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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 104, page id 1815201908:0161
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i un mnuui
et
19. 9 uin-
1
P R O GR F. S SIONF S
Constructio es umontracio.
DTuide AR in B, ICA vE siE AK ad B R, BE G IdFT: eE VE R K ad BK, SC AB
F
Fac ad BC. Dico Factum eAC quodperebatur. Cum enim sC ve AK 2d BR, AC
AB ad B Ci ertareliquum BR 2 ad reliquum C R, BE AR al BR. underacionis
b73. huiu. A B de BCterminus est K: est aurem AB ad B C, ratio eaac cam lacione
AK ad B K, id est C ad FI. ConstaciBIEE PEOBOLTuM.
Corollarium.
X hac proxoletone manifestum est, omnem magnicuac, Oes rasionum se.
PRO POSITI
GEIESCOHEICFC.
ato
 C1It. BIE C C
t
 X
1.t.51B
Aris quorcumul Lacte  aet 2, C a , L ad F, datam ma-
Elucudinem , Opotiat aludete in corpasles, quordarae lune
rationes, nempe  L. fH, MN, NO, ica re parres illa eandem dabeane
racionem, quam primi dacarum rationum cermini, A, C, F; _ praereres
Cngula parres L. MI, MN, NO singulis daris rationibus, sinc termino
continuaris, lint aquales.
l
Conpructio e demonstratio.
STAEOHFK Ohtinibus A, C, F, Equalis; et ve divila est CK, sic divide F. O in
MI _ NV: denique per 90. huius I. M ica diuide in P d 9, vesic L. P, 2d PO, ScuC
A ad B: de rationis L. P ad P O, cerminus sic M. Similicer M N. NO diuide inpun-
atis R, S, T, V secundim rationes C ad D, E ad F, ica ve rarionum NI R ad R S, IF Y
ad FV, cermini sinE N ec O. Dico factum quod pecebatur. Demonstracio ex ipla
constructione est manifesta.
A 1.
PROPOSITIO XCII.
AoA BbcB C D NF B G HI
Acto Quoccum que tationibus AB ad BC, DE ad EF, C H ad
El, ac. magnicudinem invenire, quae omneshrarum rationum, se
les progrestionum adxequet.
Constructio e demonstratio.
adaequeric; aeque omnibusillis magticudinibus, una tiac X qualis. ha C. VEPaceF, ad.
aquabicomnes series dacarum racionum.
DEx octosesimam huius invenianeur maxnicudines, qux singularum rarionum series
eRO
 pii t itise u eit t  t eet u t si et e e e pi pute et s e  e et tu  ot es te eu te s e e e     e e  t     e  o