The Egyptian Oedipus, Volume II

SECTION VII. HIEROGLYPHIC MATHEMATICS. CHAPTER II.

...the lower World gives; the middle world participates in an equal portion of light and darkness from both, although the upper is not entirely without darkness, nor the lower entirely without light, even if light in the lower World, and darkness in the upper, seem in a certain way to be absorbed. If, therefore, you look more deeply into the Diagram The "Schema" refers to the symbolic illustrations Kircher uses to map the universe, likely the "Double Pyramid" of light and shadow described in related chapters., you will experience through the descent of unity into multiplicity, and the return of multiplicity into unity, how in the highest heaven all things which belong to multiplicity proceed into unity itself; that is, the divisible into the indivisible, darkness into light, the composite into the simple, the mortal into the immortal, the changeable into the unchangeable, potentiality into actuality actum In the philosophy of the time, "act" is the perfected reality of a thing, while "potential" is its unrealized possibility., the part into the whole, and so on for the rest. You will find the contrary process in the lower World. If you investigate these things with a sharp mind, you will behold the greatest and most obscure things clearly by the brightest light, reaching even to the most hidden secrets of nature. Moreover, you must conceive the unity of any particular thing in its own perfection, and imagine the quality of darkness according to that intensity of light. From the gradations of unities, you should consider that one smaller which possesses more darkness, more multiplicity, more potentiality, and more divisibility; and that one greater which has more light, more unity, more actuality, and indivisibility. For the less a unity is in act, and the more it is in potential, the more it is subject to change. For a unity that unites original: "vnitas vniens" is more perfect than a unity that is capable of being united original: "vnitate vnibili", just as the unity of the Soul is more perfect than the unity of the body, because the end of the body's unity is the soul's unity, upon which the bodily unity depends as if upon its own principle.

The wonderful offspring of Unity.

A wondrous property of the Monad Monas A term derived from the Greek word for 'One,' used here to represent God or the primary source of all existence. and its offspring occurs to us here, which demonstrates the middle state in the three aforementioned Worlds produced by God, and reveals other remarkable mysteries, as will be said, of that almighty union; and it is as follows: The wonderful property of arithmetic progression. If any number of odd numbers are arranged in their natural order starting from unity, the half of the sum of any two numbers equally distant from the center of the progression will equal the middle term of the progression. Let the following arrangement of numbers be given in a numerical series.

In this, the middle term is 5; therefore, if you join any numbers equally distant from five into one, they will produce 10, of which the half is 5. Likewise, 3 and 7: 2 and 8: 1 and 9 joined together will constitute 10, whose half is likewise 5. From this property, therefore, it is clearly perceived how unity is the principle of numbers. Demonstration of the proposed question. Which I demonstrate thus: If unity had anything prior to itself, such as some other number, or any other distinct thing, that would be placed around the unity with 2; wherefore, according to the given proposition, unity would be the half of this aggregate; but unity itself is the half of 2. Therefore, by common intellectual notion, such an aggregate and 2 would be equal, since those things which are equally multiples of one and the same thing must be equal; but such an aggregate and the number two binarius would be equally multiples of unity, namely double, especially since unity makes up the same...