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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 30, page id 1023099829:0080
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COM BENA PTOHES.
numet 2 Ia 3 sac Ccta 3, balI6 5, nempe C, Ccu 6. Mulcieu
do quoque combinarionum numeri z in 4, aequacur cellula q, balis
5. nempe P, Peu 4. Mulcieudo denique combinationum numeri + in 4.
aeguatur cellulae 5, basis 5, nempe II, Ceu r. Igitur Cumma cellularum
balis quintae dempra exrrem a sen vnitare, aequarur lummx omnium
combinarionum quae pollune heri in 4.
Prop. 7
Summa omus combnationum quae fieri porsune innu.
mero quolibeernitare aucta, estnumerus progressionis
dupla qua abruitace lumie exordium, quippeille cu-
ius exponens est numerus proxime major quam dacus.
Sic numerus quilibet r. 8. 4. Dico summam omnium combinario-
num quae Reri poltune in 4 nempe is rnicare auctam nempe 16, clle
numerum quintum (nempeproxime majorem quam quartum) pro-
srestionis duplae quae ab rnirare Cumie exordium.
Hoc nihil aliud est quam 7 consect. trians. arith.  sic uno verbo
demonstrari posset, omnis enim balis estnumerus progressionis dupla,
sic tamen demonstro.
Summa enim combinationum omnium quae feri possune in q unica-
ce aucta, aequarur, ex lem. 6. Tumma cellularum balis quintae, ipla ve.
obalis est guintus numerus progresionis duplxe quae ab rnirare lumie
exordium, ex 7. consect. crians. arich.
Prop. 8
Summa osu cobinationum guxe Reri possune in nu-
mero quolibeernicare aucta, dupla est lumma omnium
combinationum quae fieri possune in numero proxime
minori vnicare auctx.
HLoc convenit cum b consect. triang. arith. nempe omnis ba(is du-
pla est praecedentis, sic autem ostendemus.
Sinc duo numeri proximi 4, 5, dico summam combinarionum quae
fieri polluneins nempe z vnicare auctam nempe 32, esse duplam Cum-
mae combinarionum quae heri poltune in 4 nempe is rnitare aucta
nempe 16.
Summa enim combinarionum quae heri possune in srnitare aucta,
aGUaTUT, ex PraecCd. eato numero progressionis duplae. Summa vero
combinarionum quae heri possune in 4 vnicare aucta, X quaTUC, ex ca.
dem, quinto numero progrectionis dupIX. SC.NTIS AUTEM HUWCTUS PTO-
prestionis duplx, duplus est proxime praecedenris nempe quinti.