parallel_n 60_o deg_fw-la 0_o min._n again_o let_v 10800_o segment_n be_v produce_v in_o the_o same_o parallel_n of_o 60_o deg_fw-la 0_o min._n of_o 0_o deg_fw-la 1_o min._n one_o minute_n apiece_o due_a east_n or_o west_n and_o work_v according_a to_o the_o former_a manner_n the_o last_o segment_n will_v end_v in_o 59_o deg_fw-la 57_o min._n ½_n which_o dilate_v from_o parallel_n 60_o deg_fw-la 0_o min._n but_o 2½_n minute_n wherefore_o the_o consideration_n hereof_o may_v serve_v for_o a_o sufficient_a satisfaction_n plain_o to_o prove_v that_o the_o east_n and_o west_n direct_v by_o the_o magnetical_a needle_n or_o compass_n do_v lead_v in_o a_o magnetical_a parallel_n for_o as_o great_a segment_n have_v their_o great_a variety_n and_o lesser_a segment_n have_v their_o lesser_a alteration_n correspondent_a unto_o they_o so_o by_o the_o same_o reason_n insensible_a segment_n must_v have_v insensible_a difference_n and_o the_o like_a reason_n hold_v for_o any_o other_o point_n of_o the_o compass_n as_o well_o as_o for_o the_o east_n or_o west_n as_o i_o have_v former_o show_v you_o and_o at_o our_o next_o meeting_n i_o will_v set_v you_o down_o or_o show_v you_o the_o theorem_n for_o operate_a of_o it_o but_o you_o will_v say_v here_o be_v in_o 10800_o minute_n a_o difference_n of_o 2½_n minute_n and_o segment_n of_o minute_n in_o a_o man_n judgement_n be_v so_o small_a that_o a_o ship_n can_v make_v her_o way_n in_o lesser_a segment_n and_o yet_o these_o segment_n be_v not_o void_a of_o a_o sensible_a difference_n i_o answer_v as_o before_o that_o neither_o in_o sail_v east_n or_o west_n nor_o in_o the_o spirall_n or_o melisphericall_a way_n by_o any_o other_o course_n or_o point_n of_o the_o compass_n a_o ship_n continuance_n under_o a_o great_a circle_n or_o circle_n can_v be_v terminate_v and_o whereas_o 10800_o minute_n do_v in_o the_o east_n or_o west_n from_o latitude_n 60_o deg_fw-la 0_o min._n produce_v a_o difference_n of_o 2½_n minute_n i_o say_v inrespect_n of_o â—0_n great_a a_o distance_n the_o difference_n be_v insousible_a but_o if_o you_o please_v to_o take_v so_o much_o pain_n for_o the_o former_a parallel_n of_o 60_o deg_fw-la 0_o min._n to_o make_v a_o trial_n from_o second_o to_o second_o that_o be_v 〈◊〉_d 648000_o segment_n be_v produce_v east_n or_o west_n each_o segment_n to_o contain_v one_o second_o and_o the_o end_n of_o the_o last_o segment_n shall_v not_o be_v from_o the_o first_o place_n so_o much_o as_o one_o second_o and_o thus_o have_v prove_v sufficient_o that_o the_o east_n and_o west_n be_v direct_v by_o the_o magnetical_a needle_n or_o compass_n do_v lead_v in_o a_o magnetical_a parallel_n and_o also_o that_o in_o keep_v one_o course_n the_o ship_n way_n be_v spirall_n or_o helisphericall_a and_o return_v by_o the_o opposite_a point_n thereof_o the_o ship_n shall_v again_o fall_v with_o the_o place_n of_o her_o departure_n we_o will_v finish_v this_o discourse_n and_o speak_v of_o some_o principal_a 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the_o course_n we_o may_v â—nde_v the_o difference_n of_o longitude_n and_o the_o distance_n nau._n we_o will_v sir_n suppose_v a_o ship_n to_o be_v in_o latitude_n 50_o deg_fw-la 0_o min._n north_n latitude_n sail_v south_n south-west_n ½_n point_n west_n until_o she_o be_v in_o the_o latitude_n of_o 47_o deg_fw-la 0_o min._n i_o demand_v the_o difference_n of_o longitude_n and_o the_o distance_n the_o ship_n have_v run_v the_o theorem_fw-la as_o a_o mean_a proportional_a between_o the_o fine_n of_o the_o compliment_n of_o both_o latitude_n be_v to_o the_o tangent_fw-la of_o the_o course_n so_o be_v the_o difference_n of_o latitude_n to_o the_o difference_n of_o longitude_n which_o by_o the_o logarithme_n be_v thus_o add_v the_o logarithme_n tangent_fw-la of_o the_o course_n 28_o deg_fw-la 7_o min._n to_o 〈◊〉_d logarithme_n of_o the_o difference_n of_o latitude_n 60_o league_n and_o from_o that_o sum_n subtract_v half_o the_o sine_fw-la compliment_n of_o 50_o deg_fw-la 0_o min._n 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caâ—â—_n up_o their_o traverse_n by_o difference_n of_o latitude_n and_o departure_n from_o the_o meridian_n do_v find_v their_o difference_n of_o longitude_n as_o well_o as_o their_o course_n and_o their_o distance_n from_o their_o first_o place_n where_o they_o begin_v their_o traverse_n this_o way_n geo._n i_o pray_v you_o sir_n set_v i_o down_o the_o theorem_n for_o the_o operate_n of_o this_o nau._n i_o will_v sir_n which_o be_v these_o follow_v 1_o as_o the_o sum_n of_o half_a the_o logarithme_n sin_n of_o the_o compliment_n of_o both_o latitude_n be_v to_o the_o departure_n from_o the_o meridian_n so_o be_v the_o radius_fw-la to_o the_o difference_n of_o longitude_n 2_o as_o the_o difference_n of_o latitude_n be_v to_o the_o departure_n from_o the_o meridian_n so_o be_v the_o radius_fw-la to_o the_o tangent_fw-la of_o the_o course_n 3_o as_o the_o sine_fw-la of_o the_o compliment_n of_o the_o course_n be_v to_o the_o radius_fw-la so_o be_v the_o difference_n of_o latitude_n to_o the_o distance_n that_o the_o ship_n have_v run_v from_o the_o first_o place_n where_o she_o begin_v her_o traverse_n geo._n what_o be_v the_o three_o and_o as_o i_o remember_v you_o say_v the_o last_o useful_a peoposition_n to_o be_v take_v notice_n of_o in_o the_o mariner_n practice_n nau._n by_o have_v give_v the_o latitude_n of_o two_o place_n and_o their_o difference_n of_o longitude_n to_o find_v the_o magnetical_a course_n or_o rhomb_n and_o the_o distance_n geo._n how_o can_v this_o be_v useful_a for_o a_o mariner_n in_o his_o practice_n nau._n because_o many_o time_n it_o chance_v that_o a_o mariner_n be_v to_o sail_v from_o one_o port_n who_o latitude_n and_o longitude_n he_o have_v in_o geographical_a table_n as_o in_o mr._n hugh_n his_o use_n of_o the_o globe_n or_o in_o the_o table_n of_o the_o seaman_n calendar_n and_o be_v to_o sail_v so_o another_o port_n who_o latitude_n and_o longitude_n he_o have_v also_o in_o the_o say_a table_n and_o by_o this_o proposition_n be_v may_v examine_v the_o truth_n of_o his_o sea-chart_n he_o sail_v by_o geo_n set_a i_o down_o the_o theorem_n for_o this_o proposition_n and_o i_o will_v trouble_v you_o no_o further_o at_o this_o time_n nau._n sir_n i_o be_o in_o some_o haste_n because_o the_o time_n be_v far_o spend_v than_o i_o suppose_v since_o we_o meet_v but_o i_o will_v perform_v your_o request_n and_o then_o i_o will_v take_v my_o leave_n of_o you_o for_o this_o time_n first_o as_o the_o difference_n of_o latitude_n be_v to_o the_o difference_n of_o longitude_n so_o be_v half_a the_o sin_n compliment_n of_o both_o latitude_n i_o mean_v of_o the_o logarithme_n sin_n to_o the_o tangent_fw-la of_o the_o course_n second_o as_o before_o as_o the_o sine_z compliment_n of_o the_o course_n be_v to_o radius_fw-la so_o be_v the_o difference_n of_o latitude_n to_o the_o distance_n run_v geo._n master_n nautae_fw-la i_o thank_v you_o very_o kind_o for_o your_o company_n and_o your_o conference_n you_o have_v inform_v my_o judgement_n very_o much_o in_o the_o matter_n of_o navigation_n nau._n sir_n i_o be_o very_o joyful_a of_o it_o fare_v you_o well_o finis_fw-la
our_o meridian_n which_o be_v the_o begin_n of_o our_o longitude_n our_o zenith_n be_v in_o the_o parallel_n of_o 80._o deg_fw-la north_n latitude_n i_o be_o to_o demonstrate_v sagment_n of_o a_o great_a circle_n contain_v â—0_n deg_fw-la apéece_n by_o the_o demonstrature_n north-east_n the_o end_n of_o which_o first_o sagment_n of_o 30_o degree_n shall_v touch_v the_o meridian_n in_o longitude_n eastward_o 119_o degree_n 30_o minute_n from_o the_o first_o and_o there_o likewise_o shall_v 〈◊〉_d the_o parallel_n of_o north_n latitude_n 60_o deâ—r_n and_o the_o end_n of_o the_o second_o sagment_n 160._o deg_fw-la in_o longitude_n wall_n touch_v the_o 130._o deg_fw-la â—_o min._n or_o meridian_n in_o longitude_n eastward_o from_o the_o first_o &_o there_o likewise_o touch_v the_o 36._o deg_fw-la 45._o mi._n parallel_n north_n likewise_o tâ—t_v end_v of_o the_o 3._o sagment_n at_o 90._o deg_fw-la in_o longitude_n shall_v touch_v the_o 134_o deg_fw-la 30_o min._n or_o meridian_n in_o longitude_n eastward_o from_o the_o first_o &_o there_o likewise_o touch_v the_o 7_o parallel_n north_n also_o there_o touch_v the_o horizen_n 45_o deg_fw-la either_o from_o the_o cardines_fw-la east_n or_o north_n northwest_n likewise_o the_o demonstrature_n of_o northwest_n cut_v the_o meridians_fw-la and_o paraelll_v in_o longitude_n westward_n as_o the_o demonâ—rature_n of_o north_n east_n cut_v they_o eastward_o only_o that_o it_o cut_v the_o horizon_n 45_o deg_fw-la either_o from_o the_o cardines_fw-la west_n or_o north_n example_n of_o the_o southeast_n in_o the_o same_o latitude_n 8._o deg_fw-la in_o our_o place_n of_o of_o be_v as_o aforesaid_a i_o be_o to_o demonstrate_v three_o sagment_n of_o a_o great_a circle_n contain_v 30_o deg_fw-la apéece_n by_o the_o demonstrature_n southeast_n the_o end_n of_o which_o first_o sagment_n of_o 30_o deg_fw-la shall_v touch_v the_o 35_o deg_fw-la 40_o mi._n or_o meridian_n in_o longitude_n eastward_o from_o the_o first_o and_o there_o likewise_o touch_v the_o 52_o degree_n 10_o min._n parallel_v north_n and_o the_o end_n of_o the_o second_o sagment_n of_o 60_o deg_fw-la in_o longitude_n wall_n touch_v the_o 41_o degree_n 40_o min._n or_o meridian_n in_o longitude_n eastward_o from_o the_o first_o and_o there_o likewise_o touch_v the_o 22_o degree_n â—_o min._n parallel_v north_n likewise_o the_o end_n of_o the_o three_o sagment_n at_o 90_o deg_fw-la in_o longitude_n wall_n touch_v the_o 45_o deg_fw-la 30_o min._n or_o meridian_n in_o longitude_n eastward_o from_o the_o first_o and_o there_o likewise_o touch_v the_o 7_o parallel_n south_n also_o there_o tuech_v the_o horizon_n 45_o deg_fw-la either_o from_o the_o cardines_fw-la east_n or_o south_n south-west_n likewise_o the_o demonstrature_n of_o south-west_n cut_v the_o meridians_fw-la and_o parallel_n in_o longitude_n westward_o as_o the_o demonstrature_n of_o the_o southeast_n cut_v they_o eastward_o only_o that_o it_o cut_v the_o horizon_n 45_o deg_fw-la 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a_o way_n outward_a to_o be_v 390_o degree_n of_o a_o great_a circle_n and_o to_o return_v homeward_o to_o the_o first_o place_n again_o the_o like_a distance_n upon_o the_o same_o line_n which_o shall_v be_v prove_v most_o false_a by_o the_o example_n follow_v which_o example_n shall_v be_v from_o the_o latitude_n of_o 50_o degr_n and_o from_o the_o first_o example_n as_o before_o in_o the_o latitude_n 51_o degree_n 30_o min._n yet_o these_o deliver_v not_o the_o truth_n neither_o as_o by_o example_n upon_o the_o difference_n hereafter_o follow_v the_o 1_o example_n in_o north_n latitude_n 50_o deg_fw-la in_o which_o latitude_n our_o zenith_n or_o place_n of_o be_v in_o one_o meridian_n where_o we_o make_v our_o beginning_n of_o longitude_n and_o place_n of_o departure_n i_o be_o now_o to_o deliver_v from_o this_o our_o zenith_n or_o place_n of_o be_v the_o demonstrature_n of_o northwest_n for_o one_o sagment_n of_o 30_o degree_n in_o longitude_n which_o sagment_n end_n of_o 30_o degr_n northwest_o there_o cut_v the_o 11_o degr_n 30_o minute_n or_o meridian_n westward_o in_o longitude_n and_o the_o 63_o degree_n parallel_v north_n our_o zenith_n now_o be_v alter_v and_o the_o latitude_n 63_o degree_n as_o aforesaid_a we_o will_v make_v proof_n to_o return_v back_o again_o to_o our_o first_o place_n by_o the_o line_n southeast_n the_o like_a sagment_n of_o 30_o degree_n in_o longitude_n where_o this_o sagment_n end_n cut_v the_o 26_o degree_n 20_o minute_n or_o meridian_n in_o longitude_n eastward_o and_o there_o likewise_o cut_v the_o 37_o degree_n 40_o minute_n parallel_v north_n so_o that_o this_o line_n of_o northwest_n extend_v to_o 30_o degree_n as_o aforesaid_a and_o from_o thence_o return_v southeast_n to_o 30_o degree_n likewise_o there_o be_v difference_n in_o longitude_n westward_o from_o the_o first_o meridian_n or_o place_n of_o departure_n 25_o degree_n 10_o minute_n or_o meridians_fw-la and_o in_o latitude_n southward_a from_o the_o first_o 12_o 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