The Broad Sword can be picked up from the weapon stand on the right side of the Sarcophagus in the Mansion's Study. It's the first melee weapon which Adam finds and has probably been in extensive use by Florentine and his Templar associates, considering its rusty state.
Adam: I've heard mention and seen various swords around this place. Aelf mentions a sword, too. Rebecca: A sword is mentioned in Florentine's journal which was originally in the Chamber of the Soulstone. Florentine appears to suggest that by removing it, he set into motion a series of unstoppable events. He continues to say that the sword is somehow connected to the Soulstone. Later, he is unable to hold the blade as it burns his hand. Adam: The sword of the Dragon is held aloft as a beacon - to light the way to and within the Tower. The sword.