the_o angle_n at_o a_o be_v the_o compliment_n of_o the_o latitude_n and_o the_o angle_n at_o c_o the_o vertical_a angle_n make_v between_o the_o equator_fw-la and_o the_o vertical_a circle_n pass_v by_o the_o sun_n at_o c_o perpendicular_o to_o the_o horizon_n ab_fw-la wherefore_o know_v the_o base_a ac_fw-la to_o be_v 65_o degree_n 23_o minute_n and_o the_o angle_n at_o a_o to_o be_v 37_o degree_n 30_o minute_n i_o may_v find_v the_o side_n bc_n for_o if_o i_o place_v the_o thread_n to_o the_o intersection_n of_o the_o contrary_a sine_fw-la of_o 90_o degree_n with_o the_o right_n sine_fw-la of_o 65_o degree_n 22_o minute_n it_o will_v cut_v the_o contrary_a sine_fw-la of_o 37_o degree_n 30_o minute_n at_o the_o right_n sine_fw-la of_o 33_o degree_n 36_o minute_n and_o such_o be_v the_o side_n bc_n which_o be_v require_v chap._n xxiv_o to_o find_v a_o side_n by_o know_v the_o base_a and_o the_o other_o side_n as_o the_o sine_fw-la of_o the_o compliment_n of_o the_o side_n give_v to_z 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minute_n for_o the_o hour_n from_o the_o meridian_n which_o be_v require_v the_o like_a may_v you_o do_v with_o any_o of_o the_o other_o angle_n as_o to_o find_v the_o azimuth_n or_o the_o angle_n of_o the_o sun_n position_n in_o regard_n of_o pole_n and_o zenith_n but_o you_o shall_v have_v a_o more_o speedy_a way_n to_o perform_v this_o problem_n by_o the_o planisphere_n on_o the_o back_n of_o the_o quadrat_fw-la for_o by_o know_v the_o three_o side_n of_o any_o spherical_a triangle_n you_o shall_v find_v a_o angle_n as_o speedy_o as_o if_o you_o have_v the_o other_o two_o angle_n also_o chap._n xlii_o to_o find_v a_o side_n by_o know_v the_o three_o angle_n in_o any_o spherical_a triangle_n the_o side_n may_v be_v change_v into_o angle_n and_o the_o angle_n into_o side_n by_o take_v first_o for_o any_o one_o angle_n and_o his_o subtend_a side_n the_o remainder_n to_o a_o semicircle_n then_o shall_v the_o operation_n be_v the_o same_o as_o in_o the_o former_a chapter_n thus_o in_o the_o triangle_n zp_v have_v the_o angle_n zp_v 53_o degree_n 40_o minute_n and_o zsp_v 34_o degree_n 47_o minute_n with_o s_n zp_v 113_o degree_n 17_o minute_n if_o you_o take_v the_o great_a angle_n of_o 113_o degree_n 17_o minute_n out_o of_o 180_o degree_n there_o will_v remain_v 66_o degree_n 43_o minute_n then_o as_o if_o you_o have_v a_o triangle_n of_o three_o know_a side_n one_o of_o 53_o degree_n 40_o minute_n another_o of_o 34_o degree_n 47_o minute_n and_o a_o three_o of_o 66_o degree_n 43_o minute_n you_o may_v find_v a_o angle_n opposite_a to_o any_o one_o of_o these_o side_n by_o the_o last_o chapter_n so_o shall_v the_o angle_v thus_o find_v be_v the_o side_n require_v if_o it_o be_v not_o the_o angle_n
difference_n of_o the_o same_o point_n by_o the_o 18_o chap._n to_o be_v 15_o deg_fw-la 22_o min._n if_o i_o take_v 15_o deg_fw-la 22_o min._n out_o of_o 27_o deg_fw-la 54_o min._n because_o the_o declination_n be_v north_n there_o will_v remain_v 12_o deg_fw-la 32_o min._n for_o the_o oblique_a ascension_n likewise_o if_o i_o add_v 15_o deg_fw-la 22_o min._n to_o 27_o degree_n 54_o minute_n the_o sum_n will_v be_v 43_o degree_n 16_o minute_n for_o the_o oblique_a descension_n chap._n xxii_o have_v the_o azimuth_n the_o sun_n altitude_n and_o the_o declination_n to_o find_v the_o hour_n of_o the_o day_n as_o the_o cousin_n of_o the_o declination_n to_o the_o sine_fw-la of_o the_o azimuth_n so_o be_v the_o cousin_n of_o the_o altitude_n to_o the_o sine_fw-la of_o the_o hour_n thus_o in_o the_o triangle_n zp_n ♉_o in_o the_o diagram_n of_o the_o 6_o chapter_n have_v the_o side_n p_o ♉_o the_o compliment_n of_o declination_n 78_o degree_n 30_o min._n and_o the_o side_n z_o ♉_o the_o compliment_n of_o the_o sun_n altitude_n 64_o degree_n 4_o minute_n with_o the_o outward_a angle_n ♉_o zp_n the_o azimuth_n 74_o degree_n 22_o min._n we_o may_v find_v the_o angle_n zp_n ♉_o the_o hour_n from_o the_o meridian_n by_o the_o 40_o chapter_n of_o the_o second_o book_n for_o if_o we_o place_v the_o thread_n to_o the_o intersection_n of_o the_o contrary_a sine_fw-la of_o 78_o degree_n 30_o minute_n with_o the_o right_n sine_fw-la of_o 74_o degree_n 22_o minute_n it_o will_v cut_v the_o contrary_a sine_fw-la of_o 64_o degree_n 4_o minute_n at_o the_o right_n sine_fw-la of_o 62_o degree_n 6_o minute_n and_o such_o be_v the_o angle_n zp_n ♉_o the_o hour_n from_o the_o meridian_n or_o in_o time_n 4_o hour_n 8_o minute_n which_o be_v require_v chap._n xxiii_o have_v the_o hour_n of_o the_o day_n the_o sun_n altitude_n and_o the_o declination_n to_o find_v the_o azimuth_n as_o the_o cousin_n of_o the_o sun_n altitude_n to_o the_o sine_fw-la of_o the_o hour_n from_o the_o meridian_n so_o be_v the_o cousin_n of_o the_o declination_n to_o the_o sine_fw-la of_o the_o azimuth_n thus_o in_o the_o triangle_n zp_n ♉_o of_o the_o diagram_n in_o the_o 6_o chapter_n have_v the_o side_n z_o ♉_o the_o compliment_n of_o the_o sun_n altitude_n 64_o degree_n 4_o minute_n and_o the_o side_n p_o ♉_o the_o compliment_n of_o declination_n 78_o degree_n 30_o minute_n with_o the_o angle_n zp_n ♉_o the_o hour_n from_o the_o meridian_n 62_o degree_n 6_o minute_n we_o may_v find_v the_o angle_n pz_fw-fr ♉_o the_o azimuth_n by_o the_o 40_o chapter_n of_o the_o second_o book_n for_o if_o we_o place_v the_o thread_n upon_o the_o intersection_n of_o the_o contrary_a sine_fw-la of_o 64_o degree_n 4_o minute_n with_o the_o right_n sine_fw-la of_o 62_o degree_n 6_o minute_n it_o will_v cut_v the_o contrary_a sine_fw-la of_o 78_o degree_n 30_o minute_n at_o the_o right_n sine_fw-la of_o 74_o degree_n 22_o minute_n and_o such_o be_v the_o outward_a angle_n pz_n ♉_o the_o sun_n azimuth_n from_o the_o south_n which_o be_v require_v chap._n xxiv_o the_o latitude_n of_o the_o place_n the_o altitude_n and_o declination_n of_o the_o sun_n be_v give_v to_o find_v the_o hour_n of_o the_o day_n thus_o in_o the_o oblique_a spherical_a triangle_n zp_n ♉_o in_o the_o diagram_n of_o the_o 6_o chapter_n have_v the_o three_o side_n viz._n zp_v the_o compliment_n of_o the_o latitude_n 37_o degree_n 30_o minute_n and_o z_o ♉_o the_o compliment_n of_o the_o sun_n altitude_n 64_o degree_n 4_o minute_n with_o p_o ♉_o the_o compliment_n of_o declination_n 78_o degree_n 30_o minute_n we_o may_v find_v the_o angle_n zp_n ♉_o the_o hour_n from_o the_o meridian_n by_o the_o 41_o chapter_n of_o the_o second_o book_n but_o by_o this_o instrument_n more_o ready_o thus_o first_o by_o the_o 16_o chapter_n get_v the_o sun_n height_n or_o depression_n at_o the_o hour_n of_o 6_o and_o if_o the_o declination_n be_v north_n take_v the_o distance_n betwixt_o this_o sine_fw-la and_o the_o sine_fw-la of_o the_o altitude_n give_v either_o by_o substraction_n or_o with_o your_o compass_n this_o distance_n either_o count_v or_o place_n upon_o the_o contrary_a sine_fw-la of_o the_o compliment_n of_o the_o latitude_n and_o thereto_o place_v the_o thread_n the_o thread_n be_v thus_o place_v will_v cut_v the_o contrary_a sine_fw-la of_o 90_o degree_n at_o a_o right_a sine_fw-la or_o parallel_n which_o follow_v to_o the_o contrary_a sine_fw-la of_o the_o compliment_n of_o declination_n and_o thereto_o place_v the_o thread_n so_o shall_v it_o cut_v the_o contrary_a sine_fw-la of_o 90_o degree_n at_o the_o right_n sine_fw-la of_o the_o hour_n from_o six_o for_o as_o the_o cousin_n of_o the_o latitude_n to_o the_o distance_n betwixt_o the_o sine_fw-la of_o the_o height_n at_o six_o and_o the_o sine_fw-la of_o the_o altitude_n give_v so_o be_v the_o radius_fw-la to_o a_o four_o sine_fw-la then_o as_o the_o cousin_n of_o declination_n to_o this_o four_o sine_fw-la so_o be_v the_o radius_fw-la to_o the_o sine_fw-la of_o the_o hour_n from_o six_o thus_o in_o the_o diagram_n of_o the_o 6_o chapter_n have_v the_o sun_n declination_n eglantine_n or_o ♈_o o_fw-fr 11_o degree_n 30_o minute_n and_o the_o angle_n p_o ♈_o b_o the_o latitude_n of_o the_o place_n 52_o degree_n 30_o minute_n we_o have_v by_o the_o 16_o chapter_n the_o sun_n height_n at_o 6_o ro_n 9_o deg_fw-la 6_o min._n the_o sine_fw-la whereof_o be_v 158_o the_o radius_fw-la being_n 1000_o this_o sine_fw-la be_v compare_v with_o the_o sine_fw-la of_o 25_o deg_fw-la 56_o min._n 437_o the_o sine_fw-la of_o the_o sun_n altitude_n r_o a_o and_o take_v ro_n 158_o out_o of_o r_o a_o 437_o there_o will_v remain_v o_o a_o 279_o by_o which_o and_o the_o angle_n a_o ♉_o o_o the_o compliment_n of_o the_o latitude_n with_o the_o right_a angle_n at_o a_o we_o may_v find_v ♉_o o_fw-fr the_o hour_n from_o six_o for_o if_o we_o apply_v the_o thread_n to_o the_o intersection_n of_o the_o contrary_a sine_fw-la of_o 37_o deg_fw-la 30_o min._n with_o the_o right_a parallel_n of_o 279_o it_o will_v cut_v the_o contrary_a sine_fw-la of_o 90_o degree_n at_o the_o right_n sine_fw-la of_o about_o 27¼_n degree_n but_o see_v this_o 27¼_n degree_n which_o be_v o_fw-fr ♉_o be_v but_o upon_o the_o parallel_n of_o declination_n go_v therefore_o i_o place_v the_o thread_n again_o at_o the_o intersection_n of_o this_o 27¼_n with_o the_o contrary_a sine_fw-la of_o 78_o deg_fw-la 30_o min._n the_o compliment_n of_o declination_n go_v and_o it_o will_v cut_v the_o contrary_a sine_fw-la of_o 90_o deg_fw-la at_o the_o right_n sine_fw-la of_o 27_o deg_fw-la 54_o min._n and_o so_o much_o be_v ♈_o x_o or_o the_o angle_n ♈_o px_n the_o hour_n from_o six_o which_o be_v require_v and_o here_o note_v that_o if_o the_o altitude_n give_v be_v great_a than_o the_o altitude_n at_o six_o then_o be_v the_o time_n find_v to_o the_o southward_a of_o six_o but_o if_o it_o be_v lesser_a then_o be_v it_o to_o the_o northward_a but_o if_o the_o declination_n be_v southward_o then_o add_v the_o sine_fw-la of_o his_o depression_n at_o six_o to_o the_o sine_fw-la of_o the_o altitude_n give_v and_o with_o the_o same_o proceed_v in_o all_o respect_n as_o before_o and_o you_o shall_v have_v your_o desire_n all_o these_o kind_n of_o proposition_n upon_o this_o instrument_n when_o you_o be_v well_o acquaint_v therewith_o be_v soon_o wrought_v then_o speak_v chap._n xxv_o the_o latitude_n of_o the_o place_n the_o declination_n and_o altitude_n of_o the_o sun_n be_v give_v to_o find_v the_o azimuth_n thus_o in_o the_o obliquespherical_a triang_n zp_n ♉_o in_o the_o diagram_n of_o the_o 6_o chapter_n have_v the_o three_o side_n viz._n zp_n the_o compliment_n of_o latitude_n 37_o degree_n 30_o minute_n and_o z_o ♉_o the_o compliment_n of_o the_o sun_n altitude_n 64_o degree_n 4_o minute_n with_o the_o side_n p_o ♉_o the_o compliment_n of_o the_o declination_n 78_o degree_n 30_o minute_n we_o may_v find_v the_o angle_n pz_fw-fr ♉_o by_o the_o 41_o chapter_n of_o the_o second_o book_n but_o we_o will_v proceed_v as_o follow_v little_a differ_v from_o the_o former_a chapter_n first_o therefore_o if_o the_o sun_n have_v north_n declination_n get_v his_o height_n in_o the_o vertical_a circle_n by_o the_o 13_o or_o 14_o chapter_n and_o compare_v the_o sine_fw-la thereof_o with_o the_o sine_fw-la of_o the_o altitude_n give_v take_v the_o lesser_a out_o of_o the_o great_a and_o note_v the_o remainder_n then_o say_v as_o the_o cousin_n of_o the_o latitude_n to_o this_o remainder_n so_o be_v the_o sine_fw-la of_o the_o latitude_n to_o a_o four_o sine_fw-la then_o as_o the_o cousin_n of_o the_o sun_n altitude_n to_o this_o four_o sine_fw-la so_o be_v the_o radius_fw-la to_o the_o sine_fw-la of_o the_o azimuth_n
the_o almicanter_n the_o thread_n be_v thus_o place_v upon_o the_o 11_o deg_fw-la 30_o min._n in_o the_o axletree-line_n and_o parallel_v to_o the_o horizon_n will_v cut_v at_o each_o end_n thereof_o 9_o deg_fw-la 6_o min._n among_o the_o almicanter_n and_o such_o be_v the_o height_n of_o the_o sun_n at_o the_o hour_n of_o six_o or_o if_o you_o place_v the_o equator_fw-la 52_o deg_fw-la 30_o min._n above_o the_o south_n end_n of_o the_o horizon_n and_o then_o count_v 11_o deg_fw-la 30_o min._n upon_o the_o horizon_n where_o you_o shall_v find_v meet_v you_o a_o parallel_n which_o be_v follow_v to_o the_o axletree-line_n shall_v there_o give_v you_o 9_o deg_fw-la 6_o min._n for_o the_o altitude_n of_o the_o sun_n at_o six_o as_o before_o chap._n xxxvi_o have_v the_o latitude_n of_o the_o place_n and_o the_o declination_n of_o the_o sun_n to_o find_v his_o azimuth_n at_o the_o hour_n of_o six_o first_o set_v the_o sphere_n according_a to_o the_o latitude_n give_v and_o count_v the_o declination_n upon_o the_o horizon_n and_o look_v what_o parallel_n there_o meet_v you_o the_o same_o follow_v to_o the_o axtree-line_n where_o it_o will_v show_v you_o the_o azimuth_n desire_v as_o in_o the_o latitude_n of_o 52_o deg_fw-la 30_o min._n the_o declination_n of_o the_o sun_n be_v 11_o deg_fw-la 30_o min._n first_o i_o place_v the_o equator_fw-la at_o 37_o deg_fw-la 30_o min._n above_o the_o south_n end_n of_o the_o horizon_n and_o count_v the_o declination_n 11_o deg_fw-la 30_o min_fw-mi upon_o the_o horizon_n where_o i_o find_v to_o meet_v i_o the_o parallel_n of_o 7_o deg_fw-la 4_o min._n and_o such_o be_v the_o azimuth_n from_o the_o east_n or_o west_n point_v northwards_o chap._n xxxvii_o have_v the_o latitude_n of_o the_o place_n and_o the_o declination_n of_o the_o sun_n to_o find_v the_o ascensional_a difference_n and_o consequent_o the_o time_n of_o sunrising_n and_o set_v with_o the_o diurnal_a and_o nocturnal_a arch_n first_o set_v the_o planisphere_n to_o the_o latitude_n give_v and_o reckon_v the_o declination_n upon_o the_o axletree-line_n follow_v low_o the_o parallel_n thereof_o to_o the_o horizon_n where_o you_o shall_v find_v meet_v you_o the_o meridian_n of_o the_o ascensional_a difference_n count_v from_o the_o hour_n of_o six_o and_o this_o same_o meridian_n give_v you_o the_o time_n of_o sun_n set_v count_v from_o the_o south_n part_n of_o the_o limb_n or_o general_a meridian_n and_o likewise_o the_o time_n of_o his_o rise_n count_v from_o the_o north_n part_n of_o the_o limb_n and_o now_o if_o you_o still_o note_v this_o intersection_n of_o the_o horizon_n and_o sun_n parallel_n and_o count_v the_o hour_n thereupon_o between_o the_o south_n part_n of_o the_o limb_n and_o the_o horizon_n you_o shall_v have_v the_o sun_n semidiurnal_a arch_n and_o from_o the_o horizon_n to_o the_o north_n part_n of_o the_o limb_n his_o seminocturnal_a arch_n both_o which_o be_v double_v give_v you_o both_o the_o diurnal_a and_o nocturnal_a arch_n as_o for_o example_n let_v the_o latitude_n give_v be_v 52_o degree_n 30_o minute_n and_o the_o declination_n 11_o degree_n 30_o minute_n first_o i_o set_v the_o equator_fw-la 37_o degree_n 30_o minute_n above_o the_o horizon_n then_o count_v 11_o degree_n 30_o minute_n upon_o the_o axtree-line_n i_o follow_v the_o parallel_n thereof_o to_o the_o horizon_n where_o i_o find_v meet_v i_o the_o meridian_n of_o 15_o deg_fw-la 22_o min._n and_o such_o be_v the_o difference_n of_o ascensionals_n require_v now_o upon_o the_o same_o parallel_n of_o declination_n i_o seek_v how_o many_o hour_n i_o can_v find_v betweeene_v the_o south_n part_n of_o the_o limb_n and_o the_o horizon_n which_o be_v 7_o hour_n 1_o minute_n and_o so_o much_o be_v the_o semidiurnal_a arch_n and_o the_o time_n of_o sun_n set_v which_o be_v double_v make_v 14_o hour_n 2_o minute_n the_o diurnal_a arch_n so_o likewise_o count_v the_o hour_n between_o the_o north_n part_n of_o the_o limb_n and_o the_o horizon_n i_o find_v they_o 4_o hour_n 59_o minute_n and_o such_o be_v the_o seminocturnal_a arch_n and_o the_o time_n of_o sunrising_n which_o be_v double_v give_v 9_o hour_n 58_o min._n for_o the_o nocturnal_a arch_n the_o semidiurual_a and_o seminocturnal_a arch_n of_o any_o star_n who_o declination_n be_v know_v may_v be_v find_v in_o the_o self_n same_o manner_n chap._n xxxviii_o have_v the_o latitude_n of_o the_o place_n and_o the_o declination_n of_o the_o sun_n to_o find_v the_o time_n of_o the_o beginning_n and_o end_v of_o twilight_n first_o set_v the_o sphere_n to_o the_o latitude_n give_v then_o count_v the_o declination_n upon_o the_o axtree-line_n either_o northward_o or_o southward_o according_a as_o it_o be_v and_o then_o place_v the_o thread_n parallel_n to_o the_o horizon_n to_o the_o 18_o deg_fw-la of_o depression_n below_o the_o same_o and_o note_v where_o it_o cut_v the_o parallel_n of_o declination_n for_o those_o hour_n to_o the_o southward_n of_o the_o thread_n give_v the_o time_n of_o twilight_n end_v and_o the_o other_o to_o the_o northward_o the_o time_n of_o its_o beginning_n as_o for_o example_n let_v the_o latitude_n give_v be_v 52_o degree_n 30_o minute_n and_o the_o declination_n of_o the_o sun_n 11_o deg_fw-la 30_o min._n first_o i_o set_v the_o equator_fw-la 37_o deg_fw-la 30_o min._n above_o the_o horizon_n and_o count_v 11_o deg_fw-la 30_o min._n upon_o the_o axletree-line_n northward_o because_o his_o declination_n be_v towards_o that_o pole_n i_o place_v the_o thread_n parallel_v to_o the_o horizon_n 18_o deg_fw-la below_o the_o same_o and_o i_o find_v it_o cut_v the_o say_a parallel_n of_o 11_o deg_fw-la 30_o min._n at_o 2_o hour_n 34_o minute_n from_o the_o north_n part_n of_o the_o limb_n and_o such_o be_v the_o time_n of_o the_o begin_n of_o twilight_n so_o do_v it_o likewise_o cut_v the_o same_o parallel_n at_o 9_o hour_n 26_o minute_n from_o the_o south_n part_n of_o the_o meridian_n and_o such_o be_v the_o time_n of_o the_o end_n of_o twilight_n which_o be_v require_v chap._n thirty-nine_o the_o latitude_n of_o the_o place_n the_o altitude_n and_o declination_n of_o the_o sun_n be_v give_v to_o find_v the_o hour_n of_o the_o day_n first_o place_v the_o planisphere_n to_o the_o latitude_n give_v and_o seek_v his_o declination_n on_o the_o axletree-line_n among_o the_o parallel_n of_o declination_n then_o place_v the_o thread_n parallel_n to_o the_o horizon_n to_o the_o degree_n of_o the_o sun_n altitude_n count_v from_o the_o horizon_n among_o the_o almicanter_n and_o where_o the_o thread_n so_o place_v shall_v cut_v the_o parallel_n of_o declination_n there_o pass_v by_o the_o meridian_n which_o give_v you_o the_o hour_n of_o the_o day_n as_o for_o example_n in_o the_o latitude_n of_o 52_o deg_fw-la 30_o min._n the_o declination_n of_o the_o sun_n be_v 11_o deg_fw-la 30_o min._n and_o his_o altitude_n 25_o deg_fw-la 56_o min._n i_o set_v the_o equator_fw-la 37_o deg_fw-la 30_o min._n above_o the_o horizon_n and_o count_v 11_o deg_fw-la 30_o min._n upon_o the_o axletree-line_n then_o place_v the_o thread_n to_o 25_o deg_fw-la 56_o min._n among_o the_o almicanter_n i_o find_v it_o cut_v the_o parallel_n of_o 11_o deg_fw-la 30_o min._n at_o four_o hour_n 8_o minute_n from_o the_o meridian_n and_o so_o much_o be_v the_o hour_n of_o the_o day_n if_o the_o observation_n be_v make_v in_o the_o afternoon_n but_o if_o the_o observation_n be_v make_v before_o noon_n than_o be_v it_o 7_o a_o clock_n and_o 52_o min._n in_o the_o forenoon_n again_o let_v the_o latitude_n and_o declination_n be_v the_o same_o as_o before_z and_o the_o altitude_n give_v 42_o deg_fw-la 26_o min._n now_o if_o i_o place_v the_o thread_n to_o 42_o deg_fw-la 26_o min._n among_o the_o almicanter_n it_o will_v cut_v the_o parallel_n of_o 11_o deg_fw-la 30_o min._n at_o just_a two_o hour_n from_o the_o meridian_n so_o shall_v it_o be_v either_o ten_o a_o clock_n in_o the_o morning_n or_o two_o afternoon_n according_a to_o the_o observation_n chap._n xl._n the_o latitude_n of_o the_o place_n the_o sun_n altitude_n and_o declination_n be_v give_v to_o find_v his_o azimuth_n first_o set_v the_o sphere_n to_o the_o latitude_n give_v and_o then_o count_v your_o altitude_n among_o the_o parallel_n of_o declination_n and_o your_o declination_n among_o the_o almicanter_n so_o shall_v your_o meridian_n become_v azimuth_n and_o the_o work_n will_v be_v the_o same_o as_o in_o the_o former_a chapter_n only_o here_o by_o the_o way_n i_o will_v have_v you_o note_v that_o as_o your_o parallel_n and_o almicanter_n change_v office_n so_o must_v your_o north_n and_o south_n part_n of_o the_o general_a meridian_n change_v name_n so_o that_o when_o your_o thread_n cut_v any_o parallel_n at_o any_o azimuth_n if_o you_o count_v that_o azimuth_n from_o the_o south_n part_n of_o the_o limb_n it_o shall_v
for_o the_o sun_n place_n which_o at_o the_o estimate_n time_n be_v in_o 20_o deg_fw-la 12_o min._n ♑_o i_o find_v it_o to_o stand_v against_o 8_o hour_n 30_o min._n wherefore_o i_o conclude_v that_o the_o moon_n come_v to_o the_o south_n that_o night_n at_o 8_o of_o the_o clock_n and_o 30_o min._n chap._n xliv_o to_o find_v the_o time_n of_o the_o rise_n or_o set_v of_o any_o of_o the_o fix_a star_n and_o also_o of_o the_o moon_n or_o other_o planet_n when_o you_o will_v find_v the_o time_n of_o any_o star_n rise_v first_o get_v his_o seminocturnal_a arch_n according_a to_o the_o 37_o chap._n which_o put_v unto_o 12_o hour_n and_o if_o the_o star_n be_v place_v in_o the_o instrument_n bring_v that_o number_n of_o hour_n to_o the_o star_n but_o if_o the_o star_n be_v not_o in_o the_o instrument_n find_v his_o place_n by_o the_o last_o chap._n and_o bring_v this_o sum_n of_o 12_o hour_n and_o the_o star_n seminocturnal_a arch_n thereto_o so_o shall_v the_o place_n of_o the_o sun_n point_v out_o the_o the_o time_n of_o his_o rise_n as_o for_o example_n the_o 30_o of_o december_n 1652_o let_v the_o rise_n of_o arcturus_n be_v require_v which_o i_o suppose_v may_v be_v about_o 10_o of_o the_o clock_n in_o the_o night_n at_o which_o time_n the_o sun_n be_v in_o 20_o deg_fw-la 22_o min._n of_o ♑_o first_fw-mi by_o the_o 37_o chap._n i_o find_v his_o seminocturnal_a arch_n to_o be_v 4_o hour_n 3_o min._n which_o put_v unto_o 12_o hour_n make_v 16_o hour_n 3_o min._n and_o in_o regard_n arcturus_n be_v place_v in_o the_o instrument_n i_o bring_v 16_o hour_n 3_o minunto_n he_o so_o shall_v the_o sun_n in_o 20_o deg_fw-la 22_o min._n ♑_o point-out_a 10½_n hour_n for_o the_o time_n of_o arcturus_n rise_v the_o say_v 30_o of_o december_n in_o the_o night_n and_o if_o you_o will_v have_v the_o time_n of_o his_o set_n bring_v unto_o he_o his_o semidiurnal_a arch_n which_o you_o may_v find_v to_o be_v 7_o hour_n 59_o min._n so_o shall_v the_o sun_n in_o 19_o deg_fw-la 56_o min._n ♑_o which_o be_v his_o place_n of_o the_o estimate_n time_n of_o the_o star_n set_v point_n to_o 2_o hour_n 32_o min._n in_o the_o hour_n circle_n for_o the_o time_n of_o arcturus_n set_v afternoon_n in_o the_o day_n and_o year_n aforesaid_a and_o thus_o may_v you_o find_v the_o time_n of_o any_o other_o star_n or_o planet_n rise_v or_o set_v if_o you_o first_o get_v his_o declination_n by_o the_o 41_o chap._n and_o then_o his_o semidiurnal_a and_o seminocturnal_a arch_n by_o the_o 37_o chap._n and_o then_o by_o the_o last_o chap._n find_v the_o place_n whereunto_o you_o must_v bring_v his_o semidiurnal_a or_o seminocturnal_a arch_n as_o you_o there_o do_v the_o south_n point_n for_o his_o culmination_n so_o shall_v the_o sun_n place_n at_o the_o estimate_n time_n point_v out_o the_o time_n require_v chap._n xlv_o to_o find_v the_o exact_a hour_n of_o the_o night_n speedy_o by_o the_o star_n first_o with_o your_o instrument_n observe_v the_o star_n horary_a distance_n from_o the_o meridian_n that_o be_v first_o take_v his_o height_n and_o then_o find_v his_o hour_n from_o the_o meridian_n as_o you_o do_v for_o the_o sun_n in_o the_o 39_o chap._n in_o all_o respect_n but_o here_o i_o will_v have_v you_o note_v that_o in_o take_v the_o height_n of_o a_o star_n by_o the_o common_a sight_n the_o hole_n be_v so_o small_a that_o you_o can_v perceive_v a_o star_n through_o they_o and_o therefore_o for_o this_o purpose_n you_o may_v have_v two_o great_a sight_n hole_n for_o the_o star_n and_o two_o lesser_a one_o for_o the_o sun_n or_o rather_o as_o i_o use_v to_o make_v they_o for_o myself_o and_o my_o friend_n in_o all_o my_o night_n dial_n which_o be_v thus_o in_o the_o sight_n next_o my_o eye_n i_o make_v a_o great_a hole_n and_o for_o the_o sight_n by_o the_o centre_n i_o set_v up_o a_o flat_a pin_n of_o brass_n perpendicular_a to_o the_o plate_n the_o breadth_n of_o this_o pin_n will_v be_v such_o that_o the_o shadow_n thereof_o may_v not_o full_o fill_v the_o hole_n of_o the_o other_o sight_n so_o that_o when_o the_o sun_n shine_v and_o the_o shadow_n of_o the_o pin_n fall_v upon_o the_o hole_n of_o the_o other_o sight_n there_o may_v some_o small_a light_n of_o the_o sun_n pass_v through_o the_o hole_n on_o both_o side_n of_o the_o shadow_n by_o which_o mean_v you_o may_v take_v the_o height_n of_o the_o sun_n as_o exact_o as_o by_o fine_a hole_n and_o you_o may_v take_v the_o height_n of_o a_o star_n better_o with_o this_o pin_n then_o with_o great_a sight_n hole_n but_o now_o to_o the_o matter_n in_o hand_n the_o horary_a distance_n of_o the_o star_n from_o the_o meridian_n be_v find_v seek_v it_o in_o the_o hour_n circle_n if_o the_o star_n be_v to_o the_o westward_n of_o the_o meridian_n but_o if_o the_o star_n be_v to_o the_o eastward_o take_v the_o compliment_n of_o his_o horary_a distance_n to_o 24_o hour_n and_o seek_v that_o in_o the_o hour_n circle_n which_o be_v find_v bring_v it_o to_o the_o star_n or_o to_o his_o place_n find_v as_o in_o 43_o chap._n so_o shall_v the_o place_n of_o the_o sun_n point_v out_o the_o hour_n require_v as_o for_o example_n upon_o the_o 16_o of_o november_n 1652_o it_o be_v serene_a air_n i_o desire_v to_o see_v what_o time_n of_o the_o morning_n it_o be_v for_o which_o purpose_n i_o make_v use_n of_o arcturus_n and_o by_o observation_n i_o sound_v his_o height_n to_o be_v 27_o deg_fw-la 12_o min._n towards_o the_o east_n now_o his_o declination_n be_v 21_o deg_fw-la 10_o min._n north_n i_o find_v by_o the_o 39_o chap._n that_o he_o be_v 4_o hour_n 50_o min._n from_o the_o south_n and_o in_o regard_n he_o be_v on_o the_o east_n side_n of_o the_o meridian_n i_o take_v the_o compliment_n of_o 4_o hour_n 50_o min._n to_o 24_o hour_n which_o be_v 19_o hour_n 10_o min._n this_o 19_o hour_n 10_o min._n i_o seek_v in_o the_o hour_n circle_n and_o bring_v it_o to_o arcturus_n now_o the_o sun_n at_o the_o estimate_n timebeing_n in_o 4_o deg_fw-la 40_o min._n â™_o point_v to_o 17_o hour_n in_o the_o hour_n circle_n which_o be_v direct_o 5_o of_o the_o clock_n in_o the_o morning_n the_o like_a may_v be_v do_v by_o any_o of_o the_o planet_n as_o i_o will_v make_v appear_v by_o these_o two_o example_n follow_v which_o i_o make_v in_o the_o day_n time_n by_o the_o glitter_a planet_n venus_n the_o 16_o of_o november_n 1652_o i_o make_v these_o two_o follow_a observation_n by_o the_o planet_n venus_n in_o the_o day_n time_n as_o to_o the_o find_n of_o the_o hour_n by_o the_o star_n she_o be_v about_o her_o great_a distance_n from_o the_o sun_n the_o say_v 16_o day_n be_v serene_a and_o i_o be_v abroad_o and_o in_o a_o convenient_a place_n where_o i_o may_v see_v a_o clear_a horizon_n and_o see_v venus_n shine_v so_o bright_a direct_o at_o the_o sun_n rise_v i_o can_v do_v no_o less_o then_o make_v observation_n by_o she_o to_o see_v how_o her_o longitude_n latitude_n right_a ascension_n declination_n and_o likewise_o the_o hour_n find_v by_o she_o will_v agree_v with_o the_o time_n of_o sun_n rise_v wherefore_o first_o i_o observe_v her_o altitude_n by_o my_o instrument_n which_o be_v but_o small_a i_o can_v not_o make_v so_o exact_a observation_n as_o otherwise_o imight_o have_v do_v but_o as_o it_o be_v i_o find_v her_o altitude_n just_a 30_o deg_fw-la now_o the_o estimate_n time_n be_v sun_n rise_v which_o be_v that_o morning_n at_o 8_o a_o clock_n and_o 1_o min._n in_o our_o latitude_n of_o 52_o deg_fw-la 30_o min._n i_o look_v in_o my_o almanac_n for_o the_o longitude_n and_o latitude_n of_o ♀_o which_o i_o find_v according_a to_o mr._n vincent_n wing_n ephemeris_fw-la to_o be_v in_o 18_o deg_fw-la ♎_o with_o 2_o deg_fw-la north_n latitude_n then_o by_o the_o 41_o chap._n i_o find_v her_o declination_n to_o be_v 5_o deg_fw-la 14_o min._n south_n and_o so_o by_o the_o 39_o chap._n her_o hour_n from_o the_o meridian_n to_o be_v no_o more_o but_o 57_o min._n so_o likewise_o by_o the_o 41_o chap._n i_o find_v she_o right_a ascension_n to_o be_v 13_o hour_n 9_o min._n which_o circle_n i_o follow_v to_o the_o ecliptic_a line_n where_o it_o give_v i_o 18_o deg_fw-la 45_o min._n ♎_o for_o the_o place_n of_o ♀_o in_o the_o outward_a ecliptic_a unto_o which_o 18_o deg_fw-la 45_o min._n ♎_o i_o bring_v the_o compliment_n of_o 0_o hour_n 57_o min._n which_o be_v 23_o hour_n 3_o min._n so_o do_v the_o sun_n in_o 4_o deg_fw-la 47_o min._n â™_o being_n his_o place_n at_o the_o time_n of_o his_o rise_n point_v out_o 20_o hour_n 1_o min._n for_o the_o time_n require_v agree_v exact_o with_o the_o
way_n to_o find_v the_o content_a of_o a_o cylinder_n page_n 69_o how_o otherwise_o to_o find_v the_o length_n of_o a_o foot_n of_o any_o cylinder_n page_n 70_o to_o find_v the_o solid_a content_n of_o any_o cone_n page_n 73_o to_o find_v the_o altitude_n of_o a_o cone_n page_n 77_o how_o to_o measure_n any_o segment_n of_o a_o cone_n or_o any_o round_a taper_a piece_n of_o timber_n page_n 78_o how_o to_o find_v the_o solid_a content_n of_o any_o pyramid_n or_o segment_n thereof_o be_v cut_v off_o page_z 80_o the_o content_n of_o the_o second_o book_n to_o find_v the_o chord_n of_o any_o arch_a page_n 83_o to_o find_v the_o right_n sine_fw-la of_o any_o arch_a page_n 85_o to_o find_v the_o arch_n of_o any_o sine_fw-la page_z 86_o the_o radius_fw-la be_v give_v with_o a_o straight_a line_n resemble_v a_o sine_fw-la to_o find_v the_o quantity_n of_o that_o unknown_a sine_fw-la page_z 89_o the_o use_n of_o the_o parallel_n as_o they_o signify_v natural_a sin_n and_o tangent_n page_n 90_o of_o the_o resolution_n of_o right_n line_v triangle_n page_n 95_o another_o way_n to_o resolve_v right_o line_v triangle_n page_n 102_o of_o the_o resolution_n of_o right_n angle_v spherical_a triangle_n by_o the_o foreside_n of_o the_o quadrat_fw-la page_n 116_o to_o resolve_v any_o spherical_a triangle_n whatsoever_o by_o the_o foreside_n page_n 131_o of_o the_o resolution_n of_o right_n angle_v spherical_a triangle_n by_o the_o backside_n page_n 141_o how_o to_o resolve_v any_o spherical_a triangle_n whatsoever_o by_o the_o backside_n of_o the_o instrument_n page_n 146_o the_o content_n of_o the_o three_o book_n to_o find_v the_o sun_n altitude_n by_o the_o shadow_n of_o a_o perpendicular_a gnomon_n page_n 151_o to_o find_v the_o length_n of_o the_o right_a shadow_n page_n 152_o to_o find_v the_o height_n of_o the_o sun_n by_o the_o shadow_n of_o a_o gnomon_n lie_v parallel_n to_o the_o horizon_n page_n 153_o to_o find_v the_o length_n of_o the_o contrary_a shadow_n page_n 154_o to_o find_v the_o sun_n declination_n page_n 155_o to_o find_v the_o latitude_n of_o the_o place_n page_z 156_o to_o find_v the_o declination_n of_o the_o sun_n or_o star_n by_o observation_n page_n 158_o to_o find_v the_o amplitude_n of_o the_o sun_n or_o star_n page_n 160_o to_o find_v the_o pole_n elevation_n page_n 161_o to_o find_v the_o sun_n declination_n page_n 162_o to_o find_v the_o sun_n place_n page_z 159_o to_o find_v the_o sun_n height_n in_o the_o vertical_a circle_n page_n 163_o to_o find_v the_o time_n when_o the_o sun_n will_v come_v to_o the_o due_a east_n or_o west_n page_n 164_o to_o find_v the_o sun_n altitude_n at_o the_o hour_n of_o six_o page_n 165_o to_o find_v the_o sun_n azimuch_o at_o the_o hour_n of_o six_o page_n 165_o to_o find_v the_o ascensional_a difference_n page_n 166_o to_o find_v the_o beginning_n and_o end_v of_o twilight_n page_n 167_o to_o find_v the_o sun_n right_a ascension_n page_n 170_o to_o find_v the_o oblique_a ascension_n page_n 171_o to_o find_v the_o hour_n of_o the_o day_n page_n 171_o to_o find_v the_o azimuth_n page_n 172_o to_o find_v the_o hour_n of_o the_o day_n page_n 173_o to_o find_v the_o azimuth_n page_n 175_o to_o find_v the_o sun_n place_n and_o declination_n page_n 178_o to_o find_v the_o sun_n right_a ascension_n page_n 179_o to_o find_v the_o sun_n amplitude_n page_n 179_o to_o find_v the_o amplitude_n of_o the_o star_n page_n 180_o to_o find_v the_o latitude_n of_o the_o place_n page_z 181_o to_o find_v the_o sun_n declination_n page_n 182_o to_o find_v the_o sun_n height_n in_o the_o vertical_a circle_n page_n 182_o to_o find_v the_o time_n when_o the_o sun_n will_v be_v due_a east_n or_o west_n page_n 183_o to_o find_v the_o sun_n height_n at_o the_o hour_n of_o six_o page_n 184_o to_o find_v the_o sun_n azimuth_n at_o the_o hour_n of_o six_o page_n 185_o to_o find_v the_o ascensional_a difference_n of_o the_o sun_n or_o star_n page_n 185_o to_o find_v the_o beginning_n and_o end_v of_o twilight_n page_n 187_o to_o find_v the_o hour_n of_o the_o day_n page_n 187_o to_o find_v the_o azimuth_n page_n 188_o to_o find_v the_o right_a ascension_n and_o declination_n of_o the_o planet_n or_o fix_a star_n page_n 190_o to_o find_v the_o longitude_n and_o latitude_n of_o the_o star_n page_n 191_o to_o find_v the_o culmination_n of_o any_o of_o the_o fix_a star_n moon_n or_o other_o planet_n page_n 191_o to_o find_v the_o time_n of_o the_o rise_n and_o set_v of_o any_o of_o the_o fix_a star_n moon_n or_o other_o planet_n page_n 193_o to_o find_v the_o exact_a hour_n of_o the_o night_n by_o the_o star_n page_n 194_o to_o find_v how_o many_o mile_n answer_v to_o one_o deg_fw-la of_o longitude_n in_o any_o latitude_n page_n 198_o to_o find_v what_o difference_n of_o longitude_n belong_v to_o one_o degree_n of_o distance_n in_o any_o latitude_n page_n 199_o to_o find_v how_o many_o league_n do_v answer_v to_o one_o degree_n of_o latitude_n upon_o any_o rumb_n give_v page_n 200_o to_o find_v the_o difference_n of_o latitude_n page_n 201_o to_o find_v the_o distance_n upon_o the_o rumb_n page_n 202_o to_o find_v the_o rumb_n page_n 202_o to_o find_v the_o difference_n of_o longitude_n page_n 203_o to_o find_v the_o difference_n of_o longitude_n page_n 204_o to_o find_v the_o rumb_n page_n 205_o to_o find_v the_o difference_n of_o lat_fw-la &_o long_o page_n 206_o to_o find_v the_o distance_n upon_o the_o rumb_n page_n 208_o to_o find_v the_o distance_n between_o the_o ship_n and_o the_o land_n page_n 250_o to_o find_v the_o distance_n of_o any_o ship_n from_o the_o land_n page_n 207_o to_o find_v the_o distance_n of_o two_o ship_n at_o road_n page_n 029_o the_o fore-side_n of_o the_o universal_a quadrat_fw-la the_o backside_n of_o the_o universal_a quadrat_fw-la delineavit_fw-la antonius_n thompson_n the_o first_o book_n show_v the_o description_n and_o general_a use_n of_o the_o universal_a quadrat_fw-la and_o how_o thereby_o to_o resolve_v all_o such_o proposition_n as_o may_v be_v apply_v unto_o right_a line_n as_o the_o proportion_v of_o line_n and_o superficies_n the_o measure_n of_o all_o manner_n of_o land_n board_n glass_n timber_n stone_n and_o such_o like_a chap._n i._n the_o description_n and_o make_n of_o the_o universal_a quadrat_fw-la a_o quadrat_fw-la or_o square_a geometrical_a be_v a_o figure_n of_o four_o equal_a side_n who_o angle_n be_v all_o right_a angle_n within_o the_o limit_n of_o which_o figure_n we_o intend_v to_o describe_v a_o universal_a instrument_n for_o the_o speedy_a performance_n of_o most_o mathematical_a concusion_n and_o that_o general_o for_o all_o latitude_n first_o therefore_o prepare_v a_o piece_n of_o box_n or_o brass_n and_o after_o you_o have_v make_v it_o very_o smooth_a and_o plain_a cut_v it_o direct_o four_o square_a with_o four_o equal_a side_n and_o angle_v all_o right_a your_o wood_n or_o brass_n be_v thus_o prepare_v draw_v thereupon_o four_o right_a line_n equal_o distant_a or_o parallel_a to_o the_o edge_n all_o of_o they_o cut_v one_o the_o other_o at_o right_a angle_n let_v the_o parallel_n distance_n of_o these_o line_n from_o the_o edge_n be_v so_o much_o as_o that_o you_o may_v place_v the_o figure_n to_o the_o division_n limb_n like_a as_o you_o may_v perceive_v by_o the_o figure_n this_o be_v do_v divide_v each_o side_n of_o the_o square_n into_o 100_o equal_a part_n or_o rather_o 1000_o if_o quantity_n will_v give_v leave_n for_o the_o large_a the_o instrument_n be_v the_o more_o exact_o will_v the_o conclusion_n wrought_v thereby_o be_v perform_v but_o the_o instrument_n not_o so_o portable_a then_o from_o each_o division_n of_o the_o one_o side_n draw_v parallel_a line_n to_o the_o like_a division_n on_o the_o opposite_a side_n the_o like_a do_v by_o the_o other_o two_o side_n so_o shall_v the_o whole_a face_n of_o the_o instrument_n be_v fill_v with_o parallel_a line_n both_o way_n and_o cross_v each_o other_o at_o right_a angle_n according_a to_o the_o common_a cynical_a quadrant_n and_o for_o the_o better_a distinction_n of_o these_o parallel_n you_o may_v prick_v every_o five_o so_o may_v you_o guide_v your_o eye_n along_o upon_o they_o the_o better_a this_o be_v do_v make_v choice_n of_o one_o of_o the_o angle_n for_o a_o centre_n as_o here_o we_o have_v do_v at_o a_o from_o which_o you_o shall_v number_v the_o two_o next_o side_n by_o 10_o 20_o 30_o etc._n etc._n unto_o 100_o and_o place_n figure_n to_o they_o in_o the_o margin_n as_o you_o see_v in_o the_o figure_n then_o set_v one_o foot_n of_o your_o compass_n in_o the_o centre_n a_o with_o the_o other_o open_v to_o the_o full_a length_n of_o one_o of_o the_o side_n draw_v the_o quadrant_n bc_n over_o all_o the_o parallel_n this_o quadrant_n divide_v into_o
from_o the_o east_n or_o west_n point_n either_o northward_o or_o southward_o for_o whereas_o when_o the_o altitude_n of_o the_o sun_n give_v and_o his_o height_n in_o the_o vertical_a circle_n be_v equal_a he_o be_v direct_o in_o the_o east_n or_o west_n point_n so_o when_o his_o altitude_n give_v be_v great_a then_o be_v the_o azimth_n towards_o the_o south_n and_o when_o his_o altitude_n give_v be_v the_o least_o than_o be_v the_o azimuth_n towards_o the_o north._n thus_o in_o the_o diagram_n of_o the_o 6_o chapter_n have_v by_o the_o 13_o or_o 14_o chapter_n find_v the_o height_n of_o the_o sun_n in_o the_o vertical_a circle_n ♈_o c_o 14_o deg_fw-la 33_o min._n the_o sine_z whereof_z 251_o i_o take_v out_o of_o 437_o the_o sine_fw-la of_o 25_o deg_fw-la 56_o min._n ♈_o w_n the_o height_n of_o the_o sun_n give_v and_o there_o remain_v cw_o 186_o by_o which_o and_o the_o angle_v wc_n ♉_o the_fw-fr latitude_n 52_o deg_fw-la 30_o min._n and_o w_n ♉_o c_o the_o compliment_n of_o the_o latitude_n 37_o deg_fw-la 30_o min._n we_o may_v find_v the_o side_n w_n ♉_o by_o the_o 10_o or_o 25_o chapter_n of_o the_o second_o book_n for_o if_o we_o place_v the_o thread_n to_o the_o intersection_n of_o the_o contrary_a sine_fw-la of_o 37_o deg_fw-la 30_o min._n with_o the_o right_a parallel_n or_o sine_fw-la 186_o it_o will_v cut_v the_o contrary_a sine_fw-la of_o 52_o deg_fw-la 30_o min._n at_o the_o right_n sine_fw-la of_o 14_o deg_fw-la which_o be_v the_o side_n w_n ♉_o but_o see_v the_o radius_fw-la of_o this_o 14_o deg_fw-la be_v but_o the_o cousin_n of_o the_o altitude_n iw_n therefore_o i_o place_v the_o thread_n again_o at_o the_o intersection_n of_o the_o contrary_a sine_fw-la of_o 64_o deg_fw-la 4_o min._n the_o compliment_n of_o the_o altitude_n with_o this_o right_a sine_fw-la of_o 14_o deg_fw-la and_o it_o cut_v the_o contrary_a sine_fw-la of_o 90_o deg_fw-la at_o the_o right_n sine_fw-la of_o 15_o deg_fw-la 38_o min._n and_o such_o be_v ♈_o y_fw-fr or_o the_o angle_n ♈_o zy_n the_o azimuth_n from_o the_o east_n or_o west_n and_o that_o southward_o because_o the_o give_a altitude_n of_o the_o sun_n be_v more_o than_o his_o altitude_n in_o the_o vertical_a circle_n but_o if_o the_o declination_n be_v southward_o first_o get_v the_o amplitude_n by_o the_o nine_o or_o ten_o chapter_n then_o say_v as_o the_o cousin_n of_o the_o latitude_n to_o the_o sine_fw-la of_o the_o sun_n altitude_n so_o be_v the_o sine_fw-la of_o the_o latitude_n to_o a_o four_o sine_fw-la unto_o which_o four_o sine_fw-la add_v the_o sine_fw-la of_o the_o amplitude_n and_o note_n the_o sum_n thereof_o then_o say_v again_o as_o the_o cousin_n of_o the_o altitude_n to_o this_o sum_n last_o find_v so_o be_v the_o radius_fw-la to_o the_o sine_fw-la of_o the_o azimuth_n from_o the_o east_n or_o west_n southward_a as_o for_o example_n in_o the_o latitude_n of_o 52_o deg_fw-la 30_o min._n the_o sun_n place_n give_v be_v in_o the_o begin_n of_o m_o we_o may_v by_o the_o 9_o chapter_n find_v his_o amplitude_n to_o be_v 19_o degree_n 7_o minute_n the_o sine_fw-la whereof_o be_v 327_o and_o let_v the_o sun_n altitude_n be_v 23_o degree_n 20_o minute_n now_o place_v the_o thread_n to_o the_o intersection_n of_o the_o contrary_a sine_fw-la of_o 37_o deg_fw-la 30_o min._n with_o the_o right_n sine_fw-la of_o 13_o deg_fw-la 20_o min._n it_o will_v cut_v the_o contrary_a sine_fw-la of_o 52_o deg_fw-la 30_o minute_n at_o the_o right_a parallel_n of_o 301_o unto_o which_o 301_o put_v 327_o the_o sine_fw-la of_o the_o amplitude_n and_o the_o sum_n will_v be_v 628._o wherefore_o place_n the_o thread_n again_o at_o the_o intersection_n of_o the_o contrary_a sine_fw-la of_o 76_o degree_n 40_o minute_n the_o compliment_n of_o the_o sun_n altitude_n with_o the_o right_a parallel_n of_o this_o sum_n 628_o and_o it_o will_v cut_v the_o contrary_a sine_fw-la of_o 90_o deg_fw-la at_o the_o right_n sine_fw-la of_o 40_o deg_fw-la 11_o min._n which_o be_v the_o azimuth_n from_o the_o east_n or_o west_n point_v southward_o and_o thus_o have_v i_o by_o the_o fore-side_n of_o this_o universal_a quadrat_fw-la show_v the_o work_n of_o some_o of_o the_o most_o useful_a proposition_n both_o for_o navigation_n and_o dial_v yet_o very_a many_o more_o may_v be_v resolve_v by_o the_o same_o side_n as_o the_o ingenuous_a may_v perceive_v by_o consider_v well_o of_o that_o which_o be_v write_v in_o the_o second_o book_n which_o of_o itself_o be_v able_a to_o resolve_v all_o proposition_n of_o this_o nature_n and_o now_o we_o will_v proceed_v to_o show_v a_o more_o speedy_a resolution_n by_o the_o movable_a planisphere_n on_o the_o backside_n of_o the_o quadrat_fw-la chap._n xxvi_o the_o place_n of_o the_o sun_n be_v give_v to_o find_v his_o declination_n here_o you_o have_v nothing_o to_o do_v but_o only_o to_o seek_v the_o sun_n place_n give_v in_o the_o ecliptic_a line_n for_o the_o parallel_n pass_v thereby_o show_v both_o at_o the_o limb_n and_o also_o at_o the_o axletree-line_n the_o declination_n require_v as_o for_o example_n let_v the_o sun_n place_n give_v be_v the_o beginning_n of_o ♉_o now_o if_o you_o seek_v the_o begin_n of_o ♉_o on_o the_o ecliptic_a line_n you_o shall_v find_v the_o parallel_n of_o 11_o degree_n 30_o minute_n to_o pass_v thereby_o and_o such_o be_v the_o declination_n require_v thus_o may_v you_o speedy_o find_v the_o sun_n declination_n for_o any_o day_n in_o the_o year_n his_o true_a place_n be_v give_v or_o the_o declination_n of_o any_o point_n in_o the_o ecliptic_a by_o the_o inspection_n of_o the_o instrument_n chap._n xxvii_o the_o declination_n of_o the_o sun_n be_v give_v to_o find_v his_o place_n in_o the_o ecliptic_a seek_v his_o declination_n upon_o the_o axletree-line_n or_o hour_n of_o six_o and_o follow_v the_o parallel_n thereof_o to_o the_o ecliptic_a so_o shall_v it_o there_o show_v you_o the_o place_n of_o the_o sun_n require_v as_o for_o example_n let_v the_o declination_n of_o the_o sun_n be_v 11_o deg_fw-la 30_o min._n which_o i_o seek_v upon_o the_o axletree-line_n and_o find_v it_o i_o follow_v the_o parallel_n thereof_o to_o the_o ecliptic_a and_o there_o i_o find_v it_o cut_v the_o beginning_n of_o ♉_o which_o be_v the_o sun_n place_n require_v in_o regard_n he_o possess_v that_o quarter_n of_o the_o ecliptic_a betwixt_o the_o head_n of_o ♈_o and_o ♋_o but_o if_o the_o sun_n have_v be_v in_o that_o quarter_n betwixt_o ♋_o and_o ♎_o then_o have_v his_o place_n be_v in_o the_o begin_n of_o â™_o or_o if_o it_o have_v be_v the_o quarter_n betwixt_o ♎_o and_o ♑_o then_o have_v his_o place_n be_v in_o the_o begin_n of_o â™_o or_o have_v he_o be_v between_o ♑_o and_o ♈_o then_z his_o place_n have_v be_v in_o the_o begin_n of_o ♓_o chap._n xxviii_o the_o place_n of_o the_o sun_n be_v give_v to_o find_v his_o right_a ascension_n seek_v the_o sun_n place_n give_v in_o the_o ecliptic_a and_o note_v what_o meridian_n circle_n pass_v thereby_o for_o that_o meridian_n follow_v to_o the_o equator_fw-la show_v the_o right_a ascension_n require_v as_o for_o example_n let_v the_o sun_n place_n give_v be_v in_o the_o begin_n of_o ♉_o the_o which_o if_o you_o seek_v upon_o the_o ecliptic_a you_o shall_v findepass_v thereby_o a_o meridian_n which_o follow_v to_o the_o equator_fw-la give_v 27_o degree_n 54_o min._n for_o the_o right_a ascension_n which_o be_v require_v count_v from_o the_o begin_n of_o ♈_o chap._n xxix_o have_v the_o latitude_n of_o the_o place_n with_o the_o place_n of_o the_o sun_n in_o the_o ecliptic_a to_o find_v his_o amplitude_n here_o you_o must_v first_o place_v the_o planisphere_n to_o the_o latitude_n of_o the_o place_n propose_v the_o which_o you_o may_v do_v by_o turn_v the_o sphere_n about_o until_o the_o north_n part_n of_o the_o horizon_n cut_v the_o limb_n at_o the_o quantity_n of_o the_o latitude_n count_v from_o the_o north_n pole_n or_o rather_o for_o readiness_n sake_n of_o the_o number_n set_v to_o the_o limb_n till_o the_o south_n end_n of_o the_o horizon_n cut_v the_o limb_n at_o the_o quantity_n of_o the_o equinoctial_o height_n count_v from_o the_o say_v equinoctial_a which_o be_v always_o to_o the_o compliment_n of_o the_o latitude_n this_o be_v do_v your_o instrument_n be_v ready_a fix_v to_o perform_v a_o number_n of_o conclusion_n in_o that_o latitude_n but_o now_o for_o the_o amplitude_n seek_v the_o sun_n place_n in_o the_o ecliptic_a line_n and_o look_v what_o parallel_n meet_v you_o there_o the_o same_o follow_v to_o the_o horizon_n whereon_o it_o cut_v the_o amplitude_n count_v from_o the_o centre_n show_v you_o by_o the_o way_n the_o declination_n also_o as_o for_o example_n let_v the_o place_n of_o the_o sun_n give_v be_v in_o the_o begin_n of_o ♉_o which_o point_n