A treatise of algebra, in three parts. Containing

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CHAP. II.

Fro three quations involvin an threeunknorin quantities, an et to deduce two equations

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one unknown quantityint ι hicli,illae bestlearnesis practice. EX AMPLE XIII.

is addition a m 36

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68 . est is obvious sto the ad an sinx irections in Rhat In annerso are to Mointhere are Bur, o more, unknown quantities,

and Bur, o more, equation gion comparing the give equations, ou may tWays attengili discove an quatio involvinioni one anknown quantity hich, i it is a simple equation, may tWay be resolve by the Rules of the las Chapteri e ma conclude then, that A When there are a man simple quations give a quantities required, these quantities may he discovered by the applicationis the

Disiti geo

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require than quation gion the the ques. tion is no limite to determinate quantities; but is capsile of an infinite number of sol tions.' And, I there are more quatio given than there are quantities required i mavbe impossibi to findoli quantities liat ill antae the conditions os the question ι' M- cause semesos these conditions may be inco sistent with othera.

Ι the folio in Theorems, e cud hos coeffcients of the order' that are prefixi to the fame unknown quantities in the disserent quations Thus, in Theor. a. a 44,are oscille lanae order, eing the coessicient osae also h a re of the same order, heing the messicients ola: and thos are of the sanae orderina affectis,unknown quantity. But hos are calle Ninte' coemienis that are taken eac stomis different quation,

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an fio a disserent ide os coessicients Asa, , and d, b, in the fir Theorem and

involving two unknown quantities, as

then hau an P. Where the numerator is the disserence of the products of the opposite messicient in the os

der in hic ' is Ot ound and the denominator is the difference of the products of the opposite coe tenta aliendro the ordere that involve the two unknown quantities.

For sto the fir equation, it is plain that

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EX AMPLE IL

6 87. Suppos no that there are thrae un-known quantities an three quations then calline unknowiquantities and

Where in numerator consisti, at the disserent producta that cante madesos three προ- sit coessicients ahen sim the ordere in villita is no sound and the denominator conlist ofal the producto that a be made of the three opposite