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Suppose I wanted to play a double stop on the violin. The double stop played the G string and the A string simultaneously. Is this possible? Can you play a double stop on two non-adjacent strings?

Just to add to the other answers, there's this unusual technique where you loosen the hair of the bow and play with the stick of the bow under the violin, but the hair wrapping over it. This allows you to play three or four strings simultaneously.

To play only two non-adjacent strings, I guess you'd need to somehow mute the string(s) in between. I never played violin so I don't know how feasible that would be.

As Jomiddnz points out, there's pizzicato. You could also bow one string and pluck another at the same time.

But if you want both notes played with the bow, and don't want the bow to catch the strings in between, the only way is by playing on the top and bottom strings with the bow under the strings. Here's an example (OK, the only example I've found): the last few bars of Flausino Vale's variations on Franz Lehár's Paganini. (Note also the combination of an arco note and pizzicato open strings.)

If you don't want to use that extraordinary technique, then, no.

Just to be pedantic, you could pretty easily bow the open G and A strings together by holding the D string depressed just above the bridge.

No. It is physically impossible unless you play it pizzicato.

Absolutely, but it's harder on a modern instrument

As RedLitYogi says, the convex bridge (not the fingerboard!) affects your ability to play more than two adjacent strings. A tight bow means you can only normally hit two notes at once.

Historically this was not the case though. Baroque instruments had a shallower curve to the bridge, and they also used lower tension on the bow. As a result, they were perfectly capable of treble-stopping as an advanced technique.

Its still possible with a modern instrument and bow. You need to apply extreme pressure to the bow though, which makes it impossible for anything other than forte or fortissimo.

More normally, you'd simply pivot over the D string to hit the A in a single move, resulting in an arpeggiated chord. It's worth noting that even on instruments which can play true chords (e.g guitar or piano), arpeggiated chords are often used for expression, so this does not sound in any way unusual.

These techniques all assume playing three notes at once, of course. To avoid playing the "middle" string and only sound the outer two, damp the unwanted string by touching it lightly with the fleshy part of a finger.

You most likely know this, but just in case: the instruments of the string choir (violin, viola, cello, bass violin) all have convex fingerboards. This makes it much easier to bow a single string than it would be if the strings were all on one plane as they are in guitars and lutes, etc. That is why the answer given in 13 seems to be the best. (Paganini must really have been a show-off - this is akin to Hendrix playing behind his back, etc...)

If you used two bows you could achieve the result. It would be rather tricky to hold them both, and only short strokes would be viable without some extremely dexterous right-hand work (or perhaps a bowing action which moves the bow along the strings more than across them - which wouldn't sound great), but would be more versatile than the under-the-strings solution, more musical than the high-pressure solution. A specialised bowing device (perhaps like a couple of EBows) might be an option too, depending on how determined you are.