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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 480, page id 1815201908:0537
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A R A B OF
PROPOSEETO COLXXI.
VIE ABC parabolae diamerer AD divi-
Cain E, F, C punctis ve AC, AF, AO.
AD linex line concinue proporcionales:
policilque ordinarim FB, FHI, GI, C D,
iungantur AB, AHI, AI, AC.
DicOICOMENTA AB, ABHI, ABI, ABC
in continua cAc analogia.
Demonstratio.
Q Acio sermenci AB ad sesmentum AFI eri-
plicaca est ejus quam habec: B F ad FI F. rur-
sum AB HI seomencum ad lcgmencum ABPeri-
plicacam habet rarionem FTL ad TC, et Ac de
eaeceriss led E B, FH, CT, CD linex concinue
b sunc proporcionales, quoniam AF, AF, AC, AD
b33. huu IH Continua Poluntur ana logiasigicur ee segmenra AB, AB HI, AFII, ALC lunc in
racione concinvaca. Duoderar demonstrandum.
PR OPOSIETO CCLZRII
NIE ABC parabole diamerer AB, divila in F _E F, VE A L, A F, AD
linc proporrionas, de ordinatim ponantur EB, FG, DC: iuneat
Dico seomencum BeA lesteneum CC rationem habere criplica.
cam eius, quam habec EB linea ad lincam P6.
Demonstratio.
resstons.
Ex et
elt00
a
tarque B6, CC.
proportionales UnE, R I CAtAdF D, C VE A F 2d AP,
id cM ve quadracum EB ad quadracum F Cr. led raclo
crianguli E F B ad criangulum D FiC dcompotica est
ex racIONC F E ad FD, _E ex E B ad LO; criangulum
igicur F F. B ad D B C criangulum, criplicacam Habel
racionem F B ad F Os obdem modo rriangulum F BC
ad DCC, triangulum eriplicacam habet cacionem FC
ad DC; (cum rationem habennecompostra:m ex B. F ad
FD, alciendinc ad alcieudinem s_ ex F O ad DC, id
est E B ad F C; (cum BBIFOsD C proporcionales Cin1)
igicur eocum rectilineum RB CE estad eocum rectili.
neum FCCD in criplicaca racione FB ad P C; led e
x242. nam cum E B, FC, De Poeaes, Patabola quoque F AB, F AC.
Fleomencum BC. est ad reliquum CC, in criplicaca ratione B. B ad F C. Ouod
)Vcancur FB, D G. Ouoniam AR, AF; AD line
mixtilineum E B C F est ad mixcilineum DF CC incriplicaca rarione F B ad FO,
cD AC in conrinua sunc analogia: 2cC ve ABF. parabola est ad parabolam
quinci. F AC, SIC F BC F mixcilineum est ad mixcilineum FG CD. isitur de reliquum
exar demonstrandum.
PP
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