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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 173, page id 1815201908:0230
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21
lest
CIR CV LVS
lBitur lineas AB, F F sibi inuicem normales esse. Quod fuie detonitran.
dum.
Corollarium.
lnepacer, F. F. lineam, qua circulorum sese incerlecantium cenera conjungies
bitariam quoque diuidere arcus, muruisperipheriis inTerceptOS.
P R O POSITIO XI.
A ABC crian cum, Cuper cuius bali AC, de seripEuM uo-
bet circuli segmentum; oporret super reliquis crianguli laceribus,
legmenta de scribere, similia illi, quod super base delcripeu est legmento.
Constructio es demonstrario.
Ranseat primo segmentum luper basi policum, per
Cngulacriansuli excremas describatur aurem cix-
culus per BC, vei ec per B A, qui rectaS AB, BC COn-
cingac in B. Dico factum quod postulatur. Ouo-
niam BC linca concinsic circulum ADB in B: crIE
angulo AB C, aqualis angulusa segmenti ADB. CO.
dem modo angulus sesmenci BP C, ae qualis est angu-
I0 ABC. quarc segmencorum anguli AR B, ABC,
BDC, aequales sunc incer se; de similia proinde (c.
Bmenca.
Sccundo B verrex crianguli ABC, cadac intra po-
rimetrum scomenci, super AC exstructi: productis
laceribus AB, BC, donec occurrane peripheria
circuli AF. C, in F e B. delcribantur circuli per
AF B, BF C: cricque peractum quod postulacue.
iunctis enim AP, CF. exturgent anguli AR C, AFC
eidem arcuiinsittentes aequales, ac proinde ADB.
AF C segmenca similia crunc: rurlum cum anou.
IuS AF C. SE aequalis angulo AF C, id est BF C,
CrUnE _ SCOIMENEA AF C:, BFC, incer le similia.
QuarCErIa ADB, AFC, BFC, limilia TunE.
Tercio B vercex crianguli AB C, extra sermen-
ei ambicum consticurus sic, quod super bas ex-
Rructum est; occurracque perimerer crianguli
laceribus in punctis F, _ C. Tum Per BFC,
BCA, circul describantur. Dico tactum esse
quodpecitur. lungantur AC, F.C. Quoniam an-
suli AFC, AC C aqualessun, crunc_ B Fi C.
BC A reliqui aequales. QuaTE _E AECUS AD B,
B F. C quibus insictunt, limiles func. Rursus cum
angulus ACC cam cu ansulob Ccomenci AH C.
quam cum ACB angulo, duobus rectis aque
cur demprocommuniangulo ACF C: CrunEAN
suli AGB, AHC, adeoque ex reliduorum le
smencorum anguli AD_ AC, C, aequales, e
AGC, BD A, Scomenca similia: cA aucem B F C segmoncum oltentum limile le.
smenco AD B, cria igitur segmCnEa AG C, ADB, BF C suncincer se similia.
Ouarro B punctum cadens exera segmencum baleos, constituae B A, crianguli
lacus. Contingens circulum AOC in A. lacus vero B C, cundem secet in C. per
puncta B, A, C, et A, B, O, circuli describancur; dico illos saristacere pecirioni
ium-