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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 507, page id 1815201908:0564
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1815201908&page=564
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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
# Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German.
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# After the first blank line: the recognised lines in reading order, one per line.

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erie
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sune
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P A R ABOL A.
eROPOSITIO CCCZXII.
SEO ABC paraboIX diameter AD, ad quam oFalHaH POIALCE
LCD, BF: pertectoque parallelogrammo DF, auCAEML HIICA LL,
sCCanS E B RCCEaS in G C: hancantem C F lineis equales G, BHL.
Dico HIH puncca esse ad parabolam.
Demonstratio.
Vngantur AC. quoniam DF parallelogrammum
es CuinS diaMCERi AC, FD, de RF linex eequi-
distane laceri AF, lineis F C aequales lune rectae
HI; isitur e HI B lineis x quales sunERI. dempris
isicur communibus K B, manent IB, FTK linex X.
quales: punctaisicur HI HI a ad parabola TUNE.
PROPOSITIO CCCXXV.
ISto AB C parabolae diameter AD, ad
quam ordinatim ponantur lincae CD,
BE, quas in G sccerrecta A C. descripea dein
Per A _ C, parabola C. F A quam in A recta
ContinOAE AV, _ F B diameter SIC, HanE F C lineis, pion
e rectis BC proporrionales F. I.
Dicoram H, HI puncta quam l, I ese ad parabolam.
Demonstratio.
iSc enim ve AG C rectangulum ad rectan-
oulum ACC, siC AP D rectangulum aa
rectangulum AV D: lcd vE ACC rectanou
lum estad rectangulum ACC, sic FG linca
est adb lincam F C, id est F. FT linca ad lineam
FH: ixituT _C HIF est adHIH, VE AF. D rC.
ctangulum ad rectangulum AE D: SimiliceF
octenditur, esC F I ad F T, vE A E D ECCTan-
sulum ad rectangulum AED; punctaigieur
LI, FL vei ec Y, T, cpuncca ad parabolas lunc.
PROPOSIETO CCCZZVI
DArabolam AB C concingat in A li-
L nea AF: ponatur aurem sectionis
dIaMCEer A. D, d illi parallelae F. B: dein
rectis L Bproportionales hanelinex BF.
DicoA, F, F puncta ese ad parabolam.
Demonstratio.
VeanCuF FC parallelx concingenti AF:
cumisituE bevE E B ad F B, sC BF, ad
BF, CriE quoque B F ad B F, VE F B ad F B.
sedrario FB ad B B, duplicaca est rarionis F A ad F. A, 1d est F C+ ad F Cigitut e
racio E F ad F. F, id est A C. ad AC, duplicaca eAt rarionis (r F ad Cr H: 1B1CuF A, F, t
puncta Cunc ad parabolam.
67
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B47. Mcoius.
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