Prologue

...excel that existence which is characterized by the division and composition of ratios original: logoi. In this context, it refers to both mathematical ratios and the formative principles of the soul.. This mathematical existence surpasses and encompasses the knowledge of physical substances, yet it does not fully admit the varied and discursive thoughts of the soul. Instead, it aligns itself with those simple forms of knowledge that are pure of all matter. Indeed, I say that the middle rank of mathematical objects fulfills the entirety of the "middle ground," filling the gap between the essences that are completely indivisible and those things which become divided in the realm of matter.

When we examine the principles of the whole of mathematical essence, let us ascend to those overarching principles that penetrate all beings and generate all things from themselves: I mean the Limit original: peras. The principle of definition, shape, and stability. and the Unlimited original: apeiron. The principle of plurality, growth, and potentiality.. For from these two—following the incomprehensible and totally ungraspable cause of the One—all other things were established, including mathematical natures. Those primary principles produce all things boundlessly and in a transcendent manner, while the things that exist in parts receive their progression in the proper order and appropriate rank; thus some are established as primary, others as middle, and others as final.

The primary classes of being, according to their own simplicity, first participate in the Limit and the Unlimited. On one hand, they are fulfilled by the Limit through their union, identity, and stable and firm existence. On the other hand, they receive from the Unlimited their division into plurality, their generative abundance, and their life, eternity, and progression. Now, as for mathematical objects...