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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 383, page id 1815201908:0440
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P AR ABOL H.
PROPOSTTIO XLII.
Ecehc A B Cparabolam diamerri ata quauIs AF, BB; IunctHq A,
B dlaccoum terminis, ponatur ad diametrum B D ordinacim l1-
nea C D, OcCuErOnS AB, A F lincis in F XF.
DicOFD, CD, F. D in concinua eAse analogia.
Demonstraiio.
BOnaluT ex A ordiMacim AG; veB D ad BC, HCD L Ct
ad A Cicead DF: sed BDad B C, duplicacam habec
arationem ejus quam hab et DC ad AC+, id eA DF, ta-
cioisitur DF ad D F, quoque duplicara est rationis (D C ad
DF: quaTEDF, DC, D F linex lunc in continua analo.
Bia. Quoderat demonstrandum.
Corollarium.
IIdem boluis: sequicur rectanigulum F C a
rectangulo FD, C F, cum enim FD, CD, F D propOc
cionales sInE,rE FD ad CD; SC FC eAt ad CF: rectangu-
lumisicur FDCF B aequale est roctangulo FC D. Quod
cracpropolicum.
PR OPOSTTIOXLITE
Cuo eLe loclatislum aquarirectansaoLL.
Ildem policis quae supras
Demonstratio.
a cadat F punctum extra
patabolam. Ouoniam igieur re-
eta bC i D bissecta est d ei in
directam aecta quaedam C+F. re-
deato C D, aequale est c quadraco
FD: led FD quadraro xquale CI
dangulum GF C rna cum quadra-
c 6. Secudo
rectarguium L. LD, una cum dre-
aasulosF. DF, id estrna cum qua-
drato CD Per praecedence propoligitur de rectangulo (+ F. C una cu quadraco (D,
aequale esrectanoulum P. FD una cum quadraro CD: dempro isitur communi
quadrato C D, mancc CFC rectongulo, aequale rectansulum R. FD.
Secundo cadac F punctum inera parabolam. Ouoniam CtC linca in D lecta cA
bitariam de non bitariam in F, rectangulum OF C ina cum equadraro E D, Xqua- Cs. Seeundis
le cAquadraco OD: sed GD quadraro aequale quoque est rectangulum FDF, id
eltcedanigulum BFD una cum quadraro F: D; rectangulum igitur CF C vnacum
quadraco FD aequale estrectangulo R FD; vna cum quadearo FD: quare dem
ocomumi quadao FDilae et Clla L. L1
Duoderar demonstrandum.
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