A treatise of algebra, in three parts. Containing

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cte fies termis a series that, ill converge thes iter the laser ici speet os a.

Is the reler he madesto revolve aho ut the samesquare the contram a Domi oKard C, it

sin term os a series foris, ilia converges thes ne the greater that fis And thicis the ce

tions havinite s that involve poKers of Handa it fractioηal or fur indice, by aking distances sto A in the sines AC and AB proportional to these actions an furti,' and thene determining si situation os in te so the proposed quation in the parallelogram ABCD. It is tote observe also that when the sine

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scribe a polligan Zabed avinia ter of the miration in rata os ita ingles, an includi re alline odie term Wisti it then a series may beseund foris hy supposing any tW term equalthacare places in any tWo adjacent angies of the polygon , os. Is the ruterra be made to move parallelo itseli est the term which it,illisuch at onee wil be of the same dimension osa sor the willaea the fame proportion O Oneanother a the term in the linea themselves.

moves toward U; ut more dimensions hanthey, is it moves toWard A. The term in thestraight line ZE, serve to determine the first term os the converginiseries requires Thesemith the term it muches astematas serve ode ternaine the succeeding term os the converg-

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ini ei est the rest vanishing compares With

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t viseno is supposta infinites litue. In the

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' vili Est Die inlinitet greater than 'x , Menaris infinite. . 6 1og. When the firaetermio P os thes ries is seunda the precedin melliod thena , supposi nix 46 and substitutinithis hi--miat an iis poWers oris an iis poWers, there viil ari an equatio se determinimis the seconester of the series. This ne inu ' tion a be reate in the fame manne a theequation os, and by the Rule of oa, theterm that area be compare in orde to ob

is positive o negative an alway in arithmetica progressio , bat his value ingstbstitute sor it in the proposita quation the

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arithmetica progressionis hola differenc is sithe quare cube, o any o ero of AI'

tems,herein the dimensions of wili constitute an arithmetical progression havinitii esse me com inon differetice r so these dimensions illiest, an ' an Har, o Gri c. Theresere,

consist os these dimension os ob via in M

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multiple os, an consequently that His a mor of the differenc os dimension os o in the terim E 'x' and FI α' supposingi disto'. it sellavis heresere' stat, is a common divisor

of the differences of the dimensions os, in theterm of the equation, hen o have substituted in Aroe in ali me te s.' Andris, beqssume eques to the reatus common diviser

tum tirat involveriae sam dimensions of I to 1 anissi, by whicli means you Will obtain particu Iar quations the sis os,hicli illisive A,

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is , Amor ioz. cis Bun to e . se hastis o substitute a foris in the quation, Milthe term hecome sta' , and the differences of the indic es are , , , a Whose greatest common meas ureris I so that r

No sine Φ a x, et x 'a' et o it ilows that the sum os these series involvingo must vanissa. ut that cannot be is the coenficient of ver particula term does no vanissi. For ever term here sis infinitet litile, is infinitet greater uim alie folloWing termn se hae

et is

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is everrum does no vanisti Disseis, the -- dition or subtractio of the solio in termawhicli are infinitet les than it, or of the preis cedin term Whicli are infinitet greater, an .no destrosit, and there e the whola cannot vanissi. I appears there e that PAsia' uio, is an equation sor determining q, and

gives A erat a.

in , 99.

austicis requires to expresso by a series consistinios thelowercos, at is obrious that