If a number has any part whatever, then it is measured by a number called by the same name as the part. Let the number A have any part whatever, B , and let C be a number called by the same name as the part B . I say that C measures A . Since B is a part of A called by the same name as C , and the unit D is also a part of C called by the same name as it, therefore the part B of A is the same part of the unit D of the number C . Therefore the unit D measures the number C the same number of times that B measures A .
C measures A .
Therefore, if a number has any part whatever, then it is measured by a number called by the same name as the part. This proposition is used in the proof of the next proposition.