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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)
# Folio 91, page id 1032977698:0113
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CAP. I.
Analysis Infinitorum.
OA = t, AN =1 C, NA = 0, vOCetUTeriam YO
subtansens hujus =_, Critk: t: : c: 0, _ t e = k0.
Onde AI SIEO = C + I, aC CUEVa AD F VerSuS
aXCM COnCAVA, CrIE +C = kC + KI X te- he
li, quare keminociplat.
Ouod A 0 = e = 1, CA + C == k e - ki, e kL
kC = +C, adeoque kMaiOF ip LaF.
Fc Cequens oritur currarum Aexura diagnocti.
cum incatu, quo curra subtansentialis AA a
ad currae interceptam A.  pplicata eA
Si Fuerit Subtangens le minor ipla currae expon
Cex TubtansentiF, exit cuera AD F VersuS aXCHA
CUUm COnCAVA.
Si vero k Fuerir maiox ip(aF, erit curva ADF
vertus axem Cuum Convexa. IYB. Potuisce e
hoc ex 5. 80_ 8Y elici, cum ibi demonstretur
essck: F: : B: y.
Coroll. L. Paret ex duabus praecedentibus, I
sUBtanSCNSF CUEVA ADF, cujus AexuS quaerieuI,
explicetur per intercepram A.  Teu x. commo-
dissime adhiberi peaecedentem; A vero per appli.
Catam y delionetur subtansens +, inquisitioni
curraturx porius inserrirc 5. 90.
Coroll. II. Ouo vero methodihujus ulus per
exempla PateAE, AIECUIEVA, CUjuS IntCTCCPIA X
applicata y. Subtangens s ejulque aequatio
2YX = X X = yy ad CircuLUIM. OUXTIEUE ejuS
CUEVaCUTA Versus interCeptam AQ
ea 12