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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 462, page id 1815201908:0519
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n17. bu
moiostratio.
acUEPEE A continseHS A R, Occurrens B F
Llinex in F, qua producta secet D C in C. quo-
niam ixicur xequidistANE AF, CD, VE CF ad F A
sic GF est ad FF. ponicur aurem AC in Libita
riam divila, igieur _ P. F aequalis est L G de FAF
criangulum aequale criangulo CFC: Ccd F AF
triansulo aequale est criangulum C B A. igicue e
C F Gcriangulum xequale est eriangulo AB C. quia
F B, B F linex aequales lunc: cst autem C AD qua-
8
druplum crianouli C F C: quia AD dupla est FC
ED dupla C. C isicur d quacruplum ca
guli ABC. Quod erat demonarandum.
eROPOSITIO, CCLLL
Sco ABC parabolae inscriprum eriangulum maximum ABC: in-
eribantur aurem ec reliduis legmencis criangula maxima: d hoc
Temperhat.
Dicorori criangulorum soriei equalem esse parabolam ABC.
Demonstratio.
Tenimnon sic aequalis, maiorigi
cur est vol minor. (c primum pa-
rabola maior coca criangulotum
Cerie, ec exceltus ponacur quanci-
eas C. quoniam igicur criangulum
ABC maximum estillorum, qua
parabola inscribi possune, maius
bquogue illud crie dimidio paca-
bolo cui inscripeum est. Cmilicee
triangularuo AV B, BFC maio
ra lune dimidiis seomentorum qui-
bos inscribuncur. quod cum sinc
termino concinuari possic, relin-
quetur ex cparabolaquancicas, da-
taminor, eroo deminorquanticare Ci, ergoilla exceslusnon est, quo parabola crian-
sulorum seriem excedir: ergo parabola maior non estrora criangulorum serie.
Duod vero neque minor illâ sic, manitestum est; cum eriangulorum leries, exhy-
Pochesi semper inera parabolam continuerur, ac proinde series illa quancum cunque
aucta, plurium criangulorum addicione, semper eamen parsmaneae parabolx: cum
ipicur seric crianguloru, nec maior, nec minor sic parabola, xequalis ve sirnecesse est.
P R OPOSITIO CCXZK
ode valadblam aderiangulum maximum AB C. cam h2.
bere proporcionem quam quacuor aderia.
Demonstratio.
b229. b1
docimot
Adem POlTa AguTZ:
dFX230.
Klansulum amaximum AB C, quadruplum est criangulorum maximori A P. B,
ins.
BF C quae residuis inscribuneur segmencis; e illa rurlum simul sumpes, quadeu-
Pla criangulorum reliduislesmeneis inleripeorum. aeque ica sinc cermino proceden-
do, cum ablaca semper quadrupla snc crianxulorum, qux reliduis inscribuntur se-
Bmencis,
e s eoos oesraineo oa e s  en