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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 68, page id 1815201908:0125
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prr
PROGRESSIONES
Demonstratio.
Tumpeos, SC CL ExCessibus M ec N simul Cumpeis, hoc est excessu P: Similicer
oltendemus II luperare I excestu P. Cuncixirur Cr. FP, L in Axichmeticd alalous
Duoderac demonstrandum.
loset. nt. adt 
P R OPOSITTO XX.
ISto AB. ad BC, ve BD ad DF; _ Rac ip SI BC aequaliS F. F, vbi
Dico esse ve AB alt AC, SC AD ad AF, et BD ad BF.
Erminorum seriei A, B, C, MUEVUS CxCENUSSIEMI; N, vero excesus alCeriuS; M au
tem ex N sibi addici, Facianc P: quoniam igitur A superac B excesu NI, _ D Su-
DCrAE F excestu N, A e D simul sumpri, hoc est C. Cuperabune B _ F. simu
scumquetandem cadar punctum F.
Demonstratio
aC uti
216. Fnino
Voniam eAt vE AB ad H C, ita D D ad D F, erit componendo, convercendo vE AB
at AC, ica BD ad BF: vIcerius, cum (InC FF, BC aequaleS, CrIE FOT2 AL
aequalis quaruor proportionalibus AB, B C, BD, D F: e AD aequalis pritIX e
TeKEIX, vei _ A C prime aC secundX: QUATCVE a AC ad AB, ITa AF ad AD:
e inverrendo ve AB ad AC, ita AD ad AF, ex reance otendimus, ica BD ad
DF: quod erat demonstrandum.
PROPOSIITOZXI.
Aex linc quacuor propectonales, minima AB, ICCHHOA AC, CetIIA
AD, QUATTA AF.
 piluo difterenciam primae de cercia, mhorem ele L C al-
terentia lecundae e quarix:
adllla