+ Proclus the Successor on the First

of Euclid's Elements

Book One :-

The intermediate nature of mathematical objects

Mathematical being original: ousia does not belong among the primary classes of things that exist, nor among the last. Instead, it occupies the middle ground This "middle ground" refers to the Neoplatonic idea that mathematics bridges the gap between the spiritual/intellectual world and the physical world. between indivisible, simple, uncompounded realities and those that are divisible and defined by various compositions and diverse divisions. For on one hand, the stability, immutability, and unchanging nature of the reasoning applied to mathematics shows it is superior to the types of forms found in matter. On the other hand, the discursive Greek: diexodikon. Discursive reasoning refers to thinking that moves step-by-step from premises to conclusions, rather than grasping truth all at once by intuition. nature of its mental applications, its use of the dimensions of its subjects, and its reliance on other pre-established principles,
Regarding the Order

assigns it a rank lower than that indivisible reality referring to the pure Intellect or Nous which is perfectly established within itself. For this reason, I believe, Plato also divided the ways we know things according to these levels: the first, the middle, and the last realities. To the indivisible realities he assigned the highest level of intellection original: noētikē, and after this, he placed the rank of discursive reason original: dianoētikē, considering it worthy of...