Excerpt from The Elements of Algebra, Vol. 1: Designed for the Use of Schools
1. Algebra is the science which reasons about quantities by means of letters of the Alphabet, and certain signs and symbols, which are employed to represent both the quantities themselves, and the manner in which they are connected with others.
Thus we might put a to represent 7. and then twice a would represent 14; or we might put a to represent 3, and then twice a would represent 6, three times a, 9, &c.
2. The sign = (equal) denotes that the quantities between which it stands are equal to one another.
Thus, if a = 17, then twice a = 34.
3. The sign stands for then or therefore, and for since or because.
4. The sign + (plus) denotes that the quantity before which it stands is added, and the sign - (minus) that the quantity before which it stands is subtracted.
Thus 5 + 3 = 8, 5-3 = 2; and if a = 3 and 5 = 4,
then a + b = 3 + 4 = 7, a + b + 2 = 3 + 4 + 2 = 9,
10- a = 10 - 3 = 7, 10- a - b = 10 - 3 - 4 = 7 - 4 = 3.
The sign ~ is used to denote that the less of two quantities is taken from the greater, when it is not known which is the greater.
Thus o-5 denotes the difference between a and b.
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