rise_v at_o 6_o of_o the_o clock_n and_o so_o there_o be_v no_o difference_n of_o ascension_n for_o he_o be_v then_o in_o the_o aequinoctial_a which_o cut_v the_o horizon_n in_o the_o two_o opposite_a point_n of_o east_n and_o west_n in_o this_o question_n the_o difference_n of_o ascension_n be_v o_o p_o and_o be_v a_o distance_n upon_o a_o line_n that_o go_v not_o through_o the_o centre_n therefore_o take_v half_a the_o length_n of_o the_o parallel_n i_o d_o and_o proceed_v as_o you_o do_v in_o the_o three_o question_n and_o after_o you_o have_v find_v it_o in_o degree_n and_o minute_n convert_v it_o into_o hour_n and_o minute_n of_o time_n and_o set_v it_o down_o i_o find_v it_o to_o be_v here_o 16_o deg_fw-la 18_o min._n which_o be_v 1_o hour_n 5′_n 3_o 15._o by_o the_o difference_n of_o ascension_n thus_o find_v you_o may_v find_v the_o length_n of_o the_o day_n or_o night_n the_o hour_n of_o sun_n rise_v or_o the_o hour_n of_o uns_fw-fr set_v question_n vii_o for_o the_o time_n 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it_o from_o 6_o and_o it_o give_v the_o time_n of_o sun_n set_v and_o that_o double_a be_v the_o length_n of_o the_o whole_a day_n again_o that_o subtract_v from_o 24_o hour_n be_v the_o length_n of_o the_o night_n question_v viii_o to_o find_v the_o hour_n of_o the_o sun_n be_v due_a east_n or_o west_n the_o sun_n be_v due_a east_n in_o this_o example_n or_o any_o other_o when_o he_o go_v by_o the_o east_n point_n of_o the_o horizon_n or_o west_n when_o he_o go_v by_o the_o west_n point_fw-fr in_o this_o example_n the_o sun_n parallel_n of_o declination_n cut_v the_o east_n and_o west_n azimuth_n in_o s_n which_o be_v late_a in_o the_o morning_n than_o 6_o of_o the_o clock_n by_o the_o distance_n s_o p_o therefore_o see_v what_o s_n p_o be_v by_o the_o three_o way_n of_o measure_v and_o convert_v it_o into_o time_n and_o add_v it_o to_o 6_o hour_n it_o shall_v give_v the_o hour_n of_o the_o sun_n be_v due_a east_n i_o find_v it_o in_o this_o example_n to_o be_v 6_o h._n 46′_n 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and_o it_o leave_v the_o length_n of_o the_o short_a night_n 7_o h._n 50_o min._n equal_a to_o which_o be_v the_o length_n of_o the_o short_a day_n 7_o h._n 50_o min._n but_o you_o may_v measure_v the_o length_n of_o the_o short_a day_n and_o subtract_v that_o from_o 24_o hour_n and_o it_o will_v be_v the_o length_n of_o the_o long_a night_n which_o be_v equal_a to_o the_o long_a day_n now_o the_o short_a day_n be_v when_o the_o sun_n be_v in_o the_o tropic_a of_o capricorn_n for_o than_o it_o be_v late_a before_o he_o rise_v now_o to_o measure_v it_o take_v the_o distance_n from_o 6_o of_o the_o clock_n which_o be_v t_n and_o the_o sun_n rise_v which_o be_v u_o and_o set_v it_o off_o by_o the_o three_o way_n of_o measure_v convert_v the_o degree_n into_o time_n and_o subtract_v that_o time_n from_o 6_o hour_n it_o leave_v the_o length_n of_o the_o forenoon_n which_o double_v be_v the_o length_n of_o the_o short_a day_n as_o in_o quest_n 7._o i_o have_v speak_v to_o that_o purpose_n i_o need_v say_v no_o more_o that_o 7_o the_o question_n be_v light_a sufficient_a i_o may_v do_v a_o example_n of_o what_o be_v before_o do_v in_o a_o south_n latitude_n but_o reason_n give_v that_o the_o same_o which_o the_o south_n pole_n or_o southern_a part_n of_o the_o heaven_n be_v depress_v in_o a_o northern_a latitude_n the_o same_o will_v the_o northern_a part_n of_o the_o heaven_n be_v depress_v in_o a_o latitude_n as_o far_o southerly_a so_o that_o there_o will_v be_v no_o difference_n
of_o certain_a fix_a star_n near_o the_o equinoctial_a 179_o the_o like_a for_o star_n near_o the_o north_n pole_n 180_o a_o table_n show_v how_o much_o the_o north_n star_n be_v above_o or_o below_o the_o pole_n for_o every_o several_a position_n of_o the_o former_a or_o great_a guard_n 181_o rule_n to_o find_v the_o latitude_n by_o the_o meridian_n altitude_n of_o the_o sun_n or_o star_n 182_o of_o astronomy_n wherein_o the_o application_n and_o use_v of_o the_o doctrine_n of_o spherical_a triangle_n be_v exemplify_v in_o the_o resolution_n of_o several_a proposition_n of_o the_o sphere_n which_o appertain_v to_o astronomy_n and_o navigation_n from_o page_n 185_o to_o page_n 203_o of_o arithmetic_n the_o table_n 7000000000000_o million_o of_o million_o 800000000000_o hundred_o thousand_o million_o 90000000000_o ten_o thousand_o million_o 6000000000_o thousand_o million_o 500000000_o hundred_o million_o 30000000_o ten_o million_o 2000000_o million_o 800000_o hundred_o thousand_o 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fix_v one_o foot_n of_o your_o compass_n in_o p_o and_o extend_v the_o other_o to_o sweep_v the_o horizon_n which_o be_v the_o same_o as_o though_o you_o let_v fall_v the_o perpendicular_a p_o n_z set_v it_o off_o by_o the_o second_o way_n of_o measure_v as_o be_v show_v in_o quest_n 2._o and_o apply_v it_o to_o your_o line_n of_o chord_n and_o the_o reason_n be_v because_o p_o n_z represent_v a_o part_n of_o a_o great_a circle_n and_o so_o be_v to_o be_v understand_v to_o be_v of_o the_o nature_n of_o those_o line_n that_o go_v through_o the_o centre_n of_o the_o sphere_n for_o all_o azimuth_n pass_v through_o the_o zenith_n and_o nadir_n which_o be_v two_o opposite_a point_n i_o find_v the_o sun_n be_v 10_o deg_fw-la 7_o min_fw-mi high_a at_o 6_o of_o the_o clock_n question_n v._o to_o find_v the_o sun_n height_n be_v due_a east_n or_o west_n where_o the_o sun_n parallel_n of_o declination_n cut_v the_o east_n and_o west_n azimuth_n be_v the_o place_n the_o sun_n be_v in_o when_o he_o be_v due_a east_n in_o the_o morning_n for_o you_o see_v he_o be_v then_o over_o the_o point_n of_o east_n in_o the_o horizon_n which_o be_v ♈_o or_o the_o centre_n therefore_o take_v the_o distance_n between_o that_o place_n and_o the_o centre_n which_o be_v s_n ♈_o and_o apply_v it_o to_o the_o line_n of_o sines_n but_o if_o you_o have_v no_o line_n of_o sines_n extend_v it_o to_o a_o chord_n after_o the_o manner_n of_o the_o second_o question_n which_o i_o call_v the_o the_o second_o way_n of_o measure_v for_o it_o be_v the_o distance_n of_o a_o line_n which_o go_v through_o the_o centre_n i_o find_v the_o sun_n height_n be_v due_a east_n or_o west_n be_v 17_o deg_fw-la 25_o m._n note_v that_o the_o same_o height_n that_o the_o sun_n be_v be_v over_o the_o east_n point_n so_o high_a he_o be_v be_v over_o the_o west_n point_n in_o the_o afternoon_n question_n vi_o to_o find_v the_o difference_n of_o ascension_n the_o difference_n of_o ascension_n be_v the_o portion_n of_o time_n that_o be_v between_o the_o sun_n rise_v and_o six_o of_o the_o clock_n if_o the_o day_n be_v long_o than_o the_o night_n the_o sun_n rise_v before_o 6_o but_o if_o short_a after_o 6_o but_o whether_o it_o be_v before_o or_o after_o 6_o that_o he_o rise_v so_o many_o hour_n and_o minute_n as_o it_o be_v from_o 6_o so_o much_o be_v the_o half_a day_n or_o night_n long_o or_o short_a than_o 6_o hour_n from_o whence_o it_o be_v evident_a that_o if_o the_o sun_n rise_v due_a east_n he_o
but_o in_o any_o case_n take_v this_o in_o general_a that_o if_o the_o difference_n of_o ascension_n be_v before_o 6_o of_o the_o clock_n subtract_v it_o if_o after_o 6_o add_v it_o to_o 6_o hour_n and_o you_o have_v the_o time_n of_o sun_n rise_v this_o stand_v to_o good_a reason_n forasmuch_o as_o the_o difference_n of_o ascension_n be_v the_o portion_n of_o time_n that_o the_o sun_n rise_v before_o or_o after_o 6_o of_o the_o clock_n in_o this_o example_n you_o see_v the_o difference_n of_o ascension_n be_v before_o 6_o of_o the_o clock_n 1_o hour_n 5′_n 3_o 15_o we_o will_v omit_v the_o part_n of_o a_o part_n of_o a_o minute_n i_o will_v know_v the_o time_n of_o the_o sun_n rise_v example_n subtract_v the_o difference_n of_o ascension_n 1_o h._n 5_o m._n 3_o 15_o from_o 6_o hour_n 5_o 60_o the_o remainder_n be_v the_o time_n of_o sun_n rise_v 4_o 54_o 12_o 15_o or_o â…˜_n thus_o i_o conclude_v the_o sun_n rise_v at_o 4_o a_o clock_n 54_o min._n â…˜_n if_o you_o have_v a_o desire_n to_o find_v the_o time_n of_o sun_n set_v subtract_v the_o time_n of_o sun_n rise_v from_o 12_o hour_n and_o you_o have_v it_o for_o as_o many_o hour_n and_o minute_n as_o the_o sun_n rise_v before_o 12_o so_o many_o hour_n and_o minute_n he_o set_v after_o 12._o example_n here_o the_o sun_n rise_v at_o 4_o of_o the_o clock_n 54_o m._n â…˜_n which_o we_o express_v thus_o 4_o h._n 54_o m._n â…˜_n this_o subtract_v from_o 11_o 60_o leave_n the_o time_n of_o sun_n set_v 7_o 05_o â…•_n which_o be_v 5_o min._n â…•_n past_o 7_o of_o the_o clock_n in_o the_o afternoon_n this_o double_a be_v the_o length_n of_o the_o whole_a day_n which_o be_v 14_o hour_n 10_o min_fw-mi â…–_n this_o subtract_v from_o 24_o hour_n be_v the_o length_n of_o the_o night_n 9_o hour_n 49_o min._n 8_o 5._o to_o find_v the_o length_n of_o the_o long_a day_n in_o that_o latitude_n before_o propose_v when_o the_o day_n be_v at_o the_o long_a in_o any_o north_n latitude_n the_o sun_n be_v in_o the_o tropic_a of_o cancer_n in_o a_o southern_a latitude_n in_o the_o tropic_a of_o capricorn_n this_o be_v a_o northern_a latitude_n therefore_o make_v the_o tropic_a of_o cancer_n the_o parallel_n of_o the_o sun_n declination_n as_o here_o o_o r_n be_v the_o parallel_n of_o the_o sun_n declination_n then_o must_v i_o 6_o be_v the_o difference_n of_o ascension_n which_o be_v =_o to_o f_o ♈_o in_o the_o right_a angle_a triangle_n i_o f_o ♈_o right_a angle_v at_o f_o you_o have_v i_o ♈_o f_o the_o compliment_n of_o the_o latitude_n 40_o deg_fw-la give_v and_o i_o f_o the_o sun_n declination_n 23_o deg_fw-la 30_o min._n to_o find_v f_o ♈_o find_v it_o as_o you_o be_v show_v to_o find_v the_o difference_n of_o ascension_n before_o convert_v it_o into_o time_n and_o find_v the_o length_n of_o the_o day_n as_o be_v show_v before_o this_o note_n that_o sine_fw-la s_z i_o f_o l_o be_v a_o arch_n of_o the_o meridian_n cut_v the_o horizon_n in_o that_o place_n of_o it_o where_o the_o sun_n rise_v sine_fw-la ♈_o f_o +_o radius_fw-la be_v =_o to_o tang._n i_o f_o +_o tang._n comp_n i_o ♈_o f._n tang._n ay_o f_o sun_n declination_n 23_o deg_fw-la 30_o min._n 9,638301_o tang._n come_v i_o ♈_o f_o poles_n elevation_n 40_o deg_fw-la 0_o min._n 10,076186_o sine_fw-la f_o ♈_o difference_n of_o ascension_n 31_o d._n 12_o m._n 39_o sec_fw-la 9,714487_o but_o you_o may_v ask_v all_o this_o while_n how_o this_o fraction_n be_v find_v it_o be_v thus_o find_v admit_v i_o will_v find_v the_o sine_fw-la of_o the_o arch_n answer_v to_o 9714487_o i_o look_v in_o the_o sin_n and_o find_v the_o near_o less_o than_o it_o to_o be_v  _fw-fr 9,714352_o i_o take_v the_o next_o great_a than_o it_o and_o find_v it_o to_o be_v 9,714560_o i_o subtract_v the_o lesser_a from_o the_o great_a the_o remainder_n be_v 208_o then_o from_o the_o figure_n that_o come_v forth_o 9,714487_o i_o subtract_v the_o near_a in_o the_o table_n less_o 9,714352_o and_o the_o remainder_n be_v 135_o then_o say_v as_o the_o difference_n between_o the_o near_a less_o and_o the_o near_o great_a 280_o comp_n arith_n 7,681936_o be_v to_o the_o difference_n between_o the_o same_o and_o that_o less_o 135_o 2,130333_o so_o be_v 60_o min._n 1,778151_o to_o 39_o sec_fw-la 1,590420_o the_o like_a be_v to_o be_v understand_v of_o any_o fraction_n else_o if_o you_o have_v occasion_n for_o the_o artificial_a sine_fw-la or_o tangent_fw-la of_o a_o arch_n that_o have_v a_o fraction_n to_o it_o say_v as_o 60_o second_n be_v to_o the_o second_o in_o the_o fraction_n which_o be_v here_o 39_o so_o be_v the_o difference_n between_o the_o near_o lesser_a and_o the_o near_o great_a 208_o to_o the_o fraction_n 135_o and_o this_o add_v to_o the_o lesser_a make_v the_o artificial_a sine_fw-la of_o the_o arch_n require_v 9,714352_o 9,714487_o the_o like_a be_v to_o be_v understand_v of_o a_o tangent_fw-la  _fw-fr to_o find_v the_o hour_n of_o the_o sun_n be_v due_a east_n or_o west_n latitude_n 50_o deg_fw-la 0_o min._n declination_n 13_o deg_fw-la 15_o min._n northerly_a i_o demand_v the_o time_n of_o the_o sun_n be_v due_a east_n or_o west_n and_o for_o the_o time_n of_o the_o sun_n be_v due_a west_n you_o be_v to_o subtract_v it_o from_o 6_o hour_n in_o this_o case_n and_o the_o remainder_n be_v your_o desire_n the_o reason_n be_v because_o as_o many_o hour_n as_o the_o sun_n be_v due_a east_n after_o 6_o of_o the_o clock_n in_o the_o morning_n so_o long_a time_n be_v he_o due_a west_n before_o 6_o of_o the_o clock_n in_o the_o afternoon_n i_o have_v leave_v the_o work_n of_o this_o to_o your_o own_o practice_n only_o i_o have_v set_v down_o the_o resolution_n of_o it_o the_o sun_n be_v due_a east_n 45_o min._n 9_o 15_o past_o 6_o of_o the_o clock_n the_o sun_n be_v due_a west_n 45_o min._n 9_o 15_o before_o 6_o of_o the_o clock_n which_o be_v at_o 5_o of_o the_o clock_n 14_o min._n 6_o 15._o note_v that_o if_o the_o sun_n declination_n be_v southerly_a then_o will_v he_o be_v east_n before_o 6_o so_o that_o whereas_o here_o you_o add_v there_o you_o subtract_v from_o 6_o hour_n to_o find_v the_o hour_n of_o the_o sun_n be_v due_a east_n or_o add_v to_o 6_o hour_n for_o the_o time_n of_o its_o be_v due_a west_n but_o your_o own_o reason_n if_o you_o look_v well_o on_o the_o scheme_n will_v guide_v you_o to_o know_v this_o and_o also_o to_o know_v that_o it_o be_v useless_a in_o such_o case_n for_o than_o he_o be_v not_o above_o the_o horizon_n latitude_n 50_o deg_fw-la 0_o min._n declination_n 13_o deg_fw-la 15_o min._n i_o demand_v the_o continuance_n of_o twilight_n as_o i_o have_v note_v before_o the_o sun_n be_v account_v 17_o deg_fw-la under_o the_o horizon_n when_o the_o day_n break_v therefore_o in_o the_o follow_a scheme_n let_v 17_o i_o be_v a_o arch_a parallel_n to_o the_o horizon_n 17_o deg_fw-la under_o it_o let_v d_o b_o c_o at_fw-fr be_v a_o azimuth_n cut_v the_o aequinoctial_a and_o the_o line_n of_o 17_o deg_fw-la in_o the_o place_n of_o their_o intersection_n which_o be_v at_o c_o then_o in_o 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to_o they_o wish_v good_a success_n in_o all_o their_o honest_a and_o laudable_a undertake_n and_o in_o the_o interim_n bid_v they_o farewell_o matthew_n norwood_n the_o content_n of_o arithmetic_n numeration_n 1_o addition_n 2_o subtraction_n 5_o multiplication_n 7_o division_n 10_o reduction_n 16_o the_o golden_a rule_n or_o rule_n of_o three_o 19_o the_o rule_n of_o interest_n and_o interest_n upon_o interest_n 24_o the_o rule_n of_o fellowship_n 25_o of_o geometry_n geometrical_a definition_n 28_o how_n to_o raise_v a_o perpendicular_a 30_o how_o to_o divide_v a_o line_n into_o two_o equal_a part_n 31_o how_n to_o raise_v a_o perpendicular_a on_o the_o end_n of_o a_o line_n ibid._n from_o a_o point_n give_v to_o let_v fall_v a_o perpendicular_a 32_o how_o to_o draw_v parallel_n line_n 33_o how_n to_o make_v a_o geometrical_a square_a 34_o how_o to_o make_v a_o oblong_a or_o square_a who_o length_n and_o breadth_n be_v give_v 34_o how_o to_o make_v a_o diamond-figure_n who_o side_n and_o angle_n shall_v be_v limit_v 35_o to_o make_v a_o rhomboiade_n who_o side_n and_o angle_n be_v give_v 36_o to_o find_v the_o centre_n of_o a_o circle_n 37_o to_o find_v the_o centre_n of_o that_o circle_n which_o shall_v pass_v through_o any_o three_o give_v point_n which_o be_v not_o situate_a in_o a_o straight_a line_n 37_o how_o to_o divide_v a_o circle_n into_o 2_o 4_o 8_o 16_o 32_o equal_a part_n 40_o the_o projection_n of_o the_o mariner_n compass_n 41_o the_o projection_n of_o the_o plain_a scale_n 42_o the_o projection_n of_o the_o sphere_n in_o plano_n 45_o the_o name_n and_o character_n of_o the_o sign_n with_o the_o month_n they_o belong_v to_o 48_o how_o to_o project_n the_o sphere_n 49_o the_o meaning_n of_o certain_a term_n of_o art_n 51_o how_o to_o find_v the_o sun_n meridian_n altitude_n 55_o how_o to_o find_v the_o amplitude_n of_o rise_v or_o set_v ibid._n how_o to_o find_v the_o azimuth_n at_o six_o of_o the_o clock_n 57_o to_o find_v the_o altitude_n at_o 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oblique_a triangle_n the_o application_n whereof_o be_v in_o ten_o question_n perfect_o explain_v all_o which_o question_n be_v apply_v to_o question_n in_o sail_v and_o be_v wrought_v both_o geometrical_o by_o the_o plain_a scale_n and_o also_o by_o the_o table_n of_o sines_n tangent_n and_o logarithm_n from_o page_n 113_o to_o page_n 146_o a_o table_n of_o meridional_a part_n to_o every_o three_o minute_n 146_o a_o declaration_n of_o the_o table_n 158_o the_o use_n of_o the_o table_n of_o meridional_a part_n exemplify_v in_o five_o question_n appertain_v to_o navigation_n from_o page_n 160_o to_o page_n 166_o of_o the_o longitude_n and_o latitude_n of_o place_n a_o table_n of_o they_o 167_o the_o use_n of_o they_o 171_o 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 172_o the_o name_n declination_n and_o season_n
sum_n stand_v thus_o you_o may_v have_v say_v 3_o time_n 3_o be_v 9_o from_z 8_o i_o can_v but_o 9_o from_o 18_o and_o the_o remainder_n be_v 9_o and_z 1_o for_o your_o borrow_a one_o ten_o from_o 1_o and_o there_o remain_v 0_o which_o be_v most_o easy_a for_o memory_n then_o set_v your_o divisor_n on_o place_n further_o towards_o the_o right_a hand_n in_o this_o form_n how_o many_o time_n 2_o can_v you_o have_v from_o 9_o four_o time_n then_o 4_o time_n 2_o be_v 8_o from_z 9_o and_o there_o remain_v 1_o and_z 4_o time_n 3_o be_v 12_o from_o 19_o and_o the_o remainder_n be_v 7_o and_o 1_o for_o the_o ten_o from_o 1_o and_o the_o remainder_n be_v 0_o and_o then_o your_o sum_n stand_v thus_o then_o remove_v your_o divisor_n to_o the_o next_o place_n and_o see_v how_o many_o time_n 2_o you_o can_v have_v out_o of_o 7_o which_o be_v 3_o time_n 3_o time_n 2_o be_v 6_o from_z 7_o and_o the_o remainder_n be_v 1_o and_o 3_o time_n 3_o be_v 9_o from_z 9_o and_o the_o remainder_n be_v 0_o and_o 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side_n against_o 4_o thus_o multiply_v they_o one_o by_o the_o other_o and_o they_o produce_v 20_o cast_v away_o all_o the_o nine_o from_o 20_o and_o the_o remainder_n be_v 2_o keep_v this_o 2_o in_o mind_n and_o cast_v up_o the_o remainder_n of_o the_o division_n and_o cast_v all_o the_o nine_o from_o it_o which_o if_o it_o be_v do_v in_o this_o sum_n afterward_o there_o will_v remain_v 3_o which_o add_v to_o the_o 2_o that_o be_v in_o your_o mind_n and_o it_o make_v 5_o which_o set_v down_o thus_o then_o cast_v away_o all_o the_o nine_o from_o your_o dividend_n and_o the_o remainder_n will_v answer_v to_o the_o last_o number_n you_o set_v down_o in_o the_o cross_n if_o the_o sum_n be_v right_a which_o here_o it_o be_v reduction_n reduction_n show_v how_o to_o bring_v gross_a or_o great_a denomination_n into_o small_a or_o small_a into_o great_a quest_n 1._o suppose_v a_o man_n have_v be_v at_o sea_n twenty_o five_o year_n and_o for_o every_o minute_n of_o that_o time_n he_o be_v to_o have_v on_o farthing_n i_o demand_v how_o many_o farthing_n be_v due_a to_o he_o here_o i_o see_v how_o many_o minute_n be_v in_o that_o quantity_n of_o time_n and_o so_o many_o minute_n so_o many_o farthing_n there_o be_v due_a which_o be_v 13140000_o farthing_n now_o to_o find_v this_o i_o first_o multiply_v the_o year_n by_o the_o day_n contain_v in_o one_o year_n which_o be_v 365_o and_o that_o produce_v 9125_o day_n the_o number_n of_o day_n in_o that_o number_n of_o year_n this_o multiply_v by_o 24_o give_v for_o its_o product_n 219000_o the_o number_n of_o hour_n in_o the_o whole_a time_n because_o 24_o hour_n be_v a_o day_n that_o product_v multiply_v by_o 60_o be_v the_o number_n of_o minute_n in_o the_o whole_a time_n because_o every_o hour_n be_v 60_o minute_n which_o be_v the_o last_o product_n or_o the_o thing_n require_v which_o i_o set_v down_o as_o the_o answer_n to_o my_o question_n thus_o facit_fw-la 13140000_o farthing_n quest_n 2._o pray_v tell_v i_o what_o these_o farthing_n come_v to_o in_o pound_n shilling_n and_o penny_n 1740120_o farthing_n four_o farthing_n make_v a_o penny_n therefore_o i_o divide_v the_o whole_a sum_n of_o farthing_n by_o 4_o and_o the_o quotient_n be_v ½_n of_o the_o number_n of_o farthing_n or_o the_o farthing_n reduce_v into_o penny_n 435030_o d._n of_o which_o sum_n i_o take_v the_o 1_o 12_o by_o divide_v it_o by_o 12_o which_o be_v the_o next_o quotient_n the_o number_n of_o shilling_n that_o be_v the_o farthing_n which_o
in_o the_o work_n at_o all_o and_o indeed_o my_o desire_n to_o be_v brief_a make_v i_o omit_v thing_n that_o i_o think_v may_v be_v understand_v without_o treat_v of_o they_o i_o will_v only_o touch_v upon_o a_o example_n in_o a_o sphere_n which_o have_v south_n declination_n latitude_n northerly_a 50_o deg_fw-la 00_o min._n declination_n 13_o deg_fw-la 15_o min._n southerly_a also_o if_o you_o subtract_v this_o amplitude_n v_o ♈_o from_o ♈_o h_o 90_o deg_fw-la the_o remainder_n be_v the_o sun_n azimuth_n from_o the_o south_n v_o h_n or_o if_o you_o add_v v_z ♈_o to_o ♈_o a_o 90_o deg_fw-la it_o be_v v._o a_o the_o sun_n azimuth_n of_o rise_v from_o the_o north_n forasmuch_o as_o five_o a_o be_v as_o much_o above_o 90_o deg_fw-la as_o v_z h_n want_v of_o it_o the_o same_o be_v to_o be_v understand_v in_o any_o sphere_n that_o the_o amplitude_n and_o azimuth_n of_o the_o sun_n be_v compliment_n one_o of_o a_o other_o to_o 90_o deg_fw-la in_o that_o quarter_n when_o the_o sun_n declination_n be_v southerly_a in_o any_o northern_a latitude_n the_o day_n be_v not_o so_o long_o as_o the_o night_n so_o that_o the_o sun_n can_v be_v up_o at_o 6_o of_o the_o clock_n which_o be_v at_o r_n therefore_o the_o sun_n azimuth_n at_o 6_o of_o the_o clock_n be_v of_o no_o use_n neither_o be_v he_o up_o when_o he_o pass_v the_o east_n point_n of_o the_o horizon_n which_o be_v at_o p_o so_o that_o you_o can_v take_v his_o height_n but_o you_o may_v measure_v how_o far_o he_o be_v under_o the_o horizon_n at_o either_o of_o those_o time_n or_o you_o may_v find_v his_o true_a azimuth_n at_o 6_o which_o be_v of_o no_o value_n to_o we_o that_o be_v seaman_n because_o we_o can_v have_v a_o magnetical_a azimuth_n they_o be_v measure_v as_o before_o the_o difference_n of_o ascension_n be_v here_o after_o 6_o of_o the_o clock_n as_o much_o as_o it_o be_v before_o 6_o in_o the_o last_o example_n and_o the_o reason_n be_v because_o the_o latitude_n be_v the_o same_o and_o the_o 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azimuth_n to_o 6_o of_o the_o clock_n and_o set_v it_o off_o by_o the_o three_o way_n of_o measure_v convert_v your_o degree_n and_o minute_n into_o time_n and_o subtract_v that_o time_n from_o 6_o hour_n and_o it_o give_v the_o due_a time_n of_o the_o morning_n that_o the_o sun_n cut_v the_o east_n point_n of_o the_o compass_n the_o reason_n why_o you_o subtract_v be_v because_o the_o sun_n be_v due_a east_n so_o long_o before_o 6_o of_o the_o clock_n subtract_v the_o hour_n of_o the_o sun_n be_v due_a east_n from_o 12_o hour_n and_o it_o will_v give_v the_o true_a time_n of_o the_o sun_n be_v due_a west_n for_o the_o time_n of_o day_n break_v draw_v the_o line_n 17_o ⊙_o parallel_n to_o the_o horizon_n and_o 17_o deg_fw-la under_o it_o as_o be_v show_v before_o and_o measure_n from_o p_o to_o r_n that_o be_v from_o the_o place_n where_o the_o sun_n parallel_n of_o declination_n cut_v that_o circle_n of_o 17_o deg_fw-la under_o the_o horizon_n to_o 6_o of_o the_o clock_n convert_v it_o into_o time_n and_o subtract_v it_o from_o 6_o of_o the_o clock_n and_o it_o leave_v the_o time_n of_o day_n break_v namely_o the_o time_n in_o the_o morning_n that_o the_o sun_n be_v in_o p_o you_o subtract_v because_o the_o day_n break_v so_o long_o before_o 6_o of_o the_o clock_n if_o it_o where_o so_o that_o the_o sun_n be_v in_o the_o tropic_a of_o capricorn_n you_o must_v take_v the_o distance_n s_o q._n you_o see_v the_o sun_n be_v pass_v the_o hour_n of_o 6_o before_o it_o be_v break_v of_o day_n now_o in_o this_o case_n you_o must_v add_v whereas_o before_o you_o subtract_v for_o the_o continuance_n of_o twilight_n it_o be_v measure_v as_o before_o from_o the_o place_n where_o the_o parallel_n of_o the_o sun_n declination_n cut_v the_o circle_n of_o 17_o deg_fw-la to_o the_o place_n where_o it_o cut_v the_o horizon_n convert_v it_o into_o time_n and_o set_v it_o down_o in_o this_o example_n it_o be_v p_o v._n what_o i_o have_v not_o mention_v here_o i_o have_v give_v 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superficies_n can_v show_v but_o one_o part_n of_o the_o globous_a body_n but_o you_o must_v know_v it_o be_v round_o which_o make_v the_o ecliptic_a to_o be_v divide_v on_o both_o side_n from_o ♈_o to_o ♋_o be_v 90_o deg_fw-la from_o ♋_o to_o ♎_o be_v 90_o deg_fw-la from_o ♎_o to_o ♑_o be_v 90_o deg_fw-la and_o from_o ♑_o to_o ♈_o be_v 90_o deg_fw-la every_o one_o of_o these_o quarter_n contain_v 3_o sign_n the_o ecliptic_a be_v thus_o divide_v into_o sign_n we_o may_v find_v the_o sun_n place_n and_o right_a ascension_n the_o sun_n place_n in_o the_o ecliptic_a be_v the_o near_a distance_n between_o the_o next_o aequinoctial_a point_n and_o the_o sun_n in_o the_o ecliptic_a by_o aequinoctial_a point_n be_v mean_v ♈_o and_o ♎_o the_o two_o point_n of_o intersection_n that_o the_o aequinoctial_a and_o the_o ecliptic_a make_n now_o in_o this_o case_n the_o sun_n must_v be_v near_a the_o equinoctial_a point_n at_o ♈_o because_o the_o month_n be_v belong_v to_o a_o sign_n near_o ♈_o than_o ♎_o therefore_o fix_v your_o compass_n in_o the_o point_n of_o ♈_o and_o extend_v the_o other_o foot_n to_o the_o sun_n in_o the_o ecliptic_a which_o be_v i_o and_o apply_v it_o to_o the_o line_n of_o sines_n or_o if_o you_o have_v no_o line_n of_o sines_n convert_v it_o to_o a_o chord_n by_o the_o second_o way_n of_o measure_v and_o as_o many_o degree_n as_o it_o be_v so_o far_o be_v the_o sun_n distant_a from_o the_o near_a aequinoctial_a point_n if_o it_o exceed_v 30_o deg_fw-la the_o sun_n must_v be_v in_o that_o degree_n of_o ♉_o that_o be_v above_o 30_o deg_fw-la if_o it_o exceed_v 60_o deg_fw-la the_o sun_n must_v be_v in_o that_o degree_n of_o ♊_o above_o 60_o but_o here_o i_o find_v it_o in_o less_o than_o 30_o namely_o 29_o deg_fw-la 3_o min._n therefore_o i_o conclude_v the_o sun_n be_v in_o 20_o deg_fw-la 3_o min._n of_o ♈_o but_o suppose_v it_o be_v time_n of_o year_n that_o the_o sun_n be_v return_v from_o the_o tropic_a towards_o the_o aequinoctial_a and_o be_v the_o same_o declination_n then_o will_v the_o sun_n place_n be_v the_o same_o from_o enter_v into_o ♎_o that_o it_o now_o be_v in_o ♈_o namely_o in_o 57_o min._n of_o â™_o which_o want_v 29_o deg_fw-la 3_o min._n of_o enter_v into_o ♎_o thus_o much_o for_o the_o sun_n place_n the_o sun_n right_a ascension_n be_v measure_v from_o the_o place_n where_o the_o sun_n parallel_n of_o declination_n cut_v the_o ecliptic_a to_o 6_o of_o the_o clock_n which_o be_v i_o 6_o set_v it_o off_o by_o the_o three_o way_n of_o measure_v to_o extend_v it_o to_o a_o great_a circle_n for_o the_o sine_fw-la of_o i_o
angle_n at_o e_z and_o so_o for_o the_o course_n as_o d_o e_z dist_n run_v and_o depar_n 197_o 8_o 10_o which_o be_v 1978_o ten_o comp_n arith_n 6,7037736_o be_v to_o radius_fw-la  _fw-fr  _fw-fr so_o be_v the_o difference_n of_o latitude_n d_o b_o 600_o ten_o 2,7781512_o to_o tangent_fw-la e_o 16_o deg_fw-la 53_o min._n  _fw-fr 9,4819248_o the_o compliment_n of_o which_o to_o 90_o deg_fw-la be_v e_z b_o d_o 73_o deg_fw-la 7_o min._n now_o because_o the_o angle_n p_o e_o a_o and_o p_o b_o at_fw-fr be_v equal_a subtract_v the_o angle_n e_o b_o a_o from_o e_o b_o d_o and_o the_o remainder_n be_v a_o b_o d_o the_o course_n example_n e_o b_o a_o 16_o deg_fw-la 53_o min._n equal_a to_o a_o e_o p_o subtract_v from_o e_o b_o d_o 73_o deg_fw-la 7_o min._n the_o remainder_n be_v a_o b_o d_o 56_o d._n 15_o m._n the_o course_n the_o reason_n that_o i_o take_v 3_o from_o 7_o and_z set_z down_z 5_o be_v because_o if_o you_o look_v to_o the_o absolute_a minute_n and_o part_n of_o a_o minute_n of_o the_o arch_n that_o answer_v to_o this_o artificial_a tangent_fw-la 9,4819248_o it_o will_v fall_v to_o such_o a_o fraction_n or_o to_o be_v the_o 15_o part_n of_o a_o minute_n less_o than_o 3_o as_o will_v bring_v it_o out_o but_o it_o be_v needless_a to_o be_v so_o exact_a in_o case_n or_o question_n of_o this_o nature_n i_o will_v not_o show_v how_o to_o work_v that_o till_o i_o come_v to_o a_o work_n that_o require_v such_o exactness_n here_o you_o see_v if_o you_o take_v it_o without_o allow_v for_o the_o fraction_n it_o be_v but_o 1_o min._n less_o or_o more_o which_o be_v but_o the_o 675_o the_o part_n of_o a_o point_n of_o the_o compass_n but_o to_o go_v to_o the_o exactness_n of_o it_o it_o be_v the_o same_o for_o the_o departure_n from_o the_o meridian_n a_o d._n as_o sine_fw-la comp_n the_o course_n a_o b_o d_o 56_o d._n 15_o m._n co_fw-la be_v 0,2552609_o to_o the_o difference_n of_o latitude_n 600_o ten_o b_o d_o 2,7781512_o so_o be_v the_o sine_fw-la of_o the_o course_n 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e._n in_o leag_n dep._n w._n in_o leag_n deg_fw-la min._n 6_o wednesday_n 17_o 19_o 060_o 518_o 7_o thursday_n 16_o 47_o 060_o 556_o 8_o friday_n 16_o 54_o 060_o 606_o 9_o saturday_n 16_o 29_o 060_o 643_o 10_o sunday_n 16_o 19_o 060_o 678_o 11_o monday_n 16_o 21_o 060_o 726_o 12_o tuesday_n 16_o 28_o 060_o 784_o 13_o wednesday_n 16_o 35_o 060_o 840_o 14_o thursday_n 16_o 27_o 060_o 889_o 15_o friday_n 16_o 24_o 060_o 929_o 16_o saturday_n 16_o 2_o 060_o 973_o 17_o sunday_n 16_o 44_o 060_o 1003_o guess_n be_v the_o log-line_n every_o 2_o hour_n your_o course_n and_o distance_n be_v set_v
down_o upon_o the_o logboard_n every_o 2_o hour_n whereby_o you_o may_v see_v it_o and_o work_v it_o every_o 24_o hour_n to_o find_v the_o departure_n and_o difference_n of_o latitude_n now_o whatsoever_o i_o find_v the_o departure_n to_o be_v i_o add_v it_o from_o the_o first_o day_n all_o along_o thus_o the_o departure_n when_o i_o set_v the_o lizard_n which_o be_v n_n n_o e_o 6_o league_n off_o be_v 2_o league_n west_n i_o keep_v mind_n of_o that_o till_o the_o next_o day_n at_o noon_n and_o i_o find_v what_o departure_n i_o have_v make_v from_o the_o meridian_n that_o i_o be_v in_o the_o day_n before_o at_o noon_n by_o the_o thing_n i_o have_v give_v i_o and_o here_o i_o find_v it_o be_v 19_o league_n i_o add_v it_o to_o my_o departure_n from_o the_o meridian_n west_n yesterday_o 2_o league_n and_o it_o make_v my_o whole_a departure_n west_n 21_o league_n again_o the_o next_o day_n at_o noon_n i_o work_v my_o ship_n travis_n as_o have_v be_v show_v and_o i_o find_v that_o she_o have_v depart_v from_o the_o meridian_n she_o be_v in_o yesterday_o 38_o league_n west_n which_o i_o add_v to_o what_o i_o have_v before_o which_o be_v 21_o and_o it_o make_v 59_o league_n and_o thus_o i_o go_v forward_o add_v my_o last_o day_n departure_n in_o its_o true_a column_n to_o all_o the_o rest_n which_o be_v in_o one_o sum_n and_o by_o this_o mean_v the_o last_o line_n be_v the_o whole_a reckon_a 21_o 38_o 59_o in_o the_o east_n column_n i_o set_v cipher_n to_o fill_v it_o up_o till_o i_o have_v some_o east_n departure_n to_o put_v in_o it_o and_o as_o that_o increase_v so_o i_o add_v it_o as_o the_o other_o every_o day_n also_o i_o carry_v the_o west_n departure_n along_o in_o its_o full_a number_n of_o league_n in_o the_o same_o line_n without_o increase_n or_o decrease_v till_o such_o time_n as_o i_o have_v more_o to_o increase_v it_o and_o then_o i_o increase_v that_o and_o carry_v the_o whole_a ea_n with_o it_o in_o the_o same_o line_n and_o thus_o you_o have_v need_n to_o look_v upon_o nothing_o but_o the_o last_o line_n to_o resolve_v you_o any_o thing_n that_o you_o desire_v either_o of_o your_o course_n make_v good_a since_o you_o set_v out_o your_o distance_n upon_o a_o straight_a line_n that_o you_o have_v fail_v your_o port_n bear_v from_o you_o what_o departure_n be_v yet_o between_o you_o and_o your_o port_n your_o distance_n to_o it_o upon_o a_o straight_a line_n for_o there_o you_o have_v your_o whole_a westing_n and_o your_o whole_a ea_n and_o the_o latitude_n you_o be_v in_o as_o also_o the_o latitude_n of_o the_o place_n you_o be_v bind_v to_o whereby_o as_o i_o have_v former_o show_v you_o may_v find_v they_o if_o there_o be_v longitude_n but_o one_o way_n you_o will_v see_v nothing_o but_o cipher_n in_o the_o other_o column_n this_o way_n you_o see_v be_v do_v without_o a_o plat._n i_o hold_v a_o plat_v to_o be_v necessary_a only_o to_o show_v what_o danger_n lie_v in_o your_o way_n that_o so_o you_o may_v shape_v a_o course_n clear_a by_o it_o and_o i_o shall_v use_v a_o plat_v for_o nothing_o else_o except_o it_o be_v for_o coast_v where_o it_o be_v real_o useful_a i_o common_o set_v down_o the_o ea_n or_o westing_n between_o the_o place_n i_o set_v and_o the_o place_n i_o be_o bind_v to_o at_o the_o begin_n of_o my_o reckon_n as_o also_o the_o latitude_n of_o each_o place_n as_o i_o have_v do_v here_o you_o may_v ask_v why_o i_o do_v not_o set_v down_o the_o course_n that_o i_o make_v good_a every_o day_n indeed_o that_o be_v not_o unnecessary_a but_o the_o reason_n why_o i_o omit_v it_o be_v first_o because_o i_o find_v it_o of_o little_a use_n in_o my_o reckon_a and_o second_o i_o find_v it_o can_v be_v better_o express_v in_o a_o journal_n which_o be_v keep_v with_o my_o reckon_a and_o indeed_o there_o i_o set_v it_o with_o the_o wind_n and_o the_o reason_n for_o steer_v upon_o such_o course_n but_o i_o leave_v every_o one_o to_o their_o own_o judgement_n for_o that_o as_o also_o for_o distance_n and_o wind_n for_o difference_n and_o variation_n it_o will_v have_v be_v necessary_a here_o to_o have_v set_v down_o some_o table_n to_o have_v work_v triangle_n by_o for_o as_o i_o have_v say_v sometime_o in_o 24_o hour_n you_o have_v a_o travis_n of_o 4_o or_o 5_o several_a course_n and_o to_o work_v they_o this_o way_n may_v seem_v tedious_a i_o commend_v you_o to_o my_o father_n practice_n where_o there_o be_v as_o good_a table_n as_o can_v be_v to_o every_o degree_n of_o the_o compass_n its_o use_n be_v easy_a and_o work_n to_o the_o ten_o part_n of_o a_o mile_n or_o league_n concern_v the_o variation_n of_o the_o compass_n there_o be_v always_o two_o thing_n give_v to_o find_v the_o variation_n of_o the_o compass_n that_o be_v the_o true_a amplitude_n of_o the_o sun_n rise_v and_o the_o magnetical_a amplitude_n of_o the_o sun_n rise_v or_o set_v the_o true_a amplitude_n of_o the_o sun_n rise_v be_v as_o i_o have_v say_v before_o in_o another_o place_n the_o true_a and_o absolute_a quantity_n of_o degree_n that_o the_o sun_n rise_v from_o the_o east_n either_o northwards_o or_o southwards_o or_o set_v from_o the_o west_n and_o be_v find_v as_o i_o have_v before_o show_v in_o the_o use_n of_o the_o sphere_n the_o magnetical_a amplitude_n of_o the_o sun_n be_v what_o the_o sun_n rise_v from_o the_o east_n or_o set_v from_o the_o west_n by_o the_o compass_n now_o because_o the_o first_o give_v the_o truth_n how_o far_o the_o sun_n rise_v from_o the_o east_n or_o set_v from_o the_o west_n therefore_o whatsoever_o difference_n there_o be_v between_o they_o so_o much_o be_v the_o variation_n as_o now_o suppose_v i_o find_v in_o a_o certain_a latitude_n such_o a_o day_n of_o the_o month_n by_o the_o sphere_n that_o the_o sun_n rise_v to_o the_o northwards_o of_o the_o east_n 17_o degree_n that_o be_v the_o true_a amplitude_n but_o i_o observe_v the_o sun_n at_o her_o rise_n with_o a_o azimuth_n compass_n which_o be_v make_v for_o that_o purpose_n and_o find_v that_o she_o rise_v but_o east_n 10_o degree_n northerly_a then_o i_o conclude_v the_o variation_n be_v 7_o deg_fw-la 0_o min._n or_o the_o compass_n be_v false_a so_o much_o so_o that_o whereas_o if_o i_o direct_v my_o course_n east_n 10_o degree_n northerly_a by_o the_o compass_n i_o do_v not_o go_v on_o that_o course_n but_o i_o go_v east_n and_o by_o north_n 5_o deg_fw-la 45_o min._n northerly_a which_o be_v just_a 7_o d._n from_o my_o expectation_n or_o east_n 17_o deg_fw-la northerly_a the_o true_a amplitude_n now_o that_o be_v a_o gross_a error_n and_o in_o long_a run_n may_v deceive_v a_o man_n much_o and_o perhaps_o be_v a_o mean_n to_o lose_v a_o ship_n when_o one_o little_a think_v of_o it_o and_o therefore_o it_o ought_v to_o be_v look_v to_o a_o azimuth_n compass_n be_v no_o other_o in_o effect_n but_o a_o compass_n fit_v for_o the_o exact_a take_n of_o the_o sun_n at_o her_o rise_n or_o set_v or_o upon_o other_o certain_a time_n of_o the_o day_n as_o you_o may_v have_v occasion_n in_o like_a manner_n you_o may_v find_v the_o variation_n of_o the_o compass_n at_o other_o time_n by_o take_v the_o sun_n azimuth_n at_o any_o time_n of_o the_o day_n example_n suppose_v i_o be_v in_o the_o latitude_n of_o 33_o deg_fw-la 20_o min._n northerly_a and_o upon_o the_o 8_o the_o day_n of_o november_n the_o sun_n declination_n be_v southerly_a 19_o deg_fw-la 20_o min._n i_o demand_v the_o sun_n azimuth_n at_o 8_o of_o the_o clock_n the_o sun_n azimuth_n at_o her_o rise_n as_o i_o have_v show_v be_v the_o compliment_n of_o the_o sun_n amplitude_n but_o after_o the_o sun_n be_v up_o it_o may_v be_v also_o the_o distance_n of_o the_o sun_n from_o the_o east_n and_o west_n azimuth_n now_o in_o this_o proposition_n you_o desire_v to_o know_v how_o many_o degree_n the_o sun_n be_v from_o the_o east_n and_o west_n azimuth_n which_o be_v that_o part_n of_o the_o heaven_n that_o be_v distant_a from_o the_o sun_n parallel_n to_o the_o horizon_n over_o the_o east_n point_v of_o it_o or_o if_o it_o have_v be_v at_o 4_o of_o the_o clock_n in_o the_o afternoon_n it_o will_v have_v be_v require_v from_o the_o west_n point_n for_o the_o resolve_v this_o question_n project_v a_o sphere_n as_o have_v be_v teach_v for_o the_o latitude_n propose_v with_o the_o parallel_n of_o the_o sun_n declination_n draw_v as_o it_o be_v give_v divide_v this_o parallel_n of_o declination_n into_o the_o hour_n of_o the_o day_n from_o 6_o to_o 12_o or_o which_o serve_v from_o 12_o to_o 6_o in_o the_o afternoon_n the_o way_n to_o divide_v it_o be_v thus_o from_o 6_o of_o the_o
demonstrate_v it_o as_o evident_o as_o can_v be_v for_o mercator_n use_v the_o table_n here_o insert_v the_o use_n of_o the_o forego_n table_n of_o meridional_a part_n when_o you_o work_v this_o way_n find_v first_o what_o latitude_n you_o be_v in_o if_o you_o can_v observe_v do_v it_o by_o the_o thing_n give_v that_o 24_o hour_n then_o take_v notice_n what_o latitude_n you_o be_v in_o the_o day_n before_o and_o look_v in_o the_o table_n what_o answer_v to_o each_o latitude_n set_v they_o down_o subtract_v the_o lesser_a from_o the_o great_a and_o the_o remainder_n be_v the_o meridional_a part_n contain_v between_o the_o two_o latitude_n which_o number_n make_v for_o the_o length_n of_o the_o side_n which_o contain_v the_o difference_n of_o latitude_n and_o so_o work_v according_a to_o the_o direction_n follow_v i_o will_v be_v brief_a example_n to_o find_v the_o meridional_a part_n answer_v to_o any_o latitude_n let_v the_o one_o latitude_n be_v 50_o deg_fw-la 9′_n in_o the_o table_n 3488_o 3274_o 214_o answer_n it_o let_v the_o other_o lat._n be_v 47_o deg_fw-la 48′_n in_o the_o table_n answer_v it_o subtract_v the_o lesser_a from_o the_o great_a and_o the_o remainder_n be_v the_o meridional_a part_n contain_v in_o that_o difference_n of_o latitude_n the_o same_o be_v to_o be_v understand_v of_o any_o latitude_n else_o question_n i._n the_o latitude_n of_o two_o place_n be_v give_v and_o the_o rumb_n to_o find_v the_o distance_n and_o difference_n of_o longitude_n suppose_v i_o set_v sail_n from_o a_o place_n in_o the_o latitude_n of_o 39_o deg_fw-la 12_o min._n north_n latitude_n and_o be_o bind_v to_o a_o place_n in_o the_o latitude_n of_o 13_o deg_fw-la 12_o min._n north_n latitude_n which_o bear_v s_n w_n by_o w_n from_o the_o other_o i_o demand_v the_o distance_n between_o those_o place_n and_o difference_n of_o longitude_n let_v a_o represent_v the_o northermost_a place_n c_o the_o southermost_a then_o be_v a_o and_o b_o the_o latitude_n of_o each_o place_n c_o b_o the_o difference_n of_o longitude_n b_o a_o c_o be_v the_o course_n from_o the_o northermost_a to_o the_o southermost_a place_n for_o the_o distance_n between_o the_o place_n a_o c._n as_o sine_fw-la comp_n a_o 56_o deg_fw-la 15_o min._n comp_n arith_n 0,25526_o to_o a_o b_o the_o difference_n of_o latitude_n in_o mile_n 1560_o 3,19312_o so_o be_v radius_fw-la  _fw-fr to_z the_o distance_n between_o they_o c_o a_o 2808_o mile_n 3,44838_o for_o the_o difference_n of_o longitude_n the_o meridional_a part_n answer_v to_o 39_o deg_fw-la 12_o min._n be_v 2560_o the_o meridional_a part_n answer_v to_o 13_o deg_fw-la 12_o min._n be_v 0799_o the_o meridional_a part_n contain_v between_o the_o two_o lat._n 1761_o as_o radius_fw-la  _fw-fr to_n b_o a_o 1761_o part_n 3,245759_o so_o be_v tan._n the_o rumb_n a_o 56_o deg_fw-la 15_o min._n 10,175107_o to_o c_o b_o the_o diff._n of_o longitude_n in_o minute_n 2635_o m._n 3,420866_o the_o quotient_n be_v the_o number_n of_o degree_n and_o the_o remainder_n be_v the_o number_n of_o minute_n contain_v in_o the_o difference_n of_o longitude_n 43_o deg_fw-la 55_o min._n question_v ii_o course_n and_o distance_n run_v with_o one_o latitude_n give_v to_o find_v the_o other_o latitude_n and_o the_o difference_n of_o longitude_n suppose_v i_o set_v from_o the_o latitude_n of_o 49_o deg_fw-la 9_o min._n north_n and_o sail_n s_o w_n b_o w_n 2808_o mile_n i_o demand_v the_o latitude_n i_o shall_v then_o be_v in_o and_o the_o difference_n of_o longitude_n let_v a_o be_v the_o latitude_n of_o 49_o deg_fw-la 9_o min._n let_v a_o c_o be_v the_o distance_n run_v 2808_o mile_n then_o be_v a_o b_o the_o difference_n of_o latitude_n and_o c_o b_o the_o difference_n of_o longitude_n for_o the_o difference_n of_o latitude_n a_o b._n to_o a_fw-it b_o 1560_o mile_n which_o be_v divide_v by_o 60_o the_o quotient_a and_o the_o remainder_n be_v the_o difference_n of_o latitude_n in_o degree_n and_o minute_n which_o be_v 26_o d._n 0_o m._n that_o subtract_v from_o 49_o d._n 9_o m._n leave_v the_o latitude_n you_o be_v now_o in_o 23_o d._n 9_o m._n the_o reason_n why_o there_o be_v no_o inequality_n between_o degree_n of_o latitude_n be_v because_o all_o meridian_n be_v great_a circle_n so_o that_o 60_o mile_n be_v a_o degree_n of_o they_o always_o for_o the_o difference_n of_o longitude_n the_o meridional_a part_n contain_v between_o these_o two_o latitude_n i_o find_v to_o be_v 3396_o 1428_o 1968_o pt_n as_o radius_fw-la  _fw-fr to_z a_o b_o in_o part_n 1968_o 3,294025_o so_o be_v tang._n a_o the_o rumb_n 56_o deg_fw-la 15_o min._n 10,175107_o to_o the_o difference_n of_o longitude_n 2945_o m._n 3,469133_o now_o you_o may_v ask_v a_o reason_n why_o this_o difference_n of_o longitude_n shall_v differ_v from_o the_o other_o in_o the_o last_o question_n see_v the_o difference_n of_o latitude_n course_n and_o distance_n in_o each_o question_n be_v alike_o the_o reason_n be_v because_o this_o question_n run_v between_o two_o less_o parallel_n than_o the_o other_o do_v and_o therefore_o the_o same_o thing_n must_v give_v a_o great_a part_n of_o this_o parallel_n than_o it_o do_v of_o the_o other_o though_o the_o number_n of_o mile_n of_o departure_n be_v alike_o diwide_v 2945_o min._n by_o 60_o and_o you_o have_v the_o difference_n of_o longitude_n in_o degree_n and_o minute_n 49_o deg_fw-la 5_o min._n question_n iii_o the_o latitude_n of_o two_o place_n and_o the_o distance_n between_o they_o give_v to_o find_v the_o course_n and_o difference_n of_o longitude_n let_v one_o place_n namely_o a_o be_v in_o the_o latitude_n of_o 49_o deg_fw-la 9_o min._n north_n let_v the_o other_o place_n namely_o c_o be_v in_o the_o latitude_n of_o 23_o deg_fw-la 0_o min._n north_n and_o let_v the_o course_n be_v between_o the_o south_n and_o the_o east_n the_o distance_n between_o they_o be_v a_o c_o 2808_o mile_n for_o the_o course_n a._n as_o a_o c_o dist_n 2808_o mil._n 6,551602_o be_v to_o radius_fw-la  _fw-fr so_n be_v the_o diff._n of_o lat._n a_o b_o reduce_v into_o mile_n 1560_o mile_n 3,193124_o to_o the_o sine_fw-la c_o who_o comp._n be_v a_o 9,744726_o which_o be_v 56_o deg_fw-la 15_o min._n to_o the_o eastward_n of_o the_o south_n for_o the_o difference_n of_o longitude_n b_o c._n as_o radius_fw-la  _fw-fr to_n b_o a_o in_o part_n 1968_o 3,294025_o so_o be_v tangent_fw-la the_o course_n a_o 56_o deg_fw-la 15_o min._n 10,175107_o to_o the_o difference_n of_o longitude_n in_o minute_n 2945_o 3,469133_o which_o be_v as_o it_o be_v in_o the_o last_o question_n 49_o deg_fw-la 5_o min._n question_n iu._n the_o latitude_n of_o two_o place_n and_o their_o difference_n of_o longitude_n give_v to_o find_v the_o course_n and_o distance_n provide_v the_o course_n be_v between_o the_o north_n and_o the_o west_n let_v the_o latitude_n be_v as_o before_o and_o the_o difference_n of_o longitude_n 49_o deg_fw-la 5_o min._n or_o 2945_o part_n or_o minute_n for_o the_o course_n as_o the_o diff._n of_o latitude_n in_o part_n a_o b_o 1968_o co_z be_v 6,70597_o be_v to_o radius_fw-la  _fw-fr so_n be_v the_o diff._n of_o longitude_n in_o minute_n or_o part_n b_o c_o 2945_o 3,46908_o to_o the_o tangent_fw-la of_o the_o course_n a_o 56_o deg_fw-la 15_o min._n 10,17505_o to_o the_o westward_n of_o the_o north._n as_o sine_fw-la c_o 33_o deg_fw-la 45_o min._n comp_n arith_n 0,25526_o to_o the_o difference_n of_o latitude_n in_o mile_n a_o b_o 1560_o 3,19312_o so_o be_v radius_fw-la  _fw-fr to_z the_o distance_n run_v c_o a_o 2808_o mile_n 3,44839_o question_n v._o the_o difference_n of_o longitude_n course_n and_o one_o latitude_n give_v to_o find_v the_o other_o latitude_n and_o the_o distance_n in_o the_o triangle_n cba_n let_v c_o b_o be_v the_o difference_n of_o longitude_n 49_o deg_fw-la 5_o min._n or_o 2945_o min._n a_o the_o latitude_n of_o 23_o deg_fw-la 9_o min._n north_n latitude_n c_o a_o b_o the_o angle_n of_o the_o course_n north-wester_o 56_o deg_fw-la 15_o min._n let_v it_o be_v require_v to_o find_v a_o b_o the_o difference_n of_o latitude_n which_o add_v to_o the_o latitude_n of_o a_o 23_o deg_fw-la 9_o min._n will_v be_v the_o latitude_n of_o the_o other_o place_n b_o and_o a_o c_o the_o distance_n between_o they_o here_o you_o must_v find_v your_o difference_n of_o latitude_n in_o part_n first_o which_o will_v be_v reduce_v into_o mile_n after_o the_o latitude_n of_o the_o place_n at_o b_o be_v find_v and_o then_o find_v your_o distance_n 49_o deg_fw-la 5_o min._n reduce_v into_o minute_n as_o i_o say_v in_o the_o question_n be_v 2945_o min._n the_o difference_n of_o longitude_n give_v for_o the_o difference_n of_o latitude_n in_o part_n as_o radius_fw-la  _fw-fr to_z the_o difference_n of_o longitude_n in_o part_n 2945_o part_n 3,469085_o so_o be_v tan._n comp_n
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