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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 385, page id 1815201908:0442
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 57 lines, status machine
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0
P A R A BO L A
DK _D BM A linCA XqUIAIES HIIC, LCCLALSCUM HIF O ad TAK, rectanoulum
30.
estre BF. C rectangulum ad rectangulum DM L.; d pel hurando TTF C rectan-
sulum ad rectangulum BF. C, ve DMT. rectansulen et ad tellatisatu LAR.
sed Dm L. rectangulum, id cA M D N, ob DM, NI aequales lincas, aquacuE 230. huins.
rectangulo ta K; rectansulum isicue HFC, cectanpulo BF C equale est. Guod
orac demontrandum.
PROPOSITIOLXL
Darabolam AB C secene dux guxuis diametri BD, L. F, guas IHD X F
Sccene guaecunque parallela AC, G FI.
Dico esse ve BD ad EF. SIC AD C rectangulum ad reclatis t b l. H.
Demonstratio.
ECCTF E F INCA VEIPTOdUICATFIN R VEF Ksic
aequalis BD, X Per K POnaEuT LM Paraltela
GFL, CTIEISITIED VE PR ad RF, SIC LRM rC.
ctangulum ad rectangulum GF FI. quIR VEFO F R
aequacur ips BD, CriC P R M crectangulum -
quale rectangulo AD C, igicur vE BD ad R F, SC
AD C rectangulum ad rectansulum C F. H. Ouod
exac demonstrandue.
eROPOSITIO XI
Vincicerum in ABC parabola dux quaevis diameeri BD, F. F, quas in
DF _ D secet recta quaenis AC.
Dico ADC rectangulum ese ad rectangulum AFC, ve BD ad F. F.
Demonstratio.
Filac B. F aequalis BG; X PCF C POnatur TH equI.
distans AC, eric iritur ved BG ad BD, SCIG FI
rectangulum ad rectangulum ADC: sed TOTI rC
ctangulum aequale estc rectangulo AFC, cum BC
FF linex sinc equales, igicur ve F F 2d BD, (IC AF C
rectangulum ad rectansulum ADC. Quoderac de
monstrandum.
ROPOSI
reofocct e e s poltate alamelliBF, H1C.
DicoBF ad HC duplicacam habere rarionem cius guam habet A C
adDF.
b++ tnino
CAs. tnin.
d
in
S. huius
DArabolam AB C lubrendantdux queuis parallele AC, DF, quibus
Demonratio.
duplicara rarione AF ad DG, id es AC
ad DF, scd BF Cst ad FTGESVE AF C FC-
cangulum ad rectansulum D O F; igieur
BF ad FT Cm duplicaram haber rarione eius
quam habet AC ad DF. Quoderarde.
Voniam AC, D E linex in F, X G
Dolconalet cunc accuctuace
Ereetangulum ad DCF rectangulum in
monstrandum.
+P
no
8 +6. huius