This section is from the book "The American House Carpenter", by R. G. Hatfield. Also available from Amazon: The American House Carpenter.

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.

Continue to: