The Theology of Arithmetic

...fourfold in power original: dynamei. In Greek mathematics, this refers to a number squared., but eightfold in solid original: stereō. This refers to a number cubed.; and those three-fold in length are nine-fold in power, but twenty-sevenfold in solid. In the good order of all numbers, so it is also in the case of parts: those that are halves in length are quarters in power, but eighths in solid; and those that are thirds in length are ninths in power, but twenty-seventh parts in solid. Every system of quantity is formed as a part of a subdivision according to the monad the number one; the principle of unity. For there is one decad the number ten and one chiliad the number one thousand, and conversely, one-tenth and one-thousandth, and the parts proceed to infinity. In each of these, the monad remains the same in form, but differs in magnitude.

In addition to these things, the monad generates itself out of itself, just as the cosmic reason original: logos; the rational principle governing the universe and the nature of beings do, preserving all things and not allowing them to change, to whatever it may be added. Alone among all others, in a manner similar to the saving providence of the universe, it is most suitable to reveal the discourse concerning God and to be associated with Him more than anything else, insofar as it is most proximate to Him. It happens to be the "form of forms," just as a craft is to the craftsman or intellection is to the thinker.

This was demonstrated moderately in the discussion on the "friendly" opposition between oblong and square numbers. Nicomachus Nicomachus of Gerasa (c. 60–120 AD), a mathematician whose works on arithmetic and music were foundational for later Neoplatonists like Iamblichus. says that God corresponds to the monad, as He contains "seminally" original: spermatikos; containing the potential for all future development, like a seed. all things that exist in nature, just as the monad encompasses in number—potentially—those things which seem to be most opposite in actuality original: energeia; active existence through every mode of opposition. In its ineffable nature, the monad is seen to be "all-formed" original: paneidēs; having the capacity to take on any shape or form. throughout the Introduction to Arithmetic, having encompassed the beginning, middle, and end of the whole—whether we think of it as existing by a chain of connection or by side-by-side arrangement. Just as the monad is the beginning, middle, and end of quantity, magnitude, and even every quality. For as there is simply no structure of anything without it, so also without it there is no knowledge of anything whatsoever, as it is the most sovereign of all things, like pure light, sun-like and...