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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 995, page id 1815201908:1052
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VNGVLA CXIL INDRLC.
Dico planum continsens
EFHO aequale esse superticici
vngulari cylindricae IB NL C. R.
Demonstratio.
DEmonctracum eAt in 42. huiuspla-
NUM CONTINGCNS RF FTC aequale
ese rectangulo quod lineis AD, MO
COnEINCEUT. Requi demonsteatum et-
iam est propolicione 47. Superticiem
TBNL CK xqualem esse cidem rC-
ctangulo Cub lineis A D, M O com-
prehenso. ergo planum concingens
EF HTCi superticici IBNL CK X-
quale cAt. Duod erac demonstrandum.
PR OPOSITIO LI.
TNgularem superticiem cy-
lindricam secundum datam
rationem parciri.
Constructio es demonstratio.
CIc ongularis supersicies A B CD dividenda
secundum racionem daram T ad R. AaE VE
Y ad K, IE2 AD ad D F, vel iCa AD ad F F, 8
secundum FG, F. B perpendiculares ad dia-
mecrum, ducantur plana axi colindei parallela
extribencia communes sectiones in superticie
cxlindri ongulari rectas BC CFI. Dico super-
siciem vngule AB C D ad Parrem C FTD, vel
ad parcem BGFIC candem habere propor.
tionem quam habee I ad K. Demonstracum
est enim a rectansulo AD F aequalem essevn-
sule superticiem CFTD. Demonctracum quo.
que cst b rectangulo AD, P. F xqualem eNC
superficiem B CFTC. Demonstracum quoque
estcrori ongulari (uperticici aequale esse qua
dracum AD. Cum IsIEUFF. sexEI SIEVE AD ad
DF, vel F F, ica quacleacum AD ad rectanon-
Jum ADF, vel A D, F F, erit quoque re AD ad DF, vel F F (HOC ett vE L ad. R,)
ita supersicies ingularistora ad parrem C HD vel CHC. B. precticimus igitur quod
pecebacur.
PROPOSTFIO LIY. A
Ecerurrngula ABC, cls acc Pat ane oas prans guot.
cunque axixquidistanedus e rectis ad diamerrum C.
Dico luperticies ongulates planis illis intercepras eandem itetllo
cirirationem quam parces diametri DC.
siei
Decton-
in
in.
ns o e o eEaa es a EeEaESC