In the play "Romeo and Juliet" by William Shakespeare, the phrase "One pain is lessened by another's anguish" suggests that experiencing suffering can sometimes alleviate one's own emotional distress. The idea is that when we witness others in pain, it can create a sense of shared suffering, which may help to lessen our own burdens. This connection between individuals highlights the human ability to empathize with one another, illustrating how shared experiences can provide comfort during difficult times.

The second part of the quote, "Take thou some new infection to thy eye, and the rank poison of the old will die," implies that introducing new emotions or experiences can help in overcoming past grief. It indicates that by engaging with fresh feelings or insights, one can heal from old wounds, effectively replacing negative emotions with new ones. This notion reflects the complexity of human relationships and the transformative power of love and companionship, especially in the face of loss.