Syllogism, Whole, Part

In the Politics, Aristotle asserts that the Whole is prior to the Part.  Accordingly, an example of a Syllogism that expresses such priority is: some Americans are Texans; some Texans are Houstonians;  therefore, some Americans are Houstonians.  However, no such pattern is considered in the Prior Analytics.  Instead, a pattern that he does recognize, and that is apparently equivalent, is, for example: all Houstonians are Texans; all Texans are Americans; therefore, all Houstonians are Americans.  But, in this pattern, the Part is prior to the Whole, in which case, the two patterns are not equivalent, and, of greater significance, his Logic contradicts his Political Philosophy.