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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 485, page id 1815201908:0542
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ver.
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P AR ABO L A
Demonstratio.
Ccuctal a B I, ParabOIX AF. C in K, e AD
in T, cumigicur AC bitariam in P, Sic divila.
et C D aequidister BI, crit ec A D quoqueinL bi-
tariam dinila ecordinacim ad L K diameerue posi-
ta: quia vero A C normalis ad CD, verique para-
bole estcommunis, erie A B C parabola ad serinens
tum AE D, aveB Iad I. K, (cumracionem habeane
bcompolicam exracione D Tad L R, 8 A C ad AC)
sedve BI ad PR, SC CF ad F H, GuaL K CH da1
AL D rectanontum ad rectangulum A FL D. SL VE ATC ad AF C, rectanoulum. huusi
isitur re L C+ ad F II, sic ABC parabola eA ad legmencu AF. D. Guod crac de-
onstrandum.
PROPOSIFIC
Ic ad ABC Pataveae BB, Oraam POSica A C, contingens
cidc
1.
DVeroBE, qua CIECLR CK C ATAMETLO OCCHITTALII L POLITA, AUTeI A P.
ua dxemlecerm l: e parabolam in Ci, per A, L, C parabola delcriba
cur, habensapicem in F, ponacurque ordinacim. CtI, Occlerens axiBD
N I.
Dico FLB O parabolam ad parabolam AF C duplicaram habere r2
cionem +16 2d AC.
Demonstratio.
Voniam EB, A C aquidictane, ve AF ad
LFF AC F D etC ad F B, e F B ad AD: Se d
AF,F L XQUalES (UnE, XQUANEUFIGIEuF F B, AD.
ec B Et D: quia retb dP F dupla cA CF, id cAt
BIcupla IF, eric L F B dupla GI; vnde tOL2
TIC aequalis elt F B, id est AD dimidio re.
etx AC; guate deBIadBF, id cA FD, hc
FIC est ad AC, est aucem rario parabolx HIBC
ad AFC parabolam composica exrarione c BI
C 261. DM
ad FD, _ HG ad AC: igirur ratio parabolx FIBC adparabolam AF C  M.
caca est, II C ad AC. Quoderac demonstrandum.
PROPOSITIO CCLXXIX.
IIdem Policis.
L Dico ABC parabolam, octuplam esse parabola IIBC.
Demonstratio.
Voniam AD, TTC linex aequales sunc octenta, e BD quadrupla ipsius BF
Le criangulum AB C octuplum esterianguli HIBC, sed AB C parabola est ad
parabolam HBC, ve AB C criangulum ad criangulum FIB C; octupla isitur est CEx ele-
parabola ABC, parabola FIB C. Quoderar demonstrandum.
PROPOSITIO CCLZKZ.
mentis.
CInE ABC, Be parabolarum, axeS BC, LF, diuisoque BC vecun-
que in  Mluidatur _ F. P proporrionalicer in B, ponanturq; ordi-
nacim (IO, TK.
Dico C. B H parabolam esse ad pacabolam LFHC, ve AB C parabota
est ad parabolam DFF.
eP
dr
Ba
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