There are two main areas for musical instruments with sympathetic strings. One i Europe and the other is northern India. This has resulted in that there are four different hypothesises about the origin of sympathetic strings:
The most widespread hypothesis is that sympathetic strings originated in India and was spread to Europe through seafarers. Since the viola d'amore and related instruments first are known during the 17:th century this coincides pretty well with the increased trading with India and far East. England was most successful in the East India business or at least most successful in the colonization of India nad sympathetic strings is mentioned in England very early. Michael Praetorius describes in his book Syntagma musicum II from 1619 an instrument which is called viola bastarda which is supposed to have been found in England. Sympathetic strings are not mentioned in central Europe until the end of the 17:th century but then they seem to have been more popular in Germany, Bohemia and Hungary than in England. An author called Francois-Joseph Fétis claims that there were viola d'amore in Constantinople before it came to central Europe and Fétis thought that it seems that sympathetic strings came to Europe from the Middle East.
Among the indian instruments with sympathetic strings, the Sitar is the most well known. Sympathetic strings was however not used on this instrument until the 19:th century. Such strings was probably used earlier on the Sarangi, some sources from the 17:th century mentions sympathetic strings. This is about the same time as the first evidence of sympathetic strings in Europe which makes it difficult to conclude where it was used first. India was however highly influenced by Persia and many indian instruments are of persian or arabian origin. This means that there are support for Fétis hypothesis of origin in the Middle East. The flame shaped sound holes of the viola d'amore could also be an indication of this since the flame is a symbol of Islam.