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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
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EEOMET RIC F:
Scholion.
Ota: dum in propositione dicitur, S HxeC ablatio seniper HaE, dICO FCHIIHOL CK A R
quancicarem daca tmmorem: sensum proposirionis non esse, relinqui ex AK quamila-
rem dataminorem, post ablationem terminorum in infinitum concinuatam; sue post rotam
seriem absoluram, relinqui danc quantitatem daraminorem; sed auferenu etos ex AK.
in racione ante dictas aliquanad hot auferendos, Deresidua parsrorius a3 htor sit quanei-
EaEc datd. qudd  et altam quorundam dictum sit.
ece Laata
Ata hc maghicudo quacumque AK: Si fuerie
AB ad BK, VEBC ad C, H.
AB ad AR, VE BC ad BK.
vet ZAK, BK, C H concinue proporcionales.
AB ad BC, VE BK ad OR.
AB ad BC, vE AR ad BK.
Dicomagnicudinem A R xqualem esse rori progressioni magnicudi-
num continue proportionalion, racionis A B ad BC in infinitum con:
cinuataes suc quodidem est, rationis AB ad B C in infinitum conri-
nuacae terminum esse L.
Demonstraiio.
Vin AB hC ad BK s DE BC 2d C. R, POTCNIE FATIO = A B ad BC, IHCIA MIa:
PonirdICIM AR ICIDEL CBMMMHAri, IEa DE NUIQUAM PCTUENIAEUE 24 R, 275. MIS.
Id est AK maior erie quacunque Perie Aniea rerminorum; ergo AK, non est
minor Terie coca rationS AB Sd BC: Deinde quia AB est ad BK, ve BC ad
CK SIFactO AB ad BC CEMPCF COntInUEtN, exit vE AB ad b BR, huC VEB C ad B, S. huius.
CR, HC CD ad DK _E DP ad BK, acque ira deinceps in inhnicum: Ieaque si con-
rinuecur temper ratio AB ad B C, relinquerur crandem ex AR magnicudo quauls c, 8. huins:
Aica minOT: Cuare AK nequit ene maior; serie racionis A B ad B C: nam si maioe
eset deberecaliquo excessu esemaior. ponatur is TK; isitur A L seriei rationis AB
ad CD aequalis erie: ergo rario AB ad B C quancumuis concimtaranon tranalice
unquam I. ergo relinquerur ex A R magnicudo semper muior quam IR. ergonon
minot quavis daca, concra iam demonstrara. non cricisitut A R maior serie racionis
AB ad BC: Juare cum nequeminorem esse ancea sic octensum, sequalis AEnCcCI-
(e eAt. Duod erar demonstrandum.
Religuarum hypochelium demonstraciones ad primam reducuneur. nam A Fuerie
AB ad AR ve BC ad BR; cric diuidendo AB ad BK vE BC ad C R. CrgO per
primam demonstrationem, rationis AB ad BC seMPEF COMTIUAEX cermIHUS CA
In R.
DcindeA Tuetine AK; BR; CK continux, etir diuidendo A B ad BR, ve BC
ad C R. Rurlum igicur per primam demonstracionem pacec propolicum:
Denique sfuerie AB ad BC, ve BR ad CK, vel AR ad B R; eric permutando
vel ABadBR, vEBC ad CR, vel AB 2d AK rE BC ad CR. Vnde irerum per pri.
mam demonstracionem contcicur propDAum.
R O POSI
Aca Perie continue proporrionalium AB, BC;  ul. cuiul
cumque proporcionis, et quoculsesce in genere quancicacs, cal
niremagnicudinem, qua omnibus cerminis corius serieidux in intini-
cum contunuala, il desctatts.
Con.