A.T. Robertson Commentary Acts 8:26

"But an angel of the Lord spake unto Philip, saying, Arise, and go toward the south unto the way that goeth down from Jerusalem unto Gaza: the same is desert." — Acts 8:26 (ASV)

Toward the South (κατα μεσημβριαν). Old word from μεσος and ημερα, midday or noon as in Ac 22:16, the only other example in the N.T. That may be the idea here also, though "towards the South" gets support from the use of κατα λιβα in Ac 27:12.

The same is desert (αυτη εστιν ερημος). Probably a parenthetical remark by Luke to give an idea of the way. One of the ways actually goes through a desert. Gaza itself was a strong city that resisted Alexander the Great five months. It was destroyed by the Romans after war broke out with the Jews.