In Jan van Yzeren's simple proof of Pascal's Hexagon Theorem the notation AB // CD is used, where AB and CD are lines. It doesn't mean parallel because on the first page, WX || YZ is used to show two lines are parallel. In the references in this proof, the first reference listed uses the // notation to show separation, but I'm having trouble understanding how several of these lines could be said to separate one another if that's what's meant. For example, the first instance of the notation says A1A0 // P1R // ST but a circle through P1 and R wouldn't intersect the outer circle seen below.
Thank you for any insight.
I'm certain that the expression "$A_1A_0/\,/P_1R/\,/ST$" means "$A_1A_0, P_1R\ $ and $\ ST\ $ are parallel." This follows from fact, noted in the preceding sentence, that $\ A_2T,A_2R\ $ and $\ A_2Q\ $ lie in the same proportion as $\ A_2S,A_2P_1\ $ and $\ A_2A_1\ $.