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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)
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COM BTHAYTONES.
aequatvE, ex eodem, summxe cellularum seriei 4, erianguli 6, nempe
D Y F F F, scu cellula K, Seu 15. est aurem p ad R, re + ad 3, Icu re 4
2d 6-- 3. ex consect. 11. Tr. arith.
Prop. 6.
Si sine duo numeri quilibet quorum minor in majore com-
binetur, sinc autem e alii duo hisproxime majores quo-
rum minor in majore quoque combinerur, erune mul.
cicudines combinationum inrer se, re hi ambo rleimi
MMIeri.
Sine duo quilibernumeri, 2, 4 alii vero his proxime majores, 3, 5;
Dico mulcicudinem combinarionum numeri 2 in 4 esse ad mulcirudi-
nem combinationum numeri 3 in 5, VE3, ad 5.
Consect. 12 triane. arith. hanc continet ex sie demonstratur.
Mulcicudo enim combinacionum ip(ius 2 in 4, aquacur, ex lemi.
5. Tummae cellularum seriei 2, crianguli 4, nempe p F L. 7 6, Peu cel-
lula C, Cen 6; Mulricudo vero combinationum numeri z in 5, Xqua-
cur, ex eodem, lumma cellularum seriei 3, crianguli 5, nempe A F B F C,
Seu cellula F, Peu rO; F.K aurem C ad F, Vr 3ad5, Cx T2 consect. triang.
arich.
Lemma 6.
Summa omnium cellularum basis criang. cuindlibet arich.
mericirnicace minuta, equatur lumme omnium com-
binacionum que feri pollune in numero qui proxine
minor est quam exponens balis.
Sicrriansulus quilibecarichmericus v. 8. quintus CHI u Dico lum.
mam cellularum sux batis II F F Y C Y R F u, minus vnirare, set
minus vnd ex extremis HI vel u aeguari summae omnium combina-
tionum quae heri possune in numero 4 qui proxime minor est quam
exponens basiS, 5. Id est. Dico summam cellularum R f C f F f FI.
Supprimo enim extremam u, id eAt q Y 6 Y 4 F F, Ceu 15; Xquari
mulcieudini combinacionum numeri r in 4 nempe 4; Plus muleieu.
dine combinationum numeri 2 in 4, nempe 6; Plus muleicudine com-
binarionum numeri z in 4, nempe 4; Plus mulcieudine combinatio-
num nameri 4 in 4, nempe I. Quae quidem sunt omnes combinatio-
nes quae fieri possunt in 4 superiores enim numeri, 5, 6, 7, ∞ c. non
combinantur in numero 4: major enim numerus in minore non com-
Binatur.
Mulcicudo enim combinarionum numeri Z in 4, XGUaTUE, ex S. lem.
cellula 2, balIS5, nempe R, seu 4. Mulcicudo vero combinationum