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# Title: Qua Continentur, Oratio Inauguralis. Mathesis Universalis; sive, Arithmeticum opus Integrum, tum Numerosam Arithmeticam tum Speciosam complectens. Adversus Meibomii, de Proportionibus Dialogum, Tractatus Elencticus (shelfmarks Leibn. Marg. 84:1, Stück 1; Leibn. Marg. 84:1)
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C AP. 23.
De Rationibus.
parriens. Siguem interim cerreac nominum barbaries, in voci-
buscechinicis; liberum iphi eric illis abstinere; dummodo mihi
permiccat indicare, quid alii tus nominibus incellectum ron
dunc.
Ouancicas major minoris Multiplex dicitur, Cvel mulcipla,)
quae minorem aliquocies exacte concinet; vel, cum minor me. Malriplex
cicur majorem. TIORNaTONaSIOD Nd CICOV SS EndaorO, orar ugra
pnXen) 1d5o Enaore, detinience Fuclide 2d5, e specintim
de numeris 5 d7. Hloc cA, cum minor aliquocies accepra eequa-
cur majori. Ea enim est rocis naruereci apud euclidem Bo-
nificacio. Sic enim Euclides 23d7. Numerus numerum meriri
dicitur per illum numerum quem multiplicans, vel a quo multiplicatus, il-
lum producit: Ec eodem modo Ouantitas quantieatem meciri cen-
Cenda eA. Si ergo quancicas minor per nullum numerum (inte-
orum incellige) mulciplicaca producal miorem, hanc illa non
mecicur. Iea numerus Senarius est binarii mulciplus; quia bi
marius aliquocies acceptus, nempecer, aequatur iphi lenario; sive
uc loquitur Fuclides) numerus 2 mericur 6, per 3; quia bi8
eria lunc lex. 2x 3 =- 6. Ac8 ad 3 non esse dicimus ir: - 21i0-
ne mulciplici: quia, quamris 3 in 8 aliquoties contineancue,
nempe bis; non tamen z exacte metiuncur 8, quia bis ablaca
relinguune 2, cer aucem anterri non pollunt.
Mulciplicis correlatum Cin proportione minoris aequalica Subn
eis consticurum) dicitur submulciplex. Apud Buclidem simpli-
cicer Pars dicicur 1 d5. Mep  631 uEVEd uedus n EKaNVOVN
ecCoV O, SrV HOrALE~ sd MEICOr. Magniiudo minor majoris Pars
est, quando exacte meritur majorem. Ubi aucem minor majorem
nonmecitur Cac lalrem in racione rationali conRituca EF,)
quancicasilla non hujus Pars, Ced Partes, ab Evelide diciturs
quipre ille, hic loci, per Pariem non aliam quam pariem aliquotam
incellixic; e perparres, Parcium aliquocarum aggregacum. Ou2
aurem hic Fuclides partem de partes appellac; appellane alii re-
centiores, pariem aliquotam, e pariem aliguantam. Sic SemilIS,
Priens, Quadrans, Sexcans, Clncia, dicuncur singulz, aliquota pars
Alis; quonia aliquocies accepea incegru Allem complenc. Népe
Semillis bis, Triens cer, auadrans quater, Sextans lexies, e Ulncin
duodecies, praecile, concinenine in Alle, sive integro. P. A au-
cem ouincunx, assis pars aliquanca, non aliquota: Nam quin
cunxbis acceptus, eA asse minor, nempe decemuncia; ac cex
aCCCPTUS
Pledia