A treatise of algebra, in three parts. Containing

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rations that relate to quantity. Hencerit is that any quantity ma be suppost to enter into algebraic computations Wo different Way .hichliave contruserim, esther as an inerment orasa decrement that is, as a quantityrio be addeclo as a quantityrio e subtractes. The fg Φίρμὰ isthi mar of Addition, and thesign-- minus) of Subtractio. Thus the quantityis

in represente by imporis that aris tole ded, o represent an increment, ut

imporis that icto be subtractes, and representa a decrementi hen severat suta quantities are,ined the signs serve to me whic are toleiades, and whicli are tora subtracted Thusa in denotes the quantity that artis Menando are both considere M incrementa, and there re expresses the sum os a an But-ε--- denotes the quantity that arises hensrom the quantity a the quantity bris subtracted iaud expresses the exces of labore When

crement.

66. As addition an subtramon are Opposite, o an increment is opposite to a decret-ment, there is an analogous opposition bemeen the affections os quantities that are consideredin the mathematica sciences Asietween exinces an desect betWcen in value os effect '

or Diuitias by o le

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or One ducto a man, an money due hysim, a line draWn toWard the right, and a linedra. to the lest gravit an levity elevation inove in horizon, an depressio belit. When π quantities qua in respe osmagnitude, ut of thos opposite indλ are Dinta together, and conceived testae place in the fame sub in the destineach otheesse' and thei amount is nocting. Thus IooL. ducto a man and os due by hi balancerac oster, and in estimatim his stoc may beboth neglected. Power is susulaesis an equalpowe actinion the same bod Mith a contra direction, and netther have Mct. When tWo umqua quantities of thos opposite qualium are Oinea in the fame subject in mater prevatis hy their difference. An When a greater quantit is ahen rom a lesse of the fame hind the remainder ecomes of the opposite

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mi of such a contrariet O Opposition. elino nothin analogous to it in quantityabstractly qnsidered, and anno subtracto greater quantity os matter rom a lesieri or agreater quantit os light rom a lesser. Andili applicatio of this doctrine to any ari or

science is tote derived sto the -- pri esses os the science. 67. A quantity that is to e adde is like-wis called a positive quantity4 and a quantit tobe subtracte is sal in eiserative the are uali reat, ut opposite to e Mother, se as

oni be qualis is quantity, ut of the fame quality that in ver operation the ne may

have ste sine effect a the other. A decrement. may he equa to an increment, ut it has' in alloperations a contrar effect a motion do n-Watas

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ward marte equat to a motion pWards, and the depression o a star beloin the origo maybe eques to the elevationis a star above iti cinose positioncare opposite, and the distance of the starcis meast than is one of them mas

a the horizon solas to have no elevation aboveit, o depression belo it It is, account of this contrariet that a negative quantity is seidio Maesi stan nocting, b cause it is opposite tothe positive, and diministres it when Oinexto it, Ubereas the additio of o has no effect Buta negative is to e consideres no lesilas a realquantity than the positive. Quantities that haven sign prefixe to theriare understood is epositive. 8. The number prefixest a lette is calued the numera cresscient, an steW ho ostenthe quantit represente by the lette is to be

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The other m is and definition necessam in aereis stat be explaine in thei proper

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sum a.

addes together fir ad the positive together into one sum, and then the negative se . Then ad these two sum together Iby use l.

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sum os all

. . .

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It is evident, that is subtractis tari aWaya decrement is the semesa addinia equesci

the sum is likewis In generat, the su tractionis a negative quantit is equivalent to, ita lis positive value CH AP

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zas I. When an positive quantity, is multiplied is an positive number,' tu the meminiis, That Facis ob taen a many times a thereare unita in m and the product

are unit in , and the product must

Case III. Multiplicatio by a positive minaberimplies a repeate addition hut multiplication ' a negative minpties a repote subtraction And . hen in is to e multiplied by - 1 the meaniniis, That a isto e subtracte a oster as there

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the - aris to e subtracte a octe a there are unita in n. but by