  9. jori, quot suneruicaces in ipsomajori.
  10. Verbi gracia numerus 6, in 7 combinarur sepries, d 4 in 5 quin-
  11. quies, ec. Ambo enim numeri, r, 6, aeque combinantur in agGrCGATO
  12. eorum 7, ex propr. hac, T. Sed, Y in 7 combinatur sepries, ex lemm. 3.
  13. Tgitur 6 in 7 combinatur quoque sepries.
  14. Prop. 2.
  15. Si duo numert combinentur in numero quod amborum
  16. agoregacum estrnitareminuro; Mulcitudines combina.
  17. tionum crune inter sc, ve ips numeri reciproce.
  18. Hhoc nihil aliud est quam consect. 17. trians. arith.
  19. Sine duo quilibernumeri, 3, 5, quorum summa 8, rnirareminura cA
  20. 7. Dico, multicudinem combinarionum numeri z in 7, esse ad mulci-
  21. cudinem combinarionum numeri 5 in 7, VE, 5ad 3.
  22. Mulricudo enim combinarionum numeri z in 7, equaTUE, ex G. lem.
  23. tertiae Ceriei, seprimi erianguli arich. nempe A F B F C Y co F E, Ceu 35.
  24. Mulricudo aurem combinationum numeri 5 in 7, aequarur, ex eodem,
  25. quineae Ceriei, ejuldem seprimi crianguli, nempe II Y M + R, Peu 2Y
  26. in criangulo aurem seprimo, Ceries quinta ee terria lunt incer se Vez ad
  27. 5, ex consect. 17. Triane. arirh. aggregarum enim exponencium serie.
  28. rum 5, 3 nempe 8, xquatur exponenri crianguli z rnirare auet0.
  29. Prop.
  30. Si numerus combinerur, primo in numero qui lui duplus
  31. est, deinde in iplomet numero duplo rnitace minuto,
  32. prima combinationum mulcicudo, secundae dupla crie.
  33. oc nihil aliud est quam consect. 20. trians. arith.
  34. Sic numerus quilibee 3, cuius duplus, 6, qui rnicare minurus ctt 5.
  35. Dico multicudinem combinarionum numeri 3 in 6, duplam esse mul-
  36. ticudinis combinarionum numeri z in 5.
  37. Possem uno verbo dicere omnis enim celluia divicieneis dupla est prae-
  38. cedeneis corradicalis sic autem demonstre.

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. 27. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/1023099829:0077?run=74