A treatise of algebra, in three parts. Containing

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mainder, o ma continiae the operatio byadding period os cyphersio that remes eri and sita the true mot in decimal, to any degrae sexa est.

dere eithe ho much the oneris greater hanthe ther, and what is thei disserenu or it ma he considere ho many times the oneris containe an me theri or more Senerally,

a What

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term hos ratio is enquire into is called theant dent, and that With Whic it is compared is calles thicosequon s9. When os Bur quantities the differe ehetwix the firmand secon is qua to the dis. serenoe etKix the hird and -- thesequantities are calle Arithmeti importio mussas in number 3 7, 2, 16. An the quantities a F e, e . ut quantities serma series in arithmetica proportion, he they

numbers, I, 2, 3, 4 s, and Io, 7, 3 6o. In our quantities arithmeticasi pro- 'ortiona the sum of the extrem cis equalis thesum the mean trem.' Thusa, - - Φare arithmetica proportionali, and the iam os the extremes his equa to the sum os the mea term e . Hence, to findine Burth quantity arithmeticali proportionalio an three give quantities Ad the secondand third, and Do thei sum subtra the first term the remainde stalliive the laurin ariti metical proportiones requires.

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An it is lain that Deach term he adde tocte term aboverit, the sum Willi a bis qualto the sum of theirst term cand the last term x. From hicli it is lain that citi sum fallube term os an arithmetica progression is equaIlithe sumin thesis and las ta en hal as Uten Muere are tems, that is the sum os an arithmetica progression is qua to the sum of the first and la term multiplied by alf the num- her of terms Thus in the precediniseries, isn e the number of terms, the sum o at the

term

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dent, that the sum os an numher os arithmetica proportionals eginia ingrato in Othing, is equa to half the sum os as an term equalto the greatet term .

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sal tot in Geometrical proportion. Iuch areth number 2 6, 4, 12 and the quantitiesur, A r; hicli are expresse aster this

In seu quantities geometricali proportional the produnt of the extremescis equalis ibe produn of the widdis terms.' hus brar And is it is require t find4Murthproportional to any three ive quantities, multipo the secon , Ibe hird, and divide Ihe produn by the frsi, he quotient Rau Iive thesura proportiona requireri' Thus, o find asturtii proportional to , ' and I multis lyari b, and divide the product et Hyby the fit sttermis, the quotient bHis thes uri proportional

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Then mali in te sie in due orderi and youare o proce. amor linito the rute, in plying the seconi by the ibita, and dividinsthei product by the fisi

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ber of the terms, and the common ratio, Dumaseasii find the sum os est the terms. Is it is a decreastra series hostium is in be

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ialem.

An quatio gives the valla os a quantity, when that quantit is alone o one id of the equation and that value sanown is ali thoselliat are o the other side areanown. Thus E

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For that is in divide bovi sides of the quatio by the fame quantity, and when Didivide eques quantulas is die fame quantit, ille M tiems must beχροα Thus,

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