The penis, a “ridiculous petitioner,” as the novelist William Gass has called it, “unreliable, though everything depends on it, easily teased, insulted, betrayed, abandoned, yet pretending to be invulnerable, a weapon which confers magical powers upon its possessor.”

In ancient Greece, Sophocles believed that to possess a penis is to be “chained to a madman.”

Why is that? Five hundred years ago, Leonardo da Vinci, the outstanding genius of the Renaissance, explain...