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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 979, page id 1815201908:1036
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VN GVLA CXLINDRTCA
Demonstratio.
X Ccholio 27. Pacec involucrum corius ungu.
Ie cuius alcicudo est diameter AD produci CX
ductu plani AEBFDB A in plarum quod
compolicum est Cx planO A F B F D B A, _E EOEO
circulo cuius diameter AD: involuerum vero
parris rngularis nalci ex ductu plani IKBML. BI,
in planum quod ConsZaC planO TRBML BI, e
toro cireulo, cuius diameter AD. Ergorinvolu-
crum corius rngulae est ad inuoluerum partis in
criplicaea ratione eius, quam habec F. B adRB,
hoc est eius quam habee F. F a+ RMI, hoc CA
eius quam habec AD ad IL. Aequi eriam rngula
EOTa _ B D C es ad paTECM VngUIATETONLBI
in criplicaca bracione eius, quam HabCE AD ad
TE: ergo involuerum eocius rngulxe est ad invo.
lucrum parcis, veongula coca est ad parcem; Per
mucando isicur, involuerum cocius vnsulx est ad
cocam ongulam, reinuoluerum parcis rngularis
ad iplam parremongularem. Ouod erat demon.
ctrandum.
PROPOSITIO XXIA.
AEUM SIE AF BIICGDF inuo-
lucrum vnoulae ADC, cuius alei-
cudo par (ic diametro AC: ducaneur q
BA, BC.
e
Dico involuerum dacum rnoulate
aequari duabus prramidibus qua pro-
ducantur ex triangulis AF B, C BII,
Cingulis in se ipla ductis.
Demonstratio.
aequatur c criansulo BCHI ducto in (c-
ipsum. Similicer planum mixcilincum ABP.
ductum in planum BF A O EquaEuE B AP,
criangulo in se ducto. Ergo cocum planum
mixcilincum CI B A F B FT C ductum in to-
cum planum F AOC FI, hoc cst per ca qux
in Scholio 27. huius demonstrauimus, inuo-
luerum dacum rngulare AEBHCODF,
aequacur duobus criangulis BCFI, B A F du-
ctis in scipsa, duabus nimirum prramidibus quae ex illis ductibus oriuneur. Ogod
crac demonstrandum.
Corollarium.
ancaame
ud
huius.
Duct
rigura. ipole verin piua hocum, Cumeue atas Cononet tau panos
nempe inuoluerum, noca lic, noca exie et altera quxe est ipla vnsula.
TIncalia rurlum nabetut ieca Cudacura. Cum eu Copou Ca otac
L R O
  ui uu u s ue i  ue ate  e  e eie u tite t  u      t    . t. e    A   et      1  p t i         u