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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 55, page id 1815201908:0112
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D-
X
M
p.
D.
2.
Ecrupulose obseruari volo, quam à Geometris omnibus SCrIIAEUE NOMenCLLTA PTO-
Portionis, vel rationis; quarum licec alcera in duobus cerminis conlistar, alcera in plu-
ribus, nihilominus, pro arbicracu lcribencis, passim confunduneM SMMIL IBITUF hXCPEX-
mista, linon exactarum detinicionum loco, Calcem rberioris explicationis lupplemen-
c0. Dacis icagne A _ B: vel
alto A 2d B est maioris inX-
Qualicacis, vel prorlus aequalica.
cts, vel minoris inxqualitats:
Tuoeh Aanc cocinux proportio.
lates ABCD. huiusmodicon.
CMuaTIO proetelSIO VOCCEUT.
A
A
2
quoccunque candem cermini exstane.
Progressio vero Greomerrica iam explicara duplex eltta continua, alia discreca
Concinua eR cum omnes cermini rarionem connectentes, HaDCML TAtONEM AnECCC-
dencis, e consequentis; ve in Ccemarerarionum explicacarun, it lietC Gucaao-
dum A ad B; ita B ad C: ex quemadmodum B ad C, Ica C ad D, acque ica in
quovis candemnumero cerminorums huiulmodi progrelsioneM concinuam voco.
Discreca prooressio est similium rationum secundum aligum continuationem po-
sicio, ve consequences non hancancccedences. exempli calla; It hdl scemadmodum
A est ad B, ica C ad D. S
BFucric minor quam A, vel
C, calem proorelsionem in
quorlibeccandem cerminis consticura sic, voco discrecam; etiam in his terminis L. 2.
5, 10. 336, 8,16. Vbi discreca rario ralde incerrupea est, quia eAt concinuario lmiliumm
rationum.
F. F Y N
Frminus prosrettionis esleriet MMIS, det Guenula progressio per-
cinset, licet in intiumun Commuciut; led quoms inceruallo daro
Plopius ad cum accedere porerit.
Fxplicatio.
Donacur recta AB, diuita in CD E F C. ve continuent candem rationem A B,
CB, DB, EB, FB, CB. Cum siccadem racio AC aCD, d CD ad DF
acque ica deinceps, cum ea, quae reperitur incer lincas AB, CB, DB, ac. Similis
quoque eric ciuldem rationispreoressio AC 2d CD; cum propressione AB, 2d
CB. Terminus autem racionis AC 2d CD, dicicur punctum B, (ive illum incrin-
secum velis, huc extrinsecum, perme licet; nam de re nobis est hic quaeltio, non de
verbo: ad quod punctum nulla progressio percinzere valee; cum omnis progressio
incerminata pars seriei existar: nihilominus camen, porerit ad illum prooressio per
concinuationem magis ac magis accedere, ica ve vicinior vlcimus cerminus progrel-
Gonis incerminaex existac ipsicermino serici, quam sr distantia qua cunque propo.
AIca
bro secundo huius cractaeus discepeabitur, illud incerim insinnacu hoc loco delidero;
huiulmodicerminum Colum repeririin ijs profressionibus, que proporrionem maioris
inaegualicacis continuane, nam carum prooressionum quae vel cerminis semper aequa-
libusconctane, vel cerre cerminis minoris inxqualicacis, nullum alsignari poste cer-
minum, manitestumnimisest, quam ve explicacione indiocac; quandoquidem dictae
Prooressiones; i conrinuentur, magnitudinem quavis daca maiorem exhibere natae
Sinc. leaque le cundo libro, cerrio, et quarro, in quibus prosretsiones iam rerminatx
An aurem talis decur terminus progressionis, ee quo pacto investigati debeac, li-
COnC -