SUBTRACTION OF ALGEBRA.

This rule being the reverse of Addition, we change the signs of the quantities to be subtracted, or consider them as changed; that is, make negative signs affirnative, and affirmative signs negative; and then ncorporate them as in Addition.

In Ex. 1, we have 2a to be subtracted from 5a, and therefore, proceeding according to the Rule, 2a becomes 2a; then, by subtracting the similar quantities having unlike signs, and prefixing the sign of the greater, as in Addition, we have 3a for the result.

Ex. 2 and 3 are combined in the same manner; but Ex. 4, being composed of unlike quantities, requires to be written down as in Addition, with the exception of changing the sign of the quantity to be subtracted.

The answers of Ex. 8, 9, 10, may be also written thus:-Ex. 8, 2a 2. 10* * Ex. 9, 10 a c-d*.x Ex. 10, 20a3c— 8.6* — 2.d*c + 2.x*

In Ex. 9, it is evident that once the root of d.x taken from twice the root of d.x leaves once the root of d.x. And in Ex. 10, it is evident that the quantities being unlike, must be written as in addition, with the exception of changing the signs of the subtrahend.

Parentheses are used with much advantage, when any number of quantities are multiplied by the san co-efficient. Ex. gr., ax + cx — dex, may be writter thus, (a + c de); and any quantities having common multiplier can be similarly written; which. facilitates calculations considerably.

e) + x2 (b + n) + x2y (eg)
ex3 + bx2 + nx2 + cx2y - gx2y

Whenever a negative sign stands before a parenthesis, It affects each sign within it: so that if we have, -(a + b c)x, each of the signs contained within the parenthesis requires to be changed whenever we remove it, thus, (a + b

c) x

==

их

bx + cx; and again, if we wish to place this in a parenthesis, it is also required that we should change the signs, bx + cx becomes (a+b−c)x.

thus.

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Ex. 15.

THIRD BOOK.

DEFINITIONS.

1. Equal circles are those of which the diameters are

8

4. In a Circle, right lines are said to be equally distant from the centre, when perpendiculars drawn from them to the centre, are equal.

5. And that line is said to be at the greatest distance from the centre, on which the greatest perpendicular falls.

6. A Segment of a Circle, is a figure which is contained by a right line and a part of a circumference.

D

7. An Angle in a Segment, is an angle under right lines drawn from any point, in the part of the circumference, which contains the segment, to the extremities of the segment.

8. An Angle is said to stand upon the part of the circumference, or arch, which is intercepted between its legs.