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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 130, page id 1815201908:0187
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pum um mmm quue an1
11
DR OGR ESSIONES.
Demonstratio.
DEroctuas cHMaMIC.
cundam huIuS; co-
la planorum leties Ml
M ad seriem NK, ve
Placum AM ad placiu
aabesut ve plana
Enc similia; duplicatam
hiabenc racione balium
AB, BC; crgo series
MdalcemKdu-
plicaram Habet ratio.
eibi eadacte. lla
autem per corollarium
Propolc. Praecedentis.
progressionis bahum
AB, BC, aC. terminuS
es R, CrUnEIgIEUE AK
BR aC. K ereS corinuR
proporcoales. unde
l
Eit SE tCC 20NCI S 1IS..
 Et L. 11
CaciotLade L clpu
eata est rationiS AR
ad B R, idestrarionis A B ad B C: erxo series MK cM ad Ceriem NR, vi AR ad CK:
croz. A. Quare per convertionem rationis series M R, est 2d planum AM. VE A R ad C R: de.
inde quia series AB, B C, CD, DF, _C. id est linca A K, est ad seriem AB, CD, _C.
ve C A ad B A, eric alcernando AK ad C A, ve scries AB, C D, _C. ad A B: scd
serieS planOTUM MK, est ad plaNuM AMI, VE AK ad C A, cr9O FCrICS MK est ad
planum AM, releries AB, CD, aec. ad AB. Duoderat demonstraridum.
Manifestum.
Xdemonstrationis dilcurtu patertoram planorum seriem esse ad primum planum,
ivc K A ad C A. Quod quia poste a vsus veniee, lixillarim nocare placuic.
PROPOSITIO CXXVII.
IIdem poliris (IC AL differentia primX AB, X cerri C. D.
Dico cotam limilium planorum Ceriem esse ad primum planum ANI
ve A B prima balis, ad A Lprima de cerria differenciam.
Demonstratio.
13 huim. Fulaclincis A L, AB certia S P concinue proporcionalis. Ixicur S F saequalis eAtro
ei scricibasium imparium AB, CD, F F, e c. ergo per praecedentem tora series
planOruM M K est ad planum AM ve S F ad AB: Acqui ex constructione AB est
2d AI vc S F ad AB; erZo coca series cA 2d planum AM, ve AB ad AI. Quod
erac demonstrandum.
er0103t11O
212
2. hnima
HS.
Octum politis, terminum habens longicudinis, punctum RL: AaF aurem
per octuagelim ahuiusS P, aequalis seriei balium imparium AB, C O, _c.
Dico rectangulum super ST in alcicudinc AB aquari cori serici qua
dratorum M L.
Ademmanente Rgura, data sic quadrarorum series balibus in dire-
Demon-
 o ute ue e   e  iu  e se   p e  e i ue   u    p    e        .  e t  t      pnndi