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. 28

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 BTI A ETORES
  2. ulcictaoeM Combinationum numeri 3 in 6, Xquaeur ex 5. lem
  3. cellula 4, baliS 7; nempe p, seu 20, qua quidem p, medium balis oc-
  4. cupar locum, quod inde procedit quod z sit dimidium 6, unde fit vt 4
  5. proxime major quam 3, medium occupet locum in numero 7 proxime
  6. majori quam 6. Tgicur ipla cellula quarca, es est in diuidente, quare
  7. dupla est cellulae, F, Peu c ex 10. consect. triang. arith. quae quidem, co–
  8. est quoque quarta cellulabasis sertae, ideoque, ex lemm. 5, ip la co leu
  9. F aeguarur mulcicudini combinarionum numeri z in 5, eroo mulcieudo
  10. comb. 3 in 6 dupla est mulcirudinis comb. 3 in 5. 9. F. D.
  11. ProP.
  12. Si sine duo sues proximi, et alius quilibee in veroque
  13. combinetur, mulciendo combinarionum quae Rune in
  14. majore, cricad alceram mulcirudinem, vemajor nume-
  15. rus, ad iplummer majorem dempro eo qui combina-
  16. Tus eAt.
  17. Sint duo numeri vnirare differentes, 5, 6, de alius quilibet 2 combi-
  18. nerur in 5, e deinde in 6; Dico mulcicudinem combinarionum ipsIuS
  19. 2 in 6, ese ad mulcirudinem combinarionum ipsius 2 in 5, ve 6, ad
  20. 2
  21. HLOC ex 13 consect. triang. arith. est manisestum e sic ostendetur.
  22. Mulcieudo, enim, combinarionum ip(IIS 2 in 6, XGUAEUIE SUMIX
  23. cellularum seriei 2, trianguli 6, nempe o f + Y B Y R Y S, ex lemm.
  24. 5. hoc est cellula 5, Seu 15. Sed, ex eodem, mulcicudo combinarionum
  25. eiu (dem 2 in 5, xquacur lummae cellularum Periei 2, crianguli 5, nempe
  26. ∞Y + Y B Y R, Ceu cellula con Peu 10; eAt aurem cellula E ad co, V16
  27. ad 4, hoc est vr 6ad 6- 2, ex 13 conlect. rrians. arich.
  28. Prop.
  29. Si duoness proxtni, in alio quolibet combinentur, erie
  30. mulcieudo combinarionum minoris, ad alEeraM, VEIa
  31. jor numerus combinatus, ad numerum in quo ambo
  32. combinari lune demprominore numero combinaco.
  33. Sine duo quiliber numeri proximi, 3, 4, ec alius quilibet 6; Dico
  34. mulcicudinem combinationum minoris; in 6, ese ad mulcicudinem
  35. combinationum majoris 4 in 6, e 4, 2d 6= 3
  36. Thaec cum X2. consect. tr. arith. convenit ex sic ostendetur.
  37. Mlulcicudo enim combinacionum numeri z in 6, aequatur, ex lemm.
  38. 5. Summae cellularum Periei 3, crianguli 6, nempe, A Y B Y C Y con
  39. seu cellula p, Peu 20. Mutrirudo rero combinationum nummeri 4 in6,

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. 28. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/1023099829:0078?run=74