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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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AP. VII.
Analysis Infinton.
NTinm. S
Om omnis equatio unam pluresre indeterminatas
Continens per currx unius pluriumre locum sec-
merrice delipnari pOME, ita ut sinsulx OceurrenteS
indecerminaex vel tanquam applicaex diversarum linearum
ad cundem axem posiex contiderari portinc, vel eriam una
ex illis interceptam quandoque repraesentare; plurimxque
ReDETIAnEUT CUrVX (FIG. IXXXII.) ADEZ, quarum, ( 2d
rectam AZ reterantur, applicatx ex A in P perpecuo crel-
CunE, ex I in R per infinicesimum spacium distanres subA-
Htunc, ee aequales sunE, 2C ex K in Z, denuo, manenre eadem
CurVX RegnationO, ACELCCCNnE: Darer incer varios app(ICA
earum hicce in cueris valores exeremum unum dari, cym MI
mirum nec ereseunenec decreseume; d hoc quidem in calu
maximum, exreris omnibus hinc inde ab hoc exireme seu
maximo deticientibus.
Simile quid obserratur in aliis curris, aur etiam in hac
eadem, si non ad axem AZ. verum ad rectam YX ap-
plicetur, quo quidem calu applicarae ex Y in V decres-
CunE, in V e S per insinirelimam distanciam disjunctae
SIbI MUEUO RQUANEUF _E SuBSICUNE, 2C Cx S in X rursum
augeneur; unde applicararum punctis V _ S insistencium
valores omnium ad hanc curram perrinontium minimi
TUINE.
Exquibus consequicur, omnem equarionem indecermina
tas quorcunque concinentem, si unica ex illis ad valorem
extremum decerminari debeac, ad quendam exmodo dictis
currarum locis, X casum quo nec crelcunt nec decre-
cunc, adeoque sibi invicem equales sune duxe sele proxi-
meexcipientes applicara, referripolle. Ad curram scili-
cet sexlus anem suum concaram si maximum, convenam
Maximis
lit
det mimum expelacut.