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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 792, page id 1815201908:0849
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CTYS PL A NL
Dico planum R I ductum in alcirudi-
L. LLxquari F. LI plano in se ducto.
a Demonstratio.
DROnUDANEUE FI P. L paraIICLA In K, L, NI, quo.
niam ON, GP, GL proporeionales sune et
C F B Bacabola, rectae a L FI, L F, L K proporrio
nales lunc: quia vero TIF lincis aequales sane
LI recta Quoquebr. FB FIR. IK proportionales
c
quarecKY ductum in alcicudinem L. HI
corpus proterr xquale illi quod oritur ex dudu
alc.
tROPOSITIO CKXZIX
B axis parabola AF F, aqualis la-
Dceri recto; policaque ad illum ordina-
_nea F. B; luper AB ve diameero
circulus describatur AC B qui ecoruIS
cadecinera parabolam, circulum hunc
contingane linca C. C aequidictans AB,
de AG, C D. 1
DicoC L. planu ductum in G L, Equa-
ri FC plano ducto in alcicudinem AB.
Demonstratio.
Veantur ad A B paraHIelX inANIEX CiFTT. EI, iungaeur item AF. Ouoniam
AB aeguarur larerirecto, linex F B, B AC aequales sunc ec D B quadracum,
quia vero CC concingic semicirculum super AB lacere quadeari descripeim, ex ele-
mencis pacer illam a diameero quadrari A F. bilccari: adeoque rectam A V. cransire
per C punctum contactus. ex quia AC, C C continsences aquales lune, xquales
quoque obrriangulorum similicndinem crune AC, CFK: vnde AC quadcaris id cst
quadraris CK aequalia lune rectangula TCT. Sed _ CR quadracis aequalia quoque
567. parab. TunC, Frectangula FCFI: rectangula isieur F C+ FI xequalia lune rectangulis IG F.
3+6. huins. Planum igicur F. C S ductum in alcicudinem AB vel C FL equale corpus producier
illi quod emersicex YC ducto in 6L.
PROPOSITIO CXL.
VIcrurtum parabolae F. F axis A C aequalis laceri recto de super AC.
Ddiamerro delcripro circulo, contingaceum AI.
Dicoplanum F. P. ductum in P. HI gignere xquale es lindrice quadran.
ii, cuius balio BF, et alcirudo AC.
AEXCON
cersa 3
C0r
46.
2 1264a3
3. Parab
Demon.