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In a medium bowl, toss the watermelon cubes with 1 tablespoon of the vinegar and season with salt and pepper. Let stand for 5 minutes, then drain.
In a small bowl, whisk the remaining 3 tablespoons of vinegar with the olive oil. In another bowl, gently toss the arugula with 3 tablespoons of the dressing. Fan the tomato slices on 10 plates and sprinkle with salt. Scatter the arugula over the tomatoes and top with the watermelon. Drizzle the remaining dressing over the salads and serve at once.