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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 140, page id 1815201908:0197
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PROGR F SSTONFS
ar2. quimi. F MC, a sic omni quadraca, ad omnia erian sula. AEqui vE AL ad L M sic eriam est
inso
140
sula, lic rectangulum AR ad recasum L. P. Reguirectangulum AR, aequale
rohuius C cocib quadeatorum serier, enen A aqualis seriei balium imparium AB,
CD, al. a AL LB) eCumienes suaatorum octenla lic xe qualis ese rectan-
cr4. quin. 8ato R Clans colaaloutorum leriescectangulo I P caqualis cric. Quareto-
1S. ha. Trapeziorum GB, HIC, LD, _c. aequabitur: Se d crapexiorum series, a consticuie
criangulum AC R. ereo rectangulum AP criangulo AC. K xquale cA. GuoderAE
demonstrandum.
rectangulum AR ad rectangulum P. P. Igicur ve omnia quadraca, ad omniatrian-
cum rectatigulum XP. risgue lectet quacatorum ac criangulorum, hoc est scrici
rouiunt.
X discursu demonstrationis collisitur, rectangulum M L. R P, proecesionierian.
Loulorum OLII, FITL, ec. ese aquale: rectansulum vero C L. R, duplum el
se cjuldem crians c ppresionis.
eROPOS1FIOAL.
Dicorectangulum sub A, c ites C A, AB, tamquam vna con
cchtum, Ecclatisulo AL aequale cAE.
Sco, veprius, quadratorum series HK, inscripra criangulo AG R;
SCEGue A O aequalis seriei balium imparium AB, CD, QC.
Demonstram.
luidatur enim LG bifariam ini MC: iBitur linCA COmPOSITA ex C A, AB, bis
concinec lincaSL. MI. L. A. quare compolita ex ( A, L B dupla est linCK AM. ergo
rectangulum sub AO sE CompOSTA ex C A, AB, duplum es crectanguli sub AO
ee AM. Acqui per rectangulum ub A O _e AM, aguatu Hrian gulo AC K: er.
eorectangulum sub A9 se GA, AB eanquam vna IIca, duplum est crianguli
ACK. Ouare cum ee rectanoutum C+ AR, ciuldem erTaHUM OAL R _C duplum,
aequabuntur incerle, rectangulum sub AO d COMPOUTa ex C A, AB, e rectan.
Perdacta.
ACuS AR criangali AFK.
Ec dinisum per lincas la-
ceri A F parallelas, in con
cinue proporrionales AK,
BR. C R. &c.
Dico craperia FB, GC.
D. dec. eneumilia.
Demon
sulum C AK. Ouoderar demonstrandum.
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