This author really believed himself, and was in earnest. He is not the only person who has written nonsense by confounding the mathematical infinite (of quantity) with what speculators now more correctly express by the unlimited, the unconditioned, or the absolute. This tract is worth preserving, as the extreme case of a particular kind. The following is a specimen. Infinity being represented by [infinity], as usual, and f, s, g, being finite integers, the three Persons are denoted by [infinity]^{f}, (m [infinity])^{s}, [infinity]^{g}, the finite fraction m representing human nature, as opposed to [infinity]. The clauses of the Creed are then given with their mathematical parallels. I extract a couple: "But the Godhead of the Father, of the Son, and of the Holy Ghost, is all one: the glory equal, the Majesty co-eternal. "It has been shown that [infinity]^f, [infinity]^g, and (m [infinity])^s, together, are but [infinity], and that each is [infinity], and any magnitude in existence represented by [infinity] always was and always will be: for it cannot be made, or destroyed, and yet exists. {330} "Equal to the Father, as touching his Godhead: and inferior to the Father, touching his Manhood." "(m [infinity])^s is equal to [infinity]^f as touching [infinity], but inferior to [infinity]^f as touching m: because m is not infinite." I might have passed this over, as beneath even my present subject, but for the way in which I became acquainted with it. A bookseller, _not the publisher_, handed it to me over his counter: one who had published mathematical works. He said, with an air of important communication, Have you seen _this_, Sir! In reply, I recommended him to show it to my friend Mr.----, for whom he had published mathematics. Educated men, used to books and to the converse of learned men, look with mysterious wonder on such productions as this: for which reason I have made a quotation which many will judge had better have been omitted. But it would have been an imposition on the public if I were, omitting this and some other uses of the Bible and Common Prayer, to pretend that I had given a true picture of my school. [Since the publication of the above, it has been stated that the author is Mr. Oliver Byrne, the author of the _Dual Arithmetic_ mentioned further on: E. B. Revilo seems to be obviously a reversal.] LOGIC HAS NO PARADOXERS. Old and new logic contrasted: being an attempt to elucidate, for ordinary comprehension, how Lord Bacon delivered the human mind from its 2,000 years' enslavement under Aristotle. By Justin Brenan.[706] London, 1839, 12mo.