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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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C,OM BIALL = LOHL S.
Prop. 9
Summa omnium combinarionum qua heri possunt in quo-
uis numerornitare minura, dupla est lumma combina-
tionum qua feri porsune in numero proximéminori.
aec cum praecedente omnino convenit.
Sine duo numeri proximi 4, 5, Dico summam omnium combinario-
num qua heri pollune in 5, nempe 3E, rnirare minuram nempe 30, esle
duplam omnium combinarionum qua heri postune in 4 nempe 15.
Frenim ex praeced. Cumma combinar. quae Rune in s rnitare aucta,
dupla est lumma combinationum quae hune in a vnicare auctae, (I ergo
ex minori LAII a AUFCTATUErnITaS, _ ex aupla Cumma aUFeTaNEUE duX
vnicares, reliquum Cummae duplae nempe summa combinationum quae
funt in s unitare minuta, remanebie dupla relidui alterius (UMIMa
nempe summa combinationum quae fiunt in 4.
Prop. 10.
Summa omnium combinacionum qua hieri possune inquo-
libet numero minura iplometnumero, aequatur lumnia
omnium comibinacionum qua hieri poltune in singulis
numeris proxosico minoribus.
HLaec cum 8 consect. Er. arith. concurrit quae sie habet, balis quaeli-
beernicare minuca, aequatur summae omnium peaecedentium. Sic au
tem ostendo.
Sic numerus quiliber 5. Dico summam omnium combinacionum
quae possune Reri in s nempe zt ipsos minutam nempe 26, aequari
lummae omnium combinacionum quae polluncheri in 4 nempers; Plus
Cumma omnium quae possuncheri in 3 nempe 7; Plus lumma omnium
qua pollune heri in 2 nempe 3; Plus ea qua porest heri in Lnemper,
quaru aggregacus eA 26.
Ecenim, Proprium numerorum huius progrectionis duplae illud est,
ve quilibet ex ip(S V. 8. PexeuS 3E, exponence luo minurus nempe 6,
id est 26, aequecur lummae inferiorum numerorum huius progrectionis,
nempe 16 78 Y 4 f 2 = 2 vnicare minurorum nempe, 15 + 7 + 3+ 170
nempe, 26. Vndetacilis est demonstrario huius propolirionis.
Proble .
Daco quooto ee ulha co
macionum qua I a. atB.