We didn't permit -------（take）books out of the library.

Taking 因为 从用法上看.permit后接动词作宾语时,要用动名词形式,而不能用不定式.如：We don’t allow [permit] swimming in the pool.我们不许在池子里游泳.但是若其后接有名词或代词,那么其后须接不定式.
再问： 嗯嗯谢谢