No, you set the book down or lay the book down, but you don't "sat the book down"
She sat quietly in the library, reading her book.
Mark and I sat down for a meeting. "I" always goes last.
In the sentence, You sat down: You is the pronoun subject sat is the verb down is the adverb.
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The past tense of "sit down" is "sat down."
In Irish it's "Shuigh Anna síos ar an mbord"
The correct way to say that is, he sat beside her.
A spider sat down beside Miss Muffet.
"I sat" becomes "I sit".
No. Sat is a verb, as in, "I was tired, so I sat down."
The past tense of "sit" is "sat." For example, "Yesterday, I sat in the park to read a book."
SAT preperation is very important. Although a book is not always required it is in your best interest to get one.