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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 469, page id 1815201908:0526
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1815201908&page=526
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 59 lines, status machine
# Lines: 59 recognised, mean confidence 0.83
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80
BC
BC
AB;
e
1210
212.
m
um
31-
a.
du.
um
A.
P. A R A B, O L A
ad FT AT componaciir exracione eriangulu C AG
ad G AF, XE Cx G AF aaHTAI, PaECCC AC trian-
rarione erianguli, C A C ad criarbulum AAF,
e ex ratione OFI ad TB, quadrilarerum, (id ell ex
HTATcriangulum, cum L A, FT As B A proporrionaleS HNE) CNIE F. C3 quadrilacerun
ad quadrilacerum B IVE C AC erlangulum ad criangulum (L AI; igitur _ P. C qua-
deilaterum ad BY quadrilacerum rationem habec criplicacam A C. 2d A V. b
PR O PO SITTOICOIVII
BC pataDolae diaeFEF AD. Policaque aa LITAI OTALMACIII
CD, descrilatur per N e C, patabola AE C, quam in R concin-
sac AD, ponanculque ordinacim quauis FB, II C sccances A F. C Para
DICO AGUTAM CONCALAI A F P. A, ad fIGUTAM CONCAUAM A FTIA, du-
plicacam haceae lacionem parabole B AF ad parabolam C A F.
Demonstratio.
EnGANEUE AF, A P. FIgura mixcilinCA AFP. A
ad siguram AHII A eam haber rationem quam
AF. L criangulum. ad eriangulum AIFI. rarioaU-
cemtrianguli AE F ad criangulum AIFICOmPO-
SIta CCCK ratione AF 2d AHI, hoc est duplicata
rations F B ad FLG, e ex ratione F F ad TEI
hroc est duplicataracionis A F ad AFI, id est qua-
druplicata racionis FB adTIG; ISITUE AFP A
sigucd ad sguram A HL L A sexcuplicacam habet rarionem linex F B ad HO. sed x ,10 it
B AF b Parabola ad G AFI parabolam criplicatam habec rarionem FB lincae ad iu
lineam FTC: IBICUE RGUFA A F F A ad Aguram AHITA; duplicacam habec t2-
rionem parabolae B AF ad parabolam Cr AFI. Ouod erat demonstrandum.
Corollarium.
lnc parer concanuin LL R, ad concauum A FTI, etiplicacam habere rarionem
LF ad AFT; Nam A F. F criangulum ad criangulum AIEI rarionem tiabet
COmPOIITaM Ex AF ad ATI, ∞ P FadIF, id est ex duplicara rarionis AF ad AII.
PROPOSITIO COZEVIII.
IEdem posiris sinE AFI, A F, AD proporrionales, iune L QuC AC.
Dicomistilineum IP 2d F O mistilineum rationem habere sextii-
plicaram, cuius rario craperii R F ad L. D, craperium est quadruplicara.
se crianguli C AF ac
In-
erianoulum ad criarigulu FT A Fin duplicaca cacio-
nC F G ad FIF isicur cum racio crianguli C A C
sulum esse ad criangulum EY AT in criplECaC2 F2
tione F C ad FII: ouia vero racio quadrilace
ei F G 2d BIquadrilaterum, componieur ex
Facione F C ad C HI quadrilaterum; (id cA Cx
exaranaii. la
bolam in L. l I.