In the first case (Mercator), the east-west scale always equals the north-south scale. In the second case (central cylindrical), the north-south scale exceeds the east-west scale everywhere away from the equator. Each remaining case has a pair of secant lines—a pair of identical latitudes of opposite sign (or else the equator) at which the east-west scale matches the north-south-scale.
in The firsT Case (mercator), tHE east-wEsT scale alwayS equals The nOrth-South SCaLe. iN tHe sECond CaSe (CenTRAl cYlINDRIcal), The NORTH-souTh scale excEeds thE eASt-wEsT ScAlE EVeryWHERe awAy froM The Equator. eAch ReMaIning case has A paIR of secant liNeS—a Pair of iDEnticAl latitudeS of opposITe SigN (OR else The EqUator) at whiCH tHE eAsT-west scaLe mAtches ThE norTh-soUth-ScAle.