A treatise of algebra, in three parts. Containing

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let besa, a, . . . . b, b, . . . . , f; and

the productis these divisor rat sed to the power

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umty that is, it stante the true integer vinae Durat.

beinia prope fraction. a. Ι hoth cand n are irrationes; or, i thelester of the two member is rational, o mot denominate by an even number cante und. . When the greater Wiember is rationes, and the exponent ni an even number, it is ambiguous Rhether the reare member of the rootis rationa o surd. An though a root in the formis is no seund, et a mot in the

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wit the signis , changed. I this oes notsucceed, and a prime number standa unde theradica inn, o Arther tris Medie ma D. Bucis a composite number stand unde the

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SUPPLEMENT

be applied limul ut, etcause of the imaginar factor et is the moesis expressi-

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Treatis that ' eves cube or Ouae power hasas many oota real and imaginary, a there Meunita in the exponent of the power ι' particu .larly that unis iiset has the cube mota 1,

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remaining roocis et is P -3, a b ore. - may hereobserve that the operation oughtto be inridyd where it canae done, by divis inmine give binomia by the greate cubethat it containc an finding the oot of the

I in messicient of the imaginar member of the binomia has a contrar sign, themota illis the fame, illi the signs of the imaginary

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nar parti vanistin by the contrariet of their

noli a be mund by evolving the binomial a , - ρ by the Gemm in pag. 1 and summing the alternate ternis. is, in the fore

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ΤREATI SE

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power of thos equations and the operation is meret involutio, of Whicli,e have realed al- ready and whe any suci equatio is given, the simple quatio by hos multiplication iti produced is found by evolutio' o the extractionis croot. But hen the equations that are supposed ob multiplied by ach other are disserent, thenother quations than powers are generates; whichao resolve into the simpla equations whenoethenare generaled is a different operatIon rominvolution, and is halcis calle ob resolutiones equalisns.

Bucas evolution is persenne is observingandaracinibactast steps os involutioni o toe discover

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discove in rules sor the resolutio of eqiiations me must arescit obstrue thei rener Da. Suppos the unknowninti aluit tot Mand ita values in an limpie quation to ea, si c. then hos simple equations by bringin ali the term in ne side, mome

is propost tot resolves, the whole dissicuit .