of_o the_o compass_n it_o be_v to_o be_v set_v off_o in_o as_o also_o whether_o it_o be_v near_o the_o east_n or_o west_n than_o the_o north_n or_o south_n for_o if_o it_o be_v near_o the_o east_n or_o west_n than_o the_o north_n or_o south_n you_o must_v do_v the_o same_o from_o a_o parallel_n as_o here_o you_o do_v from_o a_o meridian_n for_o the_o side_n of_o a_o square_n be_v but_o the_o measure_n of_o four_o point_n which_o be_v but_o half_a the_o point_n between_o a_o meridian_n and_o a_o parallel_n this_o way_n of_o work_v may_v seem_v hard_a and_o tedious_a at_o first_o but_o you_o will_v soon_o find_v that_o it_o be_v free_a from_o mistake_n and_o both_o exact_a and_o easy_a if_o you_o practise_v it_o place_v this_o between_o page_n 112_o and_o 113._o of_o oblique_a triangle_n two_o side_n with_o a_o angle_n opposite_a to_o one_o of_o they_o give_v to_o find_v the_o other_o angles_n and_o side_n question_n i._n two_o ship_n set_v sail_n from_o the_o rock_n of_o lisbon_n one_o 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league_n from_o the_o scale_n of_o equal_a part_n and_o fix_v one_o foot_n of_o your_o compass_n in_o a_o and_o where_o the_o other_o intersect_v the_o course_n b_o c_o which_o it_o do_v in_o b_o there_o be_v the_o other_o ship_n then_o to_o measure_v the_o angle_n of_o the_o ship_n bear_v one_o from_o the_o other_o it_o be_v b_o and_z b_o c_z be_v an_z e_o n_o e_o line_n extend_v b_o a_o to_o the_o arch_n of_o 60_o deg_fw-la who_o centre_n be_v at_o b_o and_o see_v how_o many_o degree_n or_o point_n it_o be_v more_o northerly_a than_o a_o e_o n_o e_o line_n and_o so_o the_o other_o ship_n namely_o the_o ship_n at_o a_o bear_v from_o the_o ship_n at_o b_o then_o take_v the_o length_n of_o b_o c_o and_o apply_v it_o to_o your_o scale_n and_o see_v how_o many_o league_n or_o mile_n it_o be_v i_o have_v wrought_v this_o in_o league_n but_o i_o will_v work_v the_o rest_n in_o mile_n because_o it_o be_v more_o exact_a i_o find_v that_o the_o ship_n at_o a_o bear_v from_o b_o n_o e_o b_o n_o 45_o min._n easterly_n the_o distance_n run_v of_o the_o southermost_a ship_n be_v 70_o league_n by_o the_o table_n the_o proportion_n of_o this_o and_o all_o other_o of_o this_o kind_n be_v the_o same_o that_o hold_v in_o right_a angle_a triangle_n namely_o that_o the_o sine_fw-la of_o every_o angle_n be_v proportional_a to_o its_o opposite_a side_n or_o every_o side_n be_v proportional_a to_o the_o sine_fw-la of_o its_o opposite_a angle_n here_o we_o have_v give_v the_o side_n c_o a_o 38_o league_n the_o side_n a_o b_o 58_o league_n and_o the_o angle_n at_o c_z which_o be_v 5_o point_n or_o 56_o deg_fw-la 15_o min._n say_v then_o for_o the_o angle_n at_o b._n as_o a_o b_o 58_o league_n 580_o tem_n comp_n arith_n 7,2365719_o be_v to_o a_o c_o b_o 56_o deg_fw-la 15_o min._n sine_fw-la  _fw-fr 9,9198464_o so_o be_v a_o c_o 38_o league_n 380_o tem_n  _fw-fr 2,5797836_o to_o a_o b_o c_o sine_fw-la 33_o deg_fw-la 0_o min._n  _fw-fr 9,7362019_o which_o subtract_v from_o 6_o point_n or_o 67_o d._n 30_o m._n  _fw-fr 33_o 00_o remainder_n be_v the_o course_n from_o north_n 34_o d._n 30_o m._n which_o the_o ship_n a_o bear_v from_o the_o ship_n b_o which_o be_v n_n e_o b_o n_o 45_o min._n easterly_n for_o the_o distance_n run_v of_o the_o ship_n at_o b_o the_o side_n b_o c._n as_o sine_fw-la c_o 56_o deg_fw-la 15_o min._n comp_n arith_n 0,080153_o be_v to_o a_o b_o 58_o league_n  _fw-fr 2,763428_o so_o be_v sine_fw-la b_o a_o c_o 90_o deg_fw-la 45_o min._n take_v the_o sine_fw-la of_o the_o acute_a angle_n b_o a_o t_o 89_o d._n 15_o m._n 9,999961_o to_o b_o c_z 68_o 8_o 10_o  _fw-fr 2,843542_o the_o reason_n why_o you_o take_v the_o acute_a angle_n be_v because_o the_o table_n go_v no_o further_o than_o 90_o deg_fw-la neither_o indeed_o be_v any_o sine_fw-la beyond_o 90_o deg_fw-la but_o as_o my_o father_n say_v in_o his_o trigonometry_n p._n 2_o the_o sine_fw-la of_o a_o arch_n less_o than_o a_o quadrant_n be_v also_o the_o right_a sine_fw-la of_o a_o arch_n as_o much_o great_a than_o a_o quadrant_n so_o than_o the_o right_a sine_fw-la of_o the_o arch_n 90_o deg_fw-la 45_o min._n which_o be_v 45_o min._n great_a than_o a_o quadrant_n must_v be_v the_o right_n sine_fw-la of_o the_o arch_n 89_o deg_fw-la 15_o min._n which_o be_v as_o much_o less_o namely_o 45_o min._n the_o geometrical_a demonstration_n of_o it_o be_v there_o lay_v down_o you_o may_v ask_v how_o i_o come_v to_o know_v the_o angle_n b_o a_o c_o which_o be_v thus_o i_o find_v one_o of_o the_o other_o two_o angle_n namely_o b_o and_o the_o other_o i_o have_v give_v i_o i_o add_v they_o both_o together_o and_o that_o sum_n i_o subtract_v from_o 180_o deg_fw-la the_o remainder_n must_v then_o be_v the_o angle_n at_o a_o because_o 180_o deg_fw-la be_v the_o sum_n of_o the_o three_o angle_n of_o any_o right_n line_v triangle_n and_o if_o i_o subtract_v two_o of_o they_o from_o three_o of_o they_o there_o will_v remain_v one_o of_o they_o which_o be_v 90_o deg_fw-la 45_o min._n the_o three_o angle_n of_o a_o triangle_n give_v with_o one_o of_o the_o side_n to_o find_v the_o other_o two_o side_n question_n ii_o admit_v i_o set_v from_o a_o head-land_n lie_v in_o the_o latitude_n of_o 50_o deg_fw-la 00_o min._n north_n latitude_n and_o sail_v w_o s_o w_n 38_o league_n and_o then_o meet_v with_o a_o ship_n that_o come_v from_o a_o place_n which_o lie_v s_n s_o w_n from_o the_o head-land_n now_o this_o ship_n have_v sail_v n_o w._n i_o demand_v the_o distance_n of_o that_o place_n from_o the_o other_o and_o also_o the_o distance_n the_o ship_n have_v sail_v that_o come_v from_o the_o southermost_a place_n the_o distance_n between_o the_o two_o place_n be_v a_o b_o mile_n 58_o mile_n the_o distance_n that_o the_o ship_n sail_v be_v a_o o_o mile_n 44_o 4_o 10_o mile_n if_o you_o have_v occasion_n to_o find_v the_o latitude_n the_o place_n at_o a_o lie_v in_o let_v fall_v the_o perpendicular_a a_o n_n upon_o the_o south_n line_n that_o come_v from_o b_o and_o it_o cut_v it_o in_o n_n and_o leave_v the_o difference_n of_o latitude_n b_o n_n see_v how_o many_o mile_n it_o be_v and_o subtract_v it_o from_o 50_o deg_fw-la and_o you_o have_v your_o desire_n measure_v a_o n_n and_o you_o have_v the_o westing_n that_o a_o lie_v from_o the_o head-land_n b._n by_o the_o table_n here_o the_o angle_n at_o b_o be_v a_o angle_n of_o 4_o point_n or_o 45_o d._n 00_o m._n the_o angle_n at_o a_o be_v a_o angle_n of_o 6_o point_n or_o 67_o d._n 30_o m._n the_o angle_n at_o o_o be_v a_o angle_n of_o 6_o point_n or_o 67_o d._n 30_o m._n the_o side_n b_o o_fw-fr be_v 58_o mile_n  _fw-fr  _fw-fr first_n for_o the_o side_n a_o b._n the_o general_a rule_n say_v that_o the_o sine_fw-la of_o every_o angle_n be_v proportional_a to_o its_o opposite_a side_n then_o from_o this_o i_o conclude_v that_o b_o a_o shall_v be_v equal_a to_o b_o o_o because_o the_o angel_n opposite_a to_o they_o be_v equal_a and_o so_o you_o will_v find_v they_o for_o as_o sine_fw-la a_o 67_o deg_fw-la 30_o min._n comp_n arith_n 0,034384_o be_v to_o o_o b_o 58_o mile_n  _fw-fr 1,763428_o so_o be_v sine_fw-la o_fw-la 67_o deg_fw-la 30_o min._n  _fw-fr 9,965615_o to_o a_o b_o 58_o mile_n the_o two_o place_n distance_n 1,763428_o you_o see_v it_o be_v so_o exact_o for_o these_o three_o number_n add_v together_o and_o radius_fw-la cast_v away_o produce_v the_o same_o logarithm_n that_o 58_o take_v out_o of_o the_o book_n do_v and_o this_o question_n i_o do_v on_o
difference_n of_o longitude_n between_o they_o which_o thing_n may_v be_v take_v from_o such_o a_o catalogue_n as_o this_o be_v after_o the_o manner_n follow_v suppose_v i_o be_v bind_v from_o the_o lizard_n to_o barbadoes_n i_o look_v in_o the_o column_n of_o latitude_n against_o the_o lizard_n and_o find_v 50_o deg_fw-la 0_o min._n for_o its_o latitude_n and_o 25_o deg_fw-la 20_o min._n for_o its_o longitude_n from_o flower_n and_o corve_n i_o look_v in_o the_o column_n of_o latitude_n against_o barbadoes_n and_o find_v 13_o deg_fw-la 12_o min._n for_o its_o latitude_n and_o 327_o deg_fw-la 42_o min._n for_o its_o longitude_n from_o flower_n and_o corve_n here_o you_o have_v the_o latitude_n of_o each_o place_n but_o to_o find_v the_o difference_n of_o longitude_n between_o these_o place_n i_o consider_v that_o barbadoes_n have_v 327_o deg_fw-la 42_o min._n of_o east_n longitude_n from_o these_o island_n but_o if_o i_o subtract_v that_o from_o 360_o deg_fw-la the_o whole_a circumference_n there_o must_v remain_v the_o west_n longitude_n that_o be_v between_o they_o which_o i_o find_v to_o be_v 32_o do_v 18_o m._n circumf_n 360_o 00_o east_n long._n 327_o 42_o  _fw-fr 32_o 18_o to_o it_o add_v the_o longitude_n between_o the_o lizard_n and_o flower_n and_o corve_v 25_o d._n 20_o m._n that_o sum_n be_v 57_o d._n 38_o m._n the_o difference_n of_o longitude_n between_o the_o lizard_n and_o barbadoes_n the_o meridian_n of_o barbadoes_n be_v to_o the_o westward_n of_o the_o lizard_n so_o many_o degree_n and_o thus_o any_o difference_n of_o longitude_n between_o two_o place_n be_v take_v provide_v that_o one_o of_o they_o be_v near_a than_o 19_o deg_fw-la to_o the_o westward_n of_o the_o place_n you_o begin_v your_o longitude_n from_o and_o the_o other_o near_a than_o 90_o deg_fw-la to_o the_o eastward_n and_o the_o reason_n of_o this_o be_v because_o the_o longitude_n of_o all_o place_n be_v set_v down_o from_o flower_n and_o corve_n to_o the_o eastward_n so_o that_o if_o a_o place_n be_v but_o 1_o deg_fw-la to_o the_o westward_n of_o flower_n and_o corve_n it_o will_v be_v set_v down_o in_o the_o catalogue_n to_o lie_v in_o the_o 359_o deg_fw-la of_o longitude_n for_o to_o know_v the_o difference_n of_o longitude_n between_o any_o two_o place_n consider_v which_o way_n they_o be_v near_o and_o that_o take_v suppose_v there_o be_v two_o place_n one_o lie_v in_o 20_o deg_fw-la 0_o min._n of_o longitude_n the_o other_o lie_v in_o 195_o deg_fw-la of_o longitude_n i_o consider_v that_o the_o difference_n between_o they_o be_v not_o 180_o deg_fw-la and_o therefore_o i_o will_v subtract_v 20_o deg_fw-la 0_o min._n from_o 195_o deg_fw-la and_o the_o remainder_n be_v the_o difference_n of_o longitude_n between_o they_o 175_o deg_fw-la but_o if_o the_o difference_n between_o two_o place_n be_v above_o 180_o deg_fw-la as_o they_o be_v lay_v down_o in_o the_o catalogue_n subtract_v that_o difference_n from_o 360_o deg_fw-la and_o the_o remainder_n be_v the_o near_a difference_n of_o longitude_n your_o own_o reason_n will_v guide_v you_o in_o this_o and_o therefore_o i_o will_v proceed_v how_o to_o keep_v a_o reckon_a of_o the_o longitude_n and_o latitude_n a_o ship_n make_v at_o sea_n have_v find_v the_o difference_n of_o longitude_n between_o the_o place_n i_o set_v from_o and_o be_o bind_v to_o as_o also_o the_o latitude_n of_o each_o place_n i_o will_v begin_v my_o reckon_a thus_o imagine_v it_o be_v between_o the_o lizard_n and_o barbadoes_n and_o i_o set_v from_o the_o lizard_n the_o 3_o d._n of_o january_n 1658._o from_o the_o lizard_n we_o depart_v january_n 3_o 1658_o be_v bind_v to_o barbadoes_n lie_v in_o latitude_n north_n 13_o d._n 12_o m._n longitude_n be_v west_n from_o the_o meridian_n of_o the_o lizard_n 57_o d._n 38_o m._n  _fw-fr mo._n day_n week_n days_n latitude_n east_n long._n west_n long._n d._n m._n d._n m._n d._n m._n january_n 4_o friday_n 49_o 00_o 00_o 00_o 03_o 00_o  _fw-fr 5_o saturday_n 47_o 24_o 00_o 00_o 06_o 27_o  _fw-fr 6_o sunday_n 46_o 09_o 00_o 46_o 06_o 27_o  _fw-fr 7_o monday_n 45_o 00_o 01_o 05_o 06_o 27_o  _fw-fr 8_o tuesday_n 43_o 01_o 01_o 05_o 06_o 27_o  _fw-fr 9_o wednesday_n 41_o 10_o 01_o 05_o 09_o 00_o  _fw-fr 10_o thursday_n 40_o 00_o 01_o 05_o 11_o 02_o  _fw-fr 11_o friday_n 38_o 11_o 01_o 05_o 13_o 20_o  _fw-fr 12_o saturday_n 36_o 12_o 01_o 05_o 14_o 40_o  _fw-fr 13_o sunday_n 34_o 10_o 01_o 05_o 16_o 00_o  _fw-fr 14_o monday_n 32_o 20_o 01_o 05_o 18_o 47_o  _fw-fr 15_o tuesday_n 30_o 11_o 01_o 05_o 20_o 00_o  _fw-fr 16_o wednesday_n 27_o 00_o 01_o 05_o 21_o 40_o  _fw-fr 17_o thursday_n 25_o 01_o 01_o 05_o 22_o 30_o  _fw-fr 18_o friday_n 23_o 10_o 01_o 05_o 24_o 00_o  _fw-fr 19_o saturday_n 21_o 45_o 01_o 05_o 26_o 10_o  _fw-fr 20_o sunday_n 20_o 45_o 01_o 05_o 28_o 44_o  _fw-fr 21_o monday_n 19_o 00_o 01_o 05_o 31_o 00_o  _fw-fr 22_o tuesday_n 18_o 30_o 01_o 05_o 33_o 32_o  _fw-fr 23_o wednesday_n 18_o 00_o 01_o 05_o 36_o 00_o  _fw-fr 24_o thursday_n 17_o 27_o 01_o 05_o 38_o 20_o  _fw-fr 25_o friday_n 16_o 49_o 01_o 05_o 40_o 40_o  _fw-fr 26_o saturday_n 16_o 10_o 01_o 05_o 42_o 50_o  _fw-fr 27_o sunday_n 15_o 40_o 01_o 05_o 44_o 59_o  _fw-fr 28_o monday_n 15_o 00_o 01_o 05_o 47_o 00_o  _fw-fr 29_o tuesday_n 14_o 30_o 01_o 05_o 49_o 02_o  _fw-fr 30_o wednesday_n 13_o 45_o 01_o 05_o 50_o 57_o  _fw-fr 31_o thursday_n 13_o 12_o 01_o 05_o 52_o 00_o february_n 1_o friday_n 13_o 14_o 01_o 05_o 54_o 30_o  _fw-fr 2_o saturday_n 13_o 12_o 01_o 05_o 54_o 40_o  _fw-fr 3_o sunday_n 13_o 12_o 01_o 05_o 54_o 40_o  _fw-fr 4_o monday_n 13_o 12_o 01_o 05_o 55_o 30_o  _fw-fr 5_o tuesday_n 13_o 12_o 01_o 05_o 57_o 30_o  _fw-fr 6_o wednesday_n 13_o 12_o 01_o 05_o 58_o 35_o here_o in_o this_o reckon_a i_o have_v set_v down_o the_o longitude_n in_o degree_n and_o minute_n as_o before_o i_o set_v down_o the_o departure_n in_o league_n carry_v all_o in_o the_o last_o line_n the_o last_o line_n of_o my_o reckon_a say_v that_o they_o be_v in_o the_o latitude_n of_o 13_o deg_fw-la 12_o min._n and_o the_o whole_a east_n longitude_n that_o we_o have_v make_v since_o we_o set_v from_o the_o lizard_n be_v 1_o deg_fw-la 5_o min._n the_o whole_a west_n longitude_n be_v 58_o deg_fw-la 35_o min._n subtract_v the_o ea_n from_o the_o westing_n and_o the_o remainder_n be_v 57_o deg_fw-la 30_o min._n which_o lack_v but_o 8_o min._n of_o 57_o deg_fw-la 38_o min._n the_o meridian_n of_o the_o place_n also_o the_o same_o line_n say_v that_o we_o be_v in_o the_o latitude_n of_o 13_o deg_fw-la 12_o min._n which_o be_v the_o latitude_n of_o the_o place_n therefore_o i_o conclude_v i_o be_o but_o 8_o min._n from_o it_o so_o that_o i_o expect_v to_o see_v land_n there_o be_v no_o difference_n in_o the_o set_n down_o of_o this_o reckon_a from_o that_o before_o but_o only_o this_o be_v degree_n and_o minute_n that_o league_n or_o mile_n neither_o be_v there_o any_o other_o difference_n in_o their_o cast_n up_o for_o there_o your_o ea_n from_o your_o westing_n in_o league_n here_o in_o degree_n that_o there_o be_v nothing_o want_v to_o make_v i_o be_v understand_v i_o will_v here_o follow_v do_v the_o three_o first_o day_n work_v in_o three_o example_n suppose_v the_o first_o day_n i_o set_v out_o i_o sail_v s_o w_n b_o w_n 6_o deg_fw-la 25_o min._n westerly_n till_o i_o come_v into_o the_o latitude_n of_o 49_o deg_fw-la 0_o min._n which_o be_v the_o next_o day_n at_o noon_n i_o consider_v that_o i_o have_v the_o two_o latitude_n give_v i_o and_o the_o course_n to_o find_v the_o difference_n of_o longitude_n the_o meridional_a part_n answer_v to_o 50_o deg_fw-la 0_o min._n be_v 3475_o the_o meridional_a part_n answer_v to_o 49_o deg_fw-la 0_o min._n be_v 3382_o the_o meridional_a part_n contain_v between_o they_o be_v 93_o for_o the_o difference_n of_o longitude_n as_o radius_fw-la  _fw-fr to_z the_o difference_n of_o latitude_n in_o part_n 93_o 1,96848_o so_o be_v the_o tangent_fw-la of_o the_o course_n 62_o d._n 40_o m._n 10,28661_o to_o the_o difference_n of_o longitude_n in_o minute_n 180_o 2,25510_o this_o 180_o divide_v by_o 60_o produce_v 3_o deg_fw-la 0_o min._n the_o difference_n of_o longitude_n make_v that_o 24_o hour_n set_v it_o down_o in_o your_o reckon_a with_o the_o latitude_n you_o be_v in_o fill_v up_o the_o east_n column_n with_o cipher_n i_o need_v not_o show_v how_o to_o find_v the_o distance_n run_v because_o i_o suppose_v by_o what_o have_v be_v say_v before_o you_o can_v do_v it_o for_o the_o second_o day_n work_n suppose_v till_o the_o next_o day_n at_o noon_n we_o sail_v s_o w_n 10_o deg_fw-la 11_o min._n