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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 999, page id 1815201908:1056
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AOYLA CLLINDRTCA.
Sulum FDK ad superkiciem E DR FI, verecta F D est ad curuam AD P. igIeUF CF- a Demon
9
Jam pacs luperticiei rngularis LCD ad cylindricam L. RIL elere eD rccta ad) un
curuam F D. Ouodtuic demonstrandum,
eROPOSITIO CVII.
Acus Cc eylindeus NL alticudinem haven AC PAtCM diatrietrO.
Ponancur in platto peraxem ductorectangula B AC, BF. C Xqua-
liaincer se, sicq; vngula AL. II secta plano BID, quod sic ad AN diame-
trum normaliter consticurum et axi equidistans. Fact a deinde HIK, X-
quali B F per AN d K punctum, hac lectio rngularis AF R.
mili ferc
Dico AID supelkciem ingularem a qualem esse rngulari superticici
L
TFXII.
Demonsradio.
discurst
10 Arch.
medes 2si
sed demonstrarum eAtcD IFTL superticiem
aequalem esse rectangulo super BNV, ex dia- 111
mecro baleos, hoc est rectangulo N B O, igi-
Cur VE CA TIR ad HTL, ita CA TTIFR vn-
sularis luperticies ad rectansulum NBC.
sed ve TTK ad HT, hoc eA, quia BF est
exhrpocheli agualis HR. VE BF, ad TIL,
sinc BO, ica Mtojuelectangulum NBF. 2d
NBO reltansulum. Bicur rectangulum
NVBF. 2d 1DC eccangulum est er super-
ficies vnemlaris AILK ad rectanrulum
NBO. Accao ioItr NBF xqualis i
est superficies rngularis TITFR: eA aurem  ii
ex supponcione rectanbulum NF aequale
BAC, cectangulo. ISTuF HIIF K vngularis
superticies rectanoulo B A C, aegualis est. ac-
oui ostensum est d rectangulo lub B A 8
diameero, hoc est ex liypocheli rectangulo B AC, xqualem elle luperticiem rnou-
larem AFD. est icaque superticies AID ingularis aequalis FILFR Cuperticiei.
Duodtuir demonstrandum.
i Sc enim superheres vngularis FFF R ad
Cuperhciem HFDL, ve HIR ad B FTL.
AOTOSILIO LVII
est prop. 1
imens. ctt.
654. huins
c 47. Buius
d46. hu
Aca SLVngula A. B C D cuius alcicudo B C par (IE diaMCEO AD, e
arcus BL. in lemeneBD.
Oporrear (uperarcu B. apel eoe guate qua il a
qualis ingulari superticiei darae FOD.
s
1.
(e1 11
10.
Con-
   m