Does "to be on the rise" have any other meaning besides "to start", "to begin" and "to be getting momentum"?
Does "to be on the rise" have any other meaning besides "to start", "to begin" and "to be getting momentum"?
A different shade of meaning than 'gaining momentum' would be improving, advancing or gaining in some desirable trait. "My fortune is on the rise" -> my situation is improving. "His star was on the rise" -> he was becoming more famous.
I don't associate it with "starting" or "beginning", though.
I never really thought of it as a metaphor for beginning - rather, it is simply a statement that your fortunes (or those of the subject) are improving.