A treatise of algebra, in three parts. Containing

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CHA P. VII.

1 htrast the exponent an mali the differencelli exponent of the quotient. '

bis an bene Δ, expresse esse is

Wit a negative exponent. It

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the niui poWer o a' is a η . The quare of a b His Hyr, the cube is a eL the mihi ex 6 i. heressinio quantities to any oWeris called Involution an an Imple qua mili is involvet, multiplFing the exponent γ that os bero e required, as in the preceding Examples.

e re in mis asso se assed testa fame pomer is continua multiplication os iiset is

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a, , S, c. are negative. Suet. The involutionis compound quantities

is a more dissiculi operation. The powers of an binomia a 4 emund is continuat mutitiplicationis it by iueis a solio s.

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has the exponent of the poWer required that in the following terms, the exponent of a decreases gradually by the sam difference vis. unit and that in the las term it is neve muta. Thelowers of re in the contrar order it is not ound in the rst terna, ut iis exponent in the seconester is unit, in the hird term iis exponent is et and thus ita exponent increases, tilli the last term it Ecomes equat to the exponent of theio e required.' A the exponent of a thus decreast, and atine sim time thos o b increase, the sumo thei exponent is alviay the lame, and sequat to the exponent of the o e required. '

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the exponent os a decretae in iis ordo, 6, , , , I, O and thole o b increvi in the contrar omer, , , , , , , . And the stim of their ea lonent in an term is alWay 6. 6 s. o find the coessicient os an term, ille coefficient of the precedin term eing -n; ou are to divide the messicient os the precessire term by the exponent of b in thegive term an to multiply the quotient isthe exponent of a in the iam term increased by unit.' Thus to in the coemients of the

and Du kn the messicient of the fies term is unit theresere, accordinito the rute, the coenscient of the ad term millie o, 6;

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The coefiicients of ui respective terms Rc- cordinito the last rese, wili be

o. quantit consistinio three, ormore term is tome involves,'m ma disitingitisti it into two pares, consideranti as ahinomial, and rais it to any owe by the pre

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CHA P. VIII.

is given the oot must e found by dividingili exponent of the ivm po ex by the number that denominates the hin os mo thatis required.

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an impossibi or imaginar quantity '

, so. I the number that denominates theroo require is a diviser os the exponent of the give power, then mali the oot be oni alome power of the fame quantit .' A the cuberoo os et 'is et the number a that denominates the cube motieinia divisor of iet. But f the number that denominates halsor of roo is require is no a divisor os theexponent of the ive poWer theno, roureiulata Rasi bave a fracton forciis exponent'