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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 672, page id 1815201908:0729
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PTR A L IS
eROPOSITIO. V
Pappi propos. 19. collectionum Mathem. l. 4. applicatur parabola.
Anc praemiero Archi.
medais, quod primam
Spiralis proprictarem, ex ipla
eius detinicione immediare
prottuencem contincat. Pap.
pisensushic est:
Si ex spira principio A. ad
Peripheriam circuli ducaneur
reCEX AB C spiralem (ecan-
CAS D C ad ATCUM CNID.
VIE parabola ABF, cuius FaNGeNS SIE
a AD, (MbEenCa AF, ex F vero ducta
diamerer E D occurrens tangenti in D.
Ducancur aurem quorcunque rectae ABC
secanres parabolam in B, e diamerrum in
C. Ieaque punctum A, in parabola, prin-
cipium (pirx A, dIAMCTEE VeTO D E Peri
metrum circulirepraesentat.
Dico AB esse ad BC, VEDC ad CF.
Demonstratio.
DEx B ducacur diametex GBF, hoc eAt paral.
leta ad D B. Per 5. Archim. de quadr. parab. ve
OB es ad BF, AIC AF ad F F, hoc cA AB ad
BC: sed ve C B ad BF, siC DC ad CF. ErgO
AB elt ad BC, VE DC ad CF. Conneniune isicur in hac prima proprietace
helix de parabola. Ouod crar demonstrandum.
Fuius propolitionis demonstrario fere in prxecedenti demonstratione involui-
cur. Placuic eamen cam scorlm applicare, quod Pappi (c, de primam spiralispro.
prieratem concincat.
PROPOSTTIO VI.
Archimedis 12. parabola applicatur.
Bhac Archimedem delibare incipio, quod prima lic earum, quibus
lLspiralium propriecares demonstraneur.
Archimedes Sichaber: Si in spiralem una quidem circumnolurione de-
Scriptam à principio spiralis (A) rectae guortibet (AB C) cadanE que X qua-
lesincer se angulos (D AC, C AC, C AC) concincant; se le mutuo x qua,
licer hoc est excestux quali) excedenr.
S in B
AB est ad BC, vra
APPLICATIO P AR ABOL A.
e ttot12t13e 15 16 2710
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