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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 183, page id 1815201908:0240
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# Lines: 63 recognised, mean confidence 0.78
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spei
Iudie
ridistum
6, 61
tac BI
a, ett
EI adB
162d
ETMUI
ad HB
P16I
Content
EB, C
ia lime
2d
aCM
10
t
UI et
cerum
iuata
coreu
BC
dC
8
EC,
Brest
EIR CVL V S.
Demonstratio.
Enero B, inceruallo A B describatuE cireu-
IaS AC C, cui peoductx AB, A F, A F, Oc.
currancin G, FT, I: Duoniam A C. BD cieculorum
fuorum diamerrilune, anguli AHIO, AIC+ xqua-
les erune angulis D F. B, D F B, sed ec anguli B AF,
E A F aquales suncangulis BDF, FDF. quod
iisdem insistane arcubus; limilia igieur sunccrian.
sula e AFE EI AL criangulis BDB, EDLi; de
AFI, AL lince proporcionales ipsis F D, FD.
quare cum sincequales AFI, AI, rectiS 2 AF C.,
AFC, PACCEAGGrCGACUM AF, B C, ad agorcg2-
cum AF, FC, candem obtinere racionem, quam
ecta D E, ad D F. Ouod fuic demonstrandum.
eROPOSIFIO XXIV
Ontingac AB inxquales circulos, conveniens eum recta per verius.
sque cenrrum acta in A: ex quo ponacur AD occurrens circulis in
F, 6, D.
Dico AB ad AC candem concinererarionem; quam obtinet AC
ad AD, vel AF ad AF.
Demonstratic
12515
Opuncta concactuum ex centris duCaneux MIAMCHII LC, et B, nemque alix bI-
FTOL ansuli (quod HIO: IR Ctic BarAHelC,) sunr equaleS; CEAHS CLa LRK, HIOL.
EruntsimIIa, 2C proirde FTI est ad TR VEHIO ad LKL NOC elE (lcuriam oltendi)
diamerri FTNI, PNt, _ ad rectam D Anormales, guoniam isicuranguli ad B
EC recti lune, parallelae erutre tectae HB, IC. ErgBHE AB, ad AC, SC HTB ad
CC, hoc estHO ad TR. Deinde, quia anguli, TKR, TILO recti tunE, _ IRR.
DE TIB ad IC, hoc est (quoniam FTN, IM diameeri, aequantur diametris HIB, TC)
DE ITN ad LMI. MMigicur est FTI ad IR, vE FIN ad IM, etit permucando
acinvertendo NII ad PEL. ve MI ad KI, adebque quadiacum NNII ad quadea-
IONLl cu quadrato I. HI; ec pundracu MI, rectanoulom Leu quadioeci
rectangulu NL P, cum, quadraro L El est ad quadraru L. Fl. ve rectansulu MK O cu
quadraco KIadquacracK P. erso Miidendorectansulu NP P CA ad quadraFuL. FI.
cum P. FB vequadracum B(L ad quadtacum HP. se do quadrarii N FX ae quacux rect aeu. B5. secundi.