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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 100, page id 1815201908:0157
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 41 lines, status machine
# Lines: 41 recognised, mean confidence 0.86
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R O GR F SSTON FS
Periem, (praecei duosprimos cerminos) in concinua elle analogid.
Dicolecundo ANI differentiam, ad primum terminum AB, CC 1
BC lecundus terminus, ad BIC coram seriem, praecer pitulum terminum.
Dicorerrio, differentiam AM, primum CC AB, C COCaITCKICI
AU, in concinua ce analo5ld.
Demonstratio
100
roniam AK magnicudo producta est ex racione AB ad BC in intinitur
Lcontinuata, eric per praecedentem AB ad BK, vE BC ad CK: ioieur permu-
candove BK ad C K. sic AB ad BC; hoc est e uldendo AM adM B, hoC
CA BC, ve BC ad CR. quod cracprimum.
RUELUM CUIM BEVE ANI ad BC, hOc CAEM B; SiC BC AII C H, CHIC COMPOHCM-
doinverrendo, ve AB ad MB, siC BK ad C R; ex converrendo inuercendo ve
AM dd AB, ica B C ad BR. quod erat secundum.
TECrUM CUM AIE VE ANL ad AB. SiC BC ad BR, CFIE permucando, VE AM ad
BC, hoc CHt MB, sic AB aa BH, aMuccando componenao, ex icerum inuer-
cendo ve AM ad AB, sic HD au H R. quod crac ccrrio locodemonstrandum.
ROPOSITIO LXXXIV
Aex Cincleries bea  MM Lesguadee appenaedet.
cudinum Concintue plopolcoan i cadene plopotctra.
Ceriei AR, ad ML N primum cerminum lerrei Mt l.
Demonstratio.
DEroctuasesimam secudam huius AR est ad BR, ve AB ad BC, hoc Ct, (CMIII
exhypochesi AB ad BC, MN ad NO, limiles SINE rariOMCS) DEMN adNO
Sedper eandem eriam est NIR ad NTR, VEMHT ad N O, ipitur AR eA 2d BR ve
MK ad NR. indeper convertionem rationis A R cA ad AB, VE M R ad MNI.
_ permucando series AR; est ad seriem MI R, re primus cerminus A B primx Ccrieis
adprimum cerminum MW Cccunda leriei; quod erat, eC.
P R O POSITIO LXZL
Dicoleriemtoram AI, e a ee   A P e
umquam exiis, quae hablenus Tmuersaliter demonscrammus propostione octo-
esta pma noca sit proportio totius seriei, ad primam maeni-
eudinem; placuit tamen exercitii causa, norisimis quibusdam proporrionibus applica-
re maxime cum de illis saepe mentio futura sit.
DRimum isicur daca lic, quocumque in genere quancicatis, proporria
Dico rocam leriem proporcionishuus, ne cemo Conuala, Cont
Cirueremagnicudinem, que dupla sir primae maxnicudinis.
eo
dupla, AB ad BC.
 ei s e   s .  p 1 1 e t.      1      . e      s  1  e   .  te   u   se    t e   e e u   i   sta