I have said that all questions in arithmetic require nothing but
addition and subtraction. I do not mean by this that no rule should
ever be used except those given in the last section, but that all
other rules only shew shorter ways of finding what might be found,
if we pleased, by the methods there deduced. Even the last two rules
themselves are only short and convenient ways of doing what may be done
with a number of pebbles or counters.
I want to know the sum of five seventeens, or I ask the following
question: There are five heaps of pebbles, and seventeen pebbles in
each heap; how many are there in all? Write five seventeens in a
column, and make the addition, which gives 85. In this case 85 is
called the product of 5 and 17, and the process of finding the
product is called multiplication, which gives nothing more
than the addition of a number of the same quantities. Here 17 is called
the multiplicand, and 5 is called the multiplier.