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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 1037, page id 1815201908:1094
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1037
NGYY A P AR ABOLIC
Constructio es demonstratio.
Ecur isicur sphaera ABC. D Creda
secundum racionens quam habec F. a1
F, ducta sectio per aLCM AC extribeat
circulum ABC. peocllarur eius diame.
qua LK par relique C0. sed C O CH par lemiciamerro. ergo _ LR (CMITAmeETO
par elt, aeleoque dimidisel. SpHus A L. Pari modo oltendam HIR elle dimidiam
ipuS C M. Pracerca quom AC, C C ipsS FTC, TC codem discursu aequales
lunc, rectangula AGO, C GN, lunc rectangula FIC:K, ICR, ac proinde pria-
mides, quarum bales sunc rectangula AC O, CG NY, alcirudines aurem AC, CC
aequancur pyramidibus quarum bales rectangula IICFR, ICR, alcicudines vero
TIC, TC. Quare cum priores preamides sncinter lC VE F, F, crunt e posteriores
re F ad F. iam vero polteriores pyramides, quarum nempe bales lune rectangula
FTGK, TG R, alticudines FTG, TG, aequancur: Colidis quorum bases TunE PegMOnEA L LO2. H1s-
ParabolX ATG, FS T C alcicudo vero communis S P: ergo solida illa parabolica
lunc ve preamides supradicta, sed ve illa solida parabolica, ita lunc segmenta B vn- b8. huius.
sularia quorum bales porriones semicirculi AB G, OBSC: VE aurem rngularia
illa Termenta c ica lunc portiones (phxricae B AD, BCD. ergo porriones sphaeri. c77 huins.
ex lunc incer se ve supradicte prramides. Requihas oltendi lupra, dacam incer le ser-
vare racionem I ad F. Eroo eriam sphaericae portiones lune incer le ve E ad F. Poieur
sphaeram divilimus secundum dacam rationem P. ad F. Oucd fueracrequisieum.
Corollarium.
CCEVERIMGHEVE A N e CO. sinc aequales
TemidtaCEEO. AEquC ita diidatuE AC
in C, reperamis balim habens rectanou-
lum ACC, alcicudinem AC, Sic ad prra
midem cuiusbalis rectangulum CGN, al-
cicudo C C I Faliolecata P, 2d F, Bac
racione inuemoMdsC A C puncto C, Rac
per C sectio tecta ad aXem A C. DicOPaE-
cem sphaera ABD a reliduum BCD
eam habererationem suam habec P linca
2d L. Guod ex iis qua demonstraca lune
Proximis propoliciondus manifeste porest c
Contare. Crectis enint AL, C MI Perpendi-
cularibus ad axem AC, quae SnE ipS axi
aquales, IIBganEUF L.C, ALMI e normali-
FeF ad dIAM CEPUM PONANEUE GK, G R X
quales recs CO, C. N connectancurirem
AI. C R. denique inletibatur circulo maxi-
moparabora ASC anchtabens semidia-
MCEEO PS PAFCHI. VNOMAM AL, A C TIINC
Pares, Cciat 4, 6. lC Pdl CA GC. Ouare
cum toc erR pac lic toc GO, eric e reli-
recta NO, in G requadracum AC mulciplicarum per CO ad quadratum CC.
mulciplicarum per GN proterat rationem datam F ad F, dinila eric (phaera secun-
dum rationem datam. Archimedes quidem paulo alicer suam preparacionem con-
Rruic, quam non minis imperfectam reliquic, acque ea cAt quam nos exhibuimus, L. c.
etoriproimle non insraca tore exiltimo, quae hic deduximus.
DOlicaisicur recta XV O dinila in quacuor partes xequales in A, P et C, A divicatur
ot se  ut ues ete M pte e  s et t s ete  et  te A te  e e e set   t tete se   e  e tet u  u et     e e ut st te t  e t  te  e s s pe    se     u