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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 263, page id 1815201908:0320
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He
ELLIPSLS.
Demonstratio.
DOnatur A F occurrere diamecro in C de BF in
M; iunisancur que D C,AB, D A. C B. Ouoniam
DC iungICEaNGENECS DR, CR, bilecacur a 2 dia-
MEErO FIK in L, eAt verob AB parallela ad DC.
ergo e haec a diamecro bilecacur in L. quare cuco-
EA DC, AB Encc xequales, erunc ex carum dimi-
dix DL, AL aequales. cumigitur eciam DL, A, I;
sinE d Paral elae, quae eas iungune D A, TL paraIIC
Ia CruInE. ergO FIgUTA A G R D parallelogrammum
cA, proindeque D A aequalis est CR. Cimili modo
octendemus BC aequalem eAC MK. Quarecum
D A, B C, CnE C aequalOs, etiam R G KM xequales
erunc, ruum igicur idem que punctum (unt C _E NI)
in quo parallele cangentibus DC, CK, ductxe e
punctis A, B, occurrume diametro. Ouod Fuir de.
moncrandum.
R O. P O S.t Y I O, XX
Eliplim cuius CenErum A SCcCHE quaeuis dux diaMCFEI DD, CF, iun-
Setilque BC; D F ponatuF FC diametet, quae BC bitarram dividat
in H, iplIaUEEM E D Occurrat in l, cum per C de B, irem D _ L, Contin - F3+. buius:
sencesagancur, que E C diamerros occurrentin ij dem punctis F e C1.
Dicoxqualia esse incer les primo triangula AC F, AB F, Secundo crian-
Gula AC F, ADC, cerrio criangula CBF, DF C.
Demonstratio.
CcurraE F C diamieter elliph in K ex L. Ouoniam
sicur BC ex hypocheli in H diuila, est bitariam,
eric tam A CH ertangutum aequale ertangulo AITB.
quam HICF aquale eriangulo  F B, vndetorum crian-
sulum AC F, aquale CAEOTIErngulO A FB, quod c
ratprimum. Rurtum cum e BC, D F. xquidistenE e BC
in H diuila sic bitariam a diametro. FC, eric e F. D in
L bitariam divisa: quare Cum heota C B, DP sInEX qua-
les, erune et harum dimidix RC. DI aequales: quare cu
etiam unt parallelE, recte C D, IT I. qua illas innoue, lune
parallelae, criangulaigicur AC HI, ADI lune incer ca(
dem parallelas. Siine aurem ee Bales AH, A L aequales
(es enim AK aequalis; AL; ee Y R HI ipC IL.) ergorriangulum ACHI XgUIATUE L27 huuius
criansulo ADI. lam VEEO AFI, AR, A F, icemque AI, AL, AC TunCL ConcinuE. l32: huivs
quareraiiO AEI ad AEs duplicaca est Facionis AFI ad A R: ec racio AF ad A C+
duplicarararionis AL ad AC. Cum igIUF FatIOnOS AFT, 2d AR; AI ad AL;
eadem linE (A FI enim ipS A I, SE AR; ipsi AL aequalis est) CrunE d PaTiONeS
A ET ad AF, AT ad AG, catundem rarionum duplicata; exdem incerle: 2c
proinde m criangulum quoqi AFC est adcriangulum AFC, vecriansulum A TD m2. sousi.
ad crianoulum A e D. Ouare cum criangula A CHt; ADY olensa sinc aequalia;
eriani AFC, A CD aequalia CrHHE: quod etat alterum. Fx quo iam patec etiam
ECTT, CDI aqualia este, quibus si 2ddas F BFI; CF I, quae eodem plane dileur:
su ostendemus aequalia, crune cora criangula C B F, Id F. Cri a qualia. Ouod craerer-
rio loeo demonstran dum.
Corol
263
huii
hai
. Biiii.