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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
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adarRAHTLERBOL
Demonstratio.
acio parallelepipedorum ex R in Z, _ S in X, ad parallelepipeda ex P in Z
e V in e, eadem est a Caurracione parailelepipedi ex R in X ad Y in Z, ex 2 8. huim
R in X ad V in e, vlceriits exracione para llelepipedi, ex S in Y ad parallelepi-
Deaa ex T in Z, e.V in a Perpropolicionem octauam huius libri. Simili modo
ratio parallelepipedorum ex lelu. I in NV, es R in O, ad parallelepipeda ex ductu
plani L In P, et M in C. elceademb cum ratione parallelepipedi ex P in N, 2d b eercando
parallelepipeda ex I in P, c in C, smul cum rarione parallelepipedi ex R in
O ac L. in P, _ M in D. Deisqueracio pamillelepipedorum ex ductu A in L, e
B in Padparallclepipeda ex cactu C in C, ex D in FF, est eadem cum racione p2-
ralleleppedi ex ductu A in L ad parallelepipeda ex C. in C, de D in II, simul cum
ratione Patallelepipedi ca B in F, ad parallelepipeda que tune ex dueru C in C et
1
ist L
Sedracio parallelexipedi ex R in Z, ad F in Z, cories continerrationem pa-
rallesepipedi ex F in DY, ad L in P, quociestixe continoe racionem parallelexipedi
ex AI I, ad C in C, quod eodem prortus modo ostendieur quo illud in quadraru-
ra circuli propolicionibus)). e 38. d harum Corollario octensum Fuic; Cunc enim om-
nia achoc praectandum in hâc ceiam quadeatura praemissa. Simili modo ratio paralle.
lexipe ex R in X ad parallelepipedu ex V in e, cories concinet rarione parallelepi-
pedi ex Lin N, ad M in O, quocies hxec continet rationem parallelexipedi ex A in F,
ad V in FI. Acque codenmodo de rarione parallelexipedi ex ductu S in Y ad T in
Z, aS in Y ad V in d Ostendieur, quodcories continenc rationem parallelexipe.
di ex K in OadT in P, e K in O ad Min O, quocies hac cadem concinecracio-
nem Barallelexipedis quod tic ex ductu B in F, ad C in G, _ B in F, ad id quod
reluleat ex ductu D in F. loicur pacet quod racio duorum parallelepipedorum ex
R in Z, _S in Z, 2d duo parallelepipeda ex T in Z, & V in de, cories concineane
racichem parallelepipedoruum quae oriuneur ex ductu I in NI, e K in O ad pacal.
relepipeda qua AUnE CZ duCTu L in P, et MI in O, quories lxec ipsa racio concince
raciorem parallelexipedorum quae gignuneur ex ductu plani e in F, _ B in F, ad
parallelexipeda, quae hiunc ex ductu C in C, et D in FI. Duodtuir demonstrandum:
Corollarium.
e dicta sunt praecedenti propolitione de quaruor parallelepipedis ex planis
LA BC D in plana B F CFI ducris, ex reliquis; cciam sunc incelligenda de quauis
subdiettione rectangulorum corundem per parallelas in parres aequales ad Forman-
daparallelepipecta, prourn propolicione requisica Fuerunc; de quibus semper het ca
demillacio ex consequentia, quae Facca iam est, cum demonstracionis discursus scrni-
versalis, Msdemque Fundamenra semper occurrane iccranda. quare cum illae subdi-
vitiones nihil noui inferendum adducant ab co, quod iam demonstracum Fuit, sed
meram eorum repericiorrem quae praemissa sunc, molestam incelligentibus conci-
neanc, hinc propolicionem praecedentem de quacunque subdiuisione demonstra-
tam libere allumemus.
 L- la l21.
PR O POSITIO
IIdem maneMeVaS.
in parabolam concauam ZY ad Polidum ex ductu concaui parabolici
Dicorationem Colidi quod oritur ex ductu concaua parabolx R S
TV in parabolicum Z _, tollescme aconenonut, quouu ex
E. F parabolam ad corp is um ex ductu parabola convere C D in CFI.
emon
ductu trapezii IK in NO ad corpus ex ductu rrapezii L. M in P9, quo-
ciestrac ipla conciner rarionent ou es cucca patabore Conuexae AB in
e e  i .     .    . .     .   p    e    u e   tett 1       1      e   .    pei    tp  u