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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 1033, page id 1815201908:1090
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VN CVL A PAR ABOLTCA.
21137
FB ad GB, duplicara est F A ad FG. Vnde pOlFa FV quae equidistet BP, CFIE
VS hoccCLK aequalis FD, ac proinde FB dupla ST, e S T duplaTK, eAt enim
OB xe qualis a TK, cum Peomenta parabemd l equalia IBK, BR B ob aqualeS 2 FX253.
LR recta OM, cric KMIaequalis YC, d GadC LB. CquOqCBC
ab
ance preminmustoca sta CN aequarur magnirudiniinclule planis DMC.
lineas V S, FD. quia vero aequidistane recte KNY, TO sc similicer ex constructione es
hoc est RL, dupla KM; ac proince KM alsualis MM L: elt aucem Sldupla LR.
ixicur eciam RMI dupla MN, hoce  L: nam R M aqualis elt M L, e R et dupla
MN isicur NP aequalis est. MINV. Isicur K E. quadrupla eAt NL. est aucem F B ad
BG, veB C ad C O: quare B C, HBC eA R L quadcupla cA O C, hoccHN L, equa-
resigitur sune linex (C, N L hoc est NM. Ouare pyramisbalim habens trianou.
Jum ROC, e alcicudinem R N d ecace prramidihabenci balim erins  IL 1
ee alcirudinem DS, hoc est S I, hoc est R IN. quare per propolicionem quam paulo
DN C. Duod demonstrare oportuIE.
PROTOSILIOXOVIII
Idem politis:
Dicorngula Eoram AB C. D Cuverare prramidem maximam vn-
gulx inleripeam limul cu exlindri lesmenco baleos B TIED, de alricu-
dinis BC, magnitudine D M C ND bis Cumpra.
Demonstratio.
Scemet es seomencum BRC D planO DM C, in duas aegnales pactes al-bCoroll. 2
Tun eHC. quare BCM Dammidium elt legmenci cylindrici BK L. D, ac proinde D2huius.
aequale remisegmenco cylindrico A Z C B: est verocora vngula aequalis prramidi in-
scripre chimulcum duobus temlesmenris AXC B, BCM D insuper adiunetis qua. c96. huius.
cicatibus qua decerminancur patBolis AZ C, AP C _EDM C, DNO. LoituE ex-
cettus quorugula excedic lamidem inscripeam simul cum sesmenco B L KL D,
huc duobus lemilermencis crtincricis AZ C B, B C M D aequalis est duabus quan-
cicatibus quae incercipiuncur planis AZC, AP C _E DMC, DNC hoc cst
DM CHD bis sumpro. Ouodoporcuir aemonstrare.
tLOtOSL1IOZCIZ.
ortent rsa efnri paraboliciparalle lepipedum xquale extri
Constructio  demonstratio.
EC
demonstracum eAt incuper proporcionem ongule LLL  S ADC D
AB C D racionem concinet duorunt atrisilita duo: led vrgula POCN, aequacur
esse dunius aderiginca duo. lsicurrngula P OCM bis Cumpea ad toram rngulam d os. huius.
quancieatibus AZ C P Avel DM CN abasSSMMnibUS A AC L LL
SC DMCND qux SinsulX xequales l L I, ab vngola ABC D,
remanehic quanticas quae ad visgulam P C H, LatIOneM obEMCM quam crisinca
ad vritarem: est antem vnula cablaris quancicaribus A Z= C P A e D M C N D, X - c96. huius
qualispyramidi inferipee rngulae, Cmul c eemmarco quod Bastmen
BFDK sub alcicudinc B C: e noca quoque est proporcio huius segmenti BRL. D
dpramidem inscripeam rngulae, cunt es  Pata uaa  (239. hmino.
scur sicprramis habens bat D, d alchaune B C equalis prramidiin scripce
rngula ABCD, una cum lesmento B lR L. B, IeM PaS AVDBC SV
haec aequalis vngulx PO CM. bie CxuIouimus prramidem ex consequencer paral-
sulam PO C. racionem habet quam trisinta ad vnum. isicur si crigelimxe parti ba-
seos ABDY A AE Xqualis Z, a IHD L L SMe B C prramis constituacuT, CrIE
delexipedum xquale rngulx paraboliex. Ouod erat Faciendum.
Corol
n