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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 400, page id 1815201908:0457
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400
A R A B. O L A.
PROPOSITIO LXXEV.
DArabolam. ABC euius diameter BD concingae in B linea FB: ex
in F, C, A, C punctis e BD diamerrum in D e HI, demislaque ex F _
C diamerri FIE, GI, occurrane LLC Hnex in K de 1.
E 2 C1EIBLIEBC CAVEE CtrI
se
Sit est A et et:
emonsrAtO.  L C in erap
OL ad FK, SC F O est ad BF; sed
F. C 2d F F, duplicacam habet rarioné
E  ad F TI, id est b GFI ad TIF; igieur
e Cl ad FK, duplicacam haber racionem
cius quam habcc CiHlinca ad lincam HP,
erac demonctrandum.
TROPOSITIO LXZXVI.
Lpuncto F. duxe quaeuis ducancurlinex P F, F. C, secanres parabolam
Dico. CI ad F K, duplicatam habereracionem eius quam haber OH
ad FTF.  161111
EX 82.
uins
1. D
pressionibus.
esse ad quaatacum AF.
vlcerius inferimus, _ A, B puuel Contactuum coniungantur, rect 25 F E, F.C, I. C in
concinua esse analogla. ret d HIL, AG, HKlincas.
Demonstratio.
ISCenim ex TUBPOSIEOVEAD qua
aracu ad quadracu D B, siC A P
quadracum ad rectanoulum RFC:
ex permucando ve AD quadratum
ad quadracum AF, SCDB qua-
dratum ad rectangulum P F C. sed
Cest quoque ve AD quadracum ad
quadracum AF, SC DB quadrani
ad quadracum FC; igieur ee DB
quadrarum ad rectarsulum P F C, sic idem quadracum DB ad quadracum FO.
inde FC quadracum xquale cA rectangulo RF C; _ F R, F C F C linex lune in
concinuata proportione.
DArabolam ABC contingane in A d B linex AD, BD convenien-
res in D, alsumpeoque puncto F. in sectionis peripheria, agAEUF PEF P.
linea FC, Parallela rectx BDOcCumens AD linexe in F.
Dico ve quadracum BD ad quadratum AD, sic L. F C. fectangulum
Est hac ab Apollonio lib. 3. prop. 16. eodem plane modo proposita: nos aurem hanc supponendo
PROPOSIIIO LaaaI
IIdem policis ducacur de alcera C FL parallela F C, secans parabolam in
I_II.
Dicorectangulum F. F. C ad rectangulum YOHI, ese ve quacalu
F A ad C A, quadrarum.
Denton
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