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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 155, page id 1815201908:0212
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 35 lines, status machine
# Lines: 35 recognised, mean confidence 0.83
# Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German.
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e
XC. C
ac
ct
GE OM E E R IC A.
PROGRESSIONVM GEOMETRTCARVM
A R S
A R T A
Doctrinam pracedenti parte in planis demonstratam, corpori-
bus, selidisque applicat.
eROPOSITIO CLZIII
Aca sic quadratorum continue proportionalium leries, balibus in
directum polcis, cuius longicudinis cerminus sic K; Tupet singulis
aucem quadratis cubi constrnantBE.
Dico consticui leriem cuborum continue proporeionalium, quae cum-
dem quoque habeant rerminum lonsicudinis l.
Demonstratio.
CC _EC. IM Concina alalO.
porcionales. Ouod crat primumr. ex quo pacee eciam secundum: Cum eriin qua
dracorum ec cuborum series, paricer Cemper procedant, idem reriulque cerminus sit
longirudinis necesse est. Oux eran demonstranda.
Aeio cubi AN ad cubum BP
cubi BN ad cubum CO, er
AB ad BC; (ponemeur enim quadeats
aesraciBIIS A B ad BC, IECM PALIO d Ss. Babes
est rationis bBC da CB, Id eIE FATIOMS VEV. sonb
sia) quare cumraciones verxque, cubi AM ae cubum B NF; d cubi B N ad cubum
CO, triplicacae Eincrarionis AB 2d BC, eadem erunE. Suncisitur cubi ANI, BN
CO in concinuaanalosias eodem modo erune de reliqui omnes coneinue pro-
P R O DOSITIO CL XVI.
Ildchrpoliris; primae AB, e Guacta L a GualeSHaHC 15, S l: Con-
Lcinuerurque rario R S ad S F, per plures semper terminos Y V, V X, _c.
Dico cubum primum AM, esc ad quemlibet cubum serici propolur
verbigracia ad quarrum D P, vrestlinca RS ad quarcam V X.
lbito