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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 1221, page id 1815201908:1278
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Et aDRALDRA HXPERBOLA
ER O POSFTI
CXLIV
Elumatur figura similis Illi quam propolirione 133. huius expolui-
Lmus _ inter AC, AB potantur medix proporrionales AD iuxta Le.
Dico hsuram parabolicam AD ductam in sc, aequari Rigurx AB, du-
Demonstraiio.
Vmenim ex hypochesi AB, A D, AC SINE In CONEINUA, EFGO DE PALCE EK PEO-
poltione rnivertali quadras ea quinca libri de ductu plani in planum, quanci
eaS AD in se ducta Condum producer, quod aequecur magnicudini solidx, quae consi-
cicur ex duarum superlicierum B A ee A C muruo incer se ductu. Duod erardemon.
Arandum.
Corollarium.
DCArO COrpuS Orrum ex ductu sgut parabolicx B A in figuranmi parabolicam AC
Ladpataelepipedum reductum else paret, cum solidum quod nalcitur ex ductu
Parabora AD in (c, quodque corpori isti in propolicione ostensum est aequale, ad
parallelexipedum reduxerimus. Nam D A in se ductum est innoluerum Polidi quod
remanet ex exlindeo parabolico polt ablacam rngulam, est aurem ex cxlindrus para-
bolicusa de rrgula bcubaca. ergo e Colidum illu d residuum cubacum est. Ouare cum 2 Per BZ
illud solidum residuum cum suo involuero conticiac prilma rectilincum, iplum quo- de cylina
queinvoluerum eric cubarum. sed D A in Ce ductum est inuoluerum illius residui. clinir-
Frso D A ductum in sc est cubarum. Oux vero de coris illis superficiebus in Ce vel
in le mucuo ductis demonstrata sunc, eadem eciam non dissimili rarione de illarum
Parcibus aparallelislineis DB AC, C AB D incercepris; demonstraneur.
PROPOSITIO CXLV
Elum peX hyporhesi priori im lcemace constituanEur AB, C D, E F ad vide sion
sulosrectos ad communem axem CHI, occurrences sectionibus Pas. 1221
varabolicisin 1, MI, V: N, O, Z; B, D, F; de hyperbola in 7, 8, n; e lub-
Dico rarionem Colidi, quod otrrur ex ductu IRLMI, in RL ON ad
tolidit ex ductu Cuperkicici M L FY V in superticiem L. OY FI noram esse.
in Cuper hocam e actenemondi ex ductu plani RPOL in IERSL. ad
Colidum productum ex alcta L. OTHI in planum LSXHI.
Demonstratio.
norem propolicionis 131. huius libri, eric parabola DD.
etx la: AC.
centis PT, RX, in P, , Lk, S, X.
Scensum estc cui parallelepipedo equetur corpus ex ductu mutuo planorum cRerco
TRLM in RF O N, quemadmodum CtaM dC COrPOTC Cx duct ML. FIV in roll. 144.
superticiem FO Y FI. Insuper ostensunt en s Cu patasserepipeao  quecar solidum dExs. d
ino
raciopalatte cdi   lidla qude criblatio extrbilit, vc quibuo abe
propolicio. Duod crac ostendendum.
explanis RPOT _ R R SI in CC mucde u, d cocem modo elli ae qualo sic10. au s.
lidum ex superkicicbus I. OTH _ LSLI huetC ancs. Suate, C noca sic
(   u   t  pit     t 1.    i 1e   s . 1a  p e   s        se  ute  a     e      u   p  gun pput 1