Theoretic Arithmetic

by Thomas Taylor

This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1816 edition. Excerpt: ... CHAPTER I. Vn the manner in which the Pythagoreans philosophized about numbers. The Pythagoreans, turning from the vulgar paths, and delivering their philosophy in secret to those alone who were worthy to receive it, exhibited it to others through mathematical names. Hence they called forms, numbers, as things which are the first separated from impartible union; for the natures which are above forms, are also above separation.1 The all-perfect multitude of forms, therefore, they obscurely signified through the duad; but they indicated the first formal principles by the monad and duad, as not being numbers; and also by the first triad and tetrad, as being the first numbers, the one being odd, and the other even, from which by addition the decad is generated; for the sum of 1, 2, 3, and 4, is ten. But after numbers, in secondary and multifarious lives, intr oducing geometrical prior to physical magnitudes; these also they referred to numbers, as to formal causes and the principles of these; referring the point indeed, as being impartible to the monad, but. Forms subsist at the extremity of the intelligible triad, which triad consists of leing, life, and intellect. But being and life, with all they contain, subsist here involved in impartible union. See my Proclus on the Theology of Plato. Theor. At. L a line as the first interval to the duad and again, a superficies, as having a more abundant interval to the triad; and a solid to the tetrad. They also called, as is evident from the testimony of Aristotle, the first length the duad; for it is not simply length, but the first length, in order that by this they might signify cause. In a similar manner also, they denominated the first breadth, the triad; and the first depth the tetrad....

Genres: Mathematics, History, Philosophy, Metaphysics

82 pages, Paperback

First published February 1, 1972

About the author

Librarian Note: There is more than one author with this name in the Goodreads database

Thomas Taylor was an English translator and Neoplatonist, the first to translate into English the complete works of Aristotle and of Plato, as well as the Orphic fragments. He published prolifically for over 50 years.

Reviews

[Peter J. · Rating 5 out of 5]

This was an important work in my opinion. Besides being tremendously intriguing when it showed odd patterns that hint at something more to numbers than the mere assemblages of monads, it also clarified some really key concepts that are found not only in Pythagoric, but Platonic, Aristotelian, and Orphic thought.