. ▁ ▁In ▁ 1 5 6 9 , ▁Ger ard us ▁Mer c ator ▁published ▁for ▁the ▁first ▁time ▁a ▁world ▁map ▁in ▁such ▁a ▁cart ographic ▁projection ▁that ▁constant - rh umb ▁traject ories ▁were ▁pl otted ▁as ▁straight ▁lines . ▁This ▁Mer c ator ▁projection ▁would ▁be ▁widely ▁used ▁for ▁na ut ical ▁charts ▁from ▁the ▁ 1 8 th ▁century ▁on ward . ▁ ▁In ▁ 1 5 9 4 , ▁John ▁Davis ▁published ▁an ▁ 8 0 - page ▁pam ph let ▁called ▁The ▁Se aman ' s ▁Sec rets ▁which , ▁among ▁other ▁things ▁describes ▁great ▁circle ▁sail ing . ▁ ▁It ' s ▁said ▁that ▁the ▁expl orer ▁Sebastian ▁Cab ot ▁had ▁used ▁great ▁circle ▁methods ▁in ▁a ▁crossing ▁of ▁the ▁North ▁Atlantic ▁in ▁ 1 4 9 5 . ▁ ▁Davis ▁also ▁gave ▁the ▁world ▁a ▁version ▁of ▁the ▁back st aff , ▁the ▁Davis ▁quadr ant , ▁which ▁became ▁one ▁of ▁the ▁dominant ▁instruments ▁from ▁the ▁ 1 7 th ▁century ▁until ▁the ▁ad option ▁of ▁the ▁se xt ant ▁in ▁the ▁ 1 9 th ▁century . ▁ ▁In ▁ 1 5 9 9 , ▁Edward ▁Wright ▁published ▁Cert aine ▁Error s ▁in ▁Navigation , ▁which ▁for ▁the ▁first ▁time ▁explained ▁the ▁mathematical ▁basis ▁of ▁the ▁Mer c ator ▁projection , ▁with ▁calculated ▁mathematical ▁tables ▁which ▁made ▁it ▁possible ▁to ▁use ▁in ▁practice . ▁ ▁The ▁book ▁made ▁clear ▁why ▁only ▁with ▁this ▁projection ▁would ▁a ▁constant ▁bearing ▁correspond ▁to ▁a ▁straight ▁line