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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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GOMBIHATIONESS
Ex combinarionibus duarum in quatuor, nempe AB, AC, AD
BC, BD, C D, quaedam Cune in quibus ipla licrera, A, vSUEPaTUE, ve
istae AB, AC, AD; quaedam qua ipsa A carene ve iltae, BC, BD,
CD.
Porro, combinariones illae, BC, BD, CD, duarum in quaruor
A, B, C, D, quae ipso A carenE, constanc ex residuis tribus, B, C, D.
Tune ergo combinationes duarum in tribus B, C, D, ioieur combina-
tiones duarum in tribus B, C, D, Cune quoque combinationes duan
rum in quatuor A, B, C, D, nempe illae quae carene iplo A.
IIla vero combinationes AB, AC, A D, duarum in quatuor A, B,
C, D, in quibus a rsurpatur, E iplo A spolientur, relinguene res-
duas lirreras, B, C, D, qua Cunc ex tribus licreris B, C, D, luncque
combinationes unius licrerae in tribus, B, C, D, igicur combinario
nes vaius liccerae in tribus B, C, D, nempe B, C, D, aCcirO A, eA-
CInnE AB, AC, AD, quae constieuune combinariones duarum lirre-
rarum in quatuor A, B, C, D, in quibus, A, vCUIEPaTuE.
Peicur combinationes duarum liccerarum in quaruor A, B, C, D.
Formancur partim ex combinationibus vnius in tribus, B, C, D, Par
rim ex combinarionibus duarum in tribus, B, C, D; Ouare mulcieu-
do primarum aquarur multicudini reliquarum, 9. F. D.
Eodem prortus modo in reliquis ostendetur exemplis verbi graria
eoc elle combin. numeri
quoc lune comb. numeri
29 in 40
29 in 39
x insuper quorlune comb. numeri 28 in 39.
Ouacuor enim numeri, 28, 29, 39, 40, condirionem requisiram ha-
bene.
Sic eor lune comb. numeri
_C.
quoc lune comb. numeri
16 in se
26 i1 55
acinsuper quorlune comb. numeri 15 in 55.
Lemma 5.
In omni criangulo Arith. summa cellularum seriei cujusti.
bec, aequatur mulcicudini combinarionum exponenris
Ceriei, in exponente erianguli.
Sic criangulus quiliber v. 8. quartus, C D n. Dico summam cel-
lularum seriei cujuluis v. 8. Secunda a Y L F B aequari mulricudini
combinationum numeri 2, exponentis secundae seriei in numero 4
exponente quarti triangli.
Sic Dico lummam cellularum Periei v. 8. quinca crianguli v. 8. octaui
aequari mulcicudini combinarionum numeri, 5 in HUmCrO 8, RC.
Ouamuis infinici sine huius proxolirionis calus, lunc enim infiniri
erianguli, breuirer ramen demonstrabo, poliris duobus assumpris.
Primo
4