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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 973, page id 1815201908:1030
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 51 lines, status machine
# Lines: 51 recognised, mean confidence 0.83
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Y N GVLA CYLINDRKCA.
OPOSIFIO XXEL
Asi rngulari dimidium hexagoni inscripcum sic per cuius latera pla.
 Pnaponanc axi aequidiltancia AtIL, (HIO
Dico legmencunt vngula plano Cilll decullatum duotum elte le
emenci quod ablarum cM plano AVII.
  Demonstratio.
cii
VCANEUE CX CCNErO P rectA P D, F R que
bitariam lecent latera hexagonalia CFT
HIA in O _ N, Ponacurque RS parallela
ad F D. Ouoniam B A, G TI a qualeS arCUIS
incercipiune, erune parallela. Ouare cum
angulus F OFT rectHS SIC, CEIAM A F O rC-
etus cric. AEqui KS Parallela est ex contr. ad
F D. ergo etiam BS K angulus eAt rectUS. F.A
verO _ P N A rectus; anguli isICUE F SR.
F. N A xe qualessunc. P. A aucem ansulus ad R.
verigue criansulo SF.K, NVP. A communis, e
vrum lacus P A, uni laceri F. K xqualc. Igitue
SK aequatuE AN. scd TI A lacus hexagoni,
hoc est Temidiameter D P, duplum est ipsius
ANV. ErgO D E dupla quoquo cA ipsIUS RS.
AEqUI DEDF ad R S, ita a scomencum rngula-
Te GOHIF ad lesmencum vngulare FT AL F,
ereo tegmencum ∞OHIIF duplum est se-
smenci II AL I. Ouod crat demonstrandum.
eROPOSITIO XXIII.
DOnacur icerum vals igulari ten.
 hexdsou Mlcripeum ve prius, e
plana polira secundum lacera hexagoni
parallela axi decultancia eria legmienta vn-
gula.
Dicororamongulam adreliduum quod
reman(ic ablacis leomeneis habere rario-
nem octoad (ex.
Demonsiratio.
AFC, BLLL CHCoCDANCK. Ostensum eAt
CIC ABCD ungula ex lacera semihexasoni
DAE, F E, BB, Per qua planA AFG, FF FF,
BP. El axi aequidistancia auterane legmenta
AF G, FGDTTE, _ F IIB. Dicoisieur PrO-
porcionem cocius vngulae ACDB ad Colidum
claulum planis ABITC, AEF B, FP IIO,
Cmlaltor oc dibula lel aupacl
a n8. tuime
CCDUlL. cciplicacam elleracionis, quam habec AB adLL, ele aucem AB ala-
mecer dupla rectE L. F, quae lacus est lienasoni. Ixicur coca rnsula AC D B, 0d upta 
EI H
C
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