What a wonderful diagram - thank you! But, I always thought that Darcy was not actually asking Elizabeth to dance a reel - He was trying to engage in some witty banter (and actually ended up being more sarcastic than witty). I think this was his follow-up to the get-together at the Lucases - Lizzy didn't want to dance then when an impromptu gathering formed, and he suspected that she wouldn't want to dance now. I think he was just trying to make some conversation and see how she reacted - I don't think he had any desire to dance (he admitted at the Lucases that dancing "is a compliment which I never pay to any place if I can avoid it.") and felt safe that Lizzy wouldn't say yes under the circumstances. If he really wanted to dance with her, I think he would asked more straightforwardly and formally, as he did at the Lucases and the Netherfield Ball - The way he phrased his request here seems like his attempt at a little joke and/or to goad a reaction from Lizzy.