Building a bridge from one side

Your people have been displaced by war, and have wandered for many months looking for a new home. Yesterday, you came across something truly marvelous. You are camped at the edge of a huge ravine, some two miles across and a thousand feet deep. At the bottom of the ravine runs a strait connecting two seas. Suspended magically in the midst of the ravine is a floating island, the top of which is level with the precipice upon which you stand, about a quarter mile away.

Your mission is to build a bridge from your location to that island, using the minimum amount of technology possible. Or in other words... how does one build a bridge when one has access neither to the ground below, nor the opposite side? Is there a way?

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Building a bridge from one side

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