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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 270, page id 1032977698:0292
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270 Analysis Infinitorum.
CaP. VII.
SIS, CIErGet 3YY X X = 5 x  + bbcC = O, qua
est Xquatio quae ita maximum auc minimum de
tExIMAHS.
TI. Casus, cum aequatio duas continet in eodem
termino indeterminatas x ex Y, quarum altera
 ad extremum aliquod est determinanda.
Sit aequatio expolita, rt = x y + b b X X -
Cx yy O; erit currae hancce aequationem con
Aruentis requatio subtansentialis = 3 X x p+ +
2 bbX + = c97t = 2C X yy + X y; e polita
incinita, termini infinito vacui ex Schol. Cieneral.
N.. XTT. Bihilorum ad instatrciici porune, unde,
reliquis per t dirilis, oritur regnatio ad extremum
determinata - 3 X X y F 2 bb x = cγy = O; ex
qua, si ad expolitam applicetur, tum ipsius X.
cum iplius y ralor, uti nocum ett, indasari
Potect.
5. 4. Ouoniam jam in utroque hoc catu xqua-
tionem ad extremum aliquod determinatam,
non nisi termini subtansentem t continentes,
exteris eranelcentibus, insrediuntur: Patet in
expositâ qualibet aequatione, omista indetermi
nata y, quae extremum ex lispocheli designat,
Cinsulos terminos reliquam indeterminatam X
continentes per numerum porestatem ipsius X
in quolibet termino exponentem, multiplicandos
esse, de hoc Facto, ex iis terminis hoc modo
1UIL.