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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 787, page id 1815201908:0844
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N PL A N V M
IF dein quoruis ducantur GC parallela ad AB, OcCurrentes L. F HIHCIS
in C: _ E. IF rectangulis xqualia hanc rectangula C IFI.
Dico corpus ex HIF plano in alcicudinem C l aesuari magnicudini
oreae ex ductu superticici 6 F. in IF.
Demonstralio.
Noniam ETF reclanoutis id est
Lrectangulis AIB aequalia AINE
rectangula GPTT CFUNE PUNCCA ATY
aad parabolam: vlcerius CT eA ad
P G7, VE TF adHTF, adeoque e
GF, ad GI, VEFHI ad IF: vnde
FTTOT recrangula aequalia suNE
reccangulis GFIF: ex cum alcicu-
do omnibus sic eadem exie b FI F du-
ccum in GT alcicudinem aequale
OF ducco in IF. Quod fuic de-
monstrandum.
PROPOSITIO CXXVII.
Tirculum ABC secet recta quaedam A G parallela diametro C D,
Acrectaque ex K contro orthogona K L P describatuEper C L. D el
liplis concingenscirculum in C e D, dein ex C dc D cangenres erisaneur
occurrenres linex AC illiulque parallelis in O _ R.
Dico corpus ex ductu OF in FR, eam habere rationem ad COrpuS ex
ductu OC in CR, quam habet L. I5 ad FHE.
Demonstratio.
Veca quavis X V aequidistantere.
CTX TK, que circulo occurrac in
C,  Cllipsi in F AGaNEuE per G _E F
Parallele diameero CD: erie igiene
RGO rectangulum xquale ReCTAN-
sulo R FO, vnde parallelopipedum
habens balim rectansulum RCO
ex CV alcicudinem ad parallelopipe.
dum habensbalim reccagulum R F O
ex alcicudinem FV est vE C V ad FV
hoc CstveTR ad LK cEimilicer oAté-
demus intinita parallelopipeda inscripea corpori nato ex muruo duceu planorum rur ex illi
t c0
OO, CR ese ad intinita parallelexipeda in scripea corpori geniro ex duetu mu- de ellipse
ae in lib.
CUO planOTUM O F, E R VE TR ad T R. croo, rei Facile deduci porest e dilcurtu 15. ostondi.
huius, magnicudo orca ex duetu O F in F R ad quancirarem ortam ex duceu O C
in C.R, eam habec proporcionem quam habec L. K ad YK. Duod exac demOn.
AErandUM.
3
a312. parab
e R O
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