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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 1028, page id 1815201908:1085
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YNCVLA ERRRDOLIOA.
1028
vidat B Mt BHactamint, de ploducat communes sectiones AO, AVI,
Dicoisleur ab eodem plante es Bilatiam quoque dividi aggregata
prilimarum quae reliduis trulti cxlindrici segmeneis inscribuneur, hoc est
Colidum AFBGDIHAOR OZPV A, aequari lolido AVP XORO.
ARLNOLMLRA.
Demonstratio.
Voniam AF aqualis est FD, hoC ClC
L5O, e F. S aequidistat AR. CFIEA Y
aequalis T O, est aurem P B ae qualiS P MI:
excostructione; igicur parallelogrammum
CA F B P T quemadmodum e Agura
PTSM quia vero sesmenca aequalia lunE
ATIB, _ BID, HOCCAR L MI, MNO, e
GI, FEI diameeri diuiduncrectas AB,
BD bitariam in F X C, a crie criangu.
lum AFIB, aequalecriangulo BID, hoc
eA criangulo MIN O. quare cum eciam lic
alcicudo BP aequalis alcicudini MIP , Cx
constructione; pars prilmacis habens ba-
sim criangulum AHIB, _ alcicudinem BP
aequacur parri habenci balum criangulum
MNO, _ alticudinem M P. Sed etiam EO-
cum prilmahabens eandem basim eriansu-
lum ATTB, e alcicudinem BM, xquale
est prismaci Cuper bali criangulari MNO
_ alCICUdINC B MI; IgICUr AVPOMZKI
residuum cuius balis esteriangulu AVPO.
XGUAEUE PXORBGD L. alceri residuo
cuius balis es criangulum P Z OR. Eocum
isicur tolidum AFBG D TH AOROX
PV R, Xquacur ColidOCOci AV P XOR
OAKLNOYMZKA. Ouod eracde.
Corollarium primum.
VOdGTubEenSis AFI, FT B, B I. IB. bitariam rursum diuisis per diamerros inscri-
Lbaneur legmencis parabole reliduis noua rursum criangula, 2cque ita procedacur
in infinicum: actisque per lingula lacera planis inlcribancur residuis erlindripara-
bolicilesmeneis prismara alia, eodem dilcursu demonstrabimus, plano eodem illo
AF O. bitariam semperdiuidiaggregara prilinatica.
Corollarium secundum.
VO, PO, PAO, ZR, PR, 1, LP
Hlispoliris demonstrauimus in preccaen a ee coutu
E M O, bilccari plano A PO.
AocylindricO ABD O MIK, cuius aduer (a plana Cunc criangula ABD,
monstrandum.
Lterri poceric cxlindricum corpus parabolicum bitariam in parces aequales diui-
Cum esse ex eo quod in infinicum per constructionem peaescripeam inscribi possine
verisque aequales quancicares qua lemper plus dimidii residuorum auterane; unde
per caquae de progrestionibus dicta lunc, concludirur plano AP O bitariam diuilum
sc cxlinaricum lesmencum quod bali contac A B D es alcicudine MB.
PL
Yqre consequenter quories planum AP O dinidic lineam B M BiFariam recte in-