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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 43, page id 1815201908:0100
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 60 lines, status machine
# Lines: 60 recognised, mean confidence 0.80
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# After the first blank line: the recognised lines in reading order, one per line.

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POTFNLLL.
P R O P OSTYIO LAVTI.
AB, AC, AD linea Fuerinc continux, quibus aegltales tanE AF,
AL, HO, in direCFUM;
Dico DCC rectangulum, ad C B F rectangulum, elle ve D A ad B A.
Demonstratic
Enero A, inceruallis AC., AD, semicirculi
deseribanEur DFILC, CR F; crectaque ex C
normali C FI, ducatur recta AF, occuerenS Cir-
culO CKF in K, WUNSANEIEquC BR, vE AC ad
AD, HC AR ad ATI, sed vE AC ad AD SIC AB
estad AC per constructionem; igitur ve AB ad
AC, AC AK ad AFI: adeoque BK, FC linex
sune parallela, d BR recta, normalis ad lincam
AC: quare DCC rectangulum, est ad rectangulum CBF, DE TTC quadratum,
ad quadrarum KB, id est in duplicaca ratione linex IIC ad KB, id eA AC ad AB,
id estre AD, linea ad lineam A B. Ouod crac demonstrandum.
P R OPOSITIO LXVTTL
SI Fuerint quoreunque linex concinux proportionales AB, C B, DB.
DEB, FB, CB
Dico rectancula ABDE, CBDE, CBEF, DBEF, DBFC,
FBF C in concinua cscanalogia; e quidem inratione AB ad C B.
Demonstratio.
Eaangulum enim AB D E. ad rectangulum CB D P, est RE A B 2 linea, ad lineam LL. Sexti.
CB; _ CBD E rectangulum ad rectangulum CBF F, est ve b DF 2d F F, b Ibid.
id cst, ve AB ad CB; Rurlum rectangulum CBF F, ad rectangulum DBF F,
estve CB ad DB, id est AB ad C B. (qiia AB, CB, DB, SC. ponuneur conti-
nUX, e DBF F rectangulum, ad rectangulum DBF G, est vER I: 2d F G, id est
icerum AB ad CB; d lic de cereris. Pgitur rectangula ABDE, CBD B, CBBF,
ecc. in concinualunm analosia, es quidem in racione AB 2d C B. Ouod erat de-
monstrandum.
lFuerinteres ordines continue proporrionalium A, B, C, D. L, F, C,
DtI. L,K, L, M. _e AF rectangulo aquale hac quadracum N: e R
quadrarumxquale rectangulo FH; sir aurem ee lF. rectangulo, aequale
quadrarum O, _ E. B rectangulo, quadrarum S. dein e rectanguloC FI,
xquale quadracum P; ex T quadrarum, aequale rectangulo CM; denique
rectangulo L H, aequale quadrarum 1, e OD rectangulo, quadea-
cum V;
Dico quadratum N ese ad quadrarum P, ve cA quadrarum 5, 2d qua-
dracum V: e R quadrarum, ad quadrarum F, ve O quadracum 3d qua-
deacum 
A OABSITIO LXIX.
Detrot