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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 686, page id 1815201908:0743
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606
S2cR A L 13.
concluderur peopenat ica e ca parre propolicionis r4. vli lu-
mus. Iccriutecenueniune splralis e parabola. Ouod erat demon-
AuCatuE AFIK, iunGatuEG FE C. Ouibus peractis eadem ratiocinatione
Arandum.
Corollarium.
emencum L. aC P repexleutari.
Archimedis 27. applicatur parabola.
Paciorum comprehenloru sub spi.
Dralibus e rectis lineis guae in circula-
tione lune, certium quidem secundidu.
plum est: quarrum verorriplum: quin-
cum aurem quadruplu, d semper quod
sequieur, secundum numeros qui dein-
ceps lunc mulciplex est sccundi spacii.
Sumirhic Archimedes spacia non more so-
lito se d pura prourinvicem non includune. (0-
cundum isicur spacium hic est, id quoddempro
primo superest ex secundo: cerrium id quod
dempris primo ex secundo _ sc deinceps.
Sic loqui roluie archimedes ve certam nu-
merorum progrestionem haberee. Nos hac
spaciorum acceptione, quamuis eriam in
parabola ad vrsuem conveniae, quod cerrica sic nonnihil _ a Communi cOnCEpTI
aliena, hoc loco praecermissa, ea solum camparabimus qua de spaciis in-
ceoris, ad sensum detinicionis quinex libri spiral. accepcis in hac propositione de-
monstrancur: cuiulmodi est quod quarum parcium primum spacium cstF: earum
secundum (ic 7; cerrium r9; quarcum 37. _c. P. X quo de ducitur eriam illud, quod qua-
rum parcium primum est rnum, carum primum cum secundo sIC8, _ eria priim a 27.
e 4. prima 64. ux omnia parabolx ad amustim accommodabimus.
AP PL IC A FIO.
Acaline voluta quoeliber (pirarum, et parabola, diameter NIE, sub.
centa R M, cansens A P in corparres equales secta, quor spiras ha-
bec voluta. U ab aequalium dinitionum punctis, ducaneur B B, CHIH,
DLL, dlanecto pataneta, lungancurque ABHFI, A OL G, ARL M.
Dico quarum parcium segmencum primum parabola, cum ABF est
r. earum lecundum AHL NB esse7, cerrium 19. quaccum77.
A Rchimedis propositio 28. Cmili Eere ria applicabitur, cum enim CeAtor AC C d
Lcriangulo AC C repExsencetuE, manifeltuni quoque es illius PAEECM P C O F
a crapezio P C CFi ac proinde sermentum GF.  Ca mixcilinco GF C C, e se-
Demot
PROPOSITIO XVI
ti