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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 863, page id 1815201908:0920
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t 2 2 Ca L Ld
863
L6105tL1O CCKCY.
IIdem potct.
Dico rectangula M O, PFI, _ MI N C ITCUM NK C, rectangulis el-
le in concinuaratione.
Demonstratio.
)Scenum est contmuare candem racionem lincas R L, L M. MO. Igitur l2d02-
CUIF LM media TCEEIX M O, OrIeTUERN, quae cum MO, OL a exhibebi erCS 2 Per 8. lib.
proporcionales. similirer ob eandem caulam concinuabune candem rarionem P FI, de pros.
TIT, OR; ergo rectangula PHIMO, _ HTC. M N cum rectangulis GRN, crunc in
concinua analogia. Ouod erac demonstrandum.
Corollarium.
TInCcOIliSI DOTEFIEMN in OFF, planum mulciplicatum tolidum extribere quod
LLsic duplum corporis orei ex ductu LuDEFECICrUI MUTUIO MIK, K HI: nam TK L.
TTRM _ CKN, lunc proporcionalia. DcindeM O, P II _E M N, O HI cum NRO
lune proporcionalia; igieur IKI. ad PII in MO, habec duplicacam racionem cius
quam habec FIRM ad GFI, duccum in MNV, cum primus cerminus sic communis
in duabus illis seriebus erium concinuarum. (cd rario IKL. ad PHI, ductiin MO, eA
vrins ad quacuor, re constat ex discursii praecedenci demonstrarione Facto; igIEuF F2-
EiO HIKM ad HO, in MINV, e racio rnius 2d duo, camracio qua drupla sic dupla
racionis duplicaca.
VINEPaFaBOIX VE PTIUSCOMIHICuCA LuBaILCIMOABC, ADL MM: HIC,
D CB Xequales incer le, vri _ AF, E D ac proinde C F, quadratum; et
ACD, Tabalterne adiiciacur in P. FD. Deinde hac Cemicirculus AC C.
Dico corpus exorcum ex ductu HIL. in L. 1E aequale este semicylindro
super bali Cl et alcirudine AF.
eROEEIOBL
Demonstrario.
Saledenci propositione demonstrarum est solidum emergens ek et LIL. III
L R. duplum esse Colidi quod gignicur ex ductu HI in T M, blcdColidu CLuu
FT in L ML, Xquale est lemicy lindro super bali CiI, d alcirudine TMI. Igieur uLL R 
Eicaqualis A F; quae dupla est A B, vel IM, manifectom eA cOrpuS CX FIL. IN L. I
aequale esse lemicylindro CI, baleos, et alcirudinis A l. a 
RFKEE 2
RO
1
dum.
aetet1111121132215 1617 18 2O E0 2L 2L332A 33 2C 27 28
111