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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 1009, page id 1815201908:1066
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VN CVLA CZLINDRLCAI
Demonstratio.
Deodem exlindro resecetur vaeula FD C, cuius alricudo AD par Sic diame.
Lero basiS F. C. Maxinum criangulum P. AC est dimidium quadeaci circulob2-
Ccosrnstaris inscripei, adeoque quarca pars quadrati, quod sic supet diamcero FC:
Prramis igicur super bali criangula F. A C in alcicudine AD, hoc es ex hypochel F C.
quarca pars est prramidis super bali ouadrara F C, in eadem alcicudine F C. Prgo
pyramis, cujus balis estcriangulum P A C, alcicudo F C, hoc cst AD; est pars di-
midia prramidis habencis pro basi quadracum P. C, alcicudinem vero B C dimidiam
prioris F. C, hoc est semidiamerrum. Acqui haec prramis axqualis est vngulX. Crg0a 70. v0
a hitiuo
prramis cuius basis eA criangulum F AC, alcicudo AD, maxima nimirum qux in-
Scribirngulae FDC porest, dimidia est ongulae ac proinde rngula eius dupla est. Sed
veongula FD C est ad prramidem sibiinleripeam, ica rngula FM C ad sibi inseri-
Pram prramidem. Nam es rngulx per 7 huius, ex pyramides ongulis in(CeipEx PCF
elementa, sunc incer se ve alcicudines AD, AM. ergo ctiam vngula FMC maxime
pyramidis sibi interipex aupla est. Quoderac demonstrandum.
Analoeia cum sphaera.
Plam hic mirabiliter lymbolisane sphaera ex ungula. Ouemadmodum enim ano-
Lbis demonstratum e noulam pyramidis maxima sibi inseripex duplam este, ica
quoque ab Archimede demonstrarum hxmisphaerium FFIKCi duptum esse coni
maximi sibiinscripci.
PROPOSITIO LZXTI
abscilla Ccelipcum, ipsius onsulae lesquialcerum ett.
DRIImA (AENOMDE) cuiuis ongulx (ABOD) a cplindro recto
Demon-
a    te   e e  pe o   e  t e  t s u e ti e  t e test  e t     e te t  te et a  s e a   et ti  te e t et e e t   . 1  t    t t  t s lis