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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
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Il
SP IR AF I6.
Demonstratio.
Rioneula B AG, B AC cum angulum ad B aequalem habeauc, cationem Ad-
bene adinuicem composicam ex locerum AB, B C, racionibus, re demonstrac
Clauius ad 23. 6: Similiter sectores B AC, B AC adinvicem rarionem habene
compolicam ex rationibus semidiameerorum AB, AB, de arcuum BC, BC. AC-
qui ex hypocheti rario Aa B in parabola ad ABB, aqualis est racioni A a B ad
ABB in spiralis racioicem B C. diameeri ad diamerrum B aC,, carem eA cum
eacione arcus BC: ad arcum Ba C: per ANerE. 2. PropOLC. praecedenc. Ergo rario
compotira exracionibus, A aB ad ABB, e B C, od BaC, hoc est racio crian-
pulorum ABC, ABR C cadem est cum compolica exracionibus A aB ad ABB
in spirali, ee orcus B C ad arcum Bao Ci; hoc est cumracione sectoris Aa B C, ad
sectorem ABaC. Isicur permucando pacerrriangula lingula B A C Singulis B AC
sectoribus esse proporrionalia. Duodcrac demonstrandum.
Dico quinco. Singula scomenta parabolica qua lineis rectis AC, et
curuis AGC continentur, Cingulis spiralibus spaciis gua vicissim lineis
rectis AC de curuo spiralis ambiru AGC, concinentur esse proporcio-
nalia.
Nam lingula. Tegmenca parabolica per 27. huius singulis eriangulis
B AC luncproporrionalia. Rurlum per candem singula spiralia spacia
singulis sectoribus B AO proporrionalia lunc. Arqui per ANerC. Quar.
cam criangula singula B AC, sectoribus B AC. sinsulis proporcionalia
Tune. Ergo et Scemenca parabolica sexmenris spiralibus lunE propor-
cionalia. Ouod erar demonstrandum.
Scho-