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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 697, page id 1815201908:0754
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ed
SPTR A L 15.
COOSITIOCLAVI.
aca Eic parabola AMP, quam cangac AH dinila in ConC prO-
Porcionales AB, AC, AD, aec. ductisque diametris BI, C. K, D L.
E M, dec. iunsc AL, AR, AH AM, etc.
Dico leomenta omnia parabolica AP, AIR, AVL, ALL M,
AIHL. MH, esse concinue proporrionalia.
der
Demonstracio
19 5
Voniam sune in ratione estrinia linere
LA B, AC, AD, dec. oeiam cubi harum
linearum erunc in proportione concinna. AE.
qui per 18. huiussegmeta coca parabolica AI;
AKLA, ATI A, AMF A, Xc. candem inter
se proportionem habene qua cubi AB, A C,
AD, AB, ecc. Ergo eciam dictalegmenca
Cune in concinua. Ergoper r. I. nostriprosrel.
sionum eciam lunc illorum differentix, (eg
MCNEANCIIPE AI, ALR, ARL, ACOLM. deC.
concinue proporcionalia. Duod erac demon-
Arandum.
ADPETCAEDR SPIRALI.
Aea lic Spiralis AAVBIS cuins li-
nea, qua eAt in principio circula-
tionis, nempe AFI diuila licin conti-
nuc proportionales AB, AC; AD,
ac. ac cenero AinteruallIS B, C, D, F,
F, C descriptis circulis qui spiram se-
cencinT,KE, L, M, N, O, iungancur AI,
AR, AL, _c.
Dico lermenca omnia spiralia AI.
AIIL, AIKL, AIKLM, QC. cAccOn
rinue proporriogalia.Am
Demonstratio.
Terstao
 a
dem enim per 29. Acchum. de spirali, Cegmen.
ca spiralia COTA ABI, ARBA, ALBA,
AMB A, _C. ve cubi rectaTUI AL, AK, AL,
AM, SCC. hoc CArCctOTUM AB, AC, AD.
AF, _c. Sinegue hi in concinua, ob concinuam suorum lacerum rationem, etiaim
dicta Ceomenta spiralia erunc in concinua rarione; ac proinde eorum differentix se
BIEHCAneMPC AHIOa A, AONB A, ANMY R, ec c. cruncconcinue proporrio:
nalia. Ouod erac demonstrandum.
Symbolizac igicurrursum mirabilicer veraque figur2. Nam AK in Spirali ips AFF
in parabola sive AP: BLO, VerO CRR, DL. S, dec. peripheriis BI, C HE, DL, 8C.
respondenc. Vnde e legmenra seemenris respondeanenecesse eAt.
Late Cace iua inparabola, (erualis Cl
iamiildem vrrobiq; licreris: quandoqui-
PB