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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 69, page id 1815201908:0126
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au.
nul
314.
i
1B
et
D.
ad
2
G E OM F T R IC A.
6
ad BD, vel vE A C ad CF, sic BC difterenciam primae et sccunda, Fore
ae C F difterenciam difterenriarum b aCl.
Secundo (i BD minori auFeratur aequalis EF, ex C F maiori, VE AB
Demonstratio.
aVm exhypole AB sic ad AC, ve AD ad A F: isicurpermurandove AB ad
AD, SiC AC ae AE; _ diuidendo re AB ad BB, siC AC ad CF; ivicue
permutando ve AB ad AC, lic BD ad CB: aEqui A B MIMOF CIE quam AC, IBHHL
e BDminor est quam CF. Duod crarpirmum. deinde ex AHCHIEI iam FaCtO, Ve AB,
etiam AB ad AC, VE PF ad CF; ac diuidendo ve AB + BC, HC L F A FC.
de permurando ve AB ad F F, id est ve A B ad BD, Sic BC A C. F: ACGUIL CHAM VE
AB 2d BD, GC Cs AC, 2d C F, (VEanEE oRendt) 115O M AB ad BD, vel AC
ad CL, Hc est BC ad CF. Quod crac demonstrandum.
2d AC, sc CA BD ad CB; quare cum eli ex hypochel aGaSipI BD, eriE
PROPOSITIO
L AL1.
tlauadopobuateo, la AB, lecunca AC, ccilla
AD, quacta AL.
Dicopio ametena plina d lccunaa Be, minorem elle ditte
rentia DE, Tertix _ quarEX:
Secundo lex E D maiori Eollacur EF, aequalis minori BC, Fore ve
AD ad DF, sic BD differenciam primx e cerrix, ad D F differenciam
differenciarum BC, DF.
invercendos De A B a B CBHC AD ad DF: leaquo pernucanuo de AB ad
AD, SC BC ad DF. sed AB minor est AD, eroo eE BC minor eA quam D E.
Ouod erac primum. 1
Deinde cummodo ostenlum (c, esse AB ad AD, ve B C elt ad D. P; d cum LL
ponacur xequalis B C, eriam A B est ad AD, VE P F ad D P. Leaque inuercendo, ac
converrendo ve AD ad BD, SiCDE ad F D: ac demum permuLALCO VE AD 2d
DE, SC BD ad DF. Aequi eriam ve AD ad DF, sic est AB ad BC, (VE anCC
ostendi) ergove AD, ad DB, vel AB ad B C, sc est B D. aet DP. Ouod crac de
moullandum.
Demonstrario.
VIMI SC AB ad AC, vE A D ad AE, igicur inuerrendo; dividendo, rursumque
e R
CitsesC
Inc continui proportionalium processus AB, B C, CD, D L, LL. ALIUIE
ia vero quavis alia W, hac vE AB ad N, Sic N ad FII: veque BC al
N, (ICN hac ad IK, _ vEC D ad N, SIC N ad ALL, c H CMHCCPS.
Dico HIL, IK, IEL, Xc. esle in continuaanalosia.
Demon-