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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 774, page id 1815201908:0831
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V. 5. P. L
R OP OSTF10 CtV.
habere compositam ex ratione quadrari BC ad quadracum FC, _ ex
Demonstratio.
IuisiS AC, FC quadrita-
riam, actilque per divisio-
num puncta parallelis RL,
MN. demiceantur ex K e
MI ad XL OrThOBONX R O
M S: icem duCanEUE L. R, N L
tildem orthogona: brevicaris
aurom causa corpora ex duetu
mucuo parabolarum orca vo-
CCHEUT COrpOTA A, F. Duadra.
cum X O est ad quadratu BC
VE 2 O A ad C A, hOC Cst CK
const. ve P F ad GF, hoc est
ve quadracum M P ad quadra-
cum FC. CrBORRO ad BC
DE MF ad FC, _ permucan-
do RO ad NTP, ve BC ad
I. C. Eodem modo oltendam,
OT hoceA OR cMc ad PN.
hOC CA PZ VE AD, ad IIF,
hoc cA exhyp. Ve BC 2dF6.
Cum igitur racio rectanguli
KOR ad rectongulum MP X
componatur exlacerumeacio
nibusR O ad MP, OR adPT.
ad solidum quod sc extecas alo H L aucto in rectangulum PY rationem habee
composicant Cx Lactone vaus au Daum hoc eit rectaneu KOR ad rectangulum
MP T, ex racione alcicudinum 9O, P P. Cumisiror rectangula ROR, M P T sinc
ad Cc invicem ve quadratum B C ad quadracum E G; _e alticudines OO, PP, VE
BC ad quaaratum se, e AC ad l Cr. limilicer oltendam lingula reliqua Colida
facta ex rectongulis religuis X O, in reliqua O R eandem habere rationem eom
Polcam ad singula alia Colida Facta ex rocrangutis religuis NP, in recranoula reliqua
PT. ergo lingula solida inscripea corpori A sune proporcionalia Cinvulis solidis in-
B12. quonsi. lccipeis corport   e b ma u a. leapa enr.
nius ad unum rarionem osse compolicam ex racionibus quadraci BC ad quidearum
CC, X AC ad F C. ergo omna le Mcripea corpori A sunc ad omnia inscripea
c+5. hhas. Colida corpori L in dicta racione composica; cum igiture solida verique corporitol
 polline, ve deticiane d corporibus ipsis quancieare dasa minori, concludicur
codem
TnE ABC, RCD parabolae aequales de similes ad cundem axem lub
Dalterne polcx, ponantur aurem de alix quauis. duxe parabole aequales
ac limiles F. F G, F. CFI ad cundem akc Abalcerne polILX.
Suouscum ex ductu parabbla AB C in parabolam AC D id
corpus ortum ex aucca parabola L. F. C in F. C HI parabolam, rarionem
A C alcirudinc ad alcicudinem FE. 6.
cum FC: jam aucem Colidum quod tc ex ductu rectanguli KO in rectangulu OR
erit hec duplicata rationis BC ad F C; hoc est eademgua quadeati B C ad quadra-
AC, F C, quemadmodum colligituE CK HIV BOCHEH. HaBCO Llidum quodAC CxRO
in OR, ad solidum ex MI P in P P racionem compositam exracionibus quadrati
I. DePa
ola-
sa I6it re 1e EO E  333A253C2I