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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 683, page id 1815201908:0740
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ROPOSITTO XIV
Archimedis 25. applicatur purabola.
Tlaciumuoeea (BMC) ex sccun
da renolutione descripea ee recta li-
nea secunda, eius quxe est in principio
reuolucionis (B C) ad secudum circulum.
hanc habec rationem, quam habenc 7.
ad T2. quae eadem est quam habene haec
duo, nempe quod comprehendicursub
radio secundi circuli ee radio primicir-
culi, e cerria pars quadrati excesus, quo
excedie radius secundi circuli, radium
primi circuli, ad quadrarum à radio se-
cundi circuli, hoc est quam habet recta-
sulum CAB cum una cerria quadrari
BC, ad quadracum AC.
Manifesti aurem Archimedis, quoniam verbolius CMt, Gual NLLIAH
beac delcribere, sen sum paucis reddo: elto spiralis ex quacunque reuolu-
tionc Orta DF: eam habec proporrionem ad Cuum circulum F, quamre-
ccangulum D AF, vua cum quadrati D P cerria parre ad quadratum AF.
AP PLTCATIO.
cta B, IL, L, M, ad palabolam polica ducan-
tUr ABHI, AHL, AL. M. PaceE igItuTeK
Expeiant demonstraris, lesmenta paraboli-
ca ABR, AHIHHD, aec. singulasreuolucio-
nesreterre, rectas vero BB, HHI, L. L, ec.
repraelentare lingulas ordine peripherias,
ac proinde a eriangulis ABB, AIIFI,
AL L, AMM Mnglos circulos extiberi:
rectas Vet HR, AL, aec. sIVC AB, AC, RC.
diameris in spirali AB, AC, AD L. relpon.
dere.
ad eriatgulum ALLII, v27. ad 12. hoc estvE
rectansulu B AHI cum vna cerria qua-
drari BFI, ad quadratum AII.
Seo parabola AFTM, cuiusransensin
squorlibet aequales partes in punctis
B, C, D, aec. dividatur; ductilq diamerris
BB, CHH, DL. L, F. MM, ex A perpun-
Dco primo SCOMCHCHM AHNB esse
Demonstratio.
(NEPATCE CX ClEMEHCIS) quadruplum elt crianguli B A b: led criangulum B E B
PCx
VnGREUE BFI, de producatur AFI, in F, L; e BB, in O. Friangulum TIB AC
 e at  t st t. p                   e  r