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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 1118, page id 1815201908:1175
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TX18
OV ADRATVRA CTRCVEI
Ougre pacerrationem rectanguli L Z G ad rectangulum FNO, toties continere
per mulciplicationemracionem rectanguli PZ Q ad R a S, quoriestraec continerper
PROPOSITIO XXXV.
musciplicacionem rationem rectansuli E. Z M ad rectangulum N N II.
IIdem permanentibus:
Dicoparallelepipedum ex basirectangu la L. Z. C e alcirudine Z. a,
ad parallelepipedum ex bali recrangula FnO, de cadem alticudine Z a
quadruplicaram habere rarionem eius quam continet parallelepivedum
ex balirectanguta F. Z MI d alcicudinc Z. a, ad parallelepipedum lub bali
recrangulà Aa H e communi alcirudine Z. n.
Demonstratio.
. D Emonstratum es a rectangulum L. Z C ad F nO rectangulum habere quadru-
plicacam eius rarionem, quam concinee rectangulum PZ MI ad N a FI. Sunt au.
cem parallelepipeda sub hisce basibus e communi alcicudine Z. N incer (C VE ip (XMCE
bales. Paret erso veciras cheoremacis.
eROPOSITIO XXZVI.
Adem HgUTA MAMeNEC:
Dico rationem parallelexipedi quod Ac ex bali recrangula L. Z. C
ad parallelepipedum quod tc ex bali F n O recrangula, tories continere
per mulciplicationem rationem parallelexipedi luper bali recrangula
PZ O ad parallelepipedum super ba(i rectangula R a S, quories rariohaec
continet per mulciplicationem rarionem parallelexipedi luper basI re-
crangula F. Z. M ad parallelepipedum quod hr super basi N a H recrangU-
la, modo pro omnibus parallelepipedis eadem lumatur alticudo, Z X.
Demonstrario.
Fmonstracum eABrationem recranguli L. Z C ad rectangulum F NO cories co-
cinere per mulciplicarionem racionem recranguli P ZO ad R X S, quoriescon-
incrratio recranguli PZ O ad Ra Srectangulum, racionem rectanguli FZ M 2d
Ta FTreccangulum; parablelepipeda aucem de quibus agimus talem sorciuntur incer
se racionem qualem bales recrangulares super quibus crecca lunc, quoniam alcicudi.
reconvenionc en hiypochebilaler isicue vericao atteccionio.