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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)
# Folio 349, page id 826603459:0395
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C AP. 37
De Requa Aurea.
pondus a in lineam B mulciplicare, aue per lineam A divi-
dere: enate enim factum illud erie cujus lengicado cA
Linca; laciendo Dondus : auc qualis quoriens, ubi quaricur
quories pondus a contineat Lincam A :
Dicimus itaque, non hic ram comparari lineam ad pondue: F juum (o
gua quidem planc hecerogenea sunt, nec invicem comparan.
da: Sed racionem duarum inter se linearum, ad racionem der. Hl10.
orum invicem ponderum: Dux quidem rociones invicem
homogenea lune, puca dupla, cripla, sequi alcera; Tumpta
nempe denominatione a quocience ancecedencis per conte-
quencem dirila. EA aurem quociensille, uc superiuscradicum
eAt, vel numerus, vel Calcem in genere numerolo aliguid, ip.
tilque numeris homogeneum; pura numerus Fractus, auy
Curdus, aurcalc quid. Adeoque quum dicieur A. B :: a. B.
hoc cancum innuicur, rarionem A ad Bsire p, aequalem
esse rationia ad6, sire =. Vel quod rancundem valet, quon
ciencem quancitaris A per homogeneam B divilae, aequalem
esse quocienci quancicaris a per tibihomogeneam (uruc priori-
Bushecerogeneam) divile. Pura, A A sC linea Bipedalis; B,
Dedalis; eric illa hujus dupla, sive ue 2 ad 1. Icem, (I a EIE
quadripondium; B, bipondium, eric illud hujus duplum
sive ve 2adc. Ouixpeerie, cum B) A(2, cum B) a (2.
Adeoque B a = 2 = = = + _c. Cum icague nihil hic a-
liud spectetur, quam ratio, sire eriam quotiens: licebic, pro ex
posicis quancicacibus, alias cujuscunque generis substicuere.
ouxe in eadem sine ratione constituex, sive eundem quorien
tem exhibeane; utne exposicis Cinc hecerogenca. Rrichmeri.
cus icaque, quo opcrationes sux rectius constent, pro expon
Eeis quancicacibus cujuscunque generis, quarum tancum ra-
tio consideracur, numeros substiuie (sire quod numeri instae
est) in eadem racione consticuros. Puta, pro lincis A, B.
bipedali de pedalis binos quolvis in eadem ratione numerOd
Pura 27 22 vel 4, 23 vet 6, 3: ec. quia ucunque J=
3
2= B: EC, pro expoticis, aequalia Cubsiuendo; quanei
cao non immuratur; Sed uerobique rancundem clt. Proinde icaq;
du X