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hello everybody welcome to the first episode on my series of projective geometry today were going to be talking about cross ratios now before we talk about cross ratios we need to talk about a convention which is that of a signed ratio so a signed ratio is something of the form X a over X B so X a and B are points on a line and we sign this based off of a convention where X is placed relative to a and B so lets say you know you have a and B or points here so this is a this is B and this is a line so this extends out if X is here or here so if X is outside of this segment then this just this ratio is defined to be positive so its positive out here and it would be positive out here but inside if X were inside the segment a B then it would be negative in other words its basically saying you know X a youre defining the distance in that direction but X a here would be defining that the distance in that direction so the order of points matters and since these are two opposite directions