Add punctuation: Having set up this model Ptolemy then goes on to describe the mathematics which he needs in the rest of the work
A: Having set up this model, Ptolemy then goes on to describe the mathematics which he needs in the rest of the work.

Add punctuation: Current trend colors are the most popular Black is all the rage at the moment reports Martin L Petersen White is the second most popular color in Denmark while basalt gray is often requested by our German customers
A: Current trend colors are the most popular. "Black is all the rage at the moment," reports Martin L. Petersen. "White is the second most popular color in Denmark, while basalt gray is often requested by our German customers."

Add punctuation: translator Ukrainian Slovenian
A:
translator - Ukrainian - Slovenian