some_o observation_n which_o may_v be_v of_o use_n in_o all_o these_o three_o kind_n of_o sail_v have_v show_v you_o how_o to_o sail_v either_o by_o the_o rumbe_n that_o lead_v from_o one_o place_n to_o another_o or_o else_o by_o a_o arch_n of_o a_o great_a circle_n extend_v between_o two_o place_n i_o shall_v now_o lay_v down_o some_o observation_n which_o may_v be_v useful_a in_o either_o of_o these_o way_n of_o sail_v for_o sometime_o it_o be_v best_o to_o use_v the_o one_o way_n sometime_o the_o other_o in_o some_o voyage_n it_o be_v best_o to_o sail_v by_o the_o rumbe_n in_o some_o voyage_n it_o be_v best_o to_o sail_v by_o the_o arch_n in_o some_o voyage_n it_o be_v the_o best_a way_n to_o use_v both_o and_o to_o keep_v neither_o to_o the_o rumbe_n nor_o to_o the_o arch_n exact_o in_o voyage_n to_o the_o west-indies_n though_o the_o near_a way_n be_v by_o the_o arch_n of_o a_o great_a circle_n and_o though_o the_o way_n by_o the_o direct_a rumbe_n lie_v very_o well_o yet_o it_o be_v usual_a in_o these_o voyage_n to_o steer_v wide_a from_o both_o these_o near_a way_n viz_o first_o to_o steer_v much_o more_o to_o the_o southward_n than_o the_o course_n lie_v until_o they_o come_v into_o the_o latitude_n of_o the_o place_n and_o then_o to_o run_v their_o course_n west_n until_o they_o arrive_v at_o their_o desire_a port_n and_o this_o way_n be_v very_o good_a especial_o when_o you_o sail_v unto_o a_o little_a lone_a island_n wind_n to_o get_v the_o benefit_n of_o the_o wind_n for_o first_o by_o sail_v towards_o the_o line_n you_o shall_v gain_v the_o benefit_n of_o the_o tradewind_n as_o they_o call_v it_o which_o do_v most_o constant_o blow_v between_o the_o north_n and_o east_n between_o and_o near_o the_o tropic_n second_o hereby_o you_o may_v be_v sure_a not_o to_o overshoot_v the_o island_n you_o will_v sail_v to_o to_o to_o avoid_v overshoot_n the_o place_n you_o go_v to_o which_o otherways_o may_v easy_o be_v do_v for_o it_o be_v a_o hard_a matter_n in_o 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inconvenience_n to_o they_o for_o they_o be_v many_o time_n at_o their_o journey_n end_n 150_o or_o 200_o league_n before_o they_o be_v aware_a and_o so_o may_v easy_o overshoot_v their_o port_n and_o lose_v themselves_o but_o that_o they_o sail_v to_o the_o main_a land_n or_o great_a island_n that_o they_o can_v pass_v by_o parallel_n 3_o the_o inconvenience_n of_o sail_v in_o a_o parallel_n now_o as_o for_o these_o cause_v you_o sometime_o stray_v from_o the_o rumb_n or_o arch_n which_o lie_v between_o the_o two_o place_n so_o there_o be_v another_o consideration_n which_o may_v be_v a_o sufficient_a reason_n for_o a_o little_a wander_a sometime_o out_o of_o the_o way_n and_o that_o be_v the_o inconvenience_n that_o there_o be_v in_o sail_v far_o upon_o a_o course_n of_o east_n or_o west_n because_o you_o must_v always_o depend_v upon_o your_o dead_a reckon_n which_o be_v subject_a to_o much_o mistake_n have_v no_o way_n to_o correct_v it_o by_o observation_n this_o parallel_n sail_v make_v the_o journey_n many_o time_n seem_v tedious_a as_o a_o man_n that_o travail_n in_o a_o unknown_a way_n think_v the_o mile_n and_o the_o way_n to_o be_v long_o than_o indeed_o they_o be_v whereas_o he_o that_o know_v the_o road_n and_o how_o far_o it_o be_v from_o place_n to_o place_n go_v on_o more_o cheerful_o therefore_o the_o labour_n will_v not_o be_v lose_v if_o you_o go_v sometime_o a_o little_a out_o of_o your_o way_n for_o this_o consideration_n that_o so_o you_o may_v have_v the_o more_o certainty_n of_o your_o account_n indeed_o the_o way_n of_o sail_v by_o the_o arch_n of_o a_o great_a circle_n do_v very_o much_o help_v in_o this_o partly_o how_o to_o avoid_v sail_v in_o a_o parallel_n partly_o as_o i_o have_v show_v at_o large_a in_o the_o former_a chapter_n but_o yet_o if_o you_o keep_v yourself_o in_o your_o yoyage_n too_o strict_o to_o the_o arch_n you_o must_v run_v much_o of_o your_o way_n in_o a_o parallel_n or_o very_o near_o it_o as_o in_o the_o example_n of_o the_o parallel_a voyage_n in_o the_o last_o chapter_n the_o difference_n of_o longitude_n between_o the_o two_o place_n be_v 70_o degree_n if_o you_o keep_v to_o the_o arch_n you_o must_v first_o sail_n e_o n_o e_o till_o you_o alter_v your_o longitude_n 5_o degree_n then_o half_a a_o point_n more_o easterly_a till_o you_o alter_v your_o longitude_n 10_o degree_n more_o than_o you_o must_v sail_v n_n by_o e_z till_o you_o alter_v your_o longitude_n 10_o degree_n more_o that_o be_v in_o all_o 25_o degree_n but_o afterward_o the_o 7_o degree_n which_o be_v set_v down_o half_a a_o point_n off_o the_o east_n and_o the_o three_o degree_n full_a east_n be_v little_o better_a than_o a_o parallel_n course_n then_o again_o this_o be_v the_o middle_a point_n of_o your_o voyage_n you_o must_v sail_v 10_o degree_n more_o in_o the_o same_o proportional_a course_n so_o that_o of_o the_o 70_o degree_n of_o the_o whole_a voyage_n you_o must_v sail_v 20_o of_o they_o near_o the_o course_n of_o east_n and_o west_n now_o you_o shall_v see_v how_o easy_o this_o may_v be_v avoid_v total_o how_o to_o avoid_v sail_v in_o a_o parallel_n total_o and_o that_o several_a way_n first_o let_v the_o course_n be_v continue_v as_o before_o till_o you_o come_v to_o 25_o degree_n difference_n of_o longitude_n which_o be_v at_o e_o in_o the_o last_o 63._o last_o page_n 63._o chart_n then_o if_o at_o this_o point_n you_o leave_v the_o great_a circle_n a_o little_a and_o keep_v on_o your_o course_n still_o upon_o the_o 7_o rumbe_n n_n by_o e_z till_o you_o come_v to_o 35_o degree_n of_o longitude_n your_o latitude_n will_v be_v 46_o degree_n 36_o minute_n or_o 60_o part_n differ_v from_o the_o latitude_n of_o the_o arch_n 55_o minute_n but_o your_o distance_n for_o these_o 10_o degree_n of_o longitude_n will_v be_v but_o 7_o degree_n 09_o 100_o that_o be_v but_o 7_o 100_o more_o than_o the_o other_o way_n which_o make_v but_o 4_o mile_n which_o make_v 4_o mile_n which_o be_v so_o little_a that_o it_o be_v not_o to_o be_v regard_v in_o respect_n of_o the_o distance_n in_o these_o 10_o degree_n be_v 425_o mile_n again_o if_o you_o begin_v soon_o to_o swerve_v from_o the_o arch_n yet_o the_o difference_n of_o your_o way_n will_v not_o be_v much_o as_o you_o may_v see_v by_o this_o table_n which_o differ_v much_o from_o the_o other_o in_o the_o rumbe_n latitude_n and_o longitude_n but_o yet_o it_o differ_v but_o little_a in_o the_o total_a sum_n of_o the_o distance_n be_v but_o 20_o 100_o which_o be_v but_o 12_o mile_n difference_n of_o longitude_n the_o course_n or_o rumbe_n distance_n or_o way_n sail_v the_o true_a longitude_n the_o
you_o must_v do_v thus_o first_o from_o the_o point_n i_o set_v the_o first_o 40_o double_a league_n upon_o the_o rumbe_n n_o w_n by_o n_n which_o will_v end_v at_o r._n then_o from_o the_o point_n r_o draw_v the_o rumbe_n n_o e_o by_z e_z which_o be_v the_o line_n r_o q_n and_o set_v thereon_o the_o 40_o double_a league_n from_o r_n to_o q_n thus_o you_o will_v find_v q_o to_o be_v the_o place_n you_o shall_v be_v in_o according_a to_o your_o dead_a reckon_n which_o be_v in_o 5_o d._n 5_o 10_o and_o somewhat_o 55._o somewhat_o 5d._o 55._o more_o of_o north_n latitude_n whereas_o by_o your_o observation_n you_o find_v that_o you_o be_v but_o in_o 5_o deg_fw-la of_o north_n latitude_n now_o to_o know_v the_o true_a place_n where_o you_o be_v in_o respect_n of_o the_o longitude_n because_o you_o have_v sail_v upon_o two_o rumbe_n draw_v the_o line_n i_o qui_fw-fr from_o i_o the_o first_o place_n you_o set_v sail_n from_o to_o q_o the_o place_n of_o your_o dead_a reckon_n and_o then_o draw_v the_o line_n f_o e_o g_o at_o 5_o deg_fw-la of_o latitude_n according_a to_o your_o observation_n of_o the_o latitude_n mark_v where_o it_o cross_v this_o line_n i_o qui_fw-fr which_o be_v in_o the_o point_n n_n and_o this_o be_v the_o true_a place_n you_o be_v in_o who_o longitude_n be_v 6_o deg_fw-la and_o who_o latitude_n be_v 5_o deg_fw-la north_n in_o like_a manner_n if_o you_o shall_v sail_v upon_o 3_o or_o 4_o several_a rumbe_n before_o you_o can_v make_v a_o observation_n of_o the_o latitude_n your_o best_a way_n will_v be_v to_o draw_v a_o line_n from_o the_o first_o place_n of_o your_o voyage_n to_o that_o present_a place_n according_a to_o your_o dead_a reckon_n or_o at_o least_o from_o the_o last_o place_n where_o you_o make_v a_o fair_a observation_n and_o be_v thereby_o well_o assure_v both_o of_o the_o longitude_n and_o latitude_n thereof_o for_o otherwise_o you_o may_v be_v much_o mistake_v in_o the_o longitude_n of_o your_o place_n as_o for_o instance_n if_o in_o the_o last_o example_n you_o shall_v think_v you_o be_v in_o that_o place_n where_o the_o line_n of_o latitude_n f_o e_o g_o do_v cut_v the_o last_o rumbe_n you_o sail_v upon_o according_a to_o your_o dead_a reckon_n viz._n the_o line_n r_o q_n by_o this_o account_n you_o will_v be_v but_o in_o o_o which_o be_v but_o in_o 5_o deg_fw-la 35_o 100_o of_o longitude_n whereas_o you_o see_v by_o the_o other_o way_n which_o be_v the_o truth_n you_o be_v in_o 6_o deg_fw-la of_o longitude_n so_o that_o the_o difference_n be_v â—_o 100_o which_o be_v very_o considerable_a in_o so_o small_a a_o space_n proposition_n 7._o be_v to_o sail_v from_o one_o place_n to_o another_o but_o by_o reason_n of_o cross_a wind_n or_o the_o coasting_n of_o the_o land_n you_o can_v sail_v thither_o upon_o the_o direct_a point_n of_o the_o compass_n which_o lie_v between_o the_o two_o place_n but_o be_v force_v to_o alter_v your_o course_n several_a time_n yet_o how_o you_o shall_v keep_v your_o account_n of_o your_o way_n so_o that_o you_o may_v know_v at_o any_o time_n what_o longitude_n and_o latitude_n you_o be_v in_o and_o how_o the_o place_n you_o be_v bind_v to_o bear_n from_o you_o and_o how_o far_o you_o want_v to_o it_o chart._n 7._o the_o manner_n of_o keep_v your_o reckon_n upon_o the_o chart._n former_a this_o proposition_n contain_v the_o use_n and_o practice_v of_o all_o the_o former_a for_o example_n suppose_v you_o be_v to_o sail_v from_o the_o place_n i_o in_o the_o former_a chart_n which_o be_v under_o the_o equinoctial_a and_o in_o 5_o degree_n of_o longitude_n unto_o the_o place_n h_n which_o have_v 5_o deg_fw-la of_o longitude_n and_o 10_o degree_n of_o north_n latitude_n here_o the_o direct_a way_n from_o i_o to_o h_n lie_v full_a north_n but_o suppose_v that_o you_o can_v sail_v upon_o this_o point_n but_o be_v force_v first_o to_o run_v n_z w_o by_z n_z 36_o double_a league_n and_o then_o n_z e_z by_z e_z 36_o double_a league_n more_o the_o question_n be_v what_o be_v the_o longitude_n and_o latitude_n of_o this_o place_n and_o how_o far_o it_o be_v distant_a from_o the_o place_n h_n and_o upon_o what_o point_n of_o the_o compass_n it_o lie_v from_o it_o first_o from_o the_o point_n i_o draw_v the_o rumbe_n n_o w_n by_o n_n and_o set_v off_o thereon_o 36_o double_a league_n from_o i_o to_o m._n then_o from_o this_o point_n m_o draw_v the_o rumbe_n n_o e_o by_z e_z and_o set_v off_o thereon_o the_o 36_o double_a league_n which_o you_o have_v sail_v upon_o it_o from_o m_n to_o n_n thus_o you_o shall_v find_v that_o n_n be_v the_o place_n wherein_o you_o be_v who_o longitude_n be_v fix_v degree_n and_o who_o latitude_n be_v five_o degree_n now_o if_o you_o lay_v a_o ruler_n from_o this_o point_n n_n to_o the_o place_n you_o be_v bind_v to_o which_o be_v h_n and_o draw_v the_o line_n h_o n_n this_o line_n be_v the_o direct_a way_n to_o the_o place_n you_o be_v bind_v and_o by_o the_o help_n your_o circle_n or_o scale_v of_o rumbe_n you_o shall_v find_v that_o it_o lie_v north_n by_o west_n or_o the_o first_o rumbe_n from_o the_o meridian_n westward_o last_o if_o you_o set_v one_o end_n of_o your_o compass_n in_o n_n and_o open_v the_o other_o to_o h_n and_o measure_v that_o distance_n in_o the_o side_n of_o the_o chart_n you_o will_v find_v it_o to_o be_v about_o 5_o degree_n 1_o â—â—_o or_o 51_o double_a league_n and_o so_o much_o you_o want_v to_o the_o end_n of_o your_o voyage_n proposition_n 8._o how_o to_o know_v the_o distance_n of_o any_o cape_n headland_n or_o island_n from_o you_o which_o you_o can_v see_v at_o two_o distant_a place_n you_o 8._o to_o know_v the_o distance_n of_o any_o cape_n from_o you_o suppose_v that_o sail_v on_o the_o sea_n you_o espy_v a_o island_n or_o cape_n lie_v at_o the_o first_o sight_n just_a north-east_n from_o you_o and_o then_o sail_v forward_o upon_o your_o way_n which_o lie_v full_a north_n to_o the_o distance_n of_o 5_o league_n you_o then_o observe_v that_o the_o island_n lie_v full_a east_n from_o you_o the_o question_n be_v to_o know_v the_o distance_n of_o this_o isle_n from_o either_o of_o these_o two_o place_n in_o such_o question_n as_o this_o you_o may_v suppose_v each_o degree_n in_o the_o former_a chart_n to_o stand_v now_o but_o for_o a_o league_n chart_n these_o two_o follow_a proposition_n rather_o belong_v to_o the_o plain_a table_n then_o the_o chart_n and_o let_v the_o first_o place_n where_o you_o espy_v the_o island_n be_v at_o a_o now_o because_o the_o island_n lie_v north-east_n from_o this_o place_n draw_v the_o line_n a_o b_o which_o be_v n_n e_o from_o a._n then_o count_v the_o 5_o league_n which_o you_o have_v sail_v upon_o your_o course_n which_o be_v full_a north_n in_o the_o meridian_n line_n from_o a_o to_o f_o and_o because_o from_o this_o place_n the_o island_n do_v lie_v full_a east_n therefore_o from_o this_o point_n f_o draw_v the_o east_n line_n f_o e_o g_o and_o mark_v where_o this_o line_n do_v cross_v the_o former_a line_n a_o e_o of_o n_o e_o from_o a_o which_o be_v in_o the_o point_n e._n this_o therefore_o must_v needs_o be_v the_o place_n of_o the_o island_n who_o distance_n if_o you_o take_v with_o your_o compass_n and_o measure_n in_o the_o side_n of_o the_o chart_n you_o shall_v find_v that_o the_o place_n e_o be_v distant_a from_o a_o 7_o league_n and_o almost_o 1_o 15_o part_n of_o a_o league_n and_o from_o f_o just_a 5_o league_n proposition_n league_n a_o double_a use_n of_o this_o proposition_n and_o by_o this_o mean_n if_o you_o know_v the_o longitude_n and_o latitude_n of_o this_o isle_n or_o cape_n you_o may_v the_o more_o certain_o know_v the_o truth_n of_o your_o account_n and_o if_o need_v be_v correct_v it_o or_o if_o you_o know_v not_o the_o place_n before_o you_o may_v set_v it_o down_o in_o your_o chart_n by_o its_o longitude_n and_o latitude_n which_o you_o find_v it_o to_o be_v in_o according_a to_o the_o best_a account_n you_o can_v make_v by_o your_o observation_n proposition_n 9_o by_o observe_v upon_o what_o rumbe_n many_o place_n lie_v from_o you_o at_o two_o several_a station_n to_o find_v the_o distance_n of_o those_o place_n and_o their_o true_a posture_n and_o bear_v one_o from_o another_o proposition_n 9_o to_o find_v out_o the_o true_a distance_n and_o bear_v of_o many_o place_n the_o use_n of_o this_o proposition_n as_o in_o the_o former_a proposition_n you_o do_v for_o one_o place_n so_o in_o this_o you_o may_v do_v for_o many_o and_o this_o will_v be_v of_o good_a use_n for_o hereby_o sail_v in_o sight_n of_o any_o coast_n you_o may_v find_v out_o how_o the_o
place_n but_o it_o be_v only_o their_o distance_n in_o the_o rumbe_n so_o that_o if_o the_o two_o place_n be_v not_o both_o under_o the_o equinoctial_a or_o both_o in_o one_o meridian_n than_o there_o be_v somewhat_o a_o near_a cut_n between_o the_o two_o place_n than_o the_o rumbe_n point_v out_o which_o sometime_o especial_o near_o the_o pole_n be_v very_o considerable_a but_o this_o be_v not_o all_o the_o benefit_n which_o come_v by_o this_o way_n of_o sail_v way_n second_o it_o be_v the_o most_o convenient_a way_n but_o many_o time_n when_o your_o course_n lie_v near_o the_o east_n and_o west_n this_o way_n be_v far_o more_o convenient_a for_o if_o you_o shall_v sail_v full_a east_n or_o west_n you_o must_v altogether_o depend_v upon_o your_o dead_a reckon_n have_v no_o way_n to_o help_v yourself_o by_o the_o observation_n of_o the_o latitude_n but_o now_o if_o you_o sail_v by_o the_o arch_n of_o a_o great_a circle_n between_v two_o such_o place_n you_o not_o only_o go_v the_o 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as_o say_v be_v but_o the_o least_o part_n of_o the_o benefit_n that_o come_v by_o this_o way_n of_o sail_v the_o chief_a be_v this_o that_o in_o sail_v between_o two_o such_o place_n by_o the_o arch_n of_o a_o great_a circle_n you_o will_v first_o in_o the_o one_o half_a of_o the_o way_n raise_v the_o pole_n 5_o degree_n 69_o 100_o and_o then_o in_o the_o other_o half_o depress_v the_o pole_n as_o much_o so_o that_o in_o your_o whole_a voyage_n you_o will_v alter_v the_o latitude_n 11_o degree_n 38_o â—0_n &_o so_o by_o the_o observation_n of_o the_o latitude_n you_o may_v rectify_v your_o dead_a reckon_n very_o well_o which_o you_o can_v do_v sail_v in_o the_o parallel_n thus_o you_o see_v this_o way_n of_o sail_v be_v not_o only_o the_o near_a but_o the_o best_a way_n now_o concern_v this_o way_n of_o sail_v there_o have_v be_v but_o little_o write_v by_o any_o subject_n few_o have_v write_v of_o this_o subject_n and_o therefore_o i_o shall_v be_v the_o more_o large_a in_o this_o captain_n saltonstall_n in_o his_o book_n call_v the_o navigator_n have_v say_v somewhat_o how_o to_o direct_v a_o parallel_n course_n but_o for_o any_o other_o course_n he_o have_v say_v nothing_o and_o what_o he_o show_v be_v to_o be_v perform_v by_o arithmetic_n master_n norwood_n in_o his_o book_n of_o trigonometry_n have_v add_v as_o a_o appendix_n many_o problem_n of_o sail_v by_o the_o arch_n of_o a_o great_a circle_n whereby_o those_o who_o both_o can_v and_o will_v take_v the_o pain_n may_v by_o calculation_n find_v out_o all_o thing_n necessary_a in_o this_o way_n of_o sail_v but_o those_o way_n of_o calculation_n as_o they_o be_v very_o difficult_a to_o the_o unlearned_a so_o they_o be_v tedious_a to_o those_o that_o have_v the_o best_a skill_n and_o therefore_o i_o hope_v it_o will_v be_v well_o accept_v if_o i_o here_o show_v you_o how_o the_o same_o may_v be_v perform_v by_o geometry_n both_o plain_o and_o speedy_o and_o yet_o with_o as_o much_o exactness_n as_o need_v be_v require_v know_v the_o chief_a thing_n to_o be_v know_v and_o in_o the_o pursuance_n hereof_o i_o shall_v keep_v as_o close_o to_o master_n norwood_n as_o i_o can_v both_o in_o his_o proposition_n and_o example_n that_o thereby_o you_o may_v see_v how_o near_o my_o plain_a line_n will_v approach_v to_o the_o exactness_n of_o his_o calculation_n now_o if_o you_o observe_v he_o there_o be_v these_o three_o thing_n which_o must_v be_v find_v out_o in_o every_o example_n first_o the_o distance_n of_o the_o two_o place_n in_o the_o arch_n of_o a_o great_a circle_n second_o the_o angle_n of_o position_n from_o the_o one_o place_n to_o the_o other_o three_o to_o find_v out_o what_o longitude_n and_o latitude_n the_o arch_n of_o the_o great_a circle_n do_v pass_v through_o between_o the_o two_o place_n place_n to_o find_v the_o distance_n of_o two_o place_n for_o the_o first_o of_o these_o know_v the_o longitude_n and_o latitude_n of_o two_o place_n to_o find_v their_o distance_n in_o the_o arch_n of_o a_o great_a circle_n which_o be_v always_o the_o near_a distance_n i_o may_v show_v you_o how_o to_o perform_v this_o in_o the_o first_o place_n but_o i_o here_o pass_v it_o by_o for_o these_o reason_n first_o because_o master_n wright_n master_n blundevile_n and_o captain_n saltonstall_n have_v all_o of_o they_o demonstrate_v it_o in_o their_o book_n already_o and_o second_o because_o the_o chief_a benefit_n in_o this_o way_n of_o sail_v do_v not_o so_o much_o consist_v in_o save_v of_o a_o little_a way_n as_o in_o sail_v the_o most_o convenient_a way_n that_o be_v so_o as_o you_o may_v alter_v your_o latitude_n most_o and_o so_o your_o reckon_n may_v be_v the_o more_o certain_a for_o though_o near_o the_o pole_n the_o difference_n of_o the_o distance_n of_o two_o place_n in_o the_o arch_n of_o a_o great_a circle_n and_o in_o their_o rumbe_n may_v be_v considerable_a yet_o in_o most_o voyage_n it_o be_v not_o as_o in_o the_o forename_a example_n of_o two_o place_n in_o the_o parallel_n of_o 40_o degree_n the_o difference_n by_o calculation_n be_v find_v to_o be_v but_o one_o degree_n 54_o 100_o which_o be_v scarce_o considerable_a in_o the_o whole_a voyage_n be_v 52_o degree_n three_o it_o will_v be_v somewhat_o difficult_a &_o it_o require_v great_a curiosity_n in_o draw_v of_o those_o line_n prescribe_v by_o they_o so_o exact_o that_o you_o may_v come_v to_o the_o knowledge_n of_o the_o distance_n any_o thing_n near_o last_o all_o that_o trouble_n be_v needless_a for_o though_o in_o calculation_n this_o distance_n must_v be_v find_v out_o first_o that_o so_o you_o may_v find_v out_o the_o rest_n of_o the_o proposition_n follow_v yet_o in_o this_o way_n i_o be_o about_o to_o show_v that_o which_o follow_v no_o way_n depend_v upon_o the_o true_a knowledge_n of_o this_o distance_n it_o shall_v be_v sufficient_a therefore_o for_o the_o present_a to_o tell_v you_o that_o this_o way_n be_v always_o somewhat_o the_o near_a way_n for_o the_o second_o of_o these_o proposition_n which_o be_v to_o know_v the_o angle_n of_o position_n from_o the_o one_o place_n to_o the_o other_o operation_n the_o angle_n of_o position_n be_v needless_a in_o this_o operation_n though_o this_o must_v be_v find_v out_o in_o calculation_n before_o you_o can_v proceed_v any_o further_a yet_o in_o this_o work_n it_o be_v more_o needless_a than_o the_o former_a proposition_n and_o therefore_o may_v be_v very_o well_o omit_v but_o now_o for_o the_o three_o proposition_n pass_v to_o find_v out_o the_o longitude_n and_o latitude_n by_o which_o the_o great_a circle_n do_v pass_v which_o be_v the_o find_v out_o by_o what_o longitude_n and_o latitude_n the_o great_a circle_n must_v pass_v between_o the_o two_o place_n this_o be_v the_o very_a end_n aim_v at_o in_o all_o the_o work_n may_v be_v thus_o attain_v first_o draw_v the_o follow_a quadrant_n a_o d_o b_o and_o divide_v it_o into_o degree_n then_o consider_v of_o what_o length_n your_o tangent_fw-la line_n must_v be_v and_o according_o set_v off_o your_o radius_fw-la from_o a_o towards_o d_o the_o large_a rest_n large_a you_o may_v make_v your_o tangent_fw-la large_a either_o by_o make_v your_o quadrant_n large_a or_o by_o set_v your_o radius_fw-la further_o from_o the_o centre_n thus_o in_o the_o quadrant_n the_o line_n d_o k_n be_v a_o large_a tangent_fw-la line_n which_o though_o it_o reach_v but_o to_o 45_o degree_n yet_o by_o lengthen_v of_o the_o line_n you_o may_v set_v on_o the_o rest_n the_o better_o but_o in_o this_o quadrant_n the_o radius_fw-la be_v a_o r_n and_o this_o radius_fw-la be_v always_o a_o tangent_fw-la of_o 45_o degree_n then_o from_o the_o point_n r_o draw_v the_o line_n r_o t_o parallel_n to_o the_o side_n of_o the_o
of_o latitude_n and_o the_o degree_n of_o longitude_n true_o you_o shall_v not_o need_v to_o use_v any_o calculation_n though_o you_o be_v well_o skill_v therein_o for_o the_o thing_n hereby_o may_v be_v much_o more_o exact_o know_v than_o the_o course_n of_o a_o ship_n can_v be_v steer_v for_o the_o further_a explain_v of_o this_o take_v another_o example_n parallel_n a_o example_n of_o two_o place_n in_o one_o parallel_n which_o shall_v be_v of_o a_o parallel_a course_n suppose_v two_o place_n to_o be_v situate_a in_o the_o parallel_n of_o 40_o degree_n of_o north_n latitude_n and_o their_o difference_n of_o longitude_n to_o be_v 70_o degree_n the_o one_o be_v in_o 300_o the_o other_o in_o 10_o degree_n of_o longitude_n and_o it_o be_v desire_v to_o know_v what_o longitude_n and_o latitude_n the_o arch_n of_o a_o great_a circle_n be_v draw_v between_o these_o two_o place_n will_v pass_v through_o to_o perform_v this_o first_o in_o the_o line_n a_o b_o mark_v out_o the_o latitude_n 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circle_n in_o such_o a_o example_n as_o this_o yet_o his_o rule_n show_v how_o to_o do_v it_o and_o according_a to_o they_o i_o have_v calculate_v this_o table_n so_o that_o you_o may_v see_v the_o exactness_n of_o this_o way_n by_o its_o agreement_n with_o the_o table_n longitude_n latitude_n deg._n  _fw-fr de._n de._n m._n 100_o part_n 300_o or_o difference_n of_o longit_fw-la 00_o 40_o 00_o these_o minute_n be_v in_o 00_o 305_o 05_o 41_o 34_o 57_o 310_o 10_o 42_o 53_o 88_o 315_o 15_o 43_o 55_o 92_o 320_o 20_o 44_o 42_o 70_o 325_o 25_o 45_o 15_o 25_o 330_o 30_o 45_o 35_o 58_o 335_o 35_o 45_o 41_o 68_o 335_o 35_o 45_o 41_o 68_o 340_o 40_o 45_o 35_o 58_o 345_o 45_o 45_o 15_o 25_o 350_o 50_o 44_o 42_o 70_o 355_o 55_o 43_o 55_o 92_o 360_o 60_o 42_o 53_o 88_o 005_o 65_o 41_o 34_o 57_o 010_o 70_o 40_o 00_o 00_o note_n if_o you_o draw_v line_n by_o every_o degree_n of_o longitude_n in_o the_o blank_a map_n as_o there_o be_v by_o every_o degree_n of_o latitude_n you_o may_v then_o find_v out_o the_o latitude_n of_o the_o great_a circle_n for_o every_o degree_n of_o longitude_n but_o this_o pain_n will_v be_v needless_a yet_o the_o line_n may_v be_v for_o some_o use_n for_o if_o your_o two_o place_n differ_v more_o in_o latitude_n than_o they_o do_v in_o longitude_n than_o it_o will_v be_v your_o better_a way_n to_o set_v down_o by_o what_o longitude_n the_o great_a circle_n do_v pass_v at_o every_o four_o or_o five_o degree_n of_o latitude_n now_o that_o the_o longitude_n and_o latitude_n of_o a_o great_a circle_n thus_o find_v out_o will_v be_v exact_a enough_o for_o the_o seaman_n use_n enough_o the_o longitude_n &_o latitude_n of_o the_o arch_n thus_o find_v out_o will_v be_v exact_a enough_o if_o you_o be_v any_o thing_n careful_a and_o handsome_a in_o draw_v of_o the_o line_n of_o latitude_n and_o longitude_n true_a observe_v what_o mr._n end_n mr._n see_v master_n norwood_n in_o his_o problem_n of_o sal_v by_o a_o great_a circle_n prob._n 9_o latter_a end_n norwood_n say_v to_o this_o purpose_n his_o word_n be_v these_o have_v speak_v before_o the_o calculation_n hereof_o but_o notwithstanding_o all_o that_o have_v hitherto_o be_v say_v it_o may_v seem_v hard_a to_o direct_v a_o ship_n and_o to_o keep_v such_o a_o reckon_n as_o may_v be_v agreeable_a to_o this_o method_n of_o sail_v and_o indeed_o as_o it_o be_v in_o a_o manner_n impossible_a so_o neither_o be_v it_o necessary_a that_o a_o ship_n shall_v always_o persevere_v exact_o in_o the_o arch_n of_o a_o great_a circle_n it_o may_v suffice_v and_o it_o be_v almost_o the_o same_o in_o effect_n if_o a_o ship_n be_v so_o direct_v that_o she_o go_v near_o this_o arch_n which_o how_o to_o do_v he_o show_v in_o the_o next_o problem_n wherein_o i_o shall_v follow_v he_o only_o whereas_o he_o direct_v you_o to_o find_v out_o the_o longitude_n and_o latitude_n of_o the_o arch_n of_o the_o great_a circle_n by_o calculation_n i_o have_v show_v you_o how_o to_o save_v that_o labour_n and_o yet_o 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often_o you_o may_v keep_v as_o near_o to_o the_o arch_n of_o the_o great_a circle_n as_o either_o you_o need_v or_o can_v expect_v to_o do_v now_o because_o mr._n norwood_n have_v sufficient_o explain_v this_o in_o the_o example_n of_o the_o summer-iland_n and_o the_o lizard_n i_o shall_v pass_v by_o that_o example_n only_o set_v it_o down_o upon_o the_o chart_n and_o refer_v you_o to_o his_o direction_n and_o show_v you_o the_o like_a in_o a_o parallel_n course_n suppose_v you_o be_v to_o sail_v from_o the_o coast_n of_o virginia_n to_o the_o coast_n of_o portugal_n between_o two_o place_n lie_v in_o the_o parallel_n of_o 40_o degree_n north_n latitude_n and_o the_o difference_n of_o longitude_n between_o they_o be_v 70_o degree_n the_o first_o place_n be_v in_o respect_v in_o these_o place_n be_v not_o set_v down_o according_a to_o their_o true_a longitude_n it_o be_v only_o the_o difference_n of_o long._n which_o i_o respect_v 300_o degree_n of_o longitude_n and_o the_o second_o place_n in_o 10_o degree_n of_o longitude_n and_o you_o will_v sail_v by_o the_o arch_n of_o a_o great_a circle_n between_o these_o two_o place_n the_o several_a place_n where_o you_o alter_v your_o course_n the_o course_n you_o steer_v the_o do_v or_o way_n sail_v the_o longitude_n the_o latitude_n  _fw-fr  _fw-fr deg._n p._n deg._n m._n deg._n m._n p._n 1_o from_o n_n to_o a_o e_o n_o e_o 4_o 09_o 305_o 0_o 41_o 34_o 57_o 2_o from_o a_o to_o c_o ½_n 7_o 69_o 315_o 0_o 43_o 48_o 80_o 3_o from_o c_o to_o e_z e_z b_o n_z 7_o 26_o 325_o 0_o 45_o 13_o 22_o 4_o from_o e_z to_z f_o ½_n 4_o 93_o 332_o 0_o 45_o 42_o 70_o 5_o from_o f_o to_o g_o east_n 2_o
table_n hereof_o for_o every_o five_o or_o ten_o degree_n for_o at_o 10_o degree_n of_o longitude_n from_o s_n the_o arch_n pass_v through_o 39_o degree_n of_o latitude_n at_o 20_o through_o 43_o ½_n and_o so_o of_o the_o rest_n position_n the_o angle_n of_o position_n second_o if_o you_o will_v know_v the_o angle_n of_o position_n from_o s_n to_o l_o then_z observe_z in_o what_o point_n the_o arch_n s_o l_o k_n do_v cross_v the_o line_n n_o m_o which_o be_v at_o t_o then_o take_v the_o distance_n n_o t_o and_o measure_v it_o in_o the_o semidiameter_n c_o e_z from_z c_z toward_z e_z and_o it_o will_v reach_v almost_o to_o 49_o degree_n which_o show_v the_o angle_n of_o position_n to_o be_v north-easter_o almost_o 49_o degree_n place_n the_o distance_n of_o the_o place_n three_o if_o you_o will_v know_v the_o distance_n of_o the_o two_o place_n you_o must_v with_o your_o compass_n take_v the_o distance_n of_o the_o two_o place_n s_n and_o l_o and_o measure_v it_o in_o that_o meridian_n which_o agree_v with_o the_o angle_n of_o position_n viz._n 49_o degree_n you_o shall_v find_v it_o will_v reach_v from_o a_o to_o five_o now_o if_o you_o reckon_v the_o degree_n of_o the_o parallel_n of_o latitude_n from_o a_o to_o this_o point_n v_n you_o shall_v have_v the_o distance_n which_o be_v 53_o degree_n and_o a_o half_a likewise_o you_o may_v measure_v any_o part_n of_o this_o arch_n s_o l_o in_o this_o meridian_n a_o v._o if_o you_o always_o set_v one_o foot_n in_o s_o and_o open_v the_o other_o to_o the_o point_n require_v and_o then_o set_v one_o foot_n in_o a_o and_o the_o other_o will_v show_v the_o distance_n of_o that_o place_n thus_o the_o distance_n will_v be_v find_v out_o as_o exact_o as_o by_o any_o other_o geometrical_a way_n but_o in_o regard_n of_o the_o smallness_n of_o the_o projection_n you_o may_v mistake_v some_o few_o mile_n or_o league_n but_o if_o you_o be_v to_o sail_v from_o the_o lizard_n to_o the_o summer-island_n arch_n the_o difference_n in_o sail_v forward_o &_o backward_o by_o the_o arch_n than_o you_o must_v first_o set_v down_o the_o latitude_n of_o the_o lizard_n on_o the_o other_o side_n of_o the_o circle_n as_o i_o note_v before_o &_o so_o the_o work_n will_v fall_v out_o much_o as_o it_o do_v before_o for_o the_o longitude_n and_o latitude_n of_o the_o arch_n will_v be_v the_o same_o only_o account_v they_o backward_o the_o distance_n will_v be_v the_o same_o viz._n 53_o degree_n and_o a_o half_a only_o it_o must_v be_v measure_v in_o another_o meridian_n according_a to_o the_o angle_n of_o position_n from_o the_o lizard_n which_o will_v be_v about_o 81_o degree_n so_o that_o in_o effect_n all_o be_v the_o same_o only_o the_o angle_n of_o position_n which_o be_v of_o little_a use_n but_o to_o find_v out_o the_o scale_n of_o the_o distance_n so_o that_o if_o you_o regard_v it_o well_o one_o labour_n will_v serve_v to_o find_v your_o way_n outward_a and_o homeward_n i_o may_v here_o show_v you_o how_o to_o perform_v the_o parallel_n question_n but_o because_o such_o question_n may_v with_o more_o ease_n and_o certainty_n be_v perform_v by_o the_o former_a way_n i_o shall_v not_o spend_v time_n about_o it_o i_o shall_v only_o instance_n in_o two_o sort_n of_o voyage_n which_o can_v be_v perform_v by_o the_o other_o projection_n and_o in_o such_o case_n as_o these_o there_o will_v be_v some_o need_n of_o this_o way_n and_o not_o else_o first_o when_o one_o of_o the_o place_n be_v under_o the_o equinoctial_a and_o the_o other_o towards_o one_o of_o the_o pole_n the_o other_o be_v when_o the_o one_o place_n have_v north_n latitude_n and_o the_o other_o south_n suppose_v you_o be_v to_o sail_v from_o the_o island_n of_o st._n thomas_n situation_n example_n of_o 2_o place_n in_o another_o manner_n of_o situation_n which_o lie_v under_o the_o equinoctial_a and_o have_v about_o 35_o degree_n of_o longitude_n to_o the_o strait_n of_o magellan_n which_o have_v about_o 53_o degree_n of_o south_n latitude_n and_o differ_v in_o longitude_n from_o the_o former_a place_n 9â—_n degree_n to_o the_o westward_o now_o it_o be_v require_v to_o find_v out_o the_o arch_n of_o the_o great_a circle_n between_o these_o two_o place_n and_o the_o longitude_n and_o latitude_n of_o this_o arch_n with_o the_o angle_n of_o position_n and_o the_o distance_n of_o the_o two_o place_n to_o perform_v this_o first_o set_v down_o the_o isle_n of_o st._n thomas_n which_o be_v under_o the_o equinoctial_a at_o the_o one_o end_n of_o the_o equinoctial_a line_n at_o d_o then_o account_v 90_o degree_n of_o longitude_n from_o d_o to_z e_z there_o be_v the_o meridian_n of_o the_o strait_n of_o magellan_n whereupon_o you_o must_v mark_v out_o the_o latitude_n thereof_o which_o be_v 53_o degree_n at_o w_n so_o you_o shall_v have_v these_o three_o point_n d_o w_n c_o by_o which_o you_o may_v find_v the_o centre_n and_o draw_v the_o arch_n d_o w_n c_o now_o this_o part_n of_o the_o circle_n from_o d_o to_z w_o be_v the_o arch_n of_o the_o great_a circle_n which_o lie_v between_o these_o two_o place_n by_o which_o you_o may_v find_v all_o the_o other_o thing_n require_v as_o first_o for_o the_o longitude_n and_o latitude_n of_o this_o arch_n they_o be_v find_v out_o by_o note_v where_o it_o cross_v the_o circle_n of_o longitude_n and_o latitude_n in_o the_o draught_n which_o you_o shall_v find_v for_o every_o ten_o degree_n to_o be_v as_o in_o this_o table_n long_o latitude_n deg_n d._n m._n 10_o 12_o 58_o 20_o 24_o 25_o 30_o 22_o 34_o 40_o 40_o 28_o 50_o 45_o 31_o 60_o 48_o 58_o 70_o 51_o 16_o 80_o 52_o 35_o 90_o 53_o 0_o second_o for_o the_o angle_n of_o rule_n of_o the_o difference_n of_o longitude_n be_v just_a 90_o deg_fw-la the_o angle_n of_o position_n be_v ready_a measure_v in_o the_o semidiameter_n e_o b_o be_v the_o distance_n b_o w_n which_o be_v 37_o degree_n but_o at_o other_o time_n must_v follow_v the_o rule_n position_n between_o the_o two_o place_n this_o be_v show_v by_o the_o arch_n dw_n cross_v the_o semidiameter_n e_o b_o so_fw-mi that_o if_o you_o take_v the_o distance_n b_o w_n and_o measure_v it_o in_o the_o diameter_n c_o d_o it_o will_v reach_v from_o c_o to_o 37_o degree_n which_o be_v the_o angle_n require_v &_o the_o situation_n show_v it_o to_o be_v south_n westerly_a last_o for_o the_o distance_n of_o the_o two_o place_n if_o you_o take_v the_o distance_n d_o w_n and_o measure_n it_o in_o the_o 37_o meridian_n line_n according_a to_o the_o angle_n of_o of_o position_n it_o will_v reach_v from_o a_o to_o the_o equinoctial_a line_n degree_n likewise_o the_o distance_n d_o w_n need_v no_o other_o measure_v but_o must_v needs_o be_v 90_o degree_n which_o show_v the_o distance_n to_o be_v 90_o degree_n the_o last_o example_n shall_v be_v of_o two_o place_n the_o one_o be_v on_o the_o one_o side_n and_o the_o other_o on_o the_o other_o side_n of_o the_o equinoctial_a as_o suppose_v you_o be_v to_o sail_v from_o the_o summer-isle_n to_o the_o cape_n of_o good_a hope_n situation_n example_n of_o place_n in_o another_o situation_n the_o latitude_n of_o the_o summer-isle_n be_v 32_o degree_n 25_o north_n and_o the_o latitude_n of_o the_o cape_n of_o good_a hope_n be_v 35_o degree_n south_n and_o suppose_v the_o difference_n of_o longitude_n between_o these_o two_o place_n to_o be_v 90_o degree_n and_o it_o be_v require_v to_o find_v out_o the_o arch_n of_o the_o great_a circle_n between_o these_o two_o place_n according_a to_o the_o longitude_n and_o latitude_n thereof_o the_o angle_n of_o position_n and_o the_o distance_n of_o the_o two_o place_n to_o perform_v this_o first_o you_o must_v set_v down_o the_o first_o place_n according_a to_o the_o latitude_n thereof_o in_o the_o outmost_a circle_n at_o s_n and_o draw_v the_o diameter_n s_o k_n to_o which_o you_o must_v draw_v the_o line_n n_o m_o squirewise_o at_o right_a angle_n then_o count_v the_o difference_n of_o longitude_n which_o be_v 90_o degree_n from_o c_o the_o meridian_n of_o the_o cape_n of_o good_a hope_n will_v fall_v in_o the_o line_n a_o b_o which_o you_o must_v mark_v out_o according_a to_o its_o latitude_n 35_o degree_n south_n at_o x_o then_o by_o these_o three_o point_n s_n x_o k_o find_v the_o centre_n which_o will_v be_v in_o the_o line_n m_o n_n extend_v and_o so_o draw_v the_o arch_n s_o x_o k._n now_o first_o for_o the_o longitude_n and_o latitude_n of_o this_o arch_n you_o may_v find_v they_o by_o see_v how_o this_o arch_n do_v cross_v the_o circle_n of_o longitude_n and_o latitude_n in_o the_o draught_n which_o for_o every_o ten_o degree_n of_o longitude_n be_v as_o follow_v long._n latitude_n  _fw-fr deg._n deg._n m._n