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# Title: [Vera Circuli Et Hyperbolae Quadratura] Vera Circvli Et Hyperbolæ Quadratura (shelfmark Leibn. Marg. 98)
# Folio 22, page id 834940469:0030
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PACOT. LL. PROBLEMA
Oportet praedictae seriei terminationem invenire
donatur C crphra seunihilhoc est exponens rarionis ex
qualicatis, seu rationis A ad A; lique HIad libitum.
exponensrarionis B ad A: SIEVEMad N iea differencia inter
Cd FI, hoc est ipsaFT vel exponens rationis B ad A ad excel
sum quo Tsaxerac C hoc est ipsam I sed veM ad Nica ratio
Bad A eA mulciplicaca rarionis C ad A5 X isicur ExCeNUS
quo Pluperac C hoc estipsa Lest exponensrarionis C ad A.
sc veM ad O ica differeneia inter ( _ HThoceAHIad excel-
sum quo superat C hoc es iplam K, led veM adO ica rario
B ad A est mulciplicata rarionis D ad A, CUMqUEHI GCCZPO-
nensrationis Bad A, erit R exponensrarionis D ad A: ligia
tur IEic exponensracionis C ad A _ R exponens rarionis D
3d A; eric excelsus quo  luperat L exponens rarionis D ad
C. deinde sic vemt ad Nita exceNus quo K luverar Lleu expo-
nensrationis D ad C ad excessum quo R superacI, Led ve M
2d Nica ex seriei compositionerario D ad C est mestriplica-
ca rationis F ad C, atque excessus quo E luperac I eMt expo-
nensrationis D ad C; e proinde excessus quo R superat I eR
exponensracionis F ad C, atque lest exponens rarionis C
ad A. e proinde R est exponensrarionis P. ad A. deinde sIE
veM ad O ita excessus quo R superar Iad excessum quo Ssu-
perat L. sed veM adO ita ex seriei copoltione rario D ad C
est mulciplicararationis Fad C, cumque excessus quo R lu-
perac IEc exponensrationis D ad C; erit excesus quo S lu-
Perat Lexponensracionis F ad C, aque Pest exponensracio-
nis C ad A, & proindeS est exponensrationis Fad A: cum
igicur R sic exponens F ad A ec S exponensrarionis Fad A;
eric excessus ouoS superacR exponensracionis F ad F: X V-
eramque leriem concinuando, demonstrarur ve ance T esse
exponentem rarionis L ad A, et V esse exponencem rarionis
Yad A. denique lemper demonstrabieur terminos conuer-
gentes