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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
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OtC
TGVL A CYLINDRICA.
Demonstratio.
Beodem clindrotere a qua dI
Lcicudinem aequalem habeac diametro ba.
seos AD, eique circumseripeum sic prisma
AFGHIDE. F
aDF baliserianguli D F IY
dimiclia cA dianect D A, alcicudo aucem crian-
suli FFI, Pas est diame. CLAIS AIUI ISICUE
DPII quasca pals elt quadrari D A. Ergo Py.
ramis, cuius basis ckeriangulum D ETI alcitu.
do VH leu e Guucca Pats ele prramidis, cu
ius basis quadracuin  A e alcicudo DA leu
FF, ac proinde amdia est prramidis cuius
balis ele Gudcracum l alcao enctae
Ter Lb prioris dimiclia. lcdprramis, cuius ba
sis quadratum D A, alcicudo aurem FB semi
diamecer, aequalis cs 2 ungula. ergo pyramis
cuius bahseriangulum W P. HI, alcicudo D A di-
B3. mabult. Hilcta ClC vnSUIX. CC d tus prramidis prilma AP. D HI C. F criplum b est. P r8o prilma
tam vero prilma D C est ad prisma DN, VE BaLIS HIED ad BaSim MED, hoc
est +. 6, ve FT R ad M R, hoc est ve C B ad OB. per 7. durem huius eciam ongula
ACD, est ad rngulam AOD ve C B ad O B. Prgoprisina D G est ad prisma DN, ve
vnoula AC D ad rngulam AOD, et permucando reprisma DO est ad ongulam
ACD. Ecprisma D N ad vngulam AOD. Acqui ostensum eAt prilm= D C. Cosqui-
alrerum esse rngula AC D. ergo d prisma D N rnsule. AOD Cesquialcerum est.
Duodetar demonstrandum.
analoeiacum sphara.
Ahes Lectoraliam nirtum viriusque corporis similicudinem. OAendic Archi-
Lmedes exlindrum sphara circum leriprum sesquialcerum esse splixrE; _ nOS mo-
do demonstrauimus prilma vngula circum seriprum lesquialcerum efferngule.
L
PR OPOSITIO LXZILI
Aca sit quaenis exlindri recti rngula cum inuoluero suo, sive cum
prilmate ip(i circum (cripto.
Dicorres planas (uperHCieS DFH, E HOF, F A C, cplindricae rngu-
laris superticiei, quam includunt, esse se squialteras.
Demonstratio.
70. vet
huius.
unoulx lesquialcerum est.
Ectangulum quod concinctus  D A diamerro balcos, d alcicudincongula
Cs. m. DC  e rectatsuum L F FTC) aequacurc superkcici vngulari. Scdcriangula
DEIP, AFC, Cimul Cumpra, sunc dimidium rectanguli FP IICr. ergo criangula
DE EI, AF C dimidium sunc rngularis superhcici. Cum igitur rectangulum F P IIC
octenderim superhciei ongulari esse aequale, crune eres simul plana luperticies
DEHI, FBHO, FAC superficicirngularis, quam cinsune, Cesquialtere. Quod
erac demonstrandum.
Analoeia cum sphaera.
ducculuc clulatula el Aapele CMcit Dcatala atnbrecis i
Lperticici sphaericx selquialreram eAlc. IIaec eriam sphaerxe proprietas miritice
enprimiu