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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 186, page id 1815201908:0243
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11
IR CYLV S.
Demonstratio.
Lisc enim quadracu A B agua.
Lse quadracis BR n B, A, hoc
estrectansuloB CTrna cuqua-
dracis Calis L. A. Veex clemen
eis pacer: est aurem quadearum
A. aequale duobus Critis  A
ergO AB quaATACUM XquaEuE
BCl hoc est CFl rectangum
do rna cum quadraco C+. A: quod
fuic demonstrandum.
l cde a Le
IIdCTHI POMCISILAHSAMIAT ITE, FF;
L 2 l X.
Vicolimeasres HE, B tn F. F, in conrinua este analogia:
Demonstratio.
Penim FTD incelligatur produci in R, exit F R ae qualis ipA R F, VE cL Cie
eis educicur, unde _ HFF rectangulum, aequale est rectangulo BL L, id eAt qua-
draco BB. Ouoderat demonstrandum.
Ildem POlICIS:
PROPOSITIO XA1.
Dico AF ad AII, eandem habererarionem quam FG ad GHI, (1.
ve AF in C e HI diuilam, excrema e mediararione proporrionali.
Demonstratio.
Ectangulum FGFI, ona cum quadrato OA; aequatur B A a quadeato led
BA, quadraro aequale estbrectangulum F AFI, isicur FOHI rectangulum rua
cum, CA quadraco aquacur F AHL rectangulo: quadrarum aurem AC xqualo
Acrectangulis AC, H; C AH; rectanguta isicur F C FF AC HI, C, AFP, aequancur
i. FA H rectansylo: Rectanguto autem F A FI xqualia quoque sune s cectangula
GTTA, GATI. ablaco igicur communi rectanoulo (+ AFL MAnCE FCHI A re-
ctangulum, rectangulis AO FI, F C FB id est rectargulo F AC HL xequalc. vnde re
F A, 2d TI A, EC F C 2d GFI. Ouod Fuic demonstrandum.
Scholion.
Aec Propoo Pontur a lappotoro septimo proposrione 154. ed quia sort casut viaetu
applicata quo recta RD. per centrum ducta est circuliB D C. adeoque ex videatur casum
ecta A F excludere, placuit ostendere vniuersalem prorsus esse: Diio dipsum praestas apollo
nics lib. 3. Proposuione 37 sed diverso à praesensi discursit. .
R