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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 399, page id 1815201908:0456
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P A R ACB O. L A.
PROPOSITIOLLZXKII
Ademmihuenee Rgita proposicumt a daro puncto exrra lectionem
sconinee aee.  et sesiit
3 Z X3 dOB= IICLI
C1
 dadee ad  e 
Constructio es demonstratto. - 30, L:
ledacum puncum D5 Cx quo ducatur queris secanSpAt ABOL aHS I O d R: erir F, C
prima erium continuarum _ A C exceltus reliquarum: invena igieut incer
CF, F A media R P PeF F, diameter agacur BD iungancurque F B. PACCE PEF PreCC.
denrem, lincam Ld P sectionem concingere in B. a daco isicur excra pacabolam pun-
atocangenrem dusimus, dec. Quoderac quaelicum.
e
SMOire BBCEHLMM PROPOSITIO LZZLIII
Darabolim ABO cuius diameter AD, COMHSALM LLU a L. L.,  ..
qua sumpeis duobus putictis F, F. guCanEuT ex L _ L, OuX pataIICLa
tC, F C occurrentes parabole in B, C, FI, C, _ AD diamerro in D e l.
Dieo BF C trectan gulum ad rectangulum HI F C duplicaram habere
racionem linee eius quam habec P. A linea ad lincam F A.
Lg. Demonstratio. quuon
Voniamcam ZB, FB. FC 1-
Lnex, quam FFI FL, FG SunE
proporcionales, erie BRC rectan-
sulum aequale quadraco HD, &
HFO rectangulum equale qua-
Ataeo FI. isitur ve quadratum R. D
et
ad quadratum FI, sC BF C rectan-
gulum est ad rectagulum FIF C. sed
F. D quadeatum elt ad quadrarum
FY, VE A B quadracum est ad quadracum AF; igitur _ B P C fectangulum est ad
rectangulum HF C VE AR, quaceatum ad quadratum AP. hoc cAt duplicatam h2:
bencrationem E A ad F A.. Duodcrat demonstrandum.
1stes Be
eDR O P OSITIO LXXXIV.
15
Sd 21 . IIC
d
Darabolas duas AB C, D. B L. habentes communem diamerrum B F
Lcontingac in eodem puncto, linca BC, ec cx C queuis ducatur lincas
occurrens parabolis in V, A, C, E, dlamerro vero BF in F.
DicoDOFrecrangitum aequari recrangulo AC C.
Demonstratio.
HoC enim per octuages. primam huius eam
LDGF rectangulum, quam rectangulum
ACCaequalequadrato ti Cigitur d ACC.
DOF rectansula inter se equalia lunc. Duod
tuic demoncrandum.