2024 Reprint of the 1934 Edition. Full facsimile of the original edition and not reproduced with Optical Recognition software. The is the first edition thus of Thomas Taylor's remarkable treatise on the Pythagorean's philosophy of numbers - with an added Introduction by Manly P. Hall. THOMAS TAYLOR, the author of this remarkable treatise on the philosophy of numbers, was one of the greatest Platonist of the modern world. He was a prodigy of erudition and industry. He translated into English the complete works of Plato and Aristotle and authored several original treatises as well. The Theoretic Arithmetic is the most important of his works. Throughout the book, Taylor draws on the writings of ancient Greek philosophers such as Plato and Aristotle to provide a comprehensive overview of Pythagoreanism and its influence on Western thought. This book is a valuable resource for anyone interested in the history of mathematics and philosophy, as well as those seeking to deepen their understanding of Pythagoreanism and its impact on modern thought.

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....