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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 44, page id 1815201908:0101
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 55 lines, status machine
# Lines: 55 recognised, mean confidence 0.87
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  em napamm nen
L IN E A R V M
Demonstratio.
Vadracum enim N ad quadrarum P, id eA peF COn-
Lctructionem, AF rectangulum, ad rectangulum
CFI rationem habeta compolicam, Cx A ad C, id est
Perhypotheum ex duplicata racione A ad B; _E CX F
MI. adFI, id est duplicara racione F ad F; scd ratio qua-
draci S ad quadracum V, id est per hrpochelim rectan-
guli EB, ad rectangulum CFD, etiam componieur ex
ratione B ad D, id est duplicata ratione A ad B, eF CX
rarione P ad G, id est duplicata ratione P ad F, IgIEUE
requadratum es ad quadracum P: sc quadrarum 52d
quadrarum V. Fodem  Osendicur quadratum R, ad quadrarum Y CNC, vE
quadracumt C dd qladracum O. Duoderar demonstrandum.
PROPOSITIO LXX.
AC linea diuisa inx qualirer in B, oporter verim que rectas X qua
es adiicere AD, CL, Vr ABC rectangulum, ad rectangulum DBF,
Constructio ex demonstratio.
Fscripeo super A C, re diametro, Cemicirculo AF C,
eriontur ex B, nOrmalis B F; e AacvE R linea 24
S. lineam, ica BF quadrarum, ad quadratum B C.
cum centro communiTI; inceruallo TIC, delcribacur
lemicirculus DGF occurrens A C linex productx
in D _ F. DiCO AD, CF, lincas CacisFaCCrE DC-
cicioni. Rectangulum enim ABC, aequale est qua-
drato b FB, d C B quadrato, aequalc est rectangu-
lum DBF: isicur rectangulum ABC, est ad rectan-
sulum DBF, VE FB quadracum, ad quadratum B Cn
id estlinea R ad lineam S per construetionem. dacx
sicur lCa A C rectas aequales rerimque adiccimus; ec. Ouoderat praestandum.
AOPOSTFIO LXX
REo quadrato A, a lInCa D F, vecunque in E diuisâ, extribere re
ctam, quae dinila decundum rationem DF ad F F, extribeac qua-
dracum sub toca, vua camrectansulo sub segmentis, ad quadratum A,
Constructio ex demonstratio.
NDCnEA MI, mecIa inEeF B_E C , HaC vE quadra-
Lcum B ad quadeacum NI, ica D E quadratum
una cum rectangulo D R F, ad quadratum C, dein
ve C linea, ad DF lineam. AC lacus quadraci, A.
Aiac ad quandam PR; gux IER LCCCEUFINL, VED F
est divila in F. Dico IK lincam eAC quaLEam.
Ouoniam est ve C linca, ad lineam DF, Sc lacuS
quadrari A ad receam LK, CxiE inVCREendO, pCF-
mucando, DF ad TK, ve C ad lacus quadrari A.
Rurlum cum TK, D F linex proporrionalicer (InE
divita,
A.
123. denti. L.
E2
B.
C
dacam habeatrationem, R ad S.
in data ratto B au.
puasuiu  e u e u ui  su ute  s e e dit   u e e p i u .  n    e  i    pu pe ae  r du  un