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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.
Coroll. Patet hinc T. quemlibet expositae
aequationis terminum, Verb. OF. yy X, PeI
erphtam pore multiplicari, adcoque ex aequa-
tione ad extremum determinara tolli, sit enim
3
r= O Crit r = - 3. tum II, quemlibee
ex residuis. Verb. GF. bX, posse quolibet
numero tum attirmatiro tum negaciro, ut 5,
multiplicari, Caeteris ex eo determinationem
accipientious; sicenim = q. -- , d = 5, Crit (POSi-
t0 loco r invento valore = 3) ipla 5= - 7d,
adcoque d= 7: quae quideni, ni FalIOE, Ca
TunE, quae methodus suddeniana requirit.
5. 6: TTT. CacuS, Cum aquario plures, imo
quotlibet, continet indeterminatas, quarum
unica Y ad extremum determinanda est.
Sic aequatio, yy f - by Z F ccb = O; OpOrtet
iplius y ralorem extremum detinire. Ouamo-
brCI Cx S, 2. ac retentis 5. 3. Symbolis, juxta
Cap. L. 5. 35. reperiatur (consideratis scilicet
indeterminaris, tanquam currarum ad cundem
axem descripearum applicatis) ipsius xquatio
lubransencialis: 2yyfnt + y yf+1 - by Ztn
=by2 ln = O; _ pOLITa F InSIITa, AC CATETIS CX
Schol. GeneraL N. XYT. Crane(centibuS, CILICE-
set aequatio qua(Ita: y yf+l - by 2 t n = O, (Ci
(t - bZ n = 0.
Schol: F.t Haec quidem, cum nullae amplius SuPersUNE
~JH.t