A book about translation studies gives an example on how the nuance of the phrase at seeing will be lost if it is simply understood as when seeing. The sentence context is taken from The Way of the White Clouds) of Govinda, describing a monk walking on a city once containing pagodas:
But one day a lonely pilgrim, whose heart burned with the pure flame of faith, so deeply grieved at seeing the desecration and decay of this place.
What is the nuanced difference between at seeing makes and when seeing? Generally, what is this kind of grammar called, and can it be applied with other verbs (at listening, at feeling), tenses (at seen), and propositions (on seeing)?
Edit from the person who set the bounty:
I have it from OP that what was the most helpful about the accepted answer was (to make a long story short):
'When seeing' means at the moment of, or on the occasion of seeing, while 'at seeing' means because of the effect on the viewer of seeing.
If we feel sad 'when seeing' (at the time of seeing) the decline of a great sportsperson, as for instance when a great player misses an easy penalty kick, it could be argued that maybe that feeling is specific to the moment/occasion of seeing, and does not persist after the event.
They felt a strong but fleeting sense of sadness when seeing the decline of the great footballer: missing that penalty kick was an awful reminder that he had lost his cutting edge, and was on the long, slow road to sporting oblivion.
Whereas 'at seeing' implies that the feeling is caused by what is seen (here, the decline of the great sportsperson):
He felt sad at seeing the decline of the great footballer: he was reminded of it often in the next few months -- years later he would come upon some reference and relive that sadness, thinking of how that missed penalty had heralded a giant's long, slow descent into sporting oblivion.
With 'at', we feel the emotion because of the decline, not just when we see it -- meaning that we could feel the same even on other occasions when we think of it -- that's the nuanced difference.