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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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6
ENGYLA CZLENDRICA.
Demonstratio.
Alem enim Havet rarionem quadrans cxlindei ac
parallelepipeuum lub bah BEI ex alcicudine F C
qualis incer bales, quadrantem Loilicer BDFi, e Pa-
rallelogram BElareperitur: Sed octensum est b pa.
rallelogrammum BET maius esse dimidio quadeantis
DBF, igicu ettam Pacallelepipedum sub bali B II, d
alcicudine LC Mraius est dimidio quadranris cs Muel.
aetac demonstrandum.
Corollarium.
Vod t astertum de parallelepipedo sub BC H, _
alcicudine F C respectu quarcae parcis cxlindri DB B
Cclau incellisendum de parallelepipedo sub basi GK, e
alcicudine FC respectu lolidi quod sic lub Cegmenco cie-
culari D G FI, & alcirudine eadem F C, atque ira de ce
nintinieum.
PROPOSITIO XI
Adem manente Egura:
Dico (i parallelepipeda hoc modo qua-
dranti inscripea cylindrico, ab eodem quadrance lemper demmaneur, resi-
duam candem tore quancicarem omni Colida magnicudine dacaminorem.
Demonstratio.
Npraecedentis ciusque Corollario demonstracum est paralle lexipeda illa maiora
existero dimidiis quancicatum extindricarum, quibus inscribuncur. Duare _ ab his
illae collaneur, semper plys auferecur quam dimidium. Ergo perr. decimi relinguecur
candem ex quadrance exlindrieo quancicas daca minor. Ouod tuic demonstrandum.
eROPOSITTO. XII.
Vadtantis cplindrici basis ADF diuila (icre prius; sectanimirum
BD in parces aequales C, I, _c. perticiantur parallelogramma
BHI, CK, 8c. Cylindro deinde inscripea Tinc parallelexipeda ve
prius lub iidem balibus. Denique secundum rectam DB, de quoduis
punctum N in linca F C, qua est in cy lindri superticre, planUm agaTuT ex-
hibens ungulam FND.
Dico etiam ex ipla tandem rngula relinquendam quantitarem qua-
visdata minorem li cadem operario in bali cxlindri concinuetur quae lu-
periore propolicione imperata fuit.
Demonstratio.
Scenlum eAt exipso cytindro rehaHAM LONC GUAMELALEM QuABIS AATA MIMOTCH.
ledhec pars residua maior est reliduo quod remanet ex ipsa rngula. igitur cum
rnsulx residuum pars sit eius residui quod remaner ex iplo cylindrO, PATCE veritaS
propolitionis.
2
PR O