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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 1201, page id 1815201908:1258
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QV ADR ATVRA CTKCVLI
ad R, _ L ad S, siTAd PFOPOREIOCH qua CA inter rationes corporum ZX ad0
d Y ad P, veproporee, qua est incer rationes corporum MI n ad RB, e I dac
Ssi elldd proportione qua eltincerrationes corporum ZB ad 9 ∞, e Y p ac
PE: acquesdconsequemer de reliquis, et hoc quidem in omni subdiuitione diamc - 2 Per 11
erorum patbolx: intero per CorolI. proporcionis Lemmaciex luprd citacx, quod
proporrio  eltincer ratiollem agoregaci corporum MI, L, K. I, ad aggrcgacum COr-
porum 11,5, l. V X incelrationem agoresaci corporum X, Y, L. co ad aseregatum
corporu . P, O. H, Calteu cum proxorrione quae est incer rariones agoregnci
FOTPOTUI MIN, C d, Ky, IB ad agoreSacum COrpOruM R e, SS, Pu, V n. de rationem
ngeresaei corporum XB, Y P; L WV;ca ad AGBTOGAEUM COEPOTUM Q , PE; O vt Y pu
Duod fuic deandum.
PROPOSIE
12. h1s
+261
1
Dico quod rario corporis orti ex ductu parabolici legmenei
EC5 in sc iptu, alt corpus quod exsurgit ex Agura parabolica vHIF
in se ducta, sic ad rationem corporis orri ex fgura parabolica IIF eD du-
eta in seiplam ad corpus quod reTuleat ex ductu tgura EOHa in Cciplam,
veratio corporis ex ductu AguTR F. CCP in (c ducta Cubalterne, ad corpus
Oreum ex ductu Fgurx vHL Fx ductae in Ce subalcerne, est ad rationem
corporisnati ex ductu Agurx LIFae D in le lubalcerne, ad corpus quod ex-
Tursit ex tigura F O na duet à in se Cubalcerne.
Demonstratio.
PRxcedenti demonstratione ostensum cst, quod rario incer omnia parallelepipeda
M, L, K, I, e omnia parallelepipeda R, S, Y, V ad racionem incer COrPOCA X, Y
L, a _E COTPOTA O, F, O, NY AEVEFACIOINEEF COFPOTA M N, L d, Ky, IB, _ COrpOTL
Re, S0. Lu Vmeltad racionem corporum ZB, YD, Z. IV, co a ad COrpOT2O D, PE, Ov
Nu. _ hoc quidem in quauis inscriprione Agurarum per subdivitionem linearum
P. CG, HIF in infinicum incelligendum est, ex vi dilcurlus in demonstracione poliri
Cumisitur concinuacis semper divisionibus auferarurb Cemperplus dimidio relidui
corporum illorum quibus parallelepipeda inscribuntur; ac propcerea cum omnia b Per +2. e
corpora limul sumpea extiauriane corpora quibus inseribuntur, manitestum eA racio- +3. duct.
nem plani paraboliei F G2F in se ducti, ad planum parabolicum vFT Fx in Ce du-
ctum esse ad rarionem plani parabolici YIF a D in se ducti, ad planum parabolicum
F.CHa ductum in Cc, ve racio primorum corporum in le lubalcerne ductorum, est
ad rationem secundorum corporum in se subalcerne ductoruns, cum tixec ipsa corpo.
rasinc, quibusca parallelepipeda circum (cripea fuerane auc inscripias Hlaecporro
corpora, similicer acque in secunda ex cerria quadracura praecticum a nobis est, ad
corpora cxlinderca iplis aequalia reduceneur. Restac re propoliciones iam aliquorhie
subiunsam ex quibus manifectior rario circuli ad rectilineu CrHaTUF.
k OFOSITIO
X 1
Anence eadem AguTa.
X
N CircHIO ABC CONHCLLNAMENL OTMIMACI ad GTAMICCOI CLa
BD; E F aequalicer scmtora a ceuctot. Iumplo acinae alcub lcom
menlurabili cum BF ponanut oramatim btL, lR aequales.
orceac aucem L M elliplim altisnare, aa quam circulus ABC
ealem Habear racionent; guulis etla cucuu lesmeneum, ad cllip-
seos leseu, alum paralletis BM _ FO; aequaliEEF a P CCNFTO
communi alao.
Con
   e it 1    1   . e  te   1   1.  te 1  . .     e   1  1 t  1  .   e t  1 s 1 .  s 1  1. 1  1  .  e  11u.