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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. VII
Analysis Infinitorum.
Hoc aurem similirer CrenEuruM PATeE, quorcunque
modonumero Ainicx) actumexe fuerunt intinire lima.
Corol. I. Manifestum hinc est, quortibet criangula ex
intinicesimis constancia; DHF., EOC, CLI, dC,
odo numerO SInE Ainita) qua se invicem non interrupEa
luccessione sequuneur, incer se de triangulo astignabili POI
este similia; estenim t: y: : c: a: : D: N: : x: E. _ HCIn CXTC-
ris. Demonstracio ex 5. praeced. Num. I. IV. X I2. leri
nesocio coltioitur.
Corol. II. Onde sequieur, potica in criangulis hisce (-
milibus una lacerum homologorum xequalium lerie, de re-
liqua lacera, homoloeahomolosis, equaliafore,
Idemhoc ex calculo demonstratur, sinc enim omnia d X
ICu DH, F. I, CL constancer aequalia, erit ideo.
e O= X; adeOquejuxTa No. I. IV. LX. ye= ita = 1tN =  1E:
quarecandem a = po = E, seu omnia dy, vel HF, 4C, L. 13
perpecuo xqualia
Corol. TTI. Ouod s omnia dy aut omnia de perpetuo
allumancur ejusdem magnicudinis, eodem modo collise
tur, hic omnia du e dx, illic omnia de ee d x constan
rer Fore aequalia. Calculum hoc crincentem, cum supe
riori plane similissiC, omitto.
Corol. IV. Fx quibus randem consequi videtur, cum pon
sica una lacerum seu omnium dx semper aequalium serie,
omnia quoque d y sibi semper aequeneur, ac omnia do
(juxta Corol. TP.) nullam incer ipla dy auc de, sinume-
r0 sine tinica, incercessuram differenciam, cum xequalium
nulla sic disserentia; unde hoclalrem principio, quo om-
na, ni Fallor, reliqua calculi infinicesimalis penera deduer
Pollune, differentiationum secundarum tertiarum  C. ulera primano
continuationes demonstrari Requeunt.
Ne aurem hoc demonstrationis genere in re tanci me-
mentiquispiam ofendacur, cum per modum inductionis
incencum evincere studear, aliam adjunso; quem intinem
sequencia praemicto lemmarica:
Lemm. I. Si quortiber, modonumero Ruitxe, infinite
limae ad se muruo addantur, earum cumma erir quancitas
infiniresima: erincicur ex lemm. 8. Vel etiam hocmodo: