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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 1121, page id 1815201908:1178
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111IIIII
EY A D R A FVR A
Corollarium.
Tinc parec rationem parallelexipedi super FFL, TL. Sad parallelepipedum su-
DEERNK, NK C, cocies per maciplicationem continere racionem parallelexi-
DCMaPeF PTL, IL T, ad paralletePipedum sUPeF ONK, NR V, quories hxcracio
per mulciplicationem conrineclallonem parallelepipedi luper P. II, II. X, ad paral.
lelexipedum luper ONK. NKHI.
PROPOSITIO XXZIR.
IVper recta AB construantur quadrata AB C, B A D quorum diaoo
DHales SInEAC, BD: descriptisque parabOlis AF C, AFC, _BGD,
BHB quarum verrices sInE LL _ B, altumatur quaenis IR, in recta AB;
qua diuila in quaruor parres a quales in puctis L, MI, N, POnatur Per Ca Pa-
rallela laceri AD, CCagonalibus in punctis P P, OO, _ TT.
VV; Pasabolis aurem in punctis F F, R R, EE, OO, SS, 6G, XZ, TIII:
compleaneut deinde rectat ala FIL, F LMI; R MN, RNK, e IL. 5.
LMS, IMNG, NK C; himilicer recranouta L IP, NIL. P, NM O, KNO:
item recrangula lL. L, L. M P; MNV, NK V; quemadmodum _ RCCta-
SULALIE, ML E; NMO, RNO; _IL X, LMZ, M NII, NRFI.
Dicorationem duorum parallelexipedorum quae hunc ex recrangulo
FILinILS, d ex reccangulo FI.MI in L. MI S, ad duo parallelepipeda
quae Oriuneur ex planO R MIN in MNG, _ ex planO RNK in NRO
planum, tocies conrinere rarionem parallelepipedorum quae signuneur
ex ductu superficiei P II. in IL. T, _ lOPeFRCICI PL MTIn LMT, ad paral.
lelepipeda producta ex baliOMI N in MNV, _ ex baLIONK in NKV,
quocieshac iplarario concinet rarionem parallelepipedorum quae hunt
ex duccu plani F. IL in planum IL. Z, ee ex duccu plani P. L. MI in LMI X,
ad parallelexipeda Facca ex duccu plani OMN in MI N EI, ex plani ONR
In NRHI.
Demonstratio.
D contutionem vicandam omnia hxec rectan gula quae in vnam Rguram consesta
LLlunc, in rarias figuras sezregabimus, ec lingulis rectangulis Cuam licreram htel
bemus quasplorum nocicia habeatur, ve discurlus racio nonnihil subleuerur. Lcsu
igicur schema parciculare comprecatu las ileemale uea Comuas
qua terminantit in parabolis convexts La. Seclau veloconaleas
quarum cermini in figura rnivertali sune recte PO X V T. Terrium denique Aigu-
rasreplasenter concanas parabiolas FR, CS, figurarniverlalis. Anc aurem petun
Cchemari inlcripea eccatgula A. B, C. D: Xl. 1. Cl. lecundo similicer rectangula
dumigicur elelationem parallelepipcco e LC MC SI L, au pacancnpipeda
redorum quae tiunc exrectangulo L L, d lem uupulantete ipeen L inP, e
BK L, M _ NO, P, O, certio quoque rectangula R, S, T, V, X, Y, Z. e osenden-
ex T in Z, _ V in X, tories continere per mulciplicationem rarionem parallelepi-
M in O, quorieslixc ipla rario concinecracionem paralleleppeaoea ilele
Blb, ad parallelepipeda ex plano C in C, e D in FI. quodnCole. ale pa
rallerepipedorum ex k in L, _SiM L, da Patatereea ca L  c a eAt
eddem cum rarione parallelepipedi ex R in L adparallelepipea Ca u L delk
ad para L L  I O. eadem est cum rarione paralle lepipedi huius.
Kn  aet rIn C, Me Cuas Factore Palstelepipedi ex S in Y ad parallelepipeda
ex T in Z, _ ex V in 8.  Similicer rario parallelepipedorum ex Tin N, ec Cx R in O.