[CROSS- 9.] The division of any group according to more than one principle of division at the same time, so that the species cut across one another and produce confusion; an instance of such an intersecting division.
1828. Whately, Rhet., in Encycl. Metrop., 246/1. Arguments are divided according to several different principles . And these cross-divisions have proved a source of endless perplexity to the Logical and Rhetorical student.
1887. Fowler, Deduct. Logic, 60. A division of men into Frenchmen, Asiatics, the unproductive classes, and barbarians, would be a cross-division.