The original text with detailed mathematical and historical comments by Eberhard Knobloch and an updated translation by Otto Hamborg "De quadratura arithmetica circuli" (1676) by Gottfried Wilhelm Leibniz is one of the most significant works in analysis. This milestone in the history of mathematics and science addresses the arithmetic quadrature of the circle, that is, the calculation of the area of a circle using a convergent, infinite series of rational numbers, cycloids, paraboloids, hyperboloids, logarithmic functions, and more. The work laid the foundations particularly for differential and integral calculus as we still learn and use it today. Citing Archimedean rigor, it teaches how to deal with the infinite in mathematics through the well-defined concepts of "infinitesimal" and "infinite" based on curve theory.