In addition to what Mildred said about the primary connection(s), here‘s another: Euler also knew (and argued with) Voltaire during Voltaire‘s time in Prussia; Voltaire was yet another person writing a poem about Algarotti having sex (in a private letter to Friedrich). Voltaire himself probably did not have sex with Algarotti, but Algarotti stayed with him and Émilie du Chatelet several times.