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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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SPIR AL15.
PROPOSTTIO Z1
Archimedis 20. applicatur parabola.
spiralem in primareuolurione factam recta
Dlinca ceriserit non in termino spirx (B) à con-
cactu vero (C) ad principium volurxe, recta iunsa-
cur (AC,) cum cenero quidem principio voluras
incervallo vero illa iuncta (interuallonem pé AC)
circulus describaturs a principio praecerea spiralis
agatur aliqua ad rectos angulos ei, que a contactu
ad principium helicis iungicur (nempe AF, )cadet
In TANOENEOM (C F,) e eric tecta (C F) inTeTCON-
curlum de principium helicis, aequalis arcui de-
Ccripei circuli, qui intercedirinter concactum de
sectione, qua lecar deloripcus circulus principium
cctacto, Cacto in ancccedentibus arcu d
panelo, surelt in principio circumuolurionis
APPLLCAFFO.
Ata Sic spiralis ACB, et parabol2
AC B cuius axis (IC AHI, tangens
AB, diameter BB lubCensa AB. FIAE vE
inspirali AD ad DB, ica in parabola AD
ad DB, ee ducatur DC D parallela BB.
Duoniam igicur (vr octendi in 13. huius)
ADBcam Cuperior quam infcriorrepre.
sencac, primam rectam in spirali ADB,
quemadmodum recta BB refere periphe.
iam BB, ita recta D C. D reterr periphe
riam DC ID. Ex quo iam le quieur arcum
DTC exhiberi a recta DIC.
Dico igicur si recta quaepiam tangat
parabolam in C, ab lcindi ex axc producto
AFaequalem ipsI, DIC, qua repraesen-
cabac arcum DIC, plane ve in spiralitan.
sens C Fauterebat AF aequalem cidem
arcui DIC.
Demonstrario.
Veatur CC parallela ad AB, per3S. L. Conic. F A xqualis eA AG, hoC eAt DC.
Chocestarcui (DIC.)
rurlum isicur habecur similieudo. Quod erar demonstrandum.
Marifectum Archimects y. G 1) lubiungitur, eadem prortusratio
 applcanau eC.
 i     s e   u e   te t  Ae     p t   e  1 .      t t  eta   et  ti  s                   1