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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 433, page id 1815201908:0490
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p
eM
DE
13
97
c.
1d.
F
PtA R A B, O L. A
duplicata est lacianis B C ad BO5 _ ratio GB 2d G D, dplicara eAt rationis
CF ad CF, racio isicur rectanguli AC D adrectangulum AED duplicata est
eius quam habet BC. P. rectangulum ad rectangulum B CF. Quod erac demon-
strandum.
PROPOSITIO CLXLL
to e   oesit cleder
Idem posiris: eriganeut ex C_ F diamorri C L, L L Oceurrentes linet
LBE in R _ B E _ LIB LIZMS..
Dicorectanguta IE GL, BGF, FIC Iin continua clse analooid.
esstBhBROHOl
Ibs e 23nc. Demonstratio.
R Ectangulum K C L ad rectangulum B G E, ratIONEM HADCE COPOSIEAM CXKC
2d BC, _c ex CF ad OF: e BC F rectangulum ad rectangulum HOI,
sarionem habercompositam ex B, C ad FI. Cis id olt HG ad BC, d ex C+ F ad GT.
sid est C L. ac C P: rectanioulum isicur H CaL, eA ad rectangulum BG P, VE BO F.
rectangulum ad eoctangulum. IL C)I. Dyod eras demonstrandum.
25 s  es gi u
2maimondaDR OP O SI FLC, CL XIII.
West
Incrursum parabolX dux ABC, DFF: _ AB C parabolx quidem
Dapex (Ic A, parabolX veto D E F Ac apex D, in quo contingat axem
AD in D: Factilque AG, D ITlineis aequalibus, agancur per C a FL, nor-
ales ad AD3 linex F BsF C occumences parabolisin E, B, F, C.
Dico ECB rectansulum ad rectangulum F HIC quinicuplicatam ha-
bercrationem eius quam habet C B linca ad lincam IIC.
B.  Demonstratio.
Atio FGB rectaneuti ad reet 2t-
LLoutum EHC, composira cA ex
ratione F C 2d F HI, hoc est duplica-
c2 CD 22d FID; id cA AFI 2d A6,
(cum AG, FID lincx aquales LnE)
hoc est ex quadruplicara rarione C B
ad HC, de exratione GB, ad HC:
rectangulum igicur F OB Ed FHC
rectangulum quincuplicacam haber rarionem e B ad HI
dumsRX
PROBOSIF
NICABC paraBOIX axis AD, _E AP F patabera Verrex A, in quo illam
L conringat linca AD, politaque F C B ordinatM ad AD ducatuF ee
alECTA FD C, VEG B, FD rectae aequales (INE.
Dico rationem F. G ad DC
quincuplicatam esse cius quam
habet GB ad DC.
Demonstratio.
DAciO L C+ AA DC COMPOIICE
Cexrarione L C 2d F D, hoc est
duplicata AC, ad AD. hoc est qua-
sruplicata rationis CB, 2d DC, Y
i
3. tot
Quodtuir demonstran-
itititi
t121315+6 + 18 10
1
a eo