TwoDue distinctrette linesdistinte alwayssi meetincontrano sempre esattamente in exactlyun one pointpunto. Se Ifsono theyparallele, arequesto parallel,punto thatè pointil liespunto at infinityall'infinito. Per To see howvedere thisalgebricamente workscome algebraicallylavora, innello projectivespazio spaceproiettivo, thele linesrette ''x''+2''y''=3 ande ''x''+2''y''=5 aresono representedrappresentate byin thecoordinate homogeneousomogenee equationsdalle equazioni ''x''+2''y''-3''z''=0 ande ''x''+2''y''-5''z''=0. SolvingRisolvendo, wesi getha ''x''= -2''y'' ande ''z''=0, correspondingche tocorrisponde theal pointpunto (-2:1:0) in homogeneouscoordinate coordinatesomogenee. AsPoiché thela coordinata ''z''-coordinateisè 0, thisquesto pointpunto liesgiace onsulla theretta line at infinityall'infinito.
Two circles never intersect in more than two points in the plane, while Bézout's theorem predicts four. The discrepancy comes from the fact that every circle passes through the same two complex points on the line at infinity.
