The Elements of the True Arithmetic of Infinites

by a fraction which, when expanded, produces an infinite series. Those who are at all familiar with the Arithmetic of Infinites A mathematical method developed by John Wallis (1616–1703) to handle series approaching infinity. invented by Dr. Wallis well know that its entire application depends on the admission of the “last term” of an infinite series. Indeed, the greatest term of an infinite series is frequently called by Dr. Wallis the “last term”*.

I shall only add that if Aristotle’s treatise on Indivisible Lines A work traditionally attributed to Aristotle discussing the nature of points and continuity. had been studied by the moderns as it deserves, their doctrine of fluxions fluxions: Newton's term for what is now called calculus and infinite series would not be celebrated as it is at present. This will be immediately evident to those who understand that treatise and what is delivered here.

• Thus, too, Ward, in that part of his Young Mathematician's Guide in which he treats of the Arithmetic of Infinites, uses the expression “the last term” in all his Lemmas Lemma: a subsidiary proposition used to demonstrate a main theorem respecting the summation of infinite series.