  Descartes' activities during the early 1620s are not well-documented. He was in France part of the time, visiting Poitou to sell some inherited properties in 1622 and visiting Paris. He went to Italy (1623–25). Upon his return he lived in Paris,  where he was in touch with mathematicians and natural philosophers in the circle of his long-time friend and correspondent  Marin Mersenne (1588–1648). While in Paris, he worked on some mathematical problems and derived the sine law of refraction, which facilitated his work on formulating mathematically the shapes of lenses (later published in the Dioptrics). His major philosophical effort during these years was on the Rules,  a work to convey his new method.