Why do orchestras sit the way they do?

I was reading a book the other day that noted that symphony orchestras almost always are arranged with the violins to the left of the conductor, violas next to them, cello and string bass on the far right. Brass and winds generally sit directly in front of the conductor, and percussion is splayed in the far rear of the orchestra.

I can certainly see why percussion is in the back – they have their big equipment (kettle drum, tympani, bass drum, gong, etc.).

But why violins to the left and cellos to the right? What would be the downside of flutes to the left and violins to the center?