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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 700, page id 1815201908:0757
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1IIIIII
700
SPLR A L. 1S.
Demonstratio.
2 Acio BG ad BcC, componitur ex rationibus BC ad CDY, _ CDZ ad
LCDZ, e CDZ ad BaCi. Aequiracio BG ad CDF, eadem est cum ratione
ABa ad AC: e ratio C DZ ad BaO, eadem est cum ratione AC ad ABB,
ergo racio BC ad Ba C componitur ex his eribus rationibus ABa ad AC, et
SE CDY ad CDZ, _ C A au BB A. Similicer racio arcus BC ad arcum BCC
componitur, ex hiscribus racionibus, arcus nempe B C ad arcum CD V, (hoc est
recta ABa ad AC) _ arcus CDZ ad arcum Ba C (hoc est recta A C ad rectam
ABB.) Acque hacres raciones aequancur eribus prioribus; nam racio AB a ad A C,
in spirali cadlem est cum ratione AB a ad A C in parabola, e ratio ArCUS C DY ad
arcum DY DE per ANerE. P. cade est cum ratione recta C D Y ad rectam D YDZ.
adeoque eriam componendo ratio arcus CD Y ad arcum CD Z eadem est cum
ratione recta C D Y ad rectam C D Z: Denique ratio A Cad AB Z, inspirali eadem
estcum rarione AC ad ABB in parabola. Ergo cum racio rectx BC, ad B0 C1, e
racioarcus BC ad arcum Ba C+ exiiidem racionibus compONAnEUT, Cx dem lune
sive xquales. Simili discursu ostendam singulas raciones rectarum cxecerarum BCad
BO, caldem esse cum racionibus sinsulis exrerorum arcuum B C ad B G. Ouare
diametri BC, B C, arcubus BC, B C proporrionales lunE: quod crat demonstran.
dum. ectisit :. (3 23.
Dicoreriio. Singula criangula C AD, DAD, sectoribus cingulis
C AD, D AD proporcionalia esse, erianoula enim se habent ve bales
CD, DD, de sectores ve arcus CD, DD. Sed linex CD, DD, ar-
cubus per AACTE. 1. praeced. Cunc pro portionales. Erso et triangula lectori.
busproporrionalia lunt.
Dico4. Sulalalisa  ncc. Macampolcemoena
singulis sectoribus B AC, ex c. una cum circulorocoprimo proporciona.
lia cAe.
Demon-
 pt    et tit . e ti tit  ote tit e e t      t  e  to       t t t  ie e t   e    e    ite B