1. Climbing up the tree, the
little boy tore his trousers.
P1 обстоятельство времени
2. Being unable to sleep, she took a couple of sleeping pills.
P1 обстоятельство
причины
3. The programme finished, they went to bed
P2 обстоятельство времени
4. Jack almost dropped the bag on which he had been writing.
NOT POSSIBLE
5. Excited by his words, Eliza
moved along the street
P2 обстоятельство причины
6. Taking off his old shirt, he
put on a new one.
Having taken off his old shirt,
he put on a new one.
P1 обстоятельство времени; 2 правильных варианта