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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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QV ADRATVRA CTROVO
Sali pami ad sccundum aggregacums, a Lattones aggresaci certii ad aggresacum
quarci, siceadem citpoPelione, qua est inter raciones parcium aggregatorum
qux ancecedences contticuebane, e raciones parcium aBgresacorum que conlequen-
Suia vero demonstratum etc quod proporrio qux est intex rariones corpOruM (+ 286. huins.
2d L, e HL ad V, ad proporcionem quae estincer rationes corporum P ad L, X 9 ad
M. Cc Deproporrio, quae elc inct rationes corporum CZ ad Tn, e FIB ad V u, ad
DrOPOEtOnEM quE CICInCEFFACES COrpOruM, Px 2d L d, _ O D ad MB, acquC it a p eor S
consequenter b derelicsns, _ hoc quidem in omni subdiuisione diamerrorum p2ca- e
bolxsintetd per Corr. Prop. Lemmaticae lupra cicacxe, quod proxorcio quxe clEintex ins-
racionem agereeari corporum C HI, I, K, ad aggregatum corporum Y, V, X, Y, e
incer racionem aeoregaci corporunte, Q, R, Siad aggresacum corporum L, M. N.
O, cadeuccum proporcione qua elt incer rationemasgresari corporum  Z, FIB
C7. Las aclavoreracum corpotum Ta, Vun XV, ZE, e incerrationem aggresari
CorpOtUM PK, DiD. K_ Su ad aggregarum corporum L ∞, M C, NI0, Od. Duod
tuic delerandum.
eR OPO5IF1O, XC.
Adem manenre tigurarnivertali propolicionis 84. huius cum parri-
Do quod racio corporis orti ex figur 2 parabolicd A F a z in le ductâ,
ad corpusertu ex hgia patabolica C. L. n a in se ducta lic ad rarionem cor-
poris orries sua PataBolCa C. For in se ducta, ad corpus quod exlurgit
exhoura parabolica A F F Zin lc ductâ, ve rario corporis ex ductu houra
AEaZ in le lubalterne, ad corpus orcum ex ductu hgurx C Fna in se sub-
alcerne, est ad rarionem corporis orri ex ductu Rgurx C Fvr in le (ubal-
terne poliex, ad corpus ortum ex ductu Agura AF FC in le lubalcer-
HC.
Demonstratio.
DRxcedenei demonstratione olensum est quod rario omnium paralle lexipedorum
G, LBL, K, ad parallelepipeda L, V, X, Y, Sc ad rationem corporum P, G. R, S,
ad COrpOTA L, NI, NI. O, ve racO COrpOruM CZ, TTB, I7, R d ad Corpora TX, V u
Xv XE. est ad racionem corpor PX, O P, R I, Sci, ad corpora L W, M C, 10,OD.
Ee hoc Guidem in quanis intelipcione fisurarum per subdivitionem lincarum A F.
C F incelsisendum est ex vi oncursus in demonstracione polici. C um ergo continua-
eis subamitionibus, auferacur lemper plus dimidio residui corporum illorum, quibus
P. hIc
parallelexipeda interibuntum, ve demonstratum est d. in libro de ductibus: aC pFo- d +1. DC
Peerea omnia simul sumpea exhauriane corpora quibus inscribumene, manifestum est
racionem planiparabolici A FaC in se ducti, ad planum parabolicum CFi na in (c
ductum, esc ad racionem plani parabolici CFur in se ducti, ad corpus ex plano pa-
rabolico A R FC in se ducto, veracio corporis orri exductu plani A F. a C in sC subal-
cerne, ad corpus ex ductuplani C Fna in se subalterne ducti, est ad rarionem plani
CFor inse ducti siibalcerne ad planum A F F Z in Pe subalcerne ductum, cum haec
ipsa corpora ine quibus paralle lexipeda fuerane interipra.
1ct.
cluvices supplebane.
Scuraribus;
lKOTOSIIIO ACI.
DArabola AE B aris sIEB C, MICCSKIOLB, C,, Qua sCCa
BA ducta ex verriceD.
Dicoleomentum B P. A ecelum ut le sccundum lincas L.D, LC eHe
ingulam parabolledu qua au Corpusrectilincum ei xqualereducta (IE.
IEK K
Demon-
o  et  s e1  t 1e   1e e 1e e e es e te  p e s  s p t    s   Ae a e e    e p t u t e s e  e te t . t et e e  e e 1t e e e    osi se isa