1、Such an able man to help you，you will surely succeed sooner or later.
有这么能干的人来帮你, 你迟早一定会成功的。（such an able man和 to help you 之间存在着主谓关系）= Since such an able man will help you, you will surely succeed sooner or later.
2、He seating himself at the desk, his mother began to tell him a story. 他在书桌旁坐好后，他母亲开始给他讲故事。（seating himself at the desk拥有了自己的逻辑主语he，注意是“主格”）
= When he seated himself at the desk, his mother began to tell him a story.
3、The key to the bike lost, he had to walk to school. 由于丢了自行车钥匙，他只好步行去学校。（lost 的逻辑主语是the key，lost 也可以用完成式having been lost）= Because the key to the bike had been lost, he had to walk to school.
1、His mother to come tonight，he is busy preparing the dinner. 他母亲今晚要来,他正在忙着准备饭菜。（= As his mother is to come tonight, he is busy preparing the dinner.）
2、——will you go to the comcert tonight 你今晚去听音乐会吗？
——sorry.So many exerise-books to check,I rially can't afford any time. 对不起，有这多的作业要批，我真的抽不出时间。（＝Because I shall check so many exercise-books tonight,I really can't afford any time.）
3、The four of us agreed on a division of labour,each to translate a quarter of the book.
我们四人同意分工干，每人翻译全书的四分之一。 （＝The four of us agreed on a division of labour and each is to translate a quarter of the book.）
4、Many trees,flowers,and grass to be planted,our newly-built school will look even more beautiful. 种上许多的树，花和草后，我们新建的学校将看上去更美。(=If many trees,flowers,and grass are planted,our newly-built school will look even more beautiful.)
1、Being ill, he went home.由于生病,他回家了。（= As he was very ill, he went home.）
2、Seating himself at the desk, he began to read a magazine. 在课桌旁坐好后，他开始看杂志。（= When he had seated himself at the desk, he began to read a magazine.）