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SECTION III. MULTIPLICATION.

articles may be expressed thus: If a be made up of the parts x , y , and x , ma is made up of mx , my , and mz ; or,

ifa = x + y + z.

ma = mx + my + mz,

or,m(x + y + z) = mx + my + mz.

A similar result may be obtained if a, instead of being made up of x, y, and z, is made by combined additions and subtractions, such as x + y-z, x- y + z, x-y-z, &c. To take the first as an instance:

Leta = x + y - z,

thenma = mx + my - mz.

For, if a had been x + y , ma would have been mx + my . But since a is less than x + y by z , too much by z has been repeated every time that x + y

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