In comparing, in the last article, the first equation with the last, it will be seen that the same symbols are contained in each, but differently arranged: that while in the first equation b appears in the right hand member and with a minus or negative sign, in the last equation it appears in the left hand member and with a plus or positive sign. Thus it is seen that in the operation performed b has been made to pass from one member to the other, but in its passage it has been changed. A similar change may be made with another of the symbols. For example, from the last equation, let d be subtracted, or this process indicated, thus -
a + d+b - d=c - d.
The plus and minus d, in the left hand member cancel each other, therefore -
a + b = c - d, or, by numerals -
4+3=9 - 2. Reducing -
7 = 7.
By this we learn that any quantity (connected by + or - ) may be passed from one member of the equation to the other, provided the sign be changed.