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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 512, page id 1815201908:0569
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 53 lines, status machine
# Lines: 53 recognised, mean confidence 0.84
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2
ie
P A R A B L. 1.
ROPOSITIOLLCXZEI
( CA BI
Scd AB C parabolae diameter AD, ad quam ordinatim ponaneur
Lslinex BF; ducantur adc ex Blinca BF, inter se parallela, X pro.
porcionales Inels LB.
Dicopuncta A, F, F. esse ad parabolam pI1
217iOG c1 31I
ale. nC
Demonstratio.
VnSanEUE FP: Duoniam eam PB liteae incorse,
quam B. B aequidictane, anguli E, BB aequales lunc:
undecum proportionalia sine lacera s B, BP, aequales
sulos conrinencia, criangula quoque P B F incer le
limua. alleoque e FF lincaexequidittances sune
aduleem; de F B lincis proporcionales: Quadra,
nigirur L L eA ad quadrarum P F, CVE F. B, quan
racum 2a quadrarum, E B, id cst De AF linea ad
um AB: inde puncta A, F, F sunc ad parabolam:
DSITIO CCCXXEVIII
Sco ABC parabolx diamecet AD, d ordinatim ad illam potea
SeD, BF: e E B, quidem juncta AC, dividar in F: ductis aurem
parallelis B C, quae A C linCX OCCUT-
rantin C: AaEVE FB ad BG, SIC FB
ad BFI.
Dico A Es puticta eNe ad parabo-
2.
Demonstratio.
Vngancur enim DH: Ouoniam E B, BH
linex proportionales lunc, lineis FB,
B∞. et anoulus E B e communis, erign-
sulis FBC Smilia sune criangula F BFI:
sune aurem e FB C criangula quoque (-
Sto ABC parabolae avis
BD, cui parallela POnatuF
AF, Eccans parabolam in A.
ducantur aurem ad axem ordi.
natim linex F C, _C INFOF FP,
E C MediX PONANEUEF. C.
Dico A, C, B puncta esse ad
parabolam.
Demonstratio.
gula similia sunE. Ouare DE F: B ad F, B, SC F. HI ad F. HT, adeoque per praeceden.
rempuncta  ae andem sunc parabotam.
milia, cum eam PB linexe incer se, quam BG rectae aequidistenciisitur de R B FT crian-
PRO POSTTIO CCOXXXIK
4+. huius. Fi SC eniM VE A P linea ad lineam A E, siC F P. C grectangutu ad rectangulum FP C
igitur e P C quadrarum est ad quadlau e Ve A B linea ad lineam A F: qua
0 a Pra pat aLa HC.
PRO.
Su    se   s     et  su      grr. s e  e u tit  e e te t t e te  s t. t  et est e e e e e  su te       e e   t  t o e  ete tt s e    l e