The chord progression in the passage above is

The passage is written in D major (one sharp in the key signature) with common time. Analysing each vertical sonority from left to right:

Chord 1: The bass note is D, and the upper voices sound F# and A. These are the root, third, and fifth of a D major triad in root position, giving Ia.

Chord 2: The bass note is A, and the upper voices sound C# and E. These are the root, third, and fifth of an A major triad (the dominant of D major) in root position, giving Va.

Chord 3: The notes again form an A major triad in root position with A in the bass, giving another Va.

Chord 4: The passage returns to D in the bass with F# and A above, producing a D major triad in root position, Ia.

The complete chord progression is therefore Ia - Va - Va - Ia, a straightforward tonic-dominant-dominant-tonic pattern that establishes and confirms the key of D major through the strongest harmonic relationship in tonal music.