The Theories of Irrational Numbers, Part I:Incommensurables, Convergent, and Earlier Geometrical Theories

The aim of this historical und critical study is somewhat different from that of the other works that are known to us which deal with the development of the theory of convergence and allied topics. We shall, in fact, he concerned primarily with questions of principle; and the numerous and valuable deductions an to the criteria which enable us to decide whether such and such a series or class of series is convergent or not, which belong to technical mathematics, will only be shortly referred to.