 The mathematical character of Kilvington’s theory can be seen in his use of two kinds of limit for continuous sequences: an intrinsic boundary (when an element is a member of the sequence of the elements it bounds: maximum quod sic, minimum quod sic) and an extrinsic boundary (when an element which serves as a boundary stands outside the range of elements which it bounds: maximum quod non, minimum quod non). Although he did not formulate strict rules about the different types of division of continua, his study cases reveal that he approved the following conditions for the existence of limits: