Using an Apple IIe with a 386 monitor

[willson@epsilon.icsl.ucla.edu (Alan Willson)]

I just got a new Sony 17-inch monitor for a 386 pc that I use 
a lot these days, but believe it or not I still have occasion 
to use my old Apple IIe, and I've been wondering if there is 
some "reasonably elegant" way to have it share the same monitor.  
The usual answer I get to this is "no way," but I can't believe 
that.  If I got an Apple RGB card would it be compatible with 
the Sony's RGB input?  Is there some other kind of Apple video 
card that would do the trick?  Is there perhaps some kind of 
conversion box available that could put the Apple's video output 
in a form that is compatible with, say, a VGA signal?  Surely 
I'm not the first person to want to do something like this.  
Any ideas or suggestions would be appreciated.

-A. N. Willson
willson@ee.ucla.edu