Definition: Equality is the subject in which the concordance of goodness, greatness, etc., finally reposes; hence, equality is considered in opposition to majority and minority.
Clarification: Equality can be either substantial or accidental, as can its opposites that equality equalizes with all its might in existence and action against majority. There is substantial equality among goodness, greatness, etc. as their entities mutually equate in the essence of equality when they enter into substantial being as its constituent parts. And between form and matter, as equality equates active form and passive matter so they can both likewise constitute substantial being from their own substantial entity through the mutual equality of action and passion. There is equality among the elements by reason of their respective properties. Now fire, by its own nature, has fiery activity equal to the activity of the other elements like active water or active air. And there is substantial equality among the individuals of a species by reason of their species, like between one man and another. And man, in the act of procreation, equates man with himself by reason of man, and other species do likewise. And there is also accidental and substantial equality, as in the equalization that fire makes as it equalizes, as much as it can, its heat with the dryness it holds from earth and with the subject it ignites; and there is a similar equalization between sight and its act of seeing that sight equalizes with itself as much as it can, as it equalizes active sight with its intrinsic visible part, and the intrinsic visible part with the remote visible object. The same applies to the active and passive correlatives of intellect, will, etc. Likewise, accidental equality is considered in equalizing accidents. Now fire equalizes its dryness with heat as much as it can, and in air it equalizes its heat with moisture, and likewise with the other elements. And substantial equality is always simply greater than accidental equality.
Distinctions: There are successively greater substantial equalities all the way to the supreme equality in which any majority or minority is totally impossible. Such a being must necessarily exist, lest supreme equality should agree with supreme privation, and lest accidental equality be simply superior to substantial equality, and lest active form and passive matter fail to equate in their mutual equation. And likewise with all other coequal things, lest there be ultimate impossibility and contradiction. Supreme equality has its own essence and nature with essential equality of action and existence, bonifier and bonified, bonifying and bonifiable, and this essence is equally the essence of goodness, greatness, eternity etc. And the things said about goodness also apply to greatness, eternity, etc. And the supreme equality is considered in the equality of its other supreme principles that must be present in the essence of supreme equality and conversely, since they are all one and identical. Therefore, supreme equality exists in the essence of supreme concordance and in the essence of the supreme beginning, middle and end, and consequently in the essence of supreme distinction; and every lesser equality, in whatever lesser principles it may be found where majority descends to minority and minority ascends to majority, is subordinate to the supreme equality which is the effect of its own causal principle of coequation.
And this principle of equality is most necessary in this Art so that with the knowledge of its conditions the artist can coequate species abstracted from the imagination by the intellect and find a way to conclude his investigation by coequating the acts of his powers with their objects and by following the form and example provided in the above conditions of equality, and treating equality sequentially with all the principles of the Art and vice versa, as shown in the third figure.
Nature: The natural fullness of equality stands in the equalizer, equalizable and equalizing giving rise to equalized or coequated being. Without equality there can be no absolute perfection, and consequently all created things in which there is majority and minority are less than perfect.