Our attention, naturally, is most drawn to the difficult parts of an inquiry; the easier steps are apt to be overlooked. Thus, while much attention and deep thought have been bestowed on the solution of equations, on the computation of logarithms, on the construction of astronomical canons; such a simple process as the repeated addition of some known quantity, has not been considered worthy of the notice of arithmeticians. Yet the tables constructed by help of this process are much more numerous, and are as important as the others, often indeed serving as their foundation.

The case when the quantity to be added is expressed accurately in numbers, needs no remark; but when that quantity is represented only approximately, we have to consider the accumulation of that part which is unavoidably left off, and to see that this does not lead to an error of so much as the half of unit in the last place that is to be retained.