...b, c, a, b, c) where a* + b" + c* = 0 for a directrix of the Absolute. Consider now two directrices (a, b, c, a, b, c) and (a,, b,, c,, a,, b,, c,) : if a line (a, b, c, f, g, h) meets each of these, then (o+/)a + (b+g)b +(c + h)c = 0, and consequently...

...equivalent to adding a positive. A single example in numbers will illustrate this : important, are a — (b + c) = a — b — c, and a — (b — c) = a — b + c. It is plain that these apply equally to quantities of more than two terms. To subtract a quantity then...

...because each system is not limited to six or any number of points and lines. If however the points A, B, C, A', B', C' and a, b, c, a, b', c belong to tmo collinear systems, and A, a, B, b, etc. be corresponding points ; then P the point of...

...therefore only differ by the algebraical sign of the whole. Since and it follows from Art. 6 that a, b, c a, b', c a", b", c" and a, b, c a", b", c" a, b', c are of opposite algebraical sign. Hence the sign of a determinant of the third order is changed...

...of the last three terms and inclosing them in a parenthesis, with the sign — prefixed. Hence, When an expression within a parenthesis is preceded by the sign — , the parenthesis may be remaned, if the sign of every inclosed term be changed; and Any number of terms in an expression may...

...add c, the result will be correct; and the expression without the brackets should be, a — b + c. .-.a— (b + c) =a — b — c. \ and a — (b — c) = a — b + c. J ' '' As an extension of the above, take the following example : — a — (b + с — m — n + r)....

...then that 1 0 + (4 + 3) = 10 + 4 + 3, and that 10 + (4- 3) = 10 + 4 - 3 ; or, if a =10, b = 4, c = 3, a + (b + c) = a + b + c and a + (b - c) = a + b - c. Here we see that the brackets were removed without altering the value of the expression. We sum up...

...c, the result will be correct; and the expression without the brackets should be, a — b + c. ... a — (b + c) = a — b — c. \ and a — (b — c) = a — b + c, J < ' As an extension of the above, take the following example : — a — (b + с — m — и + r)....

...a— b+(c — d+e), a+( — b+c— d+e), and so on. 33. Minus Sign before the Parenthesis. — When a parenthesis is preceded by the sign — , the parenthesis may be removed if the sign of every term within the parenthesis be changed . This rule has already been illustrated...

...be enclosed within a parenthesis preceded by the sign +, without changing the sign of any term. If a parenthesis is preceded by the sign — , the parenthesis may be removed, provided the sign of every term within the parenthesis is changed, namely, + to — and — to + ; conversely, any...