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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 39, page id 1815201908:0096
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E
2a
ux
0
is
de
cC
1-
sis
POZFN EIR.
ostt atto.
leatum ∞B, agnale est quadraris AC, AD rna cuma rectangulo C AD a+ Sanm
bis lumpco: sed AD quadratum, aquale est quadraris AC, CD, vIa CUIM FC- d.
ctangulo ACD bis P sumpco; id est rna curri quadearis DF, L. F; _ C+ AD FC- BPerean
ctangulum bissumprum. aequale est rectansulis, G AC P; C AP B, id es rectan- dem.
Rurtum rectangulum Ci CB. aequale est rectangulis ( ACB, ACB: sed AC B
rectangulum aquale eA, rectangulis ACD, ACDB, ACFF, ACFB, id cst
quadratis AC, CD, DP, FP, una cum rectangulo C AC B; igicur addico qua-
deato AC, cric C C B rectangulum, una cum quadrico s C, aequale quadraco CD.
Duoderac demonstrunu.
sulo C ACB (ob C L., I B lineAS aguaseS HCa CB) igitur quadratum OD,
aequale est, quadraris AC, AC, CD, DL L F. vna cum rectangulo CA, CB.
ECetUT AB, in quoruis partes
Dico quadrata A. =, CD, DE, E B, simul cum rectangulis AC B.
EDB, DLBOIS IMMIpES, aquari quadraco torius AB.
Demonstratio
recunque in C, D, E, _c.
e
e
1b
adeacum enim AB, aquatur quadratis AC, C B et rectanguloC A C B biS c +. Scclm
Llumpeo; eodem modo quadratuim CB, aequale eAt quadeatis C D, DB, _ rC- ai.
ctangulo C DB, bissuipto; denique ee quadracum DB aequalc eAt quadraris D R,
F. B, e rectangulo D I B bis sumpro. collectis igicur in rnum quadraris AC, CD.
DE, E B, e rectangulis AC. B, CDB, D E B bis CumpEisi Ex(UITBET QULANEITAS, qua-
deato AB aequalis. Ouod Fuic demonstrandum.
Corellarium.
hecollisere licet; quod de duabus rectis lineis, quomodocum que divilis ecium
Csccundum distimillimus rationes, iudicium ferre debeamus. Ex discursi enim
polico in demonstrationc huius propolicionis constat; quadraca parrium cuiuscum-
que linex, cum rectangulis bis sinul sumpris, que sub partibus fune, secundum ce-
norem propositione conrencum, aqualia esse quadrato cocius; inde cam proportio-
nem habere necectarium est quadeita parcium vnius, Cimul cum rectagulis bis sumpeis,
ad quadeaca omnia parrium alcerius, cum rectangulis luis bis sumpris, qnam iplamet
quadraca cocarum incer se obtinent. Ouod admiratione non carec, cum vria quancica-
cum, in paucistimasparces possic dividi, alcera vero in quampluximaS.
credibile; li dicum numerum verbi gracia r00. quis iubeatur, lecum cacitus in plures
vro libitu partes parciri, deinde singularum parcium quadeaca, in vnam summam col.
recca, seponac; qua cumsa, ex pcaonos paltium incerle, lecundum len-
tum proposicione concentum, coniuneca, cerrum quendam numerum sibI Cop
carit. Alcer vero Geomerrie onarus, sponsione cum eotacta, cercet le divinacurum
cumnumerum, quem suppucatione facta, in codicillis conlcriplerir. Cres eriam
cyLOUM CapEUi masiS ACCOmMOdCCUT; cam Euliuis monmiluil deduca.
Foc eriam quod subiungam, ignorancibus Cieomerriam maxime, videbicur parum
POnaTUF