Harmonical ARITHMETIC, is so much of the doctrine of numbers as relates to the making the comparisons, reductions, &c. of musical intervals.
ARITHMETIC of Infinites, is the method of summing up a series of numbers, of which the number of terms is infinite. This method was first invented by Dr. Wallis, as appears by his treatise on that subject; where he shows its uses in geometry, in finding the areas of superficies, the contents of solids, &c. But the method of fluxions, which is a kind of universal arithmetic of infinites, performs all these more easily, as well as a great many other things, which the former will not reach.