The supplies; crappy paintbrush, Elmer's glue thinned with water, wide rubber bands.
Painting glue/water mixture along glue side of spine. Wipe off any extra that has gotten onto opposing page edge.
Banding at regular intervals to "clamp" glue. Be careful not to make the bands too tight to prevent bending the cover edge and/or inside pages.
Leave overnight, fingers crossed.
Come back tomorrow for the (hopefully) exciting results!
UPDATE: Well I am very pleased to say that this method has worked rather well, and I will be trying it on other broken paperbacks. The glue seems to be flexible, but strong, and it did not discolor any pages. The next test is to see how well it holds up through a reading. Two thumbs up!