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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 257, page id 1815201908:0314
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 57 lines, status machine
# Lines: 57 recognised, mean confidence 0.86
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EL E IP S 1S.
P R OPOSITIOAXXIN
ECenE ABC ellipsm diameeri duae AC, BD, innetaque BC, afatuIF
Dpex E cenerum diameter IL L, secans BC bitariam in DLB _ ex B e
C rectae ducantur BF, CC, ad idem diameeri punctum C secances
AC, BD lincas in FI e 1.
Dico rectangulum AHC essc ad rectansulum DIB ve quadratum
AC ad quadratum DB.
10c
Demonstratio.
otiatue ex C linea CF paralleta BD; occurreris
diaticero RF, in L, R iunse BL. quontam C L X
quidistaE D Rs EFUnE PMB; CM F crianoula inter se
similia: guta VerO C M, M B Xquales sUNF, a qualia quoq;
CFUnE ErIanBUIA CM L, R MB e laceri FM, XqualelacuS
CM: igitur in criangulis BM L, CME, duo latErA C NI.
AF. aequalia sunt duobus laceribus BNI, NI L. Ced _ an-
suliiis concenti BNI L, P. M C Eaequantor. Frzo adbiles
atgoli LBM, B O B EquaHCHT. erSO BD, CF A CunE
parallelae. Ergo BITad HK, VE L F, gd F K, hoc est
(quoniam ex constructione BL, CL sune parallelX) ve
CTadTK. Ergo TIIxquidistac CB, ex cA ve HIR adF C,
EC IF ad F B, _ componendo aC PermUEANdO VE F C
ad F B, SC HIC ad BI, s0d vr CB ad BF, sIC A C est ad
BD, cum veraque in cenero: diuisa sic bitariam; igieur
DE AC ad BDS SC HIC ad B I. ergo eciam bre RC 2d
DBs AC A EI ad D I. Quaec cum rectandulum AITC
ad rectaroulum D IB cacionem habcarcomposicam ex lacecum racionbus A HI, 2d
DIS de PIC gd B F, quae ambae loltentx lune exdem ese Eutm ratione A C ad BD;
Hoc eReadem quae qua
dracorum AC, BD. Ouod erar demonstrandum. A
PR GP, OS +Y1 O XXV.
elinex C, DF inerque elsiplim ducte occurrane diamero ellipseos
MA in codeM pancto K. Duax sine scinde binx alix diamecri
D. Ck qua ita lecencur a rectis C C, BF ux rectangulu BIB
quadratis BD, A C peSBOFTIONaIIA RINE.
Dicoiunctas THI, C B ese parallelas.
on Demonstratio.
CHK
il sucsi
odie
Voniam cM quaaracum BD ad quadracum C A, hoc est ve quadratum L. V
ad Gudaracum L. A, sic vectangulum BID ad rectangulum CII A; erir permu-
tando vt quadrarum F. D Phoc eAt rectangulum BID cum quadrato F P) ad re-
ctangulum BFD. ve quadracum R A. (hoc est rectangulum CFI R cum quadraco
F. H) ad roctansulum C ITA. ergo dividendo, rectanoulum BID est ad quadtacu
P L.vcrectaneulum C EI A ad quadrami BHI. Permurando isitur rectangulum BID
eAad rectangulum CTI A vc quadraclit I’ad guadracui F HI. sed cciam est rectan-
sulum BID ad rectangulum C II A requadratum BD ad quadracum C A, HOC
eA ve quadrarum P. D ad quadracum P. A. leaque quadracum B P est ad quadracis E. FL
vequadracum F H ad quadratum F A: adeoque rectque P I ad rectam F D, hoc est
EB, vE recta F H adrectam P A hoc eAt P. C. parallelae tuncixicur LF, C B. Ouod
exat demonstrandum.
27. hui
d
quins.
P KO