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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 114, page id 1815201908:0171
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1815201908&page=171
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FSSIOIIL
re ad toram lette proscessionis C hoc est C P, ave AB ad C D. quia aurem ex hypo
dmns. CCH LLC, BC, BD lunc continux proportionales, etc AB ad CD, bvE AC ad RC;
estigitur AP ad C P, VE AC ad B C. terminus ct8  reriulque progretsionis,
dividir AC, inratione AC ad BC: quod erat demonstrandum.
RO POSIFIO CXI
ABB F. D, E. F, Xc. diuidet magnicudiem AC, inratione AC. ad BC.
Demonstratio.
IIdem politis; cerminus alcernxe sectionis, siuc progrectionis AC, BC.
ratione AC 2d CB; ergo ex alterna progressionis AC, BC, BD, ac. terminus
in endem racione diuidermasnicudinem AC. Quod erac demonstrandum.
)Priusque proscessionis AB, BF, _ CB, DF, terminisimul sumpei sunciidem
cum cerminis progressionis AC, B C, BD, F. D, _c alcernarim sumpris. ergo
nes AB, BC a CB DF. Sedharum cerminas perpracedencem, diuidic A C, in
ProBre(SIOdErna AC; BC, BD, dl. Cundem habet cerminum quem progressio
PROPOSITIO CX
RS, Sec, diuidere L. N, inrarione AB ad BC.
Acatic continue proporrionalium series, constiens magnicudinem
AR: Scaurem L. N, aequalis AR, harque prima AB, a qualis L. M:
secundae vero BC, aequas sat LO cerrix aurem C D, sic aequalis
DE, F C, HTI, _EC. (INECK PArTCN.
MIP, _E QUATEX DE, aequalis OR: aeque hoc alcernarim Cemper AaE,
itareomnes AB, C D, EF, CFI, eC. Cnc ex parre L; omnes vero BC,
Dicocerminum huius alcerne proscessionis, AB, NO, MP, OR, PO.
ebetseddboei
Voniam AB, BC, CD, DE, sune concinux proportionales, eriam AB, CD,
LE F, ec sun continua, ex quidem in rarione duplicaca AB ad B C; VE PaTCE eK
elementis. Similicer in eadem racione duplicata AB ad BC, CrUHE COnFINUX pro-
POrtIOnateS OmneS BC, DB, F C, _C acqui omnes AB, CD, _EC. TUINE CK parre
L, _ ones, BC, DF, dc exparce HI. Igitur in magnicudine L. NI per alcernamil.
lam prosxessionem, consticuuneur dux series appoliex similes, eiusdem nempe rario-
c84. huius. nis duplicatae AB ad BC. QUAEC SCrIESEOTA LM, CMP, dcc esthdseriem toram
AO; OR, _EC VE LMI ad NO, hoc es AB ad BC. Deinde quin per series AB,
dg9. huins. C D, F. F, _C _ leries BC, DB, _ c. Cimul sumpeX, aequantur seriei AB, BC.
CD, DB, dec series quoque L, & NV, Cimul sum pexe aequabuncur leriei AB, BC.
hypochel L Claee L H  F. ex BO cum
CD, DF, ec Ouare cum haec ex hypoches consticuar inagnicudinem AK, id est ex
dem
( e i   B .  1  A. . A.  B B .  . u u s  s p 1   . H B 1 B5  p B B HEIH HB B EB  s  pP B A     , u. u  1 1