What is the meaning of "on" in the following sentence,
Einstein arrived one day at Brussels on a visit to the Belgian Queen.
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Does it mean "Einstein arrived one day at Brussels for the purpose of a visit to the Belgian Queen" ?
Does "on" in the sentence mean "for the purpose of" ?
If so, Can we replace "He went to Italy for the purpose of studying music" with "He went to Italy on studying music" ?
Can we replace "I came to Paris with the view of studying painting" with "I came to Paris on studying painting" ?
If so, What is the difference in the nuance of the meaning between "on" and "for the purpose of" ?