I contend that the second cause of Posterior Analytics II.11 expresses Aristotle's doctrine of material cause as hypothetical necessity in Physics II. Aristotle presents two formulations of the second cause in Posterior Analytics II. 11, which he "clearly" means to be equivalent. These two formulations of the second cause, taken literally without reference to the definition of the syllogism, fit Aristotle's description of a material cause being "hypothetical necessity" in Physics II - that is, a necessary means to produce a goal. In Physics II.9 Aristotle's thesis that an elementary mathematical definition is a "hypothetical necessity" for the proof of a mathematical theorem explains the application of the second cause as middle term in the mathematical syllogism of Posterior Analytics II.11.
Barker, Evelyn, "Second Cause in Posterior Analytics II.11" (1997). The Society for Ancient Greek Philosophy Newsletter. 245.