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# Title: [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 (shelfmark Nm-A 605)
# Folio 28, page id 1023099829:0078
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COM BTI A ETORES
ulcictaoeM Combinationum numeri 3 in 6, Xquaeur ex 5. lem
cellula 4, baliS 7; nempe p, seu 20, qua quidem p, medium balis oc-
cupar locum, quod inde procedit quod z sit dimidium 6, unde fit vt 4
proxime major quam 3, medium occupet locum in numero 7 proxime
majori quam 6. Tgicur ipla cellula quarca, es est in diuidente, quare
dupla est cellulae, F, Peu c ex 10. consect. triang. arith. quae quidem, co–
est quoque quarta cellulabasis sertae, ideoque, ex lemm. 5, ip la co leu
F aeguarur mulcicudini combinarionum numeri z in 5, eroo mulcieudo
comb. 3 in 6 dupla est mulcirudinis comb. 3 in 5. 9. F. D.
ProP.
Si sine duo sues proximi, et alius quilibee in veroque
combinetur, mulciendo combinarionum quae Rune in
majore, cricad alceram mulcirudinem, vemajor nume-
rus, ad iplummer majorem dempro eo qui combina-
Tus eAt.
Sint duo numeri vnirare differentes, 5, 6, de alius quilibet 2 combi-
nerur in 5, e deinde in 6; Dico mulcicudinem combinarionum ipsIuS
2 in 6, ese ad mulcirudinem combinarionum ipsius 2 in 5, ve 6, ad
2
HLOC ex 13 consect. triang. arith. est manisestum e sic ostendetur.
Mulcieudo, enim, combinarionum ip(IIS 2 in 6, XGUAEUIE SUMIX
cellularum seriei 2, trianguli 6, nempe o f + Y B Y R Y S, ex lemm.
5. hoc est cellula 5, Seu 15. Sed, ex eodem, mulcicudo combinarionum
eiu (dem 2 in 5, xquacur lummae cellularum Periei 2, crianguli 5, nempe
∞Y + Y B Y R, Ceu cellula con Peu 10; eAt aurem cellula E ad co, V16
ad 4, hoc est vr 6ad 6- 2, ex 13 conlect. rrians. arich.
Prop.
Si duoness proxtni, in alio quolibet combinentur, erie
mulcieudo combinarionum minoris, ad alEeraM, VEIa
jor numerus combinatus, ad numerum in quo ambo
combinari lune demprominore numero combinaco.
Sine duo quiliber numeri proximi, 3, 4, ec alius quilibet 6; Dico
mulcicudinem combinationum minoris; in 6, ese ad mulcicudinem
combinationum majoris 4 in 6, e 4, 2d 6= 3
Thaec cum X2. consect. tr. arith. convenit ex sic ostendetur.
Mlulcicudo enim combinacionum numeri z in 6, aequatur, ex lemm.
5. Summae cellularum Periei 3, crianguli 6, nempe, A Y B Y C Y con
seu cellula p, Peu 20. Mutrirudo rero combinationum nummeri 4 in6,