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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 370, page id 1815201908:0427
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d1. Sexti.
L AL
Corollarium secundum.
GF B exians ula Xqualia. PaFCE, CUM F F, P B aequales sine octenla, _ AFF.
lROCOsIcIaCA.
Demonstratio.
IE ABC parabolx axis AD, cui in P OCCurraC
contingens B E, policaque AC parallela con-
tingene B F, demitracur ex B, linca B C aequidi.
stans axi, ponacurBF, C FTD ordinacim ad axem
AD, _BC producta occurrat concingenci per
A ductxe in K: Ouoniam B F. coringens cst e BF
ordinacim adaxem AD applicara, aequalessune
linex 2 F A, F A. _ quia B F communis alcieudo
est, triangulum F. BF, b parallelogrammo B A x-
quale cst: TUrSUM VE AF aet AV, SICC F B qua-
deacum ad quadracum CD, _ FK paralleloora.
mum ad parallelogrammum DK: ve quadracum
igieur F B ad quadracum C D cAt, (iC FK paraIIC.
loccammum dadparallelogrammum DR, Led ve
FB quadracum ad quadracum CD, AC F BA
19. Sonsi: eriangulum cadcriangulum C. A VSitur ve F K parallelostammum ad parallelo.
Grammum DR, Sic F BF criangulum est ad criangulum A CD: _ permurando ve
FR paralleloxrammum ad criane IH B F F, SiC D K parallelogrammum est ad
criangulum ACD: aequalia aurem ostensa sunc, criangulum BF F. _ parallelo-
exammum FK; xequalia igicur lunc DK parallelogrammum ec triangulum A C D:
ex ablaco communi AOFTD, aequalla remanent. criangula AGR, CFTG. vndo
cum similia quoque sinc ob AK, OLL aequidistances, xgualia sUnE LaFCTA FK G, C: FF
_ CC, C A: diuisa igitur bifariam est AC. eodem modo si TK ponatur aequidi-
AanS C A, _ Cx R diamerer pontAHC L. K occurrens B F. concissenti in L, oAten-
decur TR in MI, bissecari a HCd B C: diamerer sisicur sectionis eAt B C: quare
cum FB concingens sc qux cunque, alleoque et B HI queuis aequidistans axi, patee
Ex quo sequicur diametros omnes inparabola cAe parallelas.
Fanitur secundo rectas F A, G B, iECI AF, O F equales esse adeoque _ A F L,
G F B criangula similia ob GB, F A aequidistances.
Nparabola diamerri omnes xquidistane axi.
.toniu
Exorele
Metta.
diameeros omnes axi aequidistare. Ouod erac demonstrandum.
PROPOSITIO XZ
nlscontinseas pel callo
nacalem ocamaciu pola
ductas cumnus alanenoio
uenH.
Demonstratio
Orca Mamerer BD, de ad illatu
otcualim applicara C. aalurqu
per A concingens, dico illam B D dia
MClioCCiece: ductaenim diame
na. Fam quoque D B, Proalca  II. Duod erac demonstrandum.
Perole
hEg. huius, ErO A F ha quidistabit illa B D, vnaC CM A L lCCEC A L aequidistancium rnam, alce
C0r01
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