Elements of Algebra

CHAP. II. OF ALGEBRA. 3 CHAP. II. *Explanation of the Signs $+$ Plus and $-$ Minus.* 8. When we have to add one given number to another, this is indicated by the sign $+$, which is placed before the second number, and is read *plus*. Thus $5+3$ signifies that we must add 3 to the number 5, in which case, every one knows that the result is 8; in the same manner $12+7$ make 19; $25+16$ make 41; the sum of $25+41$ is 66, &c. 9. We also make use of the same sign $+$ *plus*, to connect several numbers together; for example, $7+5+9$ signifies that to the number 7 we must add 5, and also 9, which make 21. The reader will therefore understand what is meant by $8+5+13+11+1+3+10$, viz. the sum of all these numbers, which is 51. 10. All this is evident; and we have only to mention, that in Algebra, in order to generalise numbers, we represent them by letters, as $a, b, c, d$, &c. Thus, the expression $a+b$, signifies the sum of two numbers, which we express by $a$ and $b$, and these numbers may be either very great, or very small. In the same manner, $f+m+b+x$, signifies the sum of the numbers represented by these four letters. If we know therefore the numbers that are represented by letters, we shall at all times be able to find, by arithmetic, the sum or value of such expressions. 11. When it is required, on the contrary, to subtract one given number from another, this operation is denoted by the sign $-$, which signifies *minus*, and is placed before the number to be subtracted: thus, $8-5$ signifies that the number 5 is to be taken from the number 8; which being done, there remain 3. In like manner $12-7$ is the same as 5; and $20-14$ is the same as 6, &c. 12. Sometimes also we may have several numbers to subtract from a single one; as, for instance, $50-1-3-5-7-9$. This signifies, first, take 1 from 50, and there remain 49; take 3 from that remainder, and there will remain 46; take away 5, and 41 remain; take away 7, and 34 remain; lastly, from that take 9, and there remain 25: this last remainder is the value of the expression. But as the numbers 1, 3, 5, 7, 9, are all to be subtracted, it is the B 2