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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 611, page id 1815201908:0668
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1815201908&page=668
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 63 lines, status machine
# Lines: 63 recognised, mean confidence 0.77
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BI
endi
tuie
qui.
C
ta
II. II.
HY PF KBOCA
MucPROPOSTTIO CEVI
IIdem posicis; ducancur D FI, DF patallela alymptoris.
Dicosesmentum DHLCC, ad DI A F Segmentum, candem habere
racionem; quam  C. M N Ceomencum haber ad segmencum F A L. O.
Demonstratio.
Acio DC ad DEI aid EA BH ad BC, dupdcata est rationis b H B ad C F, a1a. huiui-
id est BIc ad B A, id est AF ad IDs legmencumiieur DHC C, ddupluim rabola
est sesmenti AF LV. sed in precedenei propositione ostensum est lexinentum e, + huins
GC AM duplum quoque esse sesmenti LOF A. vrigitur OCNM legencuin ac (d 12. hu-
Sesencum L. OFA, SIC DHICC segmencum eA ad segnictrum F ADI. Ouog
erat demonstrandums
P R OPOSITIO CNVI
Osiris denvo AB, B C alympTONShyPCt BOLE DCLI a Parabola;
veprius, occurrence hyperbola in B, ducantus FC, et Parallela
alrmproro AB acancestirperbolam in Hl. e 6.
11
Bicoracionem LIad FC, cories mulciblicare racionem D I dd EIS
quories superlicies CC mulciplex est superticiei D l.1
Demonstratio.
Atio HC, 2d C,F, id E cl.
Fad BC, dyplicaca est racionis
sF L, ad F C; ex racio C I ad D K
duplicaca est rarionis D K ad R I.
sicurquoriesmusciplicarrario HIC
2d CI, racionem CT ad DK. 10-
cies mulciplicae racio F I ad F C
racionem DK, 3d F Y: sed osten-
1
Cum estcories mulciplicare rarionem HIC ad G b, rarionem C F ad DR, squories BIg. hu-
mulciplex est fgura FII, figurx ID. Igirurrories mulaplicar rario F. I ad F C, 1d.
cionem DH ad F. I quories mulriplex est quantiras EL I, quancicaris LB. Quodtuse
depronsranaum.
1e 1SC. CNP et SB OHBM  eEgnO.
PROPOSIF
e
113 CSO 31Ct 
=2113DO ETC
InE AB, B C alympeori duarum hyperbolatum DEF, GHI, le-
actarum parabol2 BD G, in D _ C; cuius axis BC: e ducta BK;
qua occurrachyperbolis in F. ex HIp ponatur KC. parallela alyimpeoro
secars hypetholas in I, C. iunsancurque BD, BG, BI, BL.
Dico hxurami DBF ad F. B L camdem habererarionem, quam Rgu--
ta, GBFL ad HI B I, AOUFAMIS
aupoa cor. AC. l 1s. 23rii 1112.  Ben
3.11 1h EBOiONOTY~). BCLAEL. Lil
EsTC) FE.LEd iian eeir I
es p sscne: L et AR. P ACL, LE M . S.:  Y
J. F, 9125S 3IF IP. LE CANCNSI BISCMMOS
1e3ite esbaidit. CF. Ahsi D H cirioisur : S13 _3s iigsmI (e H  Br .s 3YF. WP cAT. L BE
DeMon
1
depa-
c7+ huius
bot
s s   e   e  t s o e  u  sa sr