A treatise of algebra, in three parts. Containing

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o FRACTIO NASeta the la Chapter it a seid that the quotient os an quantit adiridesby is expressed by placinia a veismali me aia, unde it, thus, These quotients are also ealled tactions and the dividen or quantityplaeed above the in is calle ili Numerator of the fraction, and the diviser o quantityplaces unde the line is calle the Denominsitor. Thuc expresses the quotient os et divides by aiand a is the numeratoriando the denominator os the fraction. leta. 1 Genumerator os a fractio is qualio irae deno nator, irinobe fractum is qua loario. 'bus and nare equalis umit. V δει numerator is rearer iba is denominarer, uoue fractio is greater reo unit. In both thesecases, the fraction is called improper But is thenumerator is se tha the eno=Frinator Iben Ibefra locis os ban unit, an is calle properi

rhus Pis an imprope fraction, ut fand

are proper fractions. A mist quantit is thata Whereos

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CHAP. 6. ALGEBRA. Whereos one par is an isteger and the ther a

PROBLEM II.

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Thus the fractions , , a, are respectivelyequa to thei fractions whichliave the fame denominator bes And the fractions

PROBLE IV.

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ID mixtinuantit is to e multiplied firstreduce it in the fori os a si action by Prob. I. Andas, integer is iste multiplied by a fraction, o ma reduce it to the s in os a fra tioni placinginit unde it.

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are respectivel equa to since isyo divide V by dy the quotient viilli thei amesaco a divide by P an divide bydY ives the sanie quotient asu dividedi d. and bd divides by bd the fame quotient ase divide by f. a. Fractions reduce to the sam denomina

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shbscribtiag the common denominator. I say

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There Vis in greate common meas ure required. The ground of this operatio is, That any quantity that measures the diviso and the re- mainde si there is any must alis me ure thedividend becisse the dividen is eques to thesum of the diviser multipliel into th quotient, and of the rei inde adde together . Thus in the last example, a meas ures the divisor - 4 , and the remainde etab lab' it must heresere likewise measure thei sum a aab 4'. o must observe in his operationto mahe that the dividend whicli has the highestpowers of the letter, accordinito hicli thequantities are ranged.

PROBLE VIII.

Me Chap. XIV.

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io the rivo stamen expresse in re uas

of the number an quantities, then the fractionis atready ii iis loWest te s. Thus a Minotbe reducta loWer. An nul)ahers, hos greatest common ine sure is unit, are seid tote moesto one amothetiya Is it is requiressito reduce a oveniaction to a fractio equa to it tha naal have a

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there are iniue divideo more rean in the diviseri Andri division the quotient a b contini di an degree os exactness ou lose, is add-ing cyphos to the dividend. The round of these operations is easily underDod stomahe generes rules for adding, multipliing, an divi ling