Answer: Root progression by ascending fourth (or, same thing, descending fifth) is the strongest there is - basically you're taking the dominant-tonic relationship and applying a similar relationship to other chord pairs.

The chords starting halfway through measure 3 are mostly examples of root progression by ascending fourth and end on a resolution to C minor.

I think what you might have heard was someone referring to this as "extending the tonic-dominant relationship." It's a common device in baroque music and somehow very pleasing.

In the illustration I've used the modern key signature for C minor, 3 flats. In old scores for Corelli you'll see the key presented baroque-style with one less flat - leaving out the flatted sixth degree, as if in Dorian.

Let's let people hear it: