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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 25, page id 1815201908:0082
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POTEN TIF.
P ROPOSITIO XZZ.
Acoangulo ABC, e D puncto extra li-
neas datas: rectam D F ponere quae rectas
EB BF auterac, in daca ratione C ad FI.
Constructio ex demonstratio.
TTac vEG2d FT, ica B A ad B C. iunctae que AC duCaTK
DF aequidistans: pacet ex elementis factum esse quod
DCCIEUT.
P R OPOSITTO ZXXI.
SEo ABC trianouli BaIIS AC; qua diuisa in D, vED E recta aequi-
distans lateri BC, media quoque SIC, inFeF A D, D C: duCaEuF quX
vis GF, parallela basi A C, occurrens F D linexe in FT.
Dico GHIF rectangulum, aquari rectansulo DF II.
Demonstratio.
Sc enim ve A D ad DB, SiC GTTadFTF;
Lquia AD, CFT linex requidistane; sed ve
AD adt DE, sIC D F es ad DC, ex hy-
Dochel; ergo eciam veOTI ad FTF, ACDF
ad DC: est aucem FI F ips D C a aqualis,
igitur ve GFT ad HIE, sC D F ad FTF: e
OFTF rectanoulum, b aequale rectanoulo
DE FI. Ouod fuic demonstrandum.
PROPOSITIOZZXII
Sto ABC crianguli balIS AC, Bifariam aIMIIa IM D; act àque per
sD linca F F, occurrente crianguli AB C laceribus, in F _ F, du-
cacur quadam HIC varallela recta F. F, ve IIL illius dimidia, media
quoque SIEInECF F. D _DF;
Dico CBHI criangulum, aequale csc triangulo ABC.
Demonstratio.
Cti perD ex Y, linea KE, eri-
LLoantur ex Ie D linCOTML, DN:
ec IMTquidem laceri C Bi D N verO
AB laceri paraIlela. VCFD ad ∞ 1,
sc GT est ad D F per hypochesim,
scd ve FD ad GF, sic DK est 2d
TK, _ VETFI adDF, SCTF ad
DL, IgIEUT DE DR ad TR, siC TL
ad D L, e diuidendo veD Tad TR,
sC DP ad DL: Quare IK, DI. li-
nex Cunc incer  sc aequales. dc
proinde cum (ve ex constructione
DACCE,) criaNSULA RMT, DNTP, Cin-
gula criangulo RBL Similia AINE,
crune e incer se Cimilia, adcoque
(CuM TK, D I reCtR AQUeNEUT) crunE
de inter se aequalia; Lacusque RM L
+.Lrimia
B17 Sexii
lacexi
ruimi.