ABSTRACT

Nicholas of Cusa was an extraordinary philosopher. He invented the principle of the coincidence of opposites according to which, in the domain of infinity, opposites come together. His most important contribution consists in breaking the prevailing Aristotelism with a new kind of logic. He hoped to resolve the problems of infinity with the principle of the coincidence of the opposites. To prove his principle, he bravely decided to experiment with it in a scientific field: mathematics. He thought that there was a continuity between the metaphysical truth and the mathematical truth. He decided to use the principle of the coincidence of the opposites on the problem of the quadrature of the circle. For fourteen years, from 1445 until 1459, he tried to resolve this problem. He vainly sought to ‘transmute’ curved lines into straight ones from some simple propositions that are false or unfounded.