Nicholas of Cusa, answered from the texts and cited to the page.
The coincidentia oppositorum is the doctrine that the absolute Maximum coincides with the absolute Minimum, that the center coincides with the circumference, that God is "beyond all affirmation and all negation" (DI I.4).1 It is not the violation of the principle of non-contradiction that Wenck charged in De Ignota Litteratura and that I answered in the Apologia Doctae Ignorantiae.
It is not paradox-for-paradox's-sake in the way some readers of the apophatic tradition have presented it. It is not, finally, the dialectical synthesis-aufhebung that Hegel saw in it. The doctrine is a higher-order claim about the structure of the absolute and the limits of finite reasoning. Ratio — discursive reason — operates under the principle of non-contradiction, and rightly so; that is its proper domain. Intellectus — the higher faculty that grasps the coincidence — sees that the principle of non-contradiction is the law of the finite and does not bind the infinite Maximum that is "beyond all contraction." The center coincides with the circumference because at the level of the absolute, the distinction between center and circumference (which is itself a perspective-bound spatial relation) does not hold.23
The Maximum coincides with the Minimum because at the level of the absolute, the distinction between greater and lesser (which is itself a relation of comparative magnitude) does not hold.4 The doctrine does not violate non-contradiction; it locates non-contradiction at its proper level and recognizes that the absolute, by definition, is not at that level.
Therefore, De Docta Ignorantia I, 4 we see incomprehensibly, beyond all rational inference, that Absolute Maximality (to which nothing is opposed and with which the Minimum coincides) is infinite.De Docta Ignorantia I, p. 10
But when he wonders about how it is that (in the case of things which have limits to their magnitude) if a similarity is posited, then a greater similarity can always be posited ad infinitum: let him consider the dividing of a finite line. For in this case we do not come to an indivisible point, even though we seem to approach it through [dividing] the parts of parts.Apologia Doctae Ignorantiae, pp. 479–480
Teacher had in this way made these statements, whose substance I believe you have heard from him at different times, I said: "Our opponent does not seem to have understood what you meant by 'coincidence of contradictories.' For, as you heard, he ascribes to you (howbeit, falsely) the statement that the creature coincides with the Creator; and he attacks this claim." To these [words] the Teacher [replied]: "I said…Apologia Doctae Ignorantiae, p. 470
Since the unqualifiedly and absolutely Maximum (than which there cannot be a greater) is greater than we can comprehend (because it is Infinite Truth), we attain unto it in no other way than incomprehensibly. For since it is not of the nature of those things which can be comparatively greater and lesser, it is beyond all that we can conceive.De Docta Ignorantia I, p. 9
The coincidence of opposites is the doctrinal feature that generated the contemporary attack from Wenck and the formal defense in the Apologia Doctae Ignorantiae. Wenck's charge — that the doctrine violates the principle of non-contradiction and amounts to pantheism — has been answered many times by modern scholars but has also been revived in various forms. Hegel saw in the doctrine a precursor of his own dialectical logic, with mixed accuracy. Bruno appropriated the doctrine and pushed it in directions Cusa would not have followed. The modern scholarly consensus, articulated by Beierwaltes, Hopkins, Harries, Casarella, and Hudson, defends the doctrine as a coherent higher-order claim that respects non-contradiction at the level of ratio while transcending it at the level of intellectus contemplating the Maximum. The pantheism charge has been thoroughly rebutted: the absolute Maximum is not the cosmos but the Creator, and the contractio relation between Maximum and contracted maximum (cosmos) preserves the Creator/ creature distinction.