Theoretic Arithmetic, in Three Books: Containing the Substance of All That Has Been Written on This Subject by Theo of Smyrna, Nicomachus, Iamblichus, and Boetius, Together With Some Remarkable

Theoretic Arithmetic, IN THREE BOOKS; by Thomas Taylor introduces a revival of a classic mathematical philosophy. It presents the substance of theoretical arithmetic as taught by ancient authorities Theo of Smyrna, Nicomachus, Iamblichus, and Boethius, and includes remarks on perfect and amicable numbers and the Pythagorean mysticism surrounding numbers. The text argues for arithmetic as a path to purification of the mind and ascent to intellectual truth, following Plato’s ideal of philosophy and the Platonic tradition. Taylor weaves introduction and notes that place arithmetic within a broader metaphysical program, merging number theory with harmony, geometry, and theology. The three books cover topics such as the monad and the duad, the division of numbers into even, odd, and composite classes, the theory of perfect numbers, amicable numbers, and the various kinds of proportion (arithmetic, geometric, harmonic). It also includes discussions on the sieve of Eratosthenes, and on the cognitive role of mathematics in philosophy.