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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 990, page id 1815201908:1047
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TNGVLA CXLINDRTCA.
PR OPOSITIO XLIII.
Ine AB, C D contingentes circulum
AL.C incerminiseance eu
circulus balis est vnsulae AF LC cylin-
drorecto decultatx, habencis alricudi-
nem FL diantetto AC patc. Ponio
HID circumdance circulum ACC, sic ve
eius lacera in contactu bilecentur, pla
nilq pertes per lincas polygoni axi pa-
rallelis, qua concurrencia cum plano el.
liprico vngulari AFC FOrMENEIR, K L.
L.Ml, communes incerlectiones, secene
vero sele muruo secundum rectas DI,
HIK, CL, BN.
Dicohxdras omnes DTRKH, HIRLC,
CLMB, ingulam ambiences simul
sumpras exclulis criangulis AB M, C DI
aequari quadrato AC.
Demonstratio.
PSc enim in praecedenei demonstratum re-
Loctarulo AC N aeguari reccitincum DHTEL.
Ibidem octentum estrectangulo AC, NO aequari rectilincum GHIRL, d rectili-
neo BO LM aequarirectangulum suPCE A C e AO; igicur cum rectangulis AC
NC., AONO, AC AO aequetur quadrarum AC; eriam omnibus tiguris rectili-
neis DFTKI, GiHKL, GBL. M simul sumpris xquatur quadratum AC. Ouod
crac demonstrandum.
PR OPOSITIO XLIV.
AEx Cu bina vngula a cylindris rectis decusacx, quarum alticudi-
nes, sinc balium circularium diameerispares, ee ip (x criam bales cir-
culares a quales linc. Circa verumque aurem circulum polygona descri-
bancur, sedinae qualium numero lacerum, circa vrum circulum exempli
pracia polygonum decem larerum, circa alcerum verolacerum mille: pon
nancur in Cuper plana per lacera polygonorum que axibus aequidistent,
concurrencia cum planis ellipricis ongulas rerminancibus.
Dico omnia plana unam ingulam ambiencia simul sumpea, aequalia
esc planis simul lumpris alceram circumdancibus, si criangularia verim.
QuC OMIETANEUT.
Demonstratio.
demde quocunque polysonoB6, CHI.
La tnius. FiX demonaratis erim. constac congeriem planorum singulas vneulas ambien-
um, dempriscriansulis xequalem ene quadraco circularis diamerri quae in balell
onsule, extspocheti aurem onsularum bales, adeoque  diameri balium aquales
TuNE.