A treatise of algebra, in three parts. Containing

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os an gia in equation by the soliowing

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sed is of sive dimensions then Iouisust 1Ῥ- pinxiae And2on. να8. When the secon term in an equation is vianting, it follows that the quation has oth Ermative an negative oois,' and that the sum os the affirmative root is qualm in sum of the negative mors is hichmeans the coemient of the secondae , whichis inessum os est the rosis of both seris, vanishes, and mahes the second term vanissa. In generat, the messicient of the secondier is the disserenoe etween the sum of the Ermative r is and the sum of the negative mois:' and the operations, have give serveoni to diministi ai the root when the sum os the assirmative is realest, or increas theis mulie in sum os in negative is gre test, so

Diuitiae b

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M to alance them, an reduce them to an equality. It is obvious, that in a quadrati equationthat Uno the secon teriri, there must be onemo assirmative an one negative and thesemus besequat omne another. In a cubi equation that want the secondierim, there must be either, ino affirmative motaequat, tinen together, to a thita motalia musthe negativi or mo negatio equescio a third that natast be positive. - Let an quationis j x in x obe propoled, and let it be no required in exte minare the third te . B supposing - the coefficient of thethird ei in the equation offici ound see equation AP to belae' 2pe F q. Suppost that co--cient equa to nothing, and by resolving the quadratic equation,' 'pe o mi illsind the value o G hich substitute sor it in the equation e, Will me lio to trans-sorm the propost equatio into ne that hallvant the stird term. The quadrati a P - ape gives

Willie transformed into an equation anting the

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tion.

xion multiplied into I mae the coemient of the

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post equation multiplied by fyas requires.

Lam The transformation mentiones in thelast article is fise hen the irae ter of the quatio has a coem cient disserent romuntly sor, by it, the quatio ma be trans- sumes into one that stes have die messicientes inessi hest term unit. Is the quatio proposed is ax' pae in

o the transform the quation into one hos root are equa to the root of the pro-

posed quatio multiplied by That in

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is transsormed in to the equation

Ora Diuitiae by Go rate

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Dissilia πιν Go rate

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sequently more east. An stat endeavour tomplain the round of this an many therrullas,e mali ive in the remaining parcof this Trevise in a more simple an concise manno. than has hitherio been done. In orde to this, we must loo hac tori et . . vhere, midabat fan equation, asta px - - qx-rmo, is proposed, and ouare to trans . Armat into mollier stat mali have ire mota lassthan the value of x by any give differen e axe, yomare to assume Iis x - . an substitutingsor, ita value a in Difin the transformes equation,

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That the lait term e - pe rhis the ver equatis, urat Was propos , avinio in place os α' The coessicient of the la term ut oneis e - 2pe is hic is the quantity that arist by multiplyin every ter of the ast messicient ae pes by the index of ein acti term an dividing the productue ape by the quantit e that is common to

Where againcit is obvious that the last term is the quatio that a proposis, avini in place of x. That the la term ut ne has sor