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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 225, page id 1815201908:0282
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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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c0d
et
De
D
c
AD SEC FTONES CONI.
ectus est, quadratis AB, BG, G F. quadiatum ducem AC xquale est quadracis
quadeatum AC, quadraco LO: quare quadratum A Li aequarur quadratis AC,
CF. vudenormalicer insictie brecta AC, ipsi G F in puncto 9. quod est in peri- b 48: primi
merro circuli habencis diameerum BD.
Secundo basis crianouli P F Contingat Cir=
culum BOD in puncto D; ducaEurque AD, A
ad punctum conactus, quod idem cA cum
cencro balis coni BTTC; IUNSANEUEQUC AF,
AF: quoniam c anguli BDF, BDF recti
TIIHE, eE F. L lacus laceri D F, ac B D Sibi ipsi
=quale cM, cciam bases BB, B Faquales c.
TUHE. CrgOqUadEaTA BF, BA, quadraris BF,
B A aequalia lunC. AEqui quadeatum FA ∞ -
quacur quadracis BF, BA, _ quadracum
E A quadracis BE, BA, quod recta AB
olano balis comi lic recta, adcoque anouli
ABF, ABR recti: quadraca igitur L A
A, dc proinde criam recta P A, F, A equan.
cur. Duare cum in Ilolcele P AP, balim bi-
CCCE AD, cric haec e perpendicularis ad
balim. leaque in hoc eriam cali perpendicula-
is AD est ad circulum BCD.
Tertio LIcrianSUIUI PEF axEM, cranLCAEPCF
AB normalem a vercicc ad balim coni du-
ctam, ac proinde ejus basis eadem sic cum B D C: tum perpendicularis a verrice ad
balim trianguli, eadem quoque erir cum perpendiculari AB que aUCIEUE A VCTEICC
ad basim coni. Ouare eciam hoc calu cerrio perpen dicularis ad balim criansul ad
circuli peripheriam exister; in conoigicur (caleno, et c. Duod tuic demonstrandum.
PR OP OSITIO V
IOnus scalenus à cuius verrice verpendicularis cadicinera conum, (1
Alececur per axem exhibens triangulum, ad cuius balim normalis du-
catur a verrice procedens:
Dico illam perimerro circuli oc-
curluram cuius diamerer aequalis erir
linex incer perpendicularem à verei-
ce coni e cenrrum baleos eiuldem
COHIITETCEPCA.
ccimin
Demonstratio.
DCOnUS AB C Q CUIUS VEFEICC Per
Pehareutaris AD demilta cadat inErS
conum; occurrens bah in D: a quo ducta
sIE D F, recta ad cenerum basc05, super qua
ve diametro circulus DHIF describatur:
deit peraxem hiac que cunque lectio exhi.
bescriangulu A L Ci: cuius BasiS F. C primo
secer circulu in F _HI, cu exverrice A dc.
miccatur AII ad rectam  C. Dico illam
in perimeerum circuli DFI F. incidere. du-
cacur enim ad punctum H, in quo CtY
circulooécurric recta D Eli iunsancurque