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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 470, page id 1815201908:0527
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P AR A B OT A.
3 aB ile B MI L L LE ~t CIBIYB l. F e1I
1 i Ddemonstratios
hers a vo An
Voniam A AF, AB,, A D linex proporcionales Cunc,
Lrectae quoque LII, BB. C. D, adeoquo fsurae a con-
CaNR A FYFA, AF F A, AD C A in concinua lunC an
logia. isieur ve AFII A figura ad figuram A F F A,, SIC
IF mistilineum est ad mistilincum F. D; sed AFII A A.
sura ad fguram AF F A, sexcuplicacam haber cationem
BHI ad CF, igicur ee PF mistilincuni ad mistilineum
sexcuplicacam habecracionem B HI ad C F. RuI.
lum, quia (A FB A F, AD proporcionales (une, criangula
quoque AK FI AI Fi, ACD in conrinua lunc an2l0-
Sia. adeoquere AK II criansulum eA ad criangulum
ALF, sIC RF crapezium est ad crapezium ID: Sec
AReC criangulum ad criangulum AL F, duplicatam
habet racionem linex AFL ad AP, hoc est quadruplicaram rarionis HIB ad F C.
isicur ex RF crapexium adrrapeum VD, quadruplicacam habet rarionem linca
HLB ad F G cuius IF mistunicum ad mistilincum s, D habex sexcuxlicacam. Quod
BLLVSII ECMACIS IO SCPLESESNCE E
R OP OSATIO COXLIX.
N parabola ACB sc AB Batoaxeos aqualis laterirecto, duetaq. A F ad
Laxem normali, ponacur guixuis FC parallela AB, secans parabolam
Dlcohas duas sese orrhosonalirer intersecare et CG, FC, OA, OB
continuè esse proporrionales.  A sucilien n
p u
Demonstratio
crac demcharandum.
b Ex B. BM-
eosenin
d EX 13.
exti.
F
in C, D dACANEUF AC, BF.
Vm. B A xqualis lic lacerirecto, crieb rectansu.
Ium B A FC aequale quadraco Fi A. lgitursunE
tres in concinua analogia FC, F A, AB: ergo cum
anguli CF A, B AF xquales sinc, similia Cunc crian-
sula CCF A, F AB. vide anguluS F A C aequalis an.
Bulo ABF. est auceangulus FAC unacum C AB.
recto xequalis; igicur eriam angulus FB A una cum
angulo C A B recto eAxequalis, ex consequenrer an-
sulus ACFB rectus cA. vlcerius cum cam angulus
AF C quam AOF rectus cA, ErCS CG, GF, C+ A
oproporcionales lunc: quia vero anguli A CB, LAB
recti lune, linex quoque LG, C A, C B proportio-
nales lunc;condem isirur concinuaneracionem CCn
FiC, C A, CB. Duod erac demonstrandum.
e. L 2 i t. L L tao
Nrer duas datas, duas medins exhibere organice.
Constructio ex demonstratio
InE duae data FTI, TK inter quas duas medias OpOrreaE exhibere, CONSIEANEIE
tae ad angulos rectos e conticiane eriangulum orthogonum FT TK. deinde _CI
bacur Parabota AC P cuius latus rectum (IE AB parS AXCOS, IUIPCF quo SeSMeNCuI
circuli comnacur Capre agare ACB aguaem 1 L. OCcuI Parabole
C a AACANEUE C 13L H aet alSMoFectOS, Ita ve CL lic aequidistans axi e iunsan-
ilt A C. BF. Dleolaccu qudd LeqituI. nam osentum est ansuloS ad G EcCtOS
eAe