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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 1000, page id 1815201908:1057
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V N CY L A CYLLN D R IC A.
Onstructio e demonstratio
JladE L L, FML normales ad diametrum
AD, e ex cylindri axc abscinde rectani
N K. verectangulum RNLaequale SIErCAd
suto ADM: ductâ deinde RLF quxe a qui-
dister NB, Aac sectio per AD lineam et FI
punctum, _ dCMIEEAEUIE F. C gua X quidi ACE
BTI. Dico superticiom HICP B aqualem
esse superticiei FOD. Es enim luperticies
CBP aequalisrect angulo a AD N I, hoc est
NTBC, sed ve superticies FBC ad FBFF
ica est B C linoa b ad linceam B IT, hoc est
rectangulum BC, NVI ad BFI, NI rCctAB-
gulum. Igicur eriam rectansulum BII, NI
hoc estrectansulum RN, NV L aequale est lu-
perticiei vngulari P. B II. Sed rectangulum
ADM eectangulO R NVI X quale cA Cx CON
Rructione. Igieur rectangutum AD M ae qua-
le estsuperticiei FBII. Acqui etiam luperti-
ongulari superticici F DFL super areu B F. constirura est aequalis. Pexsicimus er.
80 quod optabatur.
EROPOSITIO LLA.
Inc dux rngula CBO, L F O, quarum alticudines diameeris baliuti
Cinc pares. secentur aucem planis axi parallelis perpendiculariter ad
diametros, (cilicer planis L. AB, NI PIE, IDE, RFC.
Dico luperkicies hisplanis contentas, habere rationem compolicam ex
ratione diamerri C Q ad L. O diamerrum, ee exvatione ML. ad K I.
Demonstratio.
1000
7. huius
65 + toaiuo.
eA6huins. cies vngularis D F Oaequalis est rectangulo c A DMI. Pgicur eriam luperticies D FO
2 13 duiv. L.
Fmonttracum eltd superticlem igutarem ABRP C CcaDL.M
aequalem. ostentum quoque est rectansulo L. OIK X quaL. ,
titt