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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 127, page id 1815201908:0184
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en
eit
se.
uM
EEOMETRIC A.
ACMM B. R HC AA H ad _R, id est ve AB ad B C. Guoe ac PLIUMM SIIMILITOE celi-
qua quoque demonstrabimus.
Corollarium Tercilch.
e PolcS intero cercio; A F difterentia primi ec secunditermini, A B primus
Terminus, cora leries AR, lunc in continua anglogia.
Ec A Fi diftferencia, est ad AB primum cerminum, re BC secundus cerminus ad
cocamseriem dempeo primo cermino nempe ad seriem B R: _x A F differencia, BC
secundusterminus, cora series dempris duobus primis rerminis, (leries nempe CK,)
sunc in concinua analosia.
Demonstratio.
Le ML ditterencia primi de secundi cermini, in progressione M R. quoniam igitur
AB, MNT, BC, NO, aequancur, excessus quoque AF, M I, Equales erunt: de quis
iam AF ipA MI, _ AB ips MN, aqualis cA, ipAS AF, AB eadem magnicudo
cric cerria proporrionalis, qua ipsis M S, M N, vepacet ex elemencis: acqui ipsis aMIL, aBq huius.
MN. cercia proporcionalis M R: CA toca series racionis M N ad N Oergo ipsis criam
AF, AB cadem EOTA CerieS M R, cerria proporcionalis crir: acqui series AB, BC,
peccorollarium primum, candem producie magnicudinem MR, quam Ceries MI,
NO, ergo eriam productum seriei A B, BC, dec. snc tora series AK, criccerciL pro-
porcionalis ipsis AF, AB: luncicaque AF differencia, AB primus cerminus, cota
Ccries AK in continua analogia. Ouod crac primum. Similiter reliquas corollarii
Parces demonstrabimus.
Corollarium quartum.
YFdempolitis infero quarco, hic eriam valere rnivertalem illam ac criplicem constru-
ationem qua propolitione darae leriei maonicudinem equalem invenimus.
Fiac enim ve AF differencia primorum cerminorum ad AB, sic AB ad aliam ma:
enicudinem L. Dico, L. aequalem esse corisimilium maxnicudinum serici AK.
Lcbiotalte
nest Z aequalis erei sexiei, ergo alia magnicudo maior vel minor quam Z. ipR
aqualis exic; (aliqua enim magnicudo per Corollarium primum cori seriet AK X-
Qualis cH.) sicilla P. eroo per corollarium praecedens AF, A B, Y, Cunt concinux. acqui
cllam ex constructione AF, A B, Z. lunccontinuae, ervo AB est ad Z, VE A L clt ad
AB: _ AB est ad Y, VE AF cAt ad AB. candem isicut AB ad Z. ec Y cacionem
AabCE: xqualesigitur sunt Z de Y concrahypochelim: ponebacur enim Y maioraue
minor quam L. non erie ergo alia minor maiorie quam  aequalis Perici AR. crgO
Laqualis exie. Emilicet duno alias propolcionis odtunselinde telo oneo
demonstrabimus.
Corol.