10 CONSTRUCTION OF THE CANON.
less of the other, and the greater of the one to the greater of the other.
Thus let the line a b c be divided into two parts, ab and bc. Let ab lie between the limits 123.5 the greater and 123.2 the less. Also let bc lie between the limits 43.2 the greater and 43.1 the less. Then the greater being added to the greater and the less to the less, the whole line ac will lie between the limits 166.7 and 166.3.
Thus let one of the quantities ab lie between the limits 10.502 the greater and 10.500 the less. And let the other ac lie between the limits 3.216 the greater and 3.215 theless, Then 10.502 being multiplied into 3.216 and 10.500 into 3.215, the limits will become 33.774432 and 33.757500, between which the area of a b c d will lie.
and