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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 447, page id 1815201908:0504
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12
118
alus
dxi
2M
est
ata
2d
14-
in.
_I
2-
P A R A B. O L A
eROEOSITIO CRCVI
aIdem posiris, iunganeur F. B.
Dico FB quadracum aequari quadraris AO, C F, C B limul lumpris.
ui les  d Demonstratio.
Tradeatum FB, xdatC CIC quagratIS B C G F. sed F C quadrarum equale cst
gladrato AP, id est quacraris AC, C. L, quadrarum isicur L. B. aequale est qua-
drasis A C,  CB. D uod erac demonstrandtum.
eROPOSITIO CACVII.
IIdem polucis: Sccurrar L. G linea dates , C R. i LL de l.
Dico HFK lectangulum a quari rectansulo ABC.
26. 11,5.
2t 1
Demonstratio
Lquadraco FC una cum rectan-
sulo HIFK; est aurem quadraco
EIC linc BD, aequalea quadracum
AB, (cum AB aequalis ponatur l2-
Ceti recto) igitur ex quadracum AB,
aquale est quadFaTO F C Vna CUFE.
etangulo HIFK. Scd AB quadra-
um quoque CicaGuae rectangulis C AB, l+6L1
rectansulo CB A. Guadracum igieur F C vna cum rectangulo C: B A; equale elt
quadraco FC cum Lectangulo TI F K: demproisicur communi quadtuloL C, Fel-
duarectansula AD C, TI F K Cuncincer se xqualia. Ouoderac demonstrandum.
Corollarium
aX dictispaTEE FEMI rectangulum requari quadrATO A C. nam F PM rectanou-
lum ona cum quadraco L C, aequatur quadraco F C, id est A L, id cIF guadraCS
ACCL: demprossitur communi quadraco CF, mance F. P. M rectangulum X.
quale quadraco A C.
PROPOSILLO OXCVIII
Dico BFL rectar c, xquari quadrarum AC.
Demonstratio.
2due
2bC
adFaEO CF vna cum D EV 195.
Vadracum HG aequale est
AICA POlIEIS: OCCaITaLLB, Circuloin L.
PT. rectangulum xquale cMLCCLAH HIO NF F, IaCIL MHP. P. ILI M E F rectan- cCorol
alo aequale est quadracum A C: ixieur e rectansulo Bt. L. xquale ett qua d L- dabu
cum AC. Guod erac demonctrandum.