c.1500, from Latin supinus "turned or thrown backwards, inactive, indolent," related to sub "under" (see sub-). The grammatical use for "Latin verbal noun formed from the past participle stem" is from Late Latin supinum verbum "supine verb," perhaps so called because, though furnished with a noun case ending, it "falls back" on the verb.
supine su·pine (sōō-pīn', sōō'pīn')
Lying on the back; having the face upward.
Having the palm of the hand or sole of the foot upward.