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 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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
6_o be_v equal_a to_o the_o sine_fw-la of_o s_o ♈_o when_o you_o have_v measure_v it_o convert_v it_o into_o time_n and_o set_v it_o down_o i_o find_v it_o to_o be_v 1_o hour_n 44_o min._n the_o meridian_n altitude_n of_o the_o sun_n be_v give_v and_o the_o latitude_n to_o find_v the_o sun_n declination_n as_o also_o all_o the_o other_o thing_n before_o find_v latitude_n 51_o deg_fw-la northerly_a meridian_n altitude_n 52_o deg_fw-la 30_o min._n i_o demand_v the_o sun_n declination_n or_o any_o other_o thing_n that_o i_o find_v before_o for_o the_o do_n of_o this_o project_n your_o sphere_n as_o before_o be_v show_v that_o do_v i_o consider_v the_o meridian_n altitude_n of_o the_o sun_n be_v give_v to_o be_v 52_o deg_fw-la 30_o min._n i_o will_v take_v 52_o deg_fw-la 30_o min._n from_o the_o scale_n of_o chord_n and_o fix_v one_o foot_n of_o my_o compass_n in_o the_o south_n point_n of_o the_o horizon_n at_o a_o and_o extend_v the_o other_o foot_n upward_o upon_o the_o meridian_n 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to_o be_v the_o middle_a part_n and_o that_o it_o be_v a_o adjacent_a extreme_a i_o will_v apply_v the_o rule_n thus_o it_o say_v the_o sine_fw-la of_o the_o middle_a part_n which_o intimate_v that_o the_o middle_a part_n must_v be_v always_o so_o call_v as_o you_o may_v take_v the_o sine_fw-la of_o it_o now_o because_o it_o be_v note_v to_o be_v a_o compliment_n you_o must_v call_v it_o sine_fw-la compliment_n to_o find_v the_o sine_fw-la of_o it_o this_o do_v i_o will_v go_v to_o one_o of_o the_o extreme_n and_o consider_v what_o the_o axiom_n say_v for_o that_o admit_v it_o be_v the_o extreme_a c_o b_o it_o say_v the_o sine_fw-la of_o the_o middle_a part_n with_o radius_fw-la be_v equal_a to_o the_o tangent_n of_o the_o extreme_n adjacent_a from_o whence_o i_o conclude_v that_o i_o must_v call_v c_o b_o so_o as_o that_o i_o may_v have_v the_o tangent_fw-la of_o it_o now_o c_z b_o be_v not_o note_v to_o be_v a_o compliment_n and_o therefore_o i_o call_v it_o tangent_fw-la c_o b._n 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0_o min._n the_o measure_n of_o f_o ♈_o 0_o be_v e_z k_o =_o to_o t_o a_o the_o compliment_n of_o t_o s_o to_o 90_o deg_fw-la t_z s_z be_v the_o latitude_n 50_o deg_fw-la 0_o min._n and_o i_o be_o to_o find_v ♈_o 0_o the_o sun_n amplitude_n of_o rise_v i_o consider_v it_o be_v a_o opposite_a extreme_a and_o that_o be_v 0_o be_v the_o middle_a part_n sine_fw-la f_o 0_o +_o radius_fw-la be_v =_o to_o sine_fw-la ♈_o +_o sine_fw-la ♈_o 0._o sine_fw-la f_o 0_o the_o sun_n declination_n 13_o deg_fw-la 15_o min._n 9,36021_o sine_fw-la f_o ♈_o 0_o the_o come_v of_o the_o pole_n elev_n 40_o d._n co_fw-la be_v 9,19193_o sine_fw-la ♈_o 0_o the_o sun_n amplitude_n of_o rise_v or_o set_v 20_o deg_fw-la 53_o min._n 24_o sec_fw-la 9,55214_o use_v this_o way_n to_o find_v the_o sun_n true_a amplitude_n of_o rise_v upon_o occasion_n of_o find_v the_o variation_n of_o the_o compass_n the_o sun_n place_n of_o rise_v from_o the_o east_n towards_o the_o north_n namely_o east_n 20_o deg_fw-la 53_o min._n 24_o sec_fw-la northerly_a o_o ♈_o be_v the_o compliment_n of_o o_o e_o the_o sun_n azimuth_n of_o rise_v from_o the_o north_n so_o that_o if_o you_o subtract_v it_o from_o 90_o deg_fw-la ♈_o e_o the_o remainder_n be_v 69_o deg_fw-la 6_o min._n 36_o sec_fw-la o_o e_o but_o if_o you_o have_v a_o desire_n to_o find_v the_o sun_n azimuth_n by_o the_o thing_n you_o have_v give_v here_o it_o be_v in_o the_o triangle_n f_o e_o o_o and_o be_v do_v as_o in_o this_o follow_a question_n latitude_n 50_o deg_fw-la declination_n 13_o deg_fw-la 15_o min._n i_o demand_v the_o sun_n azimuth_n of_o rise_v or_o set_v let_v f_o o_o f_o p_o be_v a_o arch_n of_o the_o meridian_n cut_v the_o sun_n at_o his_o rise_n which_o be_v at_o o_o f_o o_fw-fr be_v the_o sun_n declination_n 23_o deg_fw-la 15_o min._n which_o subtract_v from_o f_o f_o 90_o deg_fw-la the_o remainder_n be_v o_o f_o 76_o deg_fw-la 45_o min._n the_o sun_n distance_n from_o the_o north_n pole_n and_o f_o e_z be_v the_o pole_n elevation_n 50_o deg_fw-la 0_o min._n and_o thus_o you_o have_v two_o side_n give_v in_o the_o right_a angle_a triangle_n o_o e_o f_o to_o find_v the_o three_o side_n o_o f_o it_o be_v a_o opposite_a extreme_a and_o f_o o_fw-fr be_v the_o middle_a part_n the_o general_a axiom_n produce_v this_o sine_fw-la come_v f_o o_o +_o radius_fw-la be_v =_o to_o sine_fw-la come_v f_o e_o +_o sine_fw-la come_v o_o e._n sine_fw-la come_v o_o f_o 76_o deg_fw-la 45_o min._n 9,360215_o sine_fw-la come_v f_o e_o 50_o deg_fw-la 0_o min._n comp_n arith_n 0,191932_o sine_fw-la come_v o_o e_o 69_o deg_fw-la 6_o min._n 36_o sec_fw-la 9,552147_o thus_o i_o find_v the_o sun_n rise_v to_o the_o eastward_n of_o the_o north_n 69_o deg_fw-la 6_o min._n 36_o sec_fw-la which_o be_v e_z b_o n_z 9_o deg_fw-la 38_o min._n 24_o sec_fw-la northerly_a the_o other_o question_n show_v the_o same_o when_o you_o find_v the_o sun_n amplitude_n latitude_n 50_o deg_fw-la declination_n 13_o deg_fw-la 15_o min._n northerly_a i_o demand_v the_o sun_n height_n at_o six_o of_o the_o clock_n let_v g_z p_o m_o n_n be_v a_o azimuth_n pass_v through_o the_o hour_n of_o 6_o now_o in_o the_o triangle_n ♈_o m_o p_o right_a angle_a at_o m_o you_o have_v give_v p_o ♈_o the_o sun_n declination_n 13_o deg_fw-la 15_o min._n and_o the_o angle_n at_o ♈_o namely_o p_o ♈_o m_o =_o to_o the_o arch_n f_o o_fw-fr for_o f_o o_fw-fr be_v the_o measure_n of_o it_o it_o be_v the_o pole_n elevation_n 50_o deg_fw-la 0_o min._n to_o find_v p_o m_o the_o sun_n height_n at_o six_o of_o the_o clock_n i_o consider_v it_o be_v a_o opposite_a extreme_a and_o the_o require_a thing_n p_o m_z be_v the_o middle_a part_n sine_fw-la p_o m_o +_o radius_fw-la be_v =_o to_o sine_fw-la p_o ♈_o +_o sine_fw-la p_o ♈_o m._n sine_fw-la p_o ♈_o the_o sun_n declination_n 13_o deg_fw-la 15_o min._n 9,360215_o sine_fw-la p_o ♈_o m_o the_o pole_n elevation_n 50_o deg_fw-la 0_o min._n 9,884254_o sine_fw-la p_o m_o the_o sun_n height_n at_o six_o of_o the_o clock_n 10_o deg_fw-la 6_o min._n 51_o see_v 9,244469_o the_o same_o thing_n give_v to_o find_v the_o sun_n azimuth_n at_o six_o of_o the_o clock_n the_o sun_n azimuth_n at_o 6_o of_o the_o clock_n be_v m_o ♈_o and_o the_o reason_n be_v for_o that_o p_o u._fw-mi in_o the_o heaven_n be_v parallel_n to_o the_o horizon_n be_v as_o many_o degree_n in_o that_o circle_n as_o ♈_o m_z be_v in_o the_o horizon_n for_o ♈_o be_v under_z m_z and_z m_z under_z p._n so_o that_o this_o question_n will_v fall_v in_o the_o same_o triangle_n as_o the_o other_o do_v and_o we_o will_v use_v the_o same_o thing_n to_o find_v it_o the_o angle_n p_o ♈_o m_o be_v 50_o deg_fw-la 0_o min._n the_o pole_n elevation_n p_o ♈_o be_v the_o sun_n declination_n 13_o d._n 15_o m._n and_o ♈_o m_o be_v require_v i_o consider_v that_o this_o be_v a_o adjacent_a extreme_a and_o that_o p_o ♈_o m_o be_v the_o middle_a part_n the_o general_a axiom_n produce_v sine_fw-la come_v p_o ♈_o m_o +_o radius_fw-la be_v =_o to_o tang._n ♈_o m_o +_o 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there_o will_v be_v this_o inference_n produce_v from_o the_o general_a axiom_n sine_fw-la i_o l_o +_o radius_fw-la be_v =_o to_o sine_fw-la i_o ♈_o l_o +_o sine_fw-la l_o ♈_o sine_fw-la i_o ♈_o l_o the_o latitude_n 50_o deg_fw-la comp_n arith_n 0,1157459_o sine_fw-la i_o l_o the_o sun_n declination_n 13_o deg_fw-la 15_o min._n 9,3602154_o sine_fw-la l_o ♈_o sun_n height_n be_v due_a east_n 17_o do_v 24′_n 34″_n 9,4759613_o the_o same_o height_n that_o the_o sun_n be_v be_v due_a east_n in_o the_o morning_n the_o same_o height_n he_o be_v when_o he_o be_v due_a west_n in_o the_o afternoon_n the_o latitude_n be_v 50_o deg_fw-la 0_o min._n declination_n 13_o deg_fw-la 15_o min._n i_o desire_v to_o know_v the_o difference_n of_o ascension_n i_o have_v show_v what_o the_o difference_n of_o ascension_n mean_v in_o this_o book_n before_o and_o if_o you_o look_v in_o the_o question_n to_o find_v the_o amplitude_n of_o the_o sun_n rise_v before_o there_o be_v the_o same_o scheme_n that_o 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convert_v into_o time_n be_v 1_o hour_n 5′_n 2_o 15_o and_o ⅔_n of_o 1_o 15_o of_o a_o minute_n the_o same_o thing_n give_v to_o find_v the_o time_n of_o sun_n rise_v for_o the_o do_n of_o this_o first_o find_v the_o difference_n of_o ascension_n as_o have_v be_v show_v in_o the_o last_o question_n and_o convert_v it_o into_o time_n which_o do_v subtract_v it_o from_o 6_o hour_n and_o you_o have_v your_o desire_n in_o this_o case_n where_o the_o declination_n and_o latitude_n be_v both_o one_o way_n