Ask at the forum if you have an Ancient or Modern Greek query!
P. and V. κατά (acc.).
Throughout: P. and V. διά (gen.), κατά (acc.), ἀνά (acc.) (rare P.).
By side of: P. and V. παρά (acc. or dat. according as motion or rest is expressed).
All along: Ar. and P. διὰ παντός.