The first textbook {written for teaching English as a foreign language} came out in the 16th century.
先分析这个句子的结构,The first textbook came out in the 16th century.主谓都有,句子结构完整,written for teaching English as a foreign language在这里相当于定语从句which was written,解释textbook,咱再看为什么要用written.这种结构叫分词做状语,一共有三种形式1,to do 2,being 3done 简单概括的说to do表示将要发生的事,用在这里表示将被谢的书,being表示正在进行的事,done表示完成和被动,在这里表示书已经被写.