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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 408, page id 1815201908:0465
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 54 lines, status machine
# Lines: 54 recognised, mean confidence 0.84
# 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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Coroll.
O5 huius
FX 70
huius.
C L. Dopro
Erettionibuo
d27. buium
P A R A BOL A.
EOEOSIFIO CVII
ito AB C parabole aneter AD, in qua alumpro exrra sectionem
sponcto quouis E, demicideur ex E lecans F F C, policisque ordinarim
O, CD, RaE AP. linca a Gualis AFI, se ex HI ordinarim ponatur HB
Dico F. C lineam extrema ee mediara.
tione proporcionali in F. _ H cNC diuilam
idest CF esse ad F. F ve CK ad R F.
Demonstratio.
EI FEIBB
VnoanCuFFF: Ouoniam A FF linea aequalis
PONICUT AF, FectX FG, BHI, a C D, PFOPOT.
cionales sunt, _ F C, TII b lincae xquales, adeo.
que _ FT parallela AF. GUarEVEF C ad RF,
sc A C ad AL, id est AD ad AFI, id est AH
ad AC, (cum AD, ATT, A C proporrionales
SInC.) id est DFI ad c FTG. id cAt CR ad RF.
Duoderas demmonstrandum.
PROPOSITIO CVTII.
Darabolam ABC cuius diameter AD, comin.
gat in B linea B C, conveniens cum diamerro in
F, ex quo recta ducatur F C, occurrens parabole in P
_ C, policaq ordinarim BD, duCaTUT A C’OcCurrens
BD linex in C, _ recta FD sccanS A C in HI.
Dico rectam A C diuilam esse in HI, d G, extrema
demedia ratione proporrionali: id cA AC, C. B: et
AHI, HLO este proporrionales.
Demonstratio.
Vugancur F O: Ononiam osensum est in praecedetri pro.
posicione FC lineam aequidistaro AF, VE AC ad Cv
sIC AF. es ad F G: sed AF cA aequalis d AD, igiTUT VE RC
ad CC, hc AD est ad F 6, id est AEL ad H1C. G yod er
demonstrandum.
EA EL. C~ CISL IHBCB IIUES TAE e
P R O P O, S, Y F PO miOVX nil 0
113 e tOO
It ad ABC patabOlX diaMHeHEBD,
ordinarim polica A C. iun ctilque AB.
E B ducacur quaenis diamocer F F. Ieur
Dico esse vE AD ad D FI, SIC. HIE ad
ct CBSe t BBBOI
Demonstratio.
lameter P F, primo AB linea Occurrarin
F exera sectionem. Ponatur per B concin-
sens IB: DE AD ad AHI, A5 DB id est 1H
OcCurrenS AC, F C, lincis in L _ H.
 u  e i t   i   u e  e  ue ete  Ae ee et u  p ei     t 1 te a  a   e         ti.  e  p 1  n       e   . 1