Counties lying adjacent to any river on the border or forming the boundary between this state and another shall have the same power, acting by and through the proper county authorities, to build and maintain bridges over such river as the counties now have to build and maintain bridges over streams lying wholly within their borders, provided that this power shall not be exercised except to cooperate with the proper authorities of the adjacent state in building and maintaining such bridges, on the principle that each state is to build simultaneously from its own bank to the middle of the river and afterwards to maintain and keep up the part of the bridge which it has built; and provided, further, that no bridge shall be erected under this Code section at any point where the river exceeds, at low-water mark, 2,000 feet in breadth.