Beat the egg whites with an electric mixer until stiff. Line a baking sheet with parchment or waxed paper. Put the sugar, corn syrup, and water in a medium-size heavy saucepan over medium-high heat. Stir to dissolve the sugar, bring to a boil and cook until the temperature reaches 260 degrees F on a candy thermometer, or the hard-ball stage, when a bit of the mixture dropped into cold water holds its shape, 10 to 15 minutes. Remove from the heat. Pour in a thin steady stream into the beaten egg whites and beat with an electric mixer on high for about 3 minutes, scraping down the sides of the bowl. Add the vanilla, and continue beating on high just until the candy starts to lose its gloss, 5 to 6 minutes. When the beaters are lifted, the mixture should fall in a ribbon that mounds on itself.