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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 379, page id 1815201908:0436
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6
P A R A B O L A.
led _ HC qualleato aquaseelt rectangulum BF; C D igicur d rectangulo L A D ~ Ex 33. hK.
aequatur rectangulum BFC D: vnde ve AF ad BF, sic CD ad AD; aequales in
aurem lunc anguli AF B; AD C. lacetibus proporcionalibus concenci, igicur cri-
angula AFB, AD C incer se similia sune, ee angulus B AF aequalis angulo
AC. D, id ect ingilo P AC: dempro ergo communiangulo: B AC, manec angulus
P. A D: aequalis ansulo C. AD. uoderat demonsrandut.
IIdem potc lecucul. LIaBla B A L. s. C. A D elle cex le similia. Pacerpor pri-
mamparrem praecedenes propoltionis...
P R OP. OSTTIO ZZXVI
IIEABC parabola diameter A D, divita in E d F VE AC, AF, AB
 Cinc proportionales, de AF media equalis laceri recto: poliris aurem
ordinatim lineis EB, FC, DC, ex A ad (, ducarux reCtL A C occur.
rens E B lineaein FI.
Dico AD, DC, FG, EB, F. LL lineas continue clle propotetonat.
Demonstratio.
Voniam AF equalis eA laceri recto, C F, F A
Lolinca aqualeS (UIME: FAEOIgITUT A F C ad AV.
id est GF ad AD; duplicaca est tationis C F ad
CD: provorrionales isitur sunE A D, CD, GF. quia
verO AD, AF, AB lunc concinux, cciam d CD,
GF, BF proportionales (une; concinuane igitF CAML
demrationem AD, CD, GF, BF. deinde cumrario
AF ad AF, id es OF ad FIF, duplicata SIC F2-
cionis C. F ad BB, proportionales quoque luncOF,
BF, HIF; concinux isicur sunc in cadem ratione
AB, CD, CF, BEHL Eiquod crac demonstrandum.
Corollarium
75
Corollariut
n
est GF ad B E, duplicata cleracionis GF ad B F, propoctionales igicur sunE AF,
BP. GF. IcaM BF ad F, sic OF eA ad CD, cum: AB, AP. A  C eiteS
nux; proporciona lesisicur sunE AP, PB, OF, CD.
. TInC sequitur AEs FB, FG, CD quoque in
Llcinua esse analogia: pario enim AF ad AF, id
AdIOSIEIKRaII
Seo AB C parabola diameter A D divila in
LE _ F, VE AF, AF, AD linea (INE PrOPOr
cionales, e AD extrema aequalis lareri recto; du
concur aurem ordinarim lince EB, FG, DC
Dico AC. ad F B, apcala habere rario.
nem cius, quam habec AP ad FG.
i1
11II
ste tu t sot  e asetit  nte