Saunière's message written on the Mona Lisa confirms his membership in the Priory brotherhood, because it quotes one of the Priory's most fundamental philosophies: "So dark the con of man."
Langdon explains to Sophie that this phrase refers to their commonly held belief that Constantine and his male successors successfully converted the world from matriarchal paganism to patriarchal Christianity by using propaganda that demonized the sacred feminine.
Sophie thinks her grandfather probably meant it as another clue.
Langdon goes off on (another) reverie about Malleus Maleficarum and how the Catholic Inquisition worked to dispose the culture of "free-thinking" women (a.k.a.: witches).
Apparently it worked really well, because the world went from revering women for their sacred powers to shunning them as devil's accomplices.
The Priory of Sion believed that this obliteration of the sacred feminine led to a "life out of balance", resulting in war, misogyny, and disrespect for Mother Earth (sound familiar?).
Langdon is called back to attention when Sophie flees as the security guard approaches, catches him, and orders him to lie facedown on the ground.