Why use 非 and 亚 for continent names? Why was 非 chosen for 非洲 (Africa) and 亚 chosen for 亚洲 (Asia)?

I can't find a particular reason to use these characters.
亚洲 is short for 亚细亚洲 while 非洲 is short for 阿非利加洲.

See the article "各大洲名称由来".