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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 733, page id 1815201908:0790
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seD
20c
Y PL A N V M
Demonstratio.
Roducta CK, perringac ad NF in Z. quoniamigitur AO, OD linex aqua
leslunc, rectangulum I.O id est CM dimidium cA AL; duo igicur rectan.
Dula CM, R N aequalia Cunc eori AT; led A P. rectangulo aequalia lunc redan-
oula OL. PR, 4S, RT, isirur ex illa quoque aquantur rectansulo ONY: crgo et
GNY maius est convexis Aguris D CL, CIFR, FF S, P B T; ad dicisivicur residuis
rectangulis FZ, P. C, rectangula CrMI, PPB, P. C inleripea maiora sunedimidio Egu-
TGCOMHExX DBC. Ouod erac demonstrandum.
PROPOSITIOXL.
DicotoEPOMCKCSla concauX de convexe inleribi fguTE, que
aequalem habeane alcicudinem, ve residuum relinquane, dato minus.
Demonstratio.
ACasEquanticasa: de in cories D diuidatur D C linca, in parres equales doncc
sub BC bali e alcicudine N C rectangulum sic minus quancicare a: tuM PeF
puncta divitionum linex ponantur parallela BC, OCCUFTenEES COnCanE EgUrX i
punctis C, F, B, per quae linca ponantur aequidistances D C, cruncisitur per 39.
huius, rectangula omnia OL, PR, 25, RY limul sumpea aequaliarectansuloR C.
adenque e minora quancicare daca a sed OD C PGF, OEH, REB rehdua A-
vuex concaue minora sunc reccangulis OL, PR, OS, KT: multo ipieur minora
sune quanticace daci a. similicer ostenditur, ablacis ex convexa figura rectangulis
CM, FH F. C, residua relinqui, daca quancicace minora. Dux erant demonistranda
ROPOSITIO XI
ACA SINE AGUIEX CONCAUX AUL CONUEKX ABC, CBD Communem
Heo rorillis inseribi posse reclat Ia (F P, F O, GR: F S, F. L,  V
aequalis atuams e Balsbuis in directum policis, ve Pihecin Peinvicem
ducta auterantur ex concauis ABC, CBD eriam ductis in se Iuicem,
relinquane quancicarem daca inorem.
Adem positâ figura:
habences alcicudinem B C, normalem ad subrentam A C D
A + 2a 3
Demon-
eo1313314 15C 17 10 10