A treatise of algebra, in three parts. Containing

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simple equation multiplied by one another that produce it, as many as there are unita in the tu est di mensis of the vinnoWn quantityio the proposed equation. 64. Bubacthere arem,other quantities,hat ver besides thele our a A e, in that substi

in the place os a Mil mahe in product vanissi i

Mixtad- 'cannot possibiy have more stan theseseu roota, and cannot admit os more silutions than Is o substitute in that producta

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6 7. I may bei sesul semetimescio consider quations a generate sto inher os in inse-

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equation hos more are the quantity a thevalue os x in the simple equation, and the tworoot of the quadraticis quation, viz.

ciis. 13. Porta And accordinias these mota are realis imposiMe, Wo 'of the oot of the cubic equation are reali impo te. 3 8 in the doctrine os involution e hewed stat the quare os an quantit positive ornegative, is alWays positive. ' and theresore, the

when is is resolve into the simple quations that produce it, the ma involve impossitae

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both involve an imaginar quantityri a thesquares is a rea qua latitu, ut iis quaremo is imaginary. Afiter the fame . manne ab uadrati equation, hen resolves, mangrue seu simple quations Och os,hicli manive

an imposithle value so the root and the famema be sat os an equatio that an e produce fro quadrati equations onis that is, Mi se dimension are of the even numbers. s. ut in cubic equation whic cannot be generate stom quadrati equations ontribu requires one simple quatio besides o produce this non os ita coemients are impossitae, Will have, at least, ne ea motr the fame with the mot of the simple equation whence itis pro luced. The quare of an impossibie quan-

is plaint imaginary. From hicli it appears, that though two simple quations involvingimpossibi expressions multiplied by one another, mangive a produc Wher no impossitae pressio ma appear; et, three suci, simple equationsae iusti plied by ach ther, ille impossibie exprestion illiso dilappeta in their K pro .

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e quationis hole coessicients are rea cannot haveat iis three roois impossitae.' io. In generat, it appears that the impon

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it is obvious that the ighest dimensio of the Uliknown quantit in thei product is qua tothe number of those simple quationsa and theterm involving the h hel dimensio is calles the si s term os the quatio generates by this

multiplication. The term involving the ext dimentio of the unknown quantity les than

the greatest is nisi is calle the uod termo the equation the term involving the nexi dimension of the unknown quantity, which is lesithan the greate hy two the Bird ter of the equation, And that tern whicli involves dimensis of the unknown quantity but issem known quantity, is calle the last ter of the equation.' The number of term is almam greater than the righes dimenso of the κη ηοwnis iniit bynmi.' And when an term is anting, anasteri cis maiae in iis place. The Ansandeocicients of equations Nil be underitoo byconsidering the solioWing TABLE, Where thesimple

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plied by one nother, an produce successivelythe higher equations.

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CuAp. et ALGEBRA. x x,sa. From me inspectionis thesesequationsit is plain stat the messicient of thesin term is

The coefficient of ne secon term is

The messicient of the Burin term is radium in the tradum reat cande made bet multipolar

one another.

i . Although in the Tabie sueti simple equations oni ala millesplied by one another as have positive mors, it is eas to ste, that the c