A treatise of algebra, in three parts. Containing

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sitive, it is negative in the value of b, and thereis only the difference of this sign in thei valueo. So that we a conclude 678. The values of . mav e discove edwithout exterminating the second term. An cubic equatio ma be reduce to thissem,

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intra I. Aia in generat, the cube

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Ex AMPLE L

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Wheres is the oessicient os, in both mo fons biit affected uit contrar signi; ecaustr

when the keond term is anting in an equation, the sum os the affirmative roon uitie equarto the sum of the negative. Compare no the pro sed equation,ith theahove producto, and the respective terin putequa to eae other Williives m

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. 6 3. O isyo want ossin the mois of the bimadratie Wit ut talaiaway the secondstrin, supposeis to Morinis se , and the values os illi , ras eques to the moesos the cubici The demonstration is deduces rom the last

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H A P. IX.

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tru roo when it is a commensurable quanti . tuti proceedi nil aster his manner, hen Ouhave two limits the ne greater tha theo si

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. and aking the Emit greater in the fame μο portion his transformatio is eas ι sor ovare onlyrio multiply the second terminio, oo, oroo , he thir term by their quares, thes riti by their cubes. Ee The equation os thela example is thus transi med into, inoox

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Me 3 7 and by bbstitutinio si x the valueo - 4x' - 63 - soris negative, and by substitutinia foris, tha quantityie me Positive, iuvescit negative, and x et gives it positive, si that the roo is et renci and Mand theresere incommensurabie. ouisa pro- ceeffas in the sorino iniex amplecto appro indate to the oota ut there are ther method by