Astronomical Images : Expanding circles approaching an infinite circle (straight line)

Nicolaus Cusanus

Astronomical Images

<p style='text-align: justify;'>Nicolaus Cusanus (c. 1401-64) completed his major philosophical treatise, <i>De docta ignorantia</i>, in Basel in 1440. Throughout the text, Cusanus employed mathematical arguments to strengthen metaphysical and theological claims, particularly his well-known doctrine of the <i>coincidentia oppositorum</i>, or 'coincidence of opposites'. According to this doctrine, seemingly opposing forms could be united; the infinitely small could be shown to coincide with the infinitely large. Although the crucial application of this theory was theological, such that the infinite God was shown to be present in all things, Cusanus explicated it in geometrical terms. This image demonstrates, for example, the apparent coincidence of two seemingly disparate geometrical forms: the circle and the straight line. The series of arcs represent a circle of increasing diameter. As the diameter of the circle increases, the arc of the smallest circle gh, becomes increasingly shallow (as represented by arcs ef and cd), eventually approximating the straight line ab. Thus, the circumference of an infinitely large circle is shown to be a straight line. In this way, Cusanus reconciled two apparently opposing geometrical forms, explaining and reinforcing his concept of <i>coincidentia oppositorum</i>. <i>De docta ignorantia</i> was to prove influential to subsequent astronomers, such as Giordano Bruno (1548-1600), who drew on Cusanus' ideas and diagrams to support his own claims for an infinite universe comprised of infinitely many solar systems.</p>