A treatise of algebra, in three parts. Containing

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thus B exterminates velf out of the quationibesides the contradiction arisinistom Amo, , hen A perhaps has Men determineffalready to be equat o seme real quantity. In orde to know ho t evite his ah surdity, letis suppos that therarit order of term in the pro sed quation are, as besere, M lm xi, and is is found wie the fissi term o aseries se then ille dimensions of Lin themist

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in Dio8, risust be the disserence of - 1in and - ns, o seme divisor of that disserence. In generat, risust be atamessuch a diviser os that

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greates common measere os these disserences. For example, is the indices ns, nh, happen tote in arithmetical progression, thenis ought to e assume equa to the com-

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mo values of x, determine sto the firmoideros rems, are equat, and thenis Go p ill bea divisor of that aggregate of the firmorder of

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mili destro each ther an vanish; so that rhesraeterm with hic the term of the seconfinia der eis ni cante compares must be that whicli

equa valuis Oscili first ter of the series.'

Ifiliis value os, is a common inrasere os alline differoces of the indices, then sit a justualue os, bucis it is non suci, a value frmuh assumta a mar measti e this and aliphe dirarences cibat in such a value a may

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Itis disserene os in indices m --s, in M, JA M, c. provide ilia difference besa mea- sine of the ther differences although therema besas an values of therar ter of the series eques a there are unita in p. or is that Mes no happen, risu be tam a se eriti equarto the rotest common meas Sosine dis