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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 380, page id 1815201908:0437
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1815201908&page=437
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 58 lines, status machine
# Lines: 58 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.

huins
27. P.
asionum
380
DC ell aplicaca.
c Coroll. 35.
huins.
AR A 80
emsonsoratio.
 A  lincae ponamire corteinua
Pentionales quoque cruic F B, F.1C, ldC: persirut
aucem AD prima serioi AB AF, A D aequalio lacer
recto, adcoquea iphi DC primae serici F. B, FO, DC
isicur b AE linoh nd lincam F. B cerria ad cerciam du-
plicacam habecracionem ejus quam haber AF ad Fci
se
unda ad tecundam; Quod erac demonttrandum
Corollarium.
Tine sequitur rectangulum. P. A F ad rectarigulum
BF C racionem hrabere criplicacam eius quam ha
vet A i linea ad lineam FC. olt en ravio rectanguli L A F. ad rectangulum
EB L C+ COPOLICA CX A R ad E B, _ AF 2d FC. Icd racio AF. ad B B, dupti-
caca clracionis AF ad FC. igicur rectangulum F. A F ad rectangulum F. B F 6.
criplicatam habet Facioeu ens quam habet AF linea ad lineam FC.
naneur aurem ordinaCM MM E LB, DC: iungancurque AB, AC.
PR OPOSITIO XXEVIII
VIE ABC parabOla diaMCTEF AD diviCa In F _ F, VE AF, AF, AD
lipex sint proporrionales, _ AF media aequalis laceri recto, po
Dico AB ad AC, rationem habere criplicacam cius; cuius FB ad
dCoral. 36. 135
C35. tuines.
ccol.
lqu
Demonstratio
Veatur ordinarim lirea F. C. Ouontam
AE, AF, AD linea proportiolale cu
1ees
a AC Iccra aequalis laceri secto, Triangula
AE B, AD CC similia lunc, ad coque vE AB
2d AE, sIc A C ad CD: X inverrendo per
mucando ve AF. ad C D, hc AB ad AC
iam voro cum AF aqualis Facta Gc lacortte.
ato, adeoque e FC cidem aequalis AB.
ABB, EO, DC erunc continux; racioiplcur
AF ad CD, priinx ad quaream eriplicura
eA racionis BP ad Fics, sccundx ad cerrium,
igicur de AB ad AC, criplicacam habeera
tionis F. B ad F C, cujus RB ad DC, chas
bec duplicacam. Quod crac demonstran.
dum.
CLCEt Liat
ZisparabOIE ABC diuisus CIECMM pL SPOLLIOHaLES; a AV
adaccco L1, 112, 1B, et, Hei Pollanut quoque, Dh.
OL, DC
Guicem media exictat incer AL, AL, 46, IIIL. CuclIq; ordinatine
Scorationem DI ad DC dupicata etus ene Gua Habet ADad
Demon.
(us  ne te ss it  1   e 1. s e t.   u s s.   A  e   1 1  ta   s  1 . 1 .  e is e t   .     t      t  1 1