SHA1 multipart calculation Is it possible to combine SHA1 digest values to get the SHA1 of the concatenated parts ? 
I know the "S1" SHA1 of "part 1" and the "S2" SHA1 of the "part 2" and I would like to know the SHA1 of the "part 1" concatenated with "part 2" calculated from "S1" and "S2". 

Is it possible ?
No.

Something similar which might be confused:

If $M$ is an unknown message and you know $h = \operatorname{hash}(M)$ and $l = \operatorname{length}(M)$, then for many hash functions it is possible to calculate the hash $h'$ a message $M' = M\ ||\ P\ ||\ X$, with $P$ only depending on $l$ (and the hash function) and $X$ arbitrary chosen by me (or by someone else).

It is still necessary to know $X$ to do the attack, mere knowledge of $\operatorname{hash}(X)$ doesn't help.

This attack (length extension) applies to many older hash functions, including MD5, SHA-1, and all hashes of the SHA-2 family. It doesn't apply to any of the SHA-3 candidates (because resistance against this was a criterion).