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# Title: [Bernhardi Nieuwentiit Analysis Infinitorum, Seu Curvilineorum Proprietates Ex Polygonorum Natura Deductae] Bernhardi Nieuwentiit Analysis Infinitorum, Seu Curvilineorum Proprietates Ex Polygonorum Natura Deductæ (shelfmark Leibn. Marg. 149)
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CAP. II. analysis Infinitorum.
4. 9
=2= 2 + 5- 1 + ZXc, 2deOque FaCO Z  Y, df
X, Crit.
=c - +
in 2
m 3
4
+ X = Y = X Y + XXY = X Y _C. in
infinitum. Elinc, quancitatibus, quarum ex-
Ponentes negatiri lunt, ad dirilores reductis,
lingulisq: terminis per er multiplicatis cmerset.
N X
X
r + X = y = p ∞ + Y rr Y _C.
Adeoque omnia re =Serieiterminorum, quo
rum Cinguli in e ducti TunF; 20 Per S I2 Omnia ye
=Y X = X X X = x  sic continuande seriem
in infinitum.
31
ere
5. 23. Tum ec eodem fonce scaturit infinica
e
series, in Figura XX ~II, quamlibet guadrantis
Circuli AO F portionem decerminans. Sic enim
radius AO: r, O8: X, QD: y, unde py
rr - X X, _ y = YYY = ∞ X = r r = 3 X, (CU Ca-
dem rr = x x ad dignitatem = crecta, hinc de-
scribendo ex eodem 5. 21. Porestatem binomii
pr = X X juxta exponentem Z, hoc CA EactOP = 
2 = rY, _C f= X X; CrunE, manentibuS gCNITUTIS,
quilibet exponentes, qui ipsi Z ec f adherent,
per 2 mulciplicandi, (cum Z _ fPerquantitates,
quae numerum binarium pro exponenti habent,
dC(18.