The Elements of the True Arithmetic of Infinites

Though I am fully persuaded that the propositions in this treatise—founded as they are on the most evident and indubitable principles—will stand the test of the most rigid scrutiny, I know well from the treatment my previous labors have received from those who set themselves up to judge their merit that I must expect gross misrepresentation and virulent abuse. I anticipate whatever hatred and envy can muster for the purpose of detraction, or whatever the cunning of malignant sophistry sophistry: deceptive or fallacious reasoning can distort. But since the propagation of truth of the highest kind is the only aim of all my work, accompanied by an earnest desire to benefit my countrymen and all mankind in the most important way, I console myself amidst all the defamation I have experienced (or may yet experience) with the consciousness of the integrity of my intentions. I hold the firm hope that what I have written for the benefit of others will always meet with the approval of the wise and good. For I have long since learned from the school of Pythagoras that the praise or blame of the stupid is equally ridiculous Original Greek: "Ηγου παντος ανοητου και τον επαινον και τον ψογον καταγελαστον." — Demophilus. Translation: "Consider both the praise and the blame of any fool to be laughable.".

As some persons may object to my use of the expression the last term of an infinite series—calling it not only paradoxical, but a perfect solecism solecism: a grammatical mistake or, in this context, a logical contradiction—I deem it necessary to observe that nothing more is meant by this expression than that term of an infinite series which, in whole numbers, is the greatest, or in fractions, the least, that can possibly exist in the series to which it belongs. This greatest or least term, as will be abundantly shown in the following treatise, can only be expressed itself...