i_o seek_v in_o the_o ecliptic_a and_o follow_v the_o parallel_n that_o pass_v thereby_o to_o the_o horizon_n i_o find_v it_o there_o to_o cut_v 19_o deg_fw-la 7_o min._n count_v from_o the_o centre_n and_o such_o be_v the_o amplitude_n require_v the_o sphere_n be_v set_v to_o the_o latitude_n of_o 52_o deg_fw-la 30_o min._n chap._n xxx_o have_v the_o latitude_n of_o the_o place_n with_o the_o declination_n of_o any_o star_n to_o find_v his_o amplitude_n first_o the_o sphere_n to_o the_o latitude_n be_v set_v if_o the_o star_n be_v therein_o place_v follow_v the_o parallel_n of_o declination_n whereon_o he_o stand_v to_o the_o horizon_n and_o if_o he_o be_v not_o in_o the_o instrument_n get_v his_o declination_n by_o the_o seven_o chap._n or_o otherwise_o by_o some_o table_n for_o that_o purpose_n which_o find_v seek_v it_o in_o the_o axletree-line_n among_o the_o parallel_n of_o declination_n &_o follow_v the_o parallel_n thereof_o to_o the_o horizon_n and_o if_o it_o cut_v the_o horizon_n it_o there_o show_v the_o amplitude_n but_o if_o it_o cut_v it_o not_o then_o do_v not_o that_o star_n set_v or_o go_v down_o under_o our_o horizon_n as_o for_o example_n let_v it_o be_v require_v to_o find_v the_o amplitude_n of_o arcturus_n i_o look_v in_o my_o instrument_n for_o arcturus_n and_o i_o find_v he_o place_v upon_o the_o parallel_n of_o 21_o d._n 10_o min._n of_o north_n declination_n as_o it_o be_v just_a in_o the_o horizon_n at_o 36_o deg_fw-la 23_o min._n from_o the_o centre_n and_o such_o be_v his_o amplitude_n and_o if_o you_o will_v have_v the_o amplitude_n of_o the_o lion_n heart_n look_v in_o your_o instrument_n and_o you_o shall_v find_v he_o place_v upon_o the_o parallel_n of_o 13_o deg_fw-la 42_o min._n of_o north_n declination_n which_o if_o you_o follow_v to_o the_o horizon_n you_o shall_v find_v it_o there_o cut_v 22_o deg_fw-la 54_o min._n and_o such_o be_v the_o amplitude_n of_o the_o lion_n heart_n in_o the_o latitude_n of_o 52_o deg_fw-la 30_o min._n but_o if_o you_o will_v seek_v the_o amplitude_n of_o the_o bright_a star_n call_v the_o harp_n you_o shall_v find_v he_o place_v upon_o the_o parallel_n of_o 38_o deg_fw-la 30_o min._n north_n declination_n but_o this_o parallel_n cut_v not_o the_o horizon_n therefore_o he_o go_v not_o under_o our_o horizon_n at_o all_o in_o the_o aforesaid_a latitude_n of_o 52_o deg_fw-la 30_o min._n but_o when_o he_o be_v in_o his_o low_a direct_o in_o the_o north_n he_o be_v just_a one_o degree_n of_o height_n chap._n xxxii_o have_v the_o declination_n and_o amplitude_n of_o the_o sun_n to_o find_v the_o latitude_n of_o the_o place_n count_n the_o declination_n upon_o the_o axletree-line_n among_o the_o parallel_n of_o declination_n and_o the_o amplitude_n upon_o the_o horizon_n from_o the_o centre_n the_o same_o way_n with_o the_o declination_n then_o move_v the_o sphere_n to_o and_o fro_o until_o the_o amplitude_n and_o the_o parallel_n of_o declination_n meet_v both_o in_o one_o point_n the_o south_n end_n of_o the_o horizon_n shall_v cut_v the_o meridian_n at_o the_o compliment_n of_o the_o latitude_n require_v as_o for_o example_n let_v the_o sun_n declination_n be_v 11_o deg_fw-la 30_o min._n and_o his_o amplitude_n 19_o deg_fw-la 7_o min._n if_o you_o move_v the_o sphere_n until_o the_o 19_o deg_fw-la 7_o min._n one_o the_o horizon_n fall_v direct_o on_o the_o parallel_n of_o 11_o deg_fw-la 30_o min._n the_o south_n end_n of_o the_o horizon_n will_v cut_v the_o limb_n at_o 37_o deg_fw-la 30._o min._n and_o such_o be_v the_o height_n of_o the_o equinoctial_a which_o be_v take_v out_o of_o 90_o deg_fw-la leave_v 52_o deg_fw-la 30_o min._n for_o the_o latitude_n of_o the_o place_n which_o be_v require_v chap._n xxxii_o the_o latitude_n of_o the_o place_n and_o the_o amplitude_n of_o the_o sun_n be_v give_v to_o find_v his_o declination_n first_o set_v the_o sphere_n to_o the_o latitude_n propose_v then_o count_v the_o amplitude_n upon_o the_o horizon_n and_o where_o it_o shall_v end_v shall_v meet_v you_o a_o parallel_n which_o be_v follow_v to_o the_o axletree-line_n will_v there_o show_v you_o the_o declination_n require_v as_o in_o the_o latitude_n of_o 52_o deg_fw-la 30_o min._n the_o amplitude_n be_v 19_o deg_fw-la 7_o min._n if_o you_o first_o place_n the_o sphere_n to_o the_o latitude_n and_o then_o count_v 19_o deg_fw-la 7_o min._n upon_o the_o horizon_n there_o shall_v meet_v you_o a_o parallel_n which_o be_v follow_v to_o the_o axletree_n line_n shall_v there_o give_v you_o 11_o deg_fw-la 30_o min._n the_o declination_n require_v chap._n xxxiii_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 height_n in_o the_o vertical_a circle_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 give_v among_o the_o almicanter_n from_o both_o end_n of_o the_o horizon_n towards_o the_o zenith_n and_o thereto_o place_v the_o thread_n parallel_v to_o the_o horizon_n and_o where_o the_o thread_n so_o place_v cut_v the_o axletree-line_n or_o six_o a_o clock_n hour-line_n there_o be_v the_o altitude_n require_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 if_o you_o count_v this_o 11._o deg_fw-la 30_o min._n from_o both_o end_n of_o the_o horizon_n among_o the_o almicanter_n and_o place_v the_o thread_n thereto_o it_o shall_v lie_v parallel_n to_o the_o horizon_n and_o cut_v the_o axle-tree-line_n at_o 14_o deg_fw-la 33_o min._n and_o such_o be_v the_o sun_n height_n when_o he_o be_v direct_o in_o the_o east_n or_o west_n point_v which_o be_v require_v or_o if_o you_o place_v the_o horizon_n to_o 52_o deg_fw-la 30_o min._n in_o the_o limb_n count_v from_o the_o equator_fw-la and_o count_v the_o declination_n upon_o the_o axletree-line_n viz._n 11_o deg_fw-la 30_o min._n the_o parallel_n thereof_o shall_v cut_v the_o horizon_n at_o 14_o deg_fw-la 33_o min._n for_o the_o height_n of_o the_o sun_n in_o the_o vertical_a circle_n the_o same_o as_o before_o chap._n xxxiv_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 his_o come_n to_o the_o east_n or_o west_n point_n first_o set_v the_o planisphere_n to_o the_o latitude_n give_v then_o place_v the_o thread_n upon_o the_o zenith_n and_o the_o nadir_n so_o shall_v it_o cut_v the_o horizon_n at_o right_a angle_n in_o the_o centre_n and_o the_o parallel_n of_o declination_n at_o the_o time_n from_o six_o count_v among_o the_o meridian_n as_o for_o example_n let_v the_o latitude_n give_v be_v 52_o deg_fw-la 30_o min._n and_o the_o sun_n declination_n 11_o deg_fw-la 30_o min._n first_o place_z the_o horizon_n to_o 37_o deg_fw-la 30_o min._n the_o compliment_n of_o the_o latitude_n below_o the_o south_n end_n of_o the_o equator_fw-la then_o place_v the_o thread_n to_o the_o zenith_n and_o nadir_n that_o be_v to_o 52_o deg_fw-la 30_o min._n above_o the_o south_n end_n of_o the_o equator_fw-la and_o as_o much_o below_o the_o north_n end_v thereof_o the_o thread_n be_v fix_v shall_v cut_v the_o horizon_n at_o right_a angle_n in_o the_o centre_n and_o also_o the_o parallel_n of_o 11_o deg_fw-la 30_o min_fw-mi at_o the_o meridian_n of_o 9_o deg_fw-la or_o in_o time_n at_o 36_o minute_n from_o the_o hour_n of_o six_o and_o such_o be_v the_o distance_n of_o time_n betwixt_o the_o hour_n of_o six_o and_o the_o sun_n come_v to_o the_o east_n or_o west_n point_n which_o be_v require_v chap._n xxxv_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 height_n at_o the_o hour_n of_o six_o first_o set_v the_o horizon_n to_o the_o compliment_n of_o the_o latititude_n below_o the_o south_n end_n of_o the_o equator_fw-la or_o the_o equator_fw-la to_o the_o compliment_n of_o the_o latitude_n above_o the_o south_n end_n of_o the_o horizon_n which_o be_v all_o one_o then_o seek_v the_o declination_n upon_o the_o axletree-line_n and_o place_v the_o thread_n thereunto_o parallel_v to_o the_o horizon_n by_o help_n of_o the_o almicanter_n at_o both_o end_n thereof_o so_o shall_v the_o thread_n show_v among_o those_o almicanter_n the_o height_n of_o the_o sun_n require_v thus_o in_o the_o latitude_n of_o 52_o deg_fw-la 30_o min._n the_o sun_n declination_n be_v 11_o deg_fw-la 30_o min._n i_o first_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 then_o place_v the_o thread_n to_o 11_o deg_fw-la 30_o min._n count_v in_o the_o axletree-line_n and_o move_v the_o end_n thereof_o to_o and_o fro_o until_o the_o thread_n lie_v parallel_n to_o the_o horizon_n which_o will_v be_v when_o both_o end_n of_o the_o thread_n cut_v like_o degree_n from_o the_o horizon_n upon_o
the_o ascensional_a difference_n 1_o hour_n 1_o minute_n add_v to_o 6_o hour_n make_v 7_o hour_n 1_o minute_n the_o semidiurnal_a arch_n or_o the_o time_n of_o sun_n set_v which_o be_v double_v give_v 14_o hour_n 2_o minute_n for_o the_o diurnal_a arch_n this_o be_v take_v out_o of_o 24_o hour_n leave_v 9_o hour_n 58_o minute_n for_o the_o nocturnal_a arch_n the_o half_a of_o which_o 9_o hour_n 58_o minute_n be_v 4_o hour_n 59_o minute_n the_o time_n of_o sun_n rise_v or_o 7_o hour_n 1_o minute_n take_v out_o of_o 12_o hour_n leave_v 4_o hour_n 59_o minute_n the_o time_n of_o sun_n rise_v but_o if_o the_o declination_n be_v southwards_o then_o take_v this_o 1_o hour_n 1_o minute_n the_o ascensional_a difference_n out_o of_o 6_o hour_n and_o there_o will_v rest_v 4_o hour_n 59_o minute_n for_o the_o semidiurnal_a arch_n which_o be_v double_v give_v 9_o hour_n 58_o minute_n for_o the_o length_n of_o the_o day_n the_o compliment_n unto_o 24_o hour_n be_v 14_o hour_n 2_o minute_n the_o length_n of_o the_o night_n the_o half_a of_o which_o be_v 7_o hour_n 1_o min._n the_o time_n of_o sunrising_n chap._n xix_o have_v the_o latitude_n of_o the_o place_n &_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 or_o end_v of_o twilight_n the_o beginning_n of_o twilight_n be_v when_o the_o sun_n approach_v within_o 18_o degree_n of_o the_o horizon_n in_o the_o east_n and_o the_o end_n of_o the_o same_o at_o 18_o deg_fw-la depression_n in_o the_o west_n wherefore_o to_o find_v the_o same_o work_n thus_o first_o by_o the_o 16_o chap._n get_v the_o height_n of_o the_o sun_n at_o the_o hour_n of_o six_o if_o the_o declination_n be_v north_n but_o if_o it_o be_v south_n take_v his_o depression_n at_o six_o for_o all_o be_v one_o thing_n if_o his_o quantity_n of_o declination_n be_v alike_o the_o height_n or_o depression_n at_o six_o be_v know_v if_o the_o declination_n be_v north_n add_v the_o sine_fw-la of_o this_o height_n to_o the_o sine_fw-la of_o 18_o deg_fw-la but_o if_o the_o declination_n be_v south_n take_v the_o difference_n betwixt_o the_o sine_fw-la of_o his_o depression_n and_o the_o sine_fw-la of_o 18_o deg_fw-la so_o shall_v the_o sum_n of_o difference_n be_v the_o second_o proportional_a number_n then_o say_v as_o the_o cousin_n of_o the_o latitude_n to_o this_o second_o proportional_a so_o be_v the_o radius_fw-la to_o a_o four_o proportional_a sine_fw-la then_o as_o the_o cousin_n of_o the_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 quantity_n of_o time_n between_o the_o beginning_n or_o end_v of_o twilight_n and_o the_o hour_n of_o six_o thus_o in_o the_o diagram_n of_o the_o 6_o chap._n have_v the_o declination_n of_o the_o sun_n ♈_o o_fw-fr 11_o deg_fw-la 30_o min._n north_n and_o thereby_o the_o sun_n height_n at_o six_o ro_n 9_o deg_fw-la 6_o min._n we_o have_v give_v we_o in_o the_o triangle_n byo_n first_o the_o angle_n ybo_n the_o compliment_n of_o the_o latitude_n 37_o deg_fw-la 30_o min._n and_o then_o the_o side_n o_fw-fr y_fw-fr 467_o the_o radius_fw-la being_n 1000_o this_o side_n be_v make_v up_o of_o the_o sine_fw-la of_o the_o sun_n height_n at_o six_o 158_o and_o the_o sine_fw-la of_o 18_o deg_fw-la 309_o or_o by_o add_v of_o or_o 158_o to_o r_o y_fw-fr 309_o we_o have_v o_o y_fw-fr 467_o for_o the_o second_o proportional_a these_o be_v know_v with_o the_o right_a angle_n at_o you_o we_o may_v find_v the_o base_a bo_z by_o the_o 10_o chapter_n or_o 27_o chap._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 37_o deg_fw-la 30_o min._n with_o the_o right_a parallel_n of_o 467_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 50_o deg_fw-la 7_o min._n which_o be_v the_o base_a bo_o but_o see_v the_o radius_fw-la of_o this_o sine_z bo_z be_v but_o the_o cousin_n of_o the_o declination_n oh_o 78_o deg_fw-la 30_o min._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 78_o deg_fw-la 30_o min._n with_o the_o right_n sine_fw-la of_o this_o 50_o degr_n 7_o min._n 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 51_o deg_fw-la 33_o min._n and_o such_o be_v the_o distance_n of_o time_n between_o the_o hour_n of_o six_o and_o the_o beginning_n or_o end_v of_o twilight_n be_v 3_o hour_n 26_o min._n now_o at_o all_o time_n if_o you_o take_v this_o distance_n out_o of_o six_o hour_n your_o remainder_n shall_v be_v the_o beginning_n of_o twilight_n and_o if_o you_o add_v this_o distance_n find_v unto_o 6_o hour_n the_o sum_n will_v be_v the_o end_n of_o the_o same_o except_o it_o be_v in_o those_o latitude_n where_o the_o depression_n of_o 6_o be_v great_a than_o 18_o deg_fw-la and_o then_o you_o must_v in_o that_o latitude_n and_o south_n declination_n who_o depression_n at_o six_o be_v more_o than_o 18_o deg_fw-la work_n by_o the_o contrary_a rule_n and_o when_o the_o sun_n have_v north_n declination_n if_o you_o take_v the_o ascensional_a difference_n out_o of_o the_o distance_n of_o time_n between_o the_o hour_n of_o six_o and_o the_o beginning_n or_o end_v of_o twilight_n you_o shall_v have_v the_o distance_n of_o time_n between_o snn_n rise_v or_o set_v and_o the_o beginning_n or_o end_v of_o twilight_n and_o when_o the_o declination_n be_v south_n add_v the_o ascensional_a difference_n to_o the_o distance_n of_o time_n find_v and_o you_o shall_v have_v the_o quantity_n of_o twilight_n as_o before_o as_o for_o example_n let_v the_o distance_n of_o time_n between_o the_o beginning_n or_o end_v of_o twilight_n and_o the_o hour_n of_o six_o be_v find_v to_o be_v 3_o hour_n 26_o min._n if_o i_o take_v this_o 3_o hour_n 26_o min._n out_o of_o 6_o hour_n there_o will_v remain_v 2_o hour_n 34_o min_fw-mi for_o the_o beginning_n of_o twilight_n and_o if_o i_o add_v this_o 3_o hour_n 26_o min._n to_o six_o hour_n it_o will_v make_v 9_o hour_n 26_o min._n for_o the_o end_n of_o twilight_n and_o now_o be_v the_o sun_n have_v north_n declination_n if_o i_o take_v the_o difference_n of_o ascension_n 1_o hour_n 1_o min._n as_o it_o be_v find_v by_o the_o last_o chapter_n out_o of_o 3_o hour_n 26_o min._n there_o will_v remain_v 2_o hour_n 25_o min._n for_o the_o quantity_n of_o twilight_n before_o or_o after_o sun_n rise_v or_o set_v chap._n xx._n have_v the_o distance_n of_o the_o sun_n from_o the_o next_o equinoctial_a point_n to_o find_v his_o right_a ascension_n as_o the_o radius_fw-la to_o the_o cousin_n of_o the_o great_a declination_n so_o be_v the_o tangent_fw-la of_o the_o distance_n to_o the_o tangent_fw-la of_o the_o right_a ascension_n thus_o in_o the_o right_a angle_a triangle_n ♈_o x_o ♉_o in_o the_o diagram_n of_o the_o 6_o chap._n have_v the_o angle_n x_o ♈_o ♉_o the_o sun_n great_a declination_n 23_o deg_fw-la 30_o min._n and_o the_o base_a ♈_o ♉_o the_o distance_n of_o the_o sun_n from_o the_o equinoctial_a point_n ♈_o 30_o deg_fw-la with_o the_o right_a angle_n at_o x_o we_o may_v find_v the_o side_n ♈_o x_o the_o sun_n right_a ascension_n by_o the_o 33_o chap._n of_o the_o second_o book_n for_o if_o we_o place_v the_o thread_n at_o the_o intersection_n of_o the_o contrary_a sine_fw-la of_o 90_o deg_fw-la with_o the_o right_n tangent_fw-la of_o 30_o deg_fw-la it_o will_v cut_v the_o contrary_a sine_fw-la of_o 66_o degree_n 30_o minute_n at_o the_o right_n tangent_fw-la of_o 27_o degree_n 54_o minute_n and_o so_o much_o be_v the_o side_n ♈_o x_o the_o right_a ascension_n require_v chap._n xxi_o have_v the_o right_a ascension_n of_o the_o sun_n or_o star_n together_o with_o the_o difference_n of_o their_o ascension_n to_o find_v the_o oblique_a ascension_n and_o descension_n if_o the_o declination_n of_o the_o sun_n or_o star_n be_v north_n subtract_v the_o ascensional_a difference_n from_o the_o right_a ascension_n and_o the_o residue_n will_v be_v the_o oblique_a ascension_n but_o if_o you_o add_v they_o together_o the_o sum_n will_v be_v the_o oblique_a descension_n but_o if_o the_o declination_n be_v south_n add_v the_o ascensional_a difference_n and_o right_a ascension_n together_o so_o will_v the_o sum_n thereof_o be_v the_o oblique_a ascension_n but_o if_o you_o take_v the_o ascensional_a difference_n out_o of_o the_o right_a ascension_n the_o remainder_n will_v be_v the_o oblique_a descension_n as_o for_o example_n the_o right_a ascension_n of_o the_o sun_n in_o the_o begin_n of_o ♉_o being_z find_v by_o the_o last_o chapter_n to_o be_v 27_o degree_n 54_o minute_n and_o the_o ascensional_a
the_o base_a 132_o inch_n and_o his_o altitude_n 9_o foot_n we_o may_v find_v his_o solid_a content_n in_o foot_n for_o if_o we_o place_v the_o the_o thread_n to_o the_o intersection_n of_o the_o contrary_a parallel_n of_o 42_o 55_o 100_o with_o the_o right_a parallel_n of_o 132_o it_o will_v cut_v the_o contrary_a parallel_n of_o 3_o which_o be_v the_o three_o part_n of_o his_o altitude_n at_o the_o right_a parallel_n of_o 9_o 3_o 10_o then_o keep_v the_o thread_n in_o the_o same_o position_n it_o will_v cut_v the_o contrary_a parallel_n of_o this_o 9_o 3_o 10_o at_o the_o right_a parallel_n of_o 28â…ž_n and_o so_o many_o solid_a foot_n be_v in_o that_o cone_n who_o base_n circumference_n be_v 132_o inch_n and_o altitude_n 9_o foot_n chap._n lix_n have_v the_o diameter_n of_o the_o base_a of_o a_o cone_fw-it give_v in_o inch_n and_o his_o altitude_n in_o foot_n to_o find_v the_o solid_a content_n in_o foot_n as_o 13_o 54_o 100_o inch_n to_o the_o diameter_n in_o inch_n so_o be_v the_o three_o part_n of_o his_o altitude_n in_o foot_n to_o a_o four_o number_n then_o as_o 13_o 54_o 100_o inch_n to_o the_o diameter_n in_o inch_n so_o be_v this_o four_o number_n to_o the_o solid_a content_n in_o foot_n thus_o in_o the_o cone_n of_o the_o 57_o chapter_n have_v the_o diameter_n of_o his_o base_a 42_o inch_n and_o his_o altitude_n 9_o foot_n we_o may_v find_v his_o solid_a content_n in_o foot_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 parallel_n of_o 13_o 54_o 100_o with_o the_o right_a parallel_n of_o 42_o inch_n it_o will_v cut_v the_o contrary_a parallel_n of_o 3_o foot_n at_o the_o right_a parallel_n of_o 9_o 3_o 10_o and_o lie_v in_o this_o same_o position_n it_o shall_v cut_v the_o contrary_a parallel_n of_o this_o 9_o 3_o 10_o at_o the_o right_a parallel_n of_o 28â…ž_n the_o solid_a content_n of_o the_o cone_n as_o before_o chap._n lx._n have_v the_o side_n and_o semidiameter_n of_o a_o cone_n to_o find_v his_o altitude_n or_o perpendicular_a fall_n from_o the_o top_n thereof_o perpendicular_o upon_o his_o base_a first_o place_v the_o bead_n to_o the_o side_n of_o the_o cone_fw-it give_v upon_o the_o side_n of_o the_o quadrat_fw-la and_o then_o open_a the_o thread_n till_o the_o bead_n fall_v direct_o upon_o the_o right_a parallel_n of_o the_o semidiameter_n of_o the_o base_a so_o shall_v the_o bead_n cut_v the_o contrary_a parallel_n of_o the_o altitude_n require_v thus_o in_o the_o cone_n of_o the_o 57_o chapter_n have_v the_o semidiameter_n of_o his_o base_a 21_o inch_n and_o his_o side_n 9_o foot_n and_o something_o better_a than_o 2_o inch_n that_o be_v 110_o inch_n if_o you_o place_v the_o bead_n to_o 110_o inch_n count_v on_o the_o side_n of_o the_o quadrat_fw-la and_o then_o open_a the_o thread_n till_o the_o bead_n fall_v direct_o upon_o the_o right_a parallel_n of_o 21_o inch_n it_o shall_v cut_v the_o contrary_a parallel_n of_o 108_o inch_n which_o be_v just_a 9_o foot_n for_o the_o altitude_n of_o the_o cone_n which_o be_v require_v chap._n lxi_o have_v the_o side_n of_o a_o segment_n of_o a_o cone_n with_o the_o semidiameter_n of_o each_o base_a or_o end_n thereof_o to_o find_v the_o altitude_n of_o tâ—e_v whole_a cone_n as_o it_o be_v before_o it_o be_v cut_v off_o with_o the_o altitude_n of_o the_o lesser_a cone_n which_o be_v cut_v off_o first_o take_v the_o lesser_a semidiameter_n out_o of_o the_o great_a and_o note_v the_o difference_n then_o say_v as_o this_o difference_n to_o the_o side_n of_o the_o segment_n of_o the_o cone_n so_o be_v the_o great_a semidiameter_n to_o the_o altitude_n of_o the_o whole_a cone_fw-mi and_o the_o less_o semidiameter_n to_o the_o altitude_n of_o the_o lesser_a cone_n which_o be_v cut_v off_o thus_o in_o the_o cone_n of_o the_o 57_o chapter_n although_o it_o shall_v be_v cut_v off_o by_o the_o plane_n of_o equidistant_o to_o the_o base_a bc_n yet_o have_v the_o side_n of_o the_o segment_n befc_n of_o the_o cone_n abc_n which_o be_v be_v or_o cf_n 6_o foot_n and_o one_o inch_n or_o 73_o 38_o 100_o inch_n with_o the_o semidiameter_n of_o the_o great_a base_a 21_o inch_n and_o the_o lesser_a 7_o inch_n we_o may_v find_v the_o perpendicular_a of_o the_o whole_a great_a cone_n as_o it_o be_v before_o it_o be_v cut_v off_o and_o also_o of_o the_o lesser_a which_o be_v cut_v off_o for_o if_o you_o take_v 7_o inch_n out_o of_o 21_o there_o will_v remain_v 14_o inch_n and_o than_o if_o you_o place_v the_o thread_n to_o the_o intersection_n of_o the_o contrary_a parallel_n of_o 14_o inch_n with_o the_o right_a parallel_n of_o 73_o 38_o 100_o inch_n it_o will_v cut_v the_o contrary_a parallel_n of_o 21_o inch_n the_o semidiameter_n of_o the_o base_a of_o the_o great_a cone_n at_o the_o right_a parallel_n of_o 108_o inch_n which_o be_v 9_o foot_n the_o altitude_n of_o the_o whole_a great_a cone_n as_o if_o it_o have_v not_o be_v cut_v off_o the_o thread_n lie_v still_o in_o the_o same_o position_n do_v likewise_o cut_v the_o contrary_a parallel_n of_o 7_o inch_n which_o be_v the_o semidiameter_n of_o the_o base_a of_o the_o lesser_a cone_n which_o be_v cut_v off_o at_o the_o right_a parallel_n of_o 36_o inch_n or_o 3_o foot_n the_o altitude_n of_o the_o lesser_a cone_n which_o be_v require_v chap._n lxii_o how_o the_o segment_n cut_v off_o from_o any_o cone_n may_v be_v measure_v the_o segment_n of_o a_o cone_n be_v no_o other_o than_o a_o round_a taper_a piece_n of_o timber_n cut_v off_o before_o it_o come_v to_o a_o point_n and_o may_v be_v measure_v by_o that_o which_o before_o be_v deliver_v when_o therefore_o at_o any_o time_n you_o meet_v with_o any_o such_o solid_a piece_n which_o will_v be_v more_o ordinary_o then_o with_o any_o other_o first_o get_v the_o length_n of_o his_o side_n and_o then_o his_o semidiameter_n at_o each_o end_n and_o so_o by_o the_o last_o chapter_n the_o altitude_n of_o the_o whole_a great_a cone_n and_o also_o of_o the_o lesser_a which_o be_v suppose_v to_o be_v add_v to_o the_o segment_n to_o make_v it_o a_o perfect_a cone_n this_o be_v do_v by_o the_o 59_o or_o 60_o chapter_n measure_v the_o content_a of_o the_o whole_a great_a cone_n and_o also_o of_o the_o lesser_a and_o take_v the_o content_a of_o the_o lesser_a out_o of_o the_o great_a the_o remainder_n without_o out_o doubt_v must_v be_v the_o content_a of_o the_o segment_n give_v as_o for_o example_n let_v the_o segment_n befc_n of_o the_o cone_n in_o the_o 57_o chapter_n be_v give_v to_o be_v measure_v let_v the_o side_n thereof_o be_v 73_o 38_o 100_o inch_n and_o the_o semidiameter_n of_o the_o great_a base_a bd_o 21_o inch_n and_o the_o semidiameter_n of_o the_o lesser_a base_a eke_o 7_o inch_n and_o so_o by_o the_o last_o chapter_n the_o altitude_n of_o the_o whole_a great_a cone_n ad_fw-la 9_o foot_n and_o the_o altitude_n of_o the_o lesser_a add_v cone_n ak_v 3_o foot_n and_o then_o by_o the_o 59_o chapter_n the_o content_a of_o the_o whole_a great_a cone_n will_v be_v 28â…ž_n foot_n and_o the_o lesser_a add_v cone_n 1_o foot_n and_o something_o better_a or_o 1_o 5_o 72_o foot_n the_o which_o if_o you_o take_v out_o of_o 28â…ž_n foot_n the_o content_a of_o the_o whole_a great_a cone_n there_o will_v remain_v 27_o 29_o 36_o foot_n for_o the_o content_a of_o the_o segment_n befc_n which_o be_v require_v chap._n lxiii_o to_o find_v the_o solid_a content_n of_o any_o pyramid_n let_v the_o base_a of_o the_o pyramid_n be_v of_o what_o manner_n it_o will_v you_o need_v do_v no_o more_o but_o take_v one_o three_o part_n of_o his_o altitude_n and_o then_o suppose_v it_o to_o be_v a_o prisma_fw-la have_v equal_a base_n like_a and_o parallel_v who_o length_n be_v equal_a to_o the_o three_o part_n of_o the_o pyramid_n you_o may_v find_v the_o solid_a content_n by_o one_o or_o other_o of_o the_o former_a chapter_n concern_v prisma_n as_o for_o example_n let_v the_o follow_v quadrangular_a pyramid_n be_v give_v to_o be_v measure_v the_o side_n of_o who_o base_a be_v 36_o inch_n and_o the_o side_n of_o the_o pyramid_n 76_o 36_o 100_o inch_n with_o the_o semidiameter_n of_o the_o circle_n enclose_v the_o base_a which_o be_v ab_fw-la 25_o 45_o 100_o inch_n by_o which_o and_o the_o side_n give_v with_o the_o help_n of_o the_o 60_o chapter_n we_o may_v find_v the_o altitude_n ad_fw-la to_o be_v 72_o inch_n or_o 6_o foot_n now_o have_v the_o side_n of_o the_o base_a in_o inch_n and_o the_o altitude_n in_o foot_n we_o may_v find_v the_o content_a in_o fect_n for_o as_o 12_o inch_n to_o the_o side_n of_o the_o base_a in_o inch_n so_o be_v the_o three_o part_n of_o the_o altitude_n in_o foot_n
to_o a_o four_o number_n and_o this_o four_o number_n to_o the_o solid_a content_n in_o foot_n wherefore_o if_o you_o apply_v the_o thread_n to_o the_o intersection_n of_o the_o contrary_a parallel_n of_o 12_o with_o the_o right_a parallel_n of_o 2_o foot_n the_o three_o part_n of_o the_o altitude_n it_o will_v cut_v the_o contrary_a parallel_n of_o 36_o inch_n the_o side_n of_o the_o base_a at_o the_o right_a parallel_n of_o 6_o the_o thread_n lie_v still_o in_o the_o same_o position_n will_v cut_v the_o contrary_a parallel_n of_o this_o 6_o at_o the_o right_a parallel_n of_o 18_o and_o such_o be_v the_o solid_a content_n of_o this_o pyramid_n in_o foot_n which_o be_v require_v now_o if_o you_o will_v measure_v any_o segment_n of_o a_o pyramid_n be_v cut_v off_o observe_v the_o former_a rule_n give_v for_o the_o measure_n of_o the_o segment_n of_o a_o cone_n and_o you_o shall_v soon_o have_v your_o desire_n for_o have_v the_o side_n of_o the_o segment_n of_o the_o pyramid_n with_o the_o semidiameter_n of_o the_o circumscribe_v circle_n at_o each_o base_a you_o may_v by_o the_o 61_o chapter_n find_v the_o altitude_n of_o the_o whole_a great_a pyramid_n as_o if_o it_o have_v not_o be_v cut_v off_o and_o also_o of_o the_o lesser_a pyramid_n which_o be_v suppose_v to_o be_v add_v to_o the_o segment_n to_o make_v it_o a_o perfect_a pyramid_n this_o be_v do_v you_o may_v by_o the_o rule_v deliver_v first_o get_v the_o content_a of_o the_o whole_a great_a pyramid_n and_o then_o of_o the_o lesser_a add_v pyramid_n and_o take_v the_o lesser_a out_o of_o the_o great_a the_o remainder_n will_v be_v the_o content_a of_o the_o give_v segment_n as_o be_v require_v the_o end_n of_o the_o first_o book_n the_o second_o book_n show_v the_o most_o plentiful_a easy_a and_o speedy_a use_n of_o the_o universal_a quadrat_fw-la in_o the_o resolution_n of_o the_o whole_a doctrine_n trigonometrical_a as_o well_o plain_a as_o spherical_a and_o that_o two_o several_a way_n upon_o the_o instrument_n with_o surpass_a facility_n and_o with_o the_o least_o intricacie_n that_o may_v be_v chap._n i._o to_o find_v the_o chord_n of_o any_o arch_n the_o radius_fw-la be_v give_v not_o exceed_v the_o side_n of_o the_o quadrat_fw-la the_o radius_fw-la of_o a_o circle_n be_v the_o semidiameter_n of_o the_o same_o circle_n or_o the_o total_a sine_fw-la or_o sine_fw-la of_o 90_o degree_n so_o ae_n be_v the_o semidiameter_n or_o radius_fw-la upon_o which_o the_o divide_a arch_n eglantine_n be_v dramn_v and_o ab_fw-la be_v the_o radius_fw-la upon_o which_o the_o arch_a bfc_n be_v draw_v and_o a_o chord_n be_v a_o right_a line_n subtend_v a_o arch_n so_o bc_n be_v the_o chord_n of_o the_o arch_a bfc_n for_o the_o find_n of_o which_o chord_n for_o any_o arch_n require_v place_v the_o radius_fw-la give_v upon_o the_o side_n of_o the_o quadrat_fw-la from_o the_o centre_n and_o note_v the_o point_n where_o the_o same_o end_v and_o there_o place_v the_o bead_n then_o open_v the_o thread_n to_o the_o arch_n give_v count_v in_o the_o quadrant_a the_o distance_n between_o the_o point_n note_v in_o the_o side_n of_o the_o quadrat_fw-la and_o the_o head_n shall_v be_v the_o chord_n require_v as_o for_o example_n let_v ab_fw-la be_v the_o radius_fw-la of_o a_o circle_n place_v upon_o the_o side_n of_o the_o quadrat_fw-la and_o let_v it_o be_v require_v to_o find_v a_o chord_n of_o 40_o degree_n first_o i_o place_v the_o bead_n at_o the_o point_n b_o where_o the_o give_v radius_fw-la end_v and_o open_v the_o thread_n to_o 40_o degree_n in_o the_o quadrant_a i_o take_v the_o distance_n betwixt_o the_o point_n b_o and_o the_o bead_n which_o be_v the_o chord_n of_o 40_o degree_n viz._n the_o chord_n of_o the_o arch_a bfc_n draw_v upon_o the_o give_v radius_fw-la ab_fw-la as_o be_v require_v and_o thus_o may_v you_o find_v the_o chord_n of_o any_o arch_n as_o well_o as_o upon_o the_o sector_n chap._n ii_o to_o find_v the_o right_n sine_fw-la of_o any_o arch_n give_v the_o radius_fw-la be_v put_v 1000_o have_v show_v the_o use_n of_o these_o parallel_a line_n as_o they_o stand_v in_o their_o own_o proper_a signification_n it_o rest_v now_o to_o show_v the_o use_n of_o they_o as_o they_o signify_v right_a fine_n and_o tangent_n and_o first_o to_o find_v the_o right_n fine_a of_o any_o arch_n seek_v the_o degree_n give_v upon_o the_o quadrant_a count_v from_o any_o side_n of_o the_o quadrant_a but_o here_o let_v it_o be_v from_o the_o begin_n of_o the_o degree_n at_o e_o so_o shall_v the_o right_a parallel_n run_v through_o the_o degree_n give_v in_o the_o quadrant_a give_v the_o number_n of_o the_o fine_a require_v but_o if_o you_o will_v have_v the_o fine_a in_o a_o right_a line_n take_v the_o length_n of_o the_o contrary_a parallel_n from_o the_o side_n of_o the_o quadrat_fw-la ae_n to_o the_o degree_n give_v in_o the_o quadrat_fw-la and_o that_o shall_v be_v your_o desire_a sine_z whereof_o the_o whole_a side_n be_v radius_fw-la as_o for_o example_n let_v it_o be_v require_v to_o find_v the_o right_n sine_fw-la of_o 53_o degree_n 8_o minute_n i_o look_v 53_o degree_n 8_o minute_n in_o the_o quadrant_a count_v from_o the_o begin_n of_o the_o degree_n at_o e_o unto_z o_o through_o which_o point_n o_o rune_v the_o right_a parallel_n of_o 800_o this_o 800_o be_v the_o right_a sine_fw-la of_o 53_o degree_n 8_o minute_n 100_o be_v radius_fw-la but_o if_o you_o will_v have_v this_o sine_fw-la in_o a_o right_a line_n take_v the_o length_n of_o the_o contrary_a paaallel_n from_o the_o point_n o_o unto_o n_n for_o the_o right_n sine_fw-la of_o 53_o degree_n 8_o minute_n which_o be_v require_v chap._n iii_o to_o find_v the_o arch_n of_o any_o sine_fw-la give_v the_o radius_fw-la be_v put_v 1000_o if_o your_o sine_fw-la be_v give_v in_o number_n seek_v the_o right_a parallel_n of_o the_o number_n give_v for_o where_o that_o parallel_n cut_v the_o quadrant_a there_o be_v the_o arch_n require_v count_v from_o the_o begin_n of_o the_o degree_n at_o e_z as_o before_z but_o if_o your_o sine_fw-la be_v give_v in_o a_o right_a line_n then_o from_o the_o side_n of_o your_o quadrat_fw-la ae_n extend_v your_o give_fw-mi sine_fw-la upon_o any_o of_o the_o contrary_a parallel_n and_o that_o right_a parallel_n that_o shall_v cut_v through_o the_o extreme_a point_n thereof_o shall_v cut_v the_o quadrant_a in_o the_o require_a arch_n as_o for_o example_n let_v 800_o be_v a_o sine_fw-la give_v unto_o which_o it_o be_v require_v to_o find_v the_o arch_n belong_v thereto_o i_o seek_v 800_o in_o the_o right_a parallel_n and_o find_v it_o i_o follow_v it_o to_o the_o quadrant_a and_o there_o i_o see_v it_o cut_v the_o arch_n of_o 53_o degree_n 8_o minute_n count_v from_o e_o which_o 53_o degree_n 8_o minute_n be_v the_o arch_n belong_v to_o the_o sine_fw-la 800_o the_o radius_fw-la being_n 1000_o but_o if_o the_o sine_fw-la be_v give_v in_o a_o right_a line_n take_v it_o betwixt_o your_o compass_n and_o set_v one_o foot_n in_o the_o side_n of_o the_o quadrat_fw-la ae_n extend_v the_o other_o upon_o any_o of_o the_o contrary_a parallel_n as_o here_o i_o set_v one_o foot_n in_o the_o point_n n_n and_o extend_v the_o other_o unto_o o_o through_o which_o point_n the_o right_a parallel_n of_o 800_o run_v and_o cut_v the_o quadrant_a in_o 53_o degree_n 8_o minute_n count_v from_o e_z as_o before_z chap._n iu._n any_o radius_fw-la not_o exceed_v the_o side_n of_o the_o quadrat_fw-la be_v give_v to_o find_v the_o right_n sine_fw-la of_o any_o arch_n or_o angle_v thereunto_o belong_v first_o take_v the_o give_v radius_fw-la and_o place_n it_o upon_o the_o contrary_a parallel_n of_o 100_o which_o be_v the_o total_a sine_fw-la and_o where_o it_o shall_v end_v there_o place_n the_o thread_n which_o be_v so_o place_v see_v where_o it_o cut_v the_o contrary_a parallel_n that_o pass_v through_o the_o give_v arch_n count_v in_o the_o quadrant_a from_o g_z for_o the_o segment_n so_o cut_v which_o lie_v between_o the_o thread_n and_o the_o side_n ae_n be_v the_o fine_a require_v let_v the_o line_n a_o be_v the_o radius_fw-la give_v and_o let_v it_o be_v require_v to_o find_v the_o sine_fw-la of_o 36_o degree_n 53_o minute_n first_o i_o take_v the_o line_n a_o and_o place_n it_o upon_o the_o contrary_a parallel_n of_o 100_o as_o from_o e_z to_z d_o upon_o which_o point_n d_o i_o place_v the_o thread_n this_o do_v i_o count_v the_o give_v arch_n viz._n 36_o degree_n 33_o minute_n from_o the_o end_n of_o the_o quadrant_a at_o g_z unto_o o_o and_o see_v what_o contrary_a parallel_n there_o i_o find_v which_o be_v 60_o intersect_v the_o thread_n at_o m_n so_o shall_v the_o distance_n nm_n be_v the_o line_n b_o the_o sine_fw-la of_o 36_o degree_n 53_o
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