24_o gr_n of_o ♉_o his_o longitude_n shall_v be_v pi_n his_o right_a ascension_n ph_n his_o declination_n he_o and_o if_o the_o place_n give_fw-mi be_v 19_o gr_n of_o ♌_o his_o longitude_n shall_v be_v pk_n his_o right_a ascension_n pn_n his_o declination_n nk_v again_o the_o declination_n bring_v to_o the_o horizon_n of_o the_o place_n shall_v there_o show_v the_o ascentionall_a difference_n amplitude_n of_o ascension_n and_o the_o like_a conclusion_n of_o the_o globe_n but_o i_o intend_v not_o here_o to_o show_v the_o use_n of_o the_o astrolabe_n but_o the_o use_n of_o the_o sector_n in_o projection_n and_o after_o this_o manner_n may_v a_o nocturnal_a be_v project_v to_o show_v the_o hour_n of_o the_o night_n whereof_o i_o will_v set_v down_o a_o type_n for_o the_o use_n of_o seaman_n it_o consist_v as_o you_o see_v of_o two_o part_n the_o one_o be_v a_o plane_n divide_v equal_o according_a to_o the_o 24_o hour_n of_o the_o day_n and_o each_o hour_n into_o quarter_n or_o minute_n as_o the_o plane_n will_v bear_v the_o line_n from_o the_o centre_n to_o xii_o stand_v for_o the_o meridian_n and_o xii_o stand_v for_o the_o hour_n of_o 12_o at_o midnight_n the_o other_o part_n be_v a_o rundle_n for_o such_o star_n as_o be_v near_o the_o north_n pole_n together_o with_o the_o twelve_o month_n and_o the_o day_n of_o each_o month_n fit_v to_o the_o right_a ascension_n of_o the_o star_n those_o that_o have_v occasion_n to_o see_v the_o south_n pole_n may_v do_v the_o like_a for_o the_o southern_a constellation_n and_o put_v they_o in_o a_o rundle_n on_o the_o back_n of_o this_o plane_n and_o so_o it_o may_v serve_v for_o all_o the_o world_n the_o use_n of_o this_o nocturnal_a be_v easy_a and_o ready_a for_o look_v up_o to_o the_o pole_n and_o see_v what_o star_n be_v near_o the_o meridian_n then_o place_v the_o rundle_n to_o the_o like_a situation_n so_o the_o day_n of_o the_o month_n will_v show_v the_o hour_n of_o the_o night_n 3_o the_o sphere_n may_v be_v project_v in_o plano_fw-la by_o circular_a line_n as_o in_o the_o particular_a astrolabe_n of_o joh._n stophlerin_n by_o help_n of_o the_o tangent_fw-la as_o before_o for_o let_v the_o circle_n give_fw-mi represent_v the_o tropic_n of_o ♑_o let_v it_o be_v divide_v into_o four_o part_n and_o cross_v at_o right_a angle_n with_o ac_fw-la the_o equinoctial_a colour_n and_o mb_v the_o solstitial_a colour_n and_o general_a meridian_n the_o centre_n p_o represent_v the_o pole_n of_o the_o world_n let_v each_o quarter_n be_v divide_v into_o 90_o gr_n and_o so_o the_o whole_a into_o 360_o begin_v from_o a_o towards_o b._n the_o meridian_n pm_n or_o pb_n may_v be_v divide_v according_a to_o the_o tangent_fw-la of_o half_a his_o ark_n so_o as_o the_o ark_n from_o the_o north_n pole_n to_o the_o tropic_n of_o ♑_o be_v 90_o gr_n and_o 23_o gr_n 30_o m._n that_o be_v 113_o gr_n 80_o m._n and_o the_o half_a ark_n 56_o gr_n 45_o m._n the_o meridian_n shall_v be_v divide_v into_o 90_o gr_n and_o 23_o gr_n 30_o m._n in_o such_o sort_n as_o the_o tangent_fw-la of_o 56_o gr_n 45_o m._n on_o the_o side_n of_o the_o sector_n be_v divide_v into_o degree_n and_o half_a degree_n of_o which_o pae_n the_o ark_n of_o the_o equator_fw-la 90_o gr_fw-la from_o the_o pole_n shall_v be_v give_v by_o the_o tangent_fw-la of_o 45_o gr_n and_o p_o 69_o the_o ark_n of_o the_o summer_n tropic_n 66_o gr_n 30_o m._n from_o the_o pole_n shall_v be_v give_v by_o the_o tangent_fw-la of_o 33_o gr_n 15_o m._n and_o the_o circle_n draw_v upon_o the_o centre_n p_o through_z ae_n and_o ♋_o shall_v be_v the_o equator_fw-la and_o the_o summer_n tropic_n have_v the_o equator_fw-la and_o both_o the_o tropique_n the_o ecliptic_a ♈_o ♋_o ♎_o ♑_o shall_v be_v draw_v from_o the_o one_o tropic_n to_o the_o other_o through_o the_o intersection_n of_o the_o equator_fw-la and_o the_o equinoctial_a colour_n and_o it_o may_v be_v divide_v first_o into_o the_o twelve_o sign_n after_o this_o manner_n pe_n the_o ark_n of_o the_o pole_n of_o the_o ecliptic_a 23_o gr_n 30_o m._n from_o the_o pole_n of_o the_o world_n shall_v be_v give_v by_o the_o tangent_fw-la of_o 11_o gr_n 45_o m._n the_o centre_n of_o the_o circle_n of_o longitude_n pass_v through_o this_o pole_n e_o ♈_o and_o ♎_o shall_v be_v find_v at_o d_o somewhat_o below_o b_o by_o the_o tangent_fw-la of_o 66_o gr_n 30_o m._n then_o through_o d_o draw_v a_o occult_a line_n parallel_n to_o ac_fw-la and_o divide_v it_o on_o each_o side_n from_o d_o in_o such_o sort_n as_o the_o tangent_fw-la be_v divide_v on_o the_o side_n of_o the_o sector_n allow_v 45_o gr_n to_o be_v equal_a to_o de._n so_o the_o thirtith_n degree_n from_o d_o towards_o the_o right_a hand_n shall_v be_v the_o centre_n of_o the_o circle_n of_o longitude_n pass_v through_o e_o ♉_o and_o â™_o the_o sixtith_n degree_n the_o centre_n of_o ♊_o e_o â™_o the_o thirtith_n degree_n from_o d_o towards_o the_o left_a hand_n the_o centre_n of_o ♓_o e_o â™_o the_o sixtith_n the_o centre_n of_o â™’_o e_o ♌_o and_o the_o other_o intermediate_v degree_n shall_v be_v the_o centre_n to_o divide_v each_o sign_n into_o 30_o gr_n if_o far_o we_o have_v respect_n unto_o the_o latitude_n we_o may_v the_o meridian_n be_v before_o divide_v number_v it_o from_o p_o northward_o unto_o h_n and_o there_o place_v the_o north_n intersection_n of_o the_o meridian_n and_o horizon_n then_o the_o compliment_n of_o the_o latitude_n be_v number_v from_o p_o southward_o unto_o z_o shall_v there_o give_v the_o zenith_n and_o 90_o gr_n from_o z_o southward_n unto_o f_o shall_v there_o give_v the_o south_n intersection_n of_o the_o meridian_n and_o horizon_n the_o middle_n between_o f_o and_o h_n shall_v be_v g_z the_o centre_n of_o the_o horizon_n ♈_o h_o ♎_o f_o pass_v through_o the_o begin_n of_o ♈_o and_o ♎_o unless_o there_o be_v some_o former_a error_n all_o parallel_n to_o the_o horizon_n may_v be_v find_v in_o like_a sort_n by_o their_o intersection_n with_o the_o meridian_n and_o the_o middle_n between_o those_o intersection_n be_v always_o the_o centre_n for_o example_n of_o this_o projection_n let_v ☉_o the_o place_n of_o the_o sun_n give_fw-mi be_v 10_o gr_n of_o ♉_o a_o right_a line_n draw_v from_o p_o through_o this_o place_n unto_o the_o equator_fw-la shall_v there_o show_v his_o right_a ascension_n ♈_o k_n and_o his_o declination_n k_o ☉_o then_o may_v we_o on_o the_o centre_n p_o and_z semidiameter_n ☉_o p_o draw_v a_o occult_a parallel_n of_o declination_n cross_v the_o horizon_n in_o l_o and_o m_o the_o meridian_n in_o g_z and_z n._n so_o the_o right_a line_n pl_z and_o pm_n produce_v shall_v show_v the_o time_n of_o the_o sun_n rise_v and_o set_v ♈_o q_o the_o difference_n of_o ascension_n ♎_o r_o the_o difference_n of_o descension_n ♈_o l_o the_o amplitude_n of_o his_o rise_n and_o ♎_o m_o the_o amplitude_n of_o his_o set_n lgm_n show_v the_o length_n of_o the_o day_n ln_o m_n the_o length_n of_o the_o night_n zg_v show_v his_o distance_n from_o the_o zenith_n at_o noon_n hn_n his_o depression_n below_o the_o horizon_n at_o midnight_n and_o then_o have_v the_o altitude_n of_o the_o sun_n at_o any_o time_n of_o the_o day_n the_o intersection_n of_o the_o parallel_n of_o altitude_n with_o the_o parallel_n of_o declination_n show_v the_o azimuth_n and_o a_o right_a line_n draw_v from_o p_o through_o this_o intersection_n give_v the_o hour_n of_o the_o day_n 4_o the_o sphere_n may_v be_v project_v in_o plano_fw-la by_o circular_a line_n after_o the_o manner_n of_o the_o old_a concave_a hemisphere_n by_o the_o help_n of_o the_o tangent_fw-la on_o the_o side_n of_o the_o sector_n for_o let_v the_o circle_n give_fw-mi represent_v the_o plane_n of_o the_o horizon_n let_v it_o be_v divide_v into_o four_o part_n and_o cross_v at_o right_a angle_n with_o sn_a the_o meridian_n and_o ev_n the_o vertical_a so_o as_o s_n may_v stand_v for_o the_o south_n n_n for_o the_o north_n e_o the_o east_n five_o the_o west_n part_n of_o the_o horizon_n and_o the_o centre_n z_o represent_v the_o zenith_n let_v each_o quarter_n of_o the_o horizon_n be_v divide_v into_o 90_o gr_n and_o so_o the_o whole_a into_o 360_o gr_n begin_n from_o n_n and_o set_v to_o the_o number_n of_o 10._o 20._o 30._o etc._n etc._n 90_o at_o e_o 180_o at_o s_n 270_o at_o five_o 360_o at_o n._n the_o semidiameter_n zn_o zs_n may_v be_v divide_v according_a to_o the_o tangent_fw-la of_o half_a their_o arke_n so_o as_o the_o ark_n from_o the_o zenith_n to_o the_o horizon_n be_v 90_o gr_n and_o the_o half_a ark_n 45_o gr_n the_o semidiameter_n be_v to_o be_v divide_v in_o such_o sort_n as_o the_o tangent_fw-la of_o 45_o gr_n as_o
northward_o with_o the_o same_o altitude_n of_o 12_o gr_n and_o like_o declination_n of_o 20_o gr_n to_o the_o northward_o it_o will_v be_v find_v to_o be_v only_o 72_o gr_n 52_o m._n though_o the_o manner_n of_o work_n be_v the_o same_o as_o before_o declin_n north_n 20_o gr_n 0_o m_o the_o distance_n be_v 70_o gr_n 0_o m._n altitude_n 12_o 0_o the_o compliment_n 78_o 0_o latitud_n north_n 51_o 30_o the_o compliment_n 38_o â—0_n  _fw-fr the_o sum_n of_o all_o three_o 186_o 30_o  _fw-fr the_o half_a sum_n 93_o 15_o  _fw-fr the_o difference_n 23_o 15_o here_o as_o the_o radius_fw-la be_v to_o the_o sine_fw-la of_o 78_o gr_n so_o the_o sine_fw-la of_o 38_o gr_n 30_o m._n to_o the_o sine_fw-la of_o 37_o gr_n 30_o m._n which_o be_v the_o four_o sine_fw-la and_o the_o same_o as_o before_o then_o as_o this_o four_o sine_fw-la of_o 37_o gr_n 30_o m._n be_v to_o the_o sine_fw-la of_o 93_o gr_n 15_o m_o so_o the_o sine_fw-la of_o 23_o gr_n 15_o m._n to_o the_o sine_fw-la of_o 40_o gr_n 20_o m._n which_o be_v the_o seven_o sine_fw-la the_o half_a way_n between_o this_o seven_o sine_z and_z the_o sine_z of_o 90_o gr_n do_v fall_n at_o 53_o gr_n 34_o m._n who_o compliment_n be_v 36_o gr_n 26_o m_o and_o the_o double_a of_o that_o be_v 72_o gr_n 52_o m._n the_o azimuth_n require_v or_o i_o may_v find_v this_o same_o azimuth_n in_o the_o line_n of_o verse_v sin_n over_o against_o the_o seven_o sine_fw-la of_o 40_o gr_n 20_o m._n 11_o have_v the_o latitude_n of_o the_o place_n the_o declination_n of_o the_o sun_n and_o the_o altitude_n of_o the_o sun_n to_o find_v the_o hour_n of_o the_o day_n add_v the_o compliment_n of_o the_o sun_n altitude_n and_o the_o distance_n of_o the_o sun_n from_o the_o pole_n and_o the_o compliment_n of_o your_o latitude_n all_o three_o together_o and_o from_o half_a the_o sum_n subtract_v the_o compliment_n of_o the_o altitude_n and_o note_v the_o difference_n 1_o as_o the_o radius_fw-la be_v in_o proportion_n to_o the_o sine_fw-la of_o the_o sun_n distance_n from_o the_o pole_n so_o the_o sine_fw-la of_o the_o compliment_n of_o the_o latitude_n to_o a_o four_o sine_fw-la 2_o as_o this_o four_o sine_fw-la be_v to_o the_o sine_fw-la of_o the_o half_a sum_n so_o the_o sine_fw-la of_o the_o difference_n to_o a_o seven_o sine_fw-la the_o mean_a proportional_a between_o this_o seven_o sine_z and_z the_o sine_z of_o 90_o gr_n will_v be_v the_o sine_fw-la of_o the_o compliment_n of_o half_a the_o hour_n from_o the_o meridian_n thus_o in_o our_o latitude_n of_o 51_o gr_n 30_o m._n the_o declination_n of_o the_o sun_n be_v 20_o gr_n northward_o and_o the_o altitude_n 12_o gr_n i_o may_v find_v the_o sun_n to_o be_v 95_o gr_n 52_o m._n from_o the_o meridian_n altitude_n 12_o gr_n 0_o m._n the_o compliment_n be_v 78_o gr_n 0_o m._n declin_n north_n 20_o 0_o the_o do_v from_o the_o pole_n 70_o 0_o latitude_n 51_o 30_o the_o compliment_n be_v 38_o 30_o  _fw-fr the_o sum_n of_o all_o three_o 186_o 30_o  _fw-fr the_o half_a sum_n 93_o 15_o  _fw-fr the_o difference_n 15_o 15_o here_o as_o the_o radius_fw-la be_v to_o the_o sine_fw-la of_o 70_o gr_n so_o the_o sine_fw-la of_o 38_o gr_n 30_o m._n to_o the_o sine_fw-la of_o 35_o gr_n 48_o m._n as_o this_o sine_fw-la of_o 35_o gr_n 48_o m._n be_v to_o the_o sine_fw-la of_o 93_o gr_n 15_o m._n so_o the_o sine_fw-la of_o 15_o gr_n 15_o m._n to_o the_o sine_fw-la of_o 26_o gr_n 40_o m._n the_o half_n may_v between_o this_o seven_o sine_fw-la of_o 26_o gr_n 40_o m._n and_o the_o sine_fw-la of_o 90_o gr_n do_v fall_n at_o 42_o gr_n 4_o m._n who_o compliment_n be_v 47_o gr_n 56_o m._n and_o the_o double_a of_o that_o 95_o gr_n 52_o m._n which_o convert_v into_o hour_n do_v give_v 6_o hour_n and_o almost_o 24_o m._n from_o the_o meridian_n or_o i_o may_v find_v these_o 95_o gr_n 52_o m._n in_o the_o line_n of_o verse_v sin_n over_o against_o the_o seven_o sine_fw-la of_o 26_o gr_n 40_o m._n 12_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 be_v to_o the_o sine_fw-la of_o the_o azimuth_n so_o 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 the_o declination_n be_v 20_o gr_n southward_o the_o altitude_n 12_o gr_n and_o the_o azimuth_n find_v by_o the_o ten_o prop._n 146_o gr_n i_o may_v find_v the_o time_n to_o be_v 35_o gr_n 36_o m._n that_o be_v 2_o hour_n 22_o m._n from_o the_o meridian_n 13_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 altitude_n be_v to_o the_o sine_fw-la of_o the_o hour_n so_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 the_o altitude_n of_o the_o sun_n be_v 12_o gr_n and_o the_o declination_n 10_o gr_n southward_o and_o the_o angle_n of_o the_o hour_n 35_o gr_n 36_o m._n i_o shall_v find_v the_o azimuth_n to_o be_v 34_o gr_n and_o so_o it_o be_v if_o it_o be_v reckon_v from_o the_o south_n but_o 146_o gr_n if_o it_o be_v take_v from_o the_o north_n part_n of_o the_o meridian_n 14_o 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 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 so_o the_o sun_n be_v in_o the_o first_o degree_n of_o â™’_o that_o be_v 59_o gr_n distant_a from_o the_o next_o equinoctial_a point_n and_o the_o great_a declination_n 23_o gr_n 30_o m._n the_o right_a ascension_n will_v be_v find_v to_o be_v 56_o gr_n 46_o m._n short_a of_o the_o begin_n of_o ♈_o and_o therefore_o 303_o gr_n 14_o m._n 15_o have_v the_o declination_n of_o the_o sun_n to_o find_v his_o right_a ascension_n as_o the_o tangent_fw-la of_o the_o great_a declination_n it_o to_o the_o tangent_fw-la of_o the_o declination_n give_v so_o the_o radius_fw-la to_o the_o sine_fw-la of_o the_o right_a ascension_n so_o the_o great_a declination_n be_v 23_o gr_n 30_o m._n and_o the_o declination_n of_o the_o sun_n give_v 20_o gr_n the_o right_a ascension_n will_v be_v find_v about_o 56_o gr_n 50_o m._n these_o be_v such_o astronomical_a proposition_n as_o i_o take_v to_o be_v useful_a for_o seaman_n for_o the_o first_o and_o second_o will_v help_v they_o to_o find_v their_o latitude_n the_o three_o to_o find_v the_o sun_n rise_v and_o set_v the_o 4.5.6.7.8.9.10.13_o prop._n to_o find_v the_o variation_n of_o their_o compass_n the_o 11_o and_o 12_o prop._n to_o find_v the_o hour_n of_o the_o day_n and_o the_o two_o last_o towards_o the_o find_n of_o the_o hour_n of_o the_o night_n for_o have_v the_o latitude_n of_o the_o place_n with_o the_o declination_n and_o altitude_n of_o any_o star_n they_o may_v find_v the_o hour_n of_o the_o star_n from_o the_o meridian_n as_o in_o the_o 11_o prop._n then_o compare_v the_o right_a 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this_o place_n be_v ♒_o ☉_o l_o and_o therefore_o the_o meridian_n altitude_n ml_o and_o the_o depression_n below_o the_o horizon_n at_o midnight_n h_n ♒_o the_o semidiurnall_a ark_n l_o ☉_o the_o seminocturnall_a ark_n o_o ♒_o the_o declination_n be_v the_o ascensionall_a difference_n r_o ☉_o the_o amplitude_n of_o ascension_n a_o ☉_o or_o if_o a_o be_v put_v to_o represent_v the_o pole_n of_o the_o world_n then_o shall_v paese_n stand_v for_o the_o equator_fw-la and_o p_o ♋_o s_o ♑_o for_o the_o ecliptic_a and_o the_o rest_n which_o before_o stand_v for_o meridians_fw-la may_v now_o serve_v for_o particular_a horizon_n according_a to_o their_o several_a elevation_n then_o suppose_v the_o place_n of_o the_o sun_n give_v to_o be_v
be_v show_v before_o in_o the_o second_o projection_n and_o if_o from_o z_o we_o draw_v circle_n through_o each_o of_o these_o division_n they_o shall_v be_v parallel_n of_o altitude_n the_o hour_n circle_n may_v be_v here_o draw_v as_o the_o azimuth_n in_o the_o three_o projection_n for_o the_o centre_n of_o epv_n the_o hour_n of_o 6_o will_v be_v find_v at_o b_o somewhat_o near_o unto_o n_n by_o the_o tangent_fw-la of_o the_o latitude_n and_o if_o through_o b_o we_o draw_v a_o occult_a line_n parallel_n unto_o ev_n and_o divide_v it_o on_o each_o side_n from_o b_o in_o such_o sort_n as_o the_o tangent_fw-la be_v divide_v on_o the_o side_n of_o the_o sector_n allow_v 45_o gr_n to_o be_v equal_a to_o bp_o and_o 15_o gr_n for_o every_o hour_n those_o division_n shall_v be_v the_o centre_n and_o the_o distance_n from_o these_o division_n unto_o p_o shall_v be_v the_o semidiameter_n whereon_o to_o describe_v the_o rest_n of_o the_o hour_n circle_n the_o ecliptic_a may_v be_v draw_v as_o 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55_o 51_o 15_o the_o side_n of_o perseus_n 48_o 28_o the_o goat_n 45_o 33_o the_o tail_n of_o the_o swan_n 44_o 0_o the_o head_n of_o medusa_n 39_o 30_o the_o harp_n 38_o 30_o castor_n 32_o 38_o pollux_n 28_o 52_o the_o north_n crown_v 28_o 0_o the_o ram_n head_n 21_o 40_o arcturus_n 21_o 10_o the_o bull_n eye_n 15_o 42_o the_o lion_n heart_n 13_o 45_o the_o vulture_n heart_n 7_o 58_o orion_n right_a shoulder_n 7_o 17_o orion_n left_a shoulder_n 5_o 57_o and_o so_o any_o other_o star_n who_o declination_n be_v know_v unto_o you_o which_o be_v do_v the_o use_n of_o this_o bow_n may_v be_v 1_o the_o day_n of_o the_o month_n be_v know_v to_o find_v the_o declination_n of_o the_o sun_n 2_o the_o declination_n be_v give_v to_o find_v the_o day_n of_o the_o month_n these_o two_o prop._n depend_v on_o the_o make_n of_o the_o bow_n if_o the_o day_n be_v know_v look_v it_o out_o in_o the_o back_n of_o the_o bow_n so_o the_o declination_n will_v appear_v in_o the_o side_n or_o if_o the_o 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hand_n hold_v the_o centre_n of_o the_o bow_n to_o your_o eye_n so_o as_o you_o may_v see_v the_o sun_n or_o star_n by_o the_o upper_a sight_n and_o with_o the_o other_o hand_n move_v the_o low_a sight_n up_o or_o down_o until_o you_o have_v bring_v one_o of_o the_o edge_n of_o it_o to_o be_v even_o with_o the_o horizon_n as_o when_o you_o observe_v with_o the_o crosse-staffe_n so_o the_o degree_n contain_v between_o that_o edge_n and_o the_o upper_a sight_n shall_v show_v the_o altitude_n require_v thus_o if_o the_o upper_a sight_n shall_v be_v at_o 80_o gr_n and_o the_o low_a sight_n at_o 50_o gr_n the_o altitude_n require_v be_v 30_o gr_n 4_o to_o find_v any_o north_n latitude_n by_o know_v either_o the_o day_n of_o the_o month_n or_o the_o declination_n of_o the_o sun_n as_o oft_o as_o you_o be_v to_o observe_v in_o north_n latitude_n place_v both_o the_o sight_n on_o the_o foreside_n of_o the_o bow_n the_o upper_a sight_n to_o the_o declination_n of_o the_o sun_n or_o the_o day_n 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come_v to_o the_o meridian_n i_o may_v set_v the_o centre_n of_o the_o bow_n to_o my_o eye_n as_o if_o i_o go_v to_o find_v the_o altitude_n of_o the_o sun_n hold_v the_o north_n end_n of_o the_o bow_n upward_o with_o the_o upper_a sight_n between_o my_o eye_n and_o the_o sun_n and_o move_v the_o low_a sight_n until_o it_o come_v to_o be_v even_o with_o the_o horizon_n if_o here_o the_o low_a sight_n shall_v stay_v aâ—_n 50_o gr_n i_o may_v well_o say_v that_o
75_o 40_o diff._n meri_fw-la 83_o 36_o do_v substy_n 9_o 32_o alti_fw-la still_o 20_o 50_o hor._n ang._n po._n arc._n pla._n gr._n m._n gr._n m._n 8_o 85_o 17_o 76_o 56_o 9_o 70_o 17_o 44_o 47_o 10_o 55_o 17_o 27_o 11_o 11_o 40_o 17_o 16_o 43_o 12_o 25_o 17_o 9_o 32_o 1_o 10_o 17_o 3_o 41_o  _fw-fr merid_n substyl_o 2_o 4_o 43_o 1_o 40_o 3_o 19_o 43_o 7_o 16_o 4_o 34_o 43_o 13_o 50_o 5_o 49_o 43_o 22_o 46_o 6_o 64_o 43_o 37_o 0_o 7_o 79_o 43_o 62_o 58_o last_o have_v find_v the_o height_n of_o the_o pole_n above_o the_o plane_n and_o gather_v the_o angle_n at_o the_o pole_n the_o ark_n of_o the_o plane_n from_o the_o substylar_n to_o the_o houre-line_n will_v be_v as_o in_o this_o table_n this_o do_v if_o we_o consider_v how_o the_o line_n do_v fall_v in_o the_o fundamental_a diagram_n we_o may_v there_o see_v how_o the_o north_n pole_n be_v elevate_v above_o the_o low_a face_n &_o the_o south_n pole_n above_o the_o upper_a face_n of_o the_o plane_n and_o according_o make_v choice_n of_o a_o centre_n draw_v the_o horizontall_a the_o meridian_n the_o substylar_n &_o the_o houre-line_n and_o set_v up_o the_o style_n as_o in_o the_o other_o plane_n a_o three_o example_n of_o a_o plane_n incline_v to_o the_o southward_n if_o in_o our_o latitude_n a_o plane_n be_v propose_v decline_v from_o the_o vertical_a 24_o gr_n 20_o m._n as_o before_o but_o incline_v to_o the_o horizon_n 14_o gr_n 20_o m._n southward_o the_o upper_a face_n be_v open_a to_o the_o north-east_n the_o low_a to_o the_o south-west_n this_o plane_n shall_v be_v here_o represent_v by_o the_o circle_n bkd_v cross_v the_o meridian_n in_o the_o point_n f_o between_o the_o equator_fw-la and_o the_o horizon_n and_o the_o proper_a meridian_n of_o this_o plane_n by_o the_o perpendicular_a ark_n pg_n let_v down_o from_o the_o pole_n to_o the_o plane_n near_o the_o hour_n of_o 11_o at_o the_o north_n part_n of_o the_o horizon_n as_o may_v partly_o appear_v by_o the_o near_a extent_n of_o the_o compass_n then_o in_o the_o triangle_n bsf_n know_v the_o side_n b_v the_o compliment_n of_o the_o declination_n with_o the_o angle_n of_o inclination_n to_o the_o horizon_n at_o b_o and_o the_o right_a angle_n at_o s_n we_o may_v find_v sf_n the_o ark_n of_o the_o meridian_n between_o the_o horizon_n and_o the_o plane_n to_o be_v 13_o gr_n 6_o m._n and_o therefore_o pf_n the_o ark_n of_o the_o meridian_n between_o the_o pole_n and_o the_o plane_n to_o the_o southward_n 115_o gr_n 24_o m._n but_o 64_o gr_n 36_o m._n to_o the_o northward_o the_o angle_n b_o fs_n or_o d_o fn_n of_o the_o inclination_n of_o the_o plane_n to_o the_o meridian_n will_v be_v find_v 84_o gr_n 9_o m_z &_o b_o f_z or_o d_o f_o the_o ark_n of_o the_o plane_n between_o the_o horizon_n &_o the_o meridian_n 66_o gr_n 20_o m._n declination_n 24_o 20_o inclination_n 14_o 20_o diff_n merid_fw-la 13_o 27_o do_v substy_n 12_o 8_o alt._n still_o 64_o 0_o hor._n ang._n po_n arc._n pla._n gr._n m._n gr._n m._n 6_o 76_o 33_o 75_o 6_o 7_o 61_o 33_o 58_o 56_o 8_o 46_o 33_o 43_o 30_o 9_o 31_o 33_o 28_o 55_o 10_o 16_o 33_o 14_o 58_o 11_o 1_o 33_o 1_o 25_o  _fw-fr merid_n substyl_o 12_o 13_o 27_o 12_o 8_o 1_o 28_o 27_o 25_o 57_o 2_o 43_o 27_o 40_o 23_o 3_o 58_o 27_o 55_o 38_o 4_o 73_o 27_o 71_o 41_o 5_o 88_o 27_o 88_o 15_o again_o in_o the_o triangle_n pgf_n know_v the_o side_n pf_n the_o ark_n of_o the_o meridian_n between_o the_o pole_n and_o the_o plane_n with_o the_o angle_n of_o inclination_n to_o the_o meridian_n at_o f_o and_o the_o right_a angle_n at_o g_o the_o angle_n fpg_n of_o the_o inclination_n of_o the_o two_o meridians_fw-la will_v be_v find_v to_o be_v 13_o gr_n 27_o m._n and_o pg_n the_o height_n of_o the_o pole_n above_o the_o plane_n about_o 64_o gr_n and_o fg_v the_o distance_n of_o the_o substylar_n from_o the_o meridian_n 12_o gr_n 8_o m._n have_v find_v the_o height_n of_o the_o pole_n above_o the_o plane_n and_o gather_v the_o angle_n at_o the_o pole_n the_o arke_n of_o the_o plane_n from_o the_o substylar_n to_o the_o houre-line_n will_v be_v find_v as_o in_o this_o table_n this_o do_v if_o we_o consider_v how_o the_o line_n do_v fall_v in_o the_o fundamental_a diagram_n we_o may_v there_o see_v how_o the_o north_n pole_n be_v elevate_v above_o the_o upper_a face_n and_o the_o south_n pole_n above_o the_o low_a face_n of_o this_o plane_n and_o according_o make_v choice_n of_o the_o centre_n draw_v the_o horizontall_a the_o meridian_n the_o substylar_n and_o the_o houre-line_n and_o set_v up_o the_o style_n as_o in_o the_o former_a plane_n chap._n xi_o to_o describe_v the_o tropique_n and_o other_o circle_n of_o declination_n in_o a_o equinoctial_a plane_n such_o circle_n as_o be_v parallel_v to_o the_o equinoctial_a and_o yet_o fall_v within_o the_o tropique_n may_v be_v describe_v on_o any_o plane_n by_o help_n of_o these_o line_n of_o proportion_n but_o after_o a_o different_a manner_n according_a as_o the_o style_n shall_v be_v either_o perpendicular_a or_o parallel_v to_o 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six_o inch_n and_o that_o parallel_n shall_v be_v the_o five_o degree_n of_o declination_n extend_v the_o compass_n from_o the_o tangent_fw-la of_o 45_o gr_n unto_o the_o tangent_fw-la of_o 5_o gr_n the_o same_o extent_n will_v reach_v in_o the_o line_n of_o number_n from_o 6.00_o unto_o about_o 0.53_o which_o show_v that_o the_o length_n of_o the_o style_n must_v be_v 53_o part_n of_o a_o inch_n divide_v into_o 100_o then_o the_o length_n of_o the_o style_n be_v know_v the_o semidiameter_n of_o the_o other_o circle_n will_v be_v find_v as_o before_o i_o begin_v here_o with_o the_o five_o parallel_n and_o thence_o proceed_v unto_o the_o tropic_n because_o the_o shadow_n of_o the_o rest_n near_o the_o equinoctial_a will_v be_v overlong_o and_o the_o equinoctial_a itself_o can_v be_v describe_v the_o parallel_n of_o north_n declination_n be_v to_o be_v set_v on_o the_o north_n face_n and_o the_o parallel_n of_o south_n declination_n on_o the_o south_n face_n of_o the_o plane_n neither_o need_v these_o parallel_n to_o be_v draw_v in_o full_a circle_n but_o only_o to_o the_o horizontall_a line_n which_o shall_v be_v describe_v in_o cap._n xviij_o have_v by_o these_o mean_v set_v up_o the_o style_n to_o his_o true_a height_n and_o draw_v the_o circle_n of_o declination_n if_o we_o shall_v place_v the_o plane_n so_o as_o it_o shall_v make_v a_o angle_n with_o the_o horizon_n equal_a to_o the_o compliment_n of_o the_o latitude_n and_o then_o turn_v it_o until_o the_o top_n of_o the_o style_n cast_v the_o shadow_n upon_o the_o parallel_n of_o declination_n belong_v to_o the_o time_n the_o meridian_n of_o the_o plane_n will_v show_v the_o meridian_n of_o the_o place_n and_o the_o shadow_n of_o the_o style_n the_o hour_n of_o the_o day_n without_o the_o help_n of_o a_o magnetical_a needle_n chap._n xii_o to_o describe_v the_o tropique_n and_o other_o circle_n of_o declination_n in_o a_o polar_n plane_n in_o all_o polar_n plane_n whether_o the_o be_v parallel_n to_o the_o 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the_o hour_n of_o 4_o after_o noon_n be_v find_v before_o to_o be_v 51_o gr_n 30_o m_o if_o you_o will_v find_v the_o distance_n between_o the_o centre_n and_o the_o equator_fw-la extend_v the_o compass_n from_o the_o sine_fw-la of_o 51_o gr_n 30_o m._n unto_o the_o sine_fw-la of_o 90_o gr_n the_o compliment_n of_o the_o declination_n the_o same_o extent_n will_v reach_v in_o the_o line_n of_o number_n from_z 12_o unto_o 15.33_o and_o such_o be_v the_o distance_n upon_o the_o houre-line_n of_o 4_o between_o the_o centre_n and_o the_o equator_fw-la if_o you_o will_v find_v the_o distance_n upon_o this_o houre-line_n between_o the_o centre_n and_o the_o inner_a tropic_n who_o declination_n be_v know_v to_o be_v 23_o gr_n 30_o m._n add_v the_o declination_n to_o the_o angle_n at_o the_o equator_fw-la so_o the_o angle_n at_o the_o parallel_n will_v be_v 75_o gr_n wherefore_o extend_v the_o compass_n from_o the_o sine_fw-la of_o 75_o gr_n unto_o the_o sine_fw-la of_o 66_o gr_n 30_o m._n 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here_o the_o hour_n fall_v between_o six_o and_o midnight_n if_o you_o add_v 23_o gr_n 30_o m._n unto_o 78_o gr_n 22_o m._n the_o sum_n will_v be_v 101_o gr_n 52_o m._n and_o the_o compliment_n to_o 180_o gr_n will_v be_v 78_o gr_n 8_o m._n for_o your_o five_o ark_n wherefore_o as_o the_o sine_fw-la of_o 78_o gr_n 22_o m._n to_o the_o sine_fw-la of_o 51_o gr_n 30_o m._n so_o the_o cousin_n of_o 78_o gr_n 8_o m._n to_o the_o sine_fw-la of_o 9_o gr_n 32_o m._n for_o the_o altitude_n require_v if_o in_o the_o same_o latitude_n of_o 51_o gr_n 30_o m._n northward_o the_o sun_n have_v 23_o gr_n 30_o m._n of_o south_n declination_n it_o be_v require_v the_o altitude_n for_o nine_o in_o the_o morning_n here_o because_o the_o latitude_n and_o declination_n be_v unlike_a the_o one_o north_n and_o the_o other_o south_n you_o may_v add_v 23_o gr_n 30_o m._n the_o ark_n of_o declination_n unto_o 60_o gr_n 39_o m._n the_o four_o ark_n belong_v to_o the_o three_o hour_n from_o the_o meridian_n so_o shall_v you_o have_v 84_o gr_n 9_o m._n for_o your_o five_o ark_n wherefore_o as_o the_o sine_fw-la of_o 60_o gr_n 39_o m._n to_o the_o sine_fw-la of_o 51_o gr_n 30_o m._n so_o the_o cousin_n of_o 84_o gr_n 9_o m._n to_o the_o sine_fw-la of_o 5_o gr_n 15_o m._n for_o the_o altitude_n require_v and_o so_o by_o one_o or_o other_o of_o these_o mean_v you_o may_v find_v the_o altitude_n of_o the_o sun_n for_o any_o point_n of_o the_o ecliptic_a at_o all_o hour_n of_o the_o day_n and_o set_v they_o down_o in_o such_o a_o table_n as_o this_o a_o table_n for_o the_o altitude_n of_o the_o sun_n in_o the_o begin_n of_o each_o sign_n at_o all_o hour_n of_o the_o day_n calculate_v for_o 51_o gr_n 30_o m._n of_o north_n latitude_n ho._n ♋_o ♊_o ♌_o ♉_o â™_o ♈_o ♎_o ♓_o â™_o â™’_o â™_o ♑_o gr._n m._n gr._n m._n gr._n m._n gr._n m._n gr._n m._n gr._n m._n gr._n m._n 12_o 62_o 0_o 58_o 42_o 50_o 0_o 38_o 30_o 27_o 0_o 18_o 18_o 15_o 0_o 11_o 1_o 59_o 43_o 56_o 34_o 48_o 12_o 36_o 58_o 25_o 40_o 17_o 6_o 13_o 52_o 10_o 2_o 53_o 45_o 50_o 55_o 43_o 12_o 32_o 37_o 21_o 51_o 13_o 38_o 10_o 30_o 9_o 3_o 45_o 42_o 43_o 6_o 36_o 0_o 26_o 7_o 15_o 58_o 8_o 12_o 5_o 15_o 8_o 4_o 36_o 41_o 34_o 13_o 27_o 31_o 18_o 8_o 8_o 33_o 1_o 15_o  _fw-fr 7_o 5_o 27_o 17_o 24_o 56_o 18_o 18_o 9_o 17_o 0_o 6_o  _fw-fr  _fw-fr 6_o 6_o 18_o 11_o 15_o 40_o 9_o 0_o 0_o 0_o  _fw-fr  _fw-fr  _fw-fr 5_o 7_o 9_o 32_o 6_o 50_o  _fw-fr  _fw-fr  _fw-fr  _fw-fr 11_o 37_o 4_o 8_o 1_o 32_o  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr 21_o 40_o last_o you_o may_v find_v what_o declination_n the_o sun_n have_v when_o he_o rise_v or_o set_v at_o any_o hour_n as_o the_o sine_fw-la of_o 90_o gr_n to_o the_o sine_fw-la of_o the_o hour_n from_o six_o so_o the_o cotangent_fw-la of_o the_o latitude_n to_o the_o tangent_fw-la of_o the_o declination_n and_o so_o in_o the_o latitude_n of_o 51_o gr_n 30_o m._n you_o shall_v find_v that_o when_o the_o sun_n rise_v either_o at_o five_o in_o the_o summer_n or_o seven_o in_o the_o winter_n his_o declination_n be_v 11_o gr_n 37_o m_o when_o he_o rise_v at_o four_o in_o the_o summer_n or_o eight_o in_o the_o winter_n his_o declination_n be_v 21_o gr_n 40_o m._n which_o may_v be_v also_o set_v down_o in_o the_o table_n that_o do_v you_o may_v there_o see_v that_o in_o this_o latitude_n the_o meridian_n altitude_n of_o the_o sun_n in_o the_o begin_n of_o ♋_o be_v 62_o gr_n in_fw-la ♊_o 58_o gr_n 42_o m._n in_fw-it ♉_o 50_o gr_n in_fw-la ♈_o 38_o gr_n 30_o m._n etc._n etc._n but_o the_o begin_n of_o ♋_o and_o ♑_o be_v represent_v by_o the_o tropique_n td_v draw_v at_o 23_o gr_n 30_o m._n of_o declination_n and_o the_o beginning_n of_o ♈_o and_o ♎_o by_o the_o equator_fw-la ef._n if_o you_o draw_v a_o occult_a parallel_n between_o the_o equator_fw-la and_o the_o tropic_n at_o 11_o gr_n 30_o m._n of_o declination_n it_o shall_v represent_v the_o beginning_n of_o ♉_o â™_o â™_o and_o ♓_o if_o you_o draw_v another_o occult_a parallel_n though_o 20_o gr_n 12_o m._n of_o declination_n it_o shall_v represent_v the_o beginning_n of_o ♊_o ♌_o â™_o and_o â™’_o then_o you_o may_v lay_v a_o ruler_n to_o the_o centre_n a_o and_o 62_o gr_n in_o the_o quadrant_a bc_n and_o note_v the_o point_n where_o it_o cross_v the_o tropic_n of_o ♋_o than_o move_v the_o ruler_n to_o 58_o gr_n 52_o m._n and_o note_v where_o it_o cross_v the_o parallel_n of_o ♊_o then_o to_o 50_o gr_n and_o note_v where_o it_o cross_v the_o parallel_n of_o ♉_o and_o again_o to_o 38_o gr_n 30_o m._n note_v where_o it_o cross_v the_o equator_fw-la so_o the_o line_n draw_v through_o these_o point_n shall_v show_v the_o hour_n of_o 12_o in_o the_o summer_n while_o the_o sun_n be_v in_o ♈_o ♉_o ♊_o ♋_o ♌_o or_o â™_o in_o like_a manner_n if_o you_o lay_v the_o ruler_n to_o the_o centre_n a_o and_o 27_o gr_n in_o the_o quadrant_a and_o note_v the_o point_n where_o it_o cross_v the_o parallel_n of_o ♓_o then_o move_v it_o to_o 18_o gr_n 18_o m._n and_o note_v where_o it_o cross_v the_o parallel_n of_o â™’_o and_o again_o to_o 15_o gr_n note_v where_o it_o cross_v the_o tropic_n of_o ♑_o the_o line_n draw_v through_o these_o point_n shall_v show_v the_o hour_n of_o 12_o in_o the_o winter_n while_o the_o sun_n be_v in_o ♎_o â™_o â™_o ♑_o â™’_o &_o ♓_o and_o so_o may_v you_o draw_v the_o rest_n of_o these_o houre-line_n only_o that_o of_o 7_o from_o the_o meridian_n in_o the_o summer_n and_o 5_o in_o the_o winter_n will_v cross_v the_o line_n of_o declination_n at_o 11_o gr_n 37_o m._n and_o that_o of_o 8_o in_o the_o summer_n and_o 4_o in_o the_o winter_n at_o 21_o gr_n 40_o m._n the_o four_o table_n for_o draw_v of_o the_o azimuth_n line_n must_v likewise_o be_v fit_v for_o the_o altitude_n of_o the_o sun_n above_o the_o horizon_n at_o every_o azimuth_n especial_o when_o he_o come_v to_o the_o equator_fw-la the_o tropique_n and_o some_o other_o intermediat_a declination_n if_o the_o sun_n be_v in_o the_o equator_fw-la and_o so_o have_v no_o declination_n as_o the_o sine_fw-la of_o 90_o gr_n to_o the_o cousin_n of_o the_o azimuth_n from_o the_o meridian_n so_o the_o cotangent_fw-la of_o the_o latitude_n to_o the_o tangent_fw-la of_o the_o altitude_n at_o the_o equator_fw-la thus_o in_o our_o latitude_n of_o 51_o gr_n 30_o m._n at_o 90_o gr_n from_o the_o meridian_n the_o sun_n will_v have_v no_o altitude_n at_o 80_o gr_n the_o altitude_n will_v be_v 7_o gr_n 52_o m_o at_o 70_o gr_n it_o will_v be_v 15_o gr_n 30_o m_o at_o 60_o gr_n it_o will_v be_v 21_o gr_n 41_o m._n if_o the_o sun_n have_v declination_n the_o meridian_n altitude_n will_v be_v easy_o find_v as_o before_o for_o the_o table_n for_o day_n and_o month_n and_o for_o all_o other_o azimuth_n as_o the_o sine_fw-la of_o the_o latitude_n to_o the_o sine_fw-la of_o the_o declination_n so_o the_o cousin_n of_o the_o altitude_n at_o the_o equator_fw-la to_o the_o sine_fw-la of_o a_o four_o ark_n when_o the_o latitude_n and_o declination_n be_v both_o alike_o in_o all_o azimuth_n from_o the_o prime_n vertical_a unto_o the_o meridian_n add_v this_o four_o ark_n unto_o the_o ark_n of_o altitude_n at_o the_o equator_fw-la when_o the_o latitude_n and_o declination_n be_v both_o alike_o and_o the_o azimuth_n more_o than_o 90_o gr_n distant_a from_o the_o meridian_n take_v the_o altitude_n at_o the_o equator_fw-la out_o of_o this_o four_o ark_n when_o the_o latitude_n and_o declination_n be_v unlike_a take_v this_o four_o ark_n out_o of_o the_o ark_n of_o altitude_n at_o the_o equator_fw-la so_o shall_v you_o have_v the_o altitude_n of_o the_o sun_n belong_v to_o the_o azimuth_n thus_o in_o our_o latitude_n of_o 51_o gr_n 30_o m._n northward_o if_o it_o be_v require_v to_o find_v the_o altitude_n of_o the_o sun_n in_o the_o azimuth_n of_o 60_o gr_n from_o the_o meridian_n when_o the_o declination_n be_v 23_o gr_n 30_o m._n nothward_o you_o may_v find_v the_o altitude_n at_o the_o equator_fw-la belong_v to_o this_o azimuth_n to_o be_v 21_o gr_n 41_o m._n by_o the_o former_a canon_n and_o by_o this_o last_o canon_n you_o may_v find_v the_o four_o ark_n to_o be_v 28_o gr_n 15_o m._n then_o because_o the_o latitude_n and_o declination_n be_v both_o alike_o to_o the_o northward_o if_o you_o add_v they_o both_o together_o you_o shall_v have_v 49_o gr_n 56_o m._n for_o the_o altitude_n require_v if_o the_o declination_n have_v be_v 23_o gr_n 30_o m._n to_o the_o southward_n you_o
be_v here_o represent_v by_o the_o ark_n figure_v with_o these_o letter_n i_o f_o m_o a_o m_o etc._n etc._n signify_v the_o month_n january_n february_n march_n april_n etc._n etc._n each_o month_n be_v divide_v unequal_o according_a to_o the_o number_n of_o the_o day_n that_o be_v therein_o 1_o the_o day_n of_o the_o month_n be_v give_v to_o find_v the_o altitude_n of_o the_o sun_n at_o noon_n let_v the_o thread_n be_v lay_v to_o the_o day_n of_o the_o month_n and_o the_o degree_n which_o it_o cut_v in_o the_o quadrant_n shall_v be_v the_o meridian_n altitude_n require_v as_o if_o the_o day_n give_fw-mi be_v the_o 15_o of_o may_n the_o thread_n lay_v on_o this_o day_n shall_v cut_v 59_o gr_n 30_o m._n in_o the_o quadrant_a which_o be_v the_o meridian_n altitude_n require_v 2_o the_o meridian_n altitude_n be_v give_v to_o find_v the_o day_n of_o the_o month_n the_o thread_n be_v set_v to_o the_o meridian_n altitude_n do_v also_o fall_v on_o the_o day_n of_o the_o month_n as_o if_o the_o altitude_n at_o noon_n be_v 59_o gr_n 30_o m._n the_o thread_n be_v set_v to_o this_o altitude_n do_v fall_v on_o the_o 15_o day_n of_o may_n and_o the_o 9_o of_o july_n and_o which_o of_o these_o two_o be_v the_o true_a day_n may_v be_v know_v by_o the_o quarter_n of_o the_o year_n or_o by_o another_o day_n observation_n for_o if_o the_o altitude_n prove_v great_a the_o thread_n will_v fall_v on_o the_o 16_o day_n of_o may_n and_o the_o 8_o of_o july_n or_o if_o it_o prove_v lesser_a the_o thread_n will_v fall_v on_o the_o 14_o of_o may_n and_o the_o 10_o of_o july_n whereby_o the_o question_n be_v full_o answer_v chap._n vi_o of_o the_o houre-line_n that_o ark_n which_o be_v draw_v upon_o the_o centre_n of_o the_o quadrant_a by_o the_o begin_n of_o declination_n do_v here_o represent_v the_o equator_fw-la that_o ark_n which_o be_v draw_v by_o 23_o gr_n 30_o m._n of_o declination_n and_o be_v next_o above_o the_o circle_n of_o month_n and_o day_n represent_v the_o tropique_n those_o line_n which_o be_v between_o the_o equator_fw-la and_o the_o tropique_n be_v undivided_a and_o number_v at_o the_o equator_fw-la by_o 6._o 7._o 8._o 9_o 10._o 11._o 12._o at_o the_o tropic_n by_o 1._o 2._o 3._o 4._o etc._n etc._n do_v represent_v the_o houre-circle_n that_o which_o be_v draw_v from_o 12_o in_o the_o equator_fw-la to_o the_o middle_n of_o june_n represent_v the_o hour_n of_o 12_o at_o noon_n in_o the_o summer_n and_o those_o which_o be_v draw_v with_o it_o to_o the_o right_a hand_n be_v for_o the_o hour_n of_o the_o day_n in_o the_o summer_n and_o the_o hour_n of_o the_o night_n in_o the_o winter_n that_o which_o be_v draw_v from_o 12_o in_o the_o equator_fw-la to_o the_o middle_n of_o december_n represent_v the_o hour_n of_o 12_o in_o the_o winter_n and_o those_o which_o be_v draw_v with_o it_o to_o the_o left_a hand_n be_v for_o the_o hour_n of_o the_o day_n in_o the_o winter_n and_o the_o hour_n of_o the_o night_n in_o the_o summer_n and_o of_o both_o these_o that_o which_o be_v draw_v from_o 11_o to_o 1_o serve_v for_o 11_o in_o the_o forenoon_n and_o 1_o in_o the_o afternoon_n that_o which_o be_v draw_v from_o 10_o to_o 2_o serve_v for_o 10_o in_o the_o forenoon_n &_o 2_o in_o the_o afternoon_n for_o the_o sun_n on_o the_o same_o day_n be_v about_o the_o same_o height_n two_o hour_n before_o noon_n as_o two_o hour_n after_o noon_n the_o like_a reason_n hold_v for_o the_o rest_n of_o the_o hour_n 1_o the_o day_n of_o the_o month_n or_o the_o height_n at_o noon_n be_v know_v to_o find_v the_o place_n of_o the_o sun_n in_o the_o ecliptic_a the_o thread_n be_v lay_v to_o the_o day_n of_o the_o month_n or_o the_o height_n at_o noon_n for_o one_o give_v the_o other_o by_o the_o former_a proposition_n mark_v where_o it_o cross_v the_o hour_n of_o 12_o and_o set_v the_o bead_n to_o that_o intersection_n then_o move_v the_o thread_n till_o the_o bead_n fall_v on_o the_o ecliptic_a and_o it_o shall_v fall_v on_o the_o place_n of_o the_o sun_n as_o if_o the_o day_n give_fw-mi be_v the_o 15_o of_o may_n or_o the_o meridian_n altitude_n 59_o gr_n 30_o m._n lay_v the_o thread_n according_o and_o put_v the_o bead_n to_o the_o intersection_n of_o the_o thread_n with_o the_o hour_n of_o 12_o then_o move_v the_o thread_n till_o the_o bead_n fall_v on_o the_o ecliptic_a and_o it_o shall_v there_o show_v the_o four_o of_o ♊_o the_o four_o of_o â™_o the_o 26_o of_o ♋_o and_o the_o 26_o of_o ♑_o and_o which_o of_o these_o be_v the_o place_n of_o the_o sun_n may_v appear_v by_o the_o quarter_n of_o the_o year_n or_o another_o day_n observation_n 2_o the_o place_n of_o the_o sun_n in_o the_o ecliptic_a be_v know_v to_o find_v the_o day_n of_o the_o month_n etc._n etc._n let_v the_o thread_n and_o bead_n be_v first_o lay_v on_o the_o place_n of_o the_o sun_n in_o the_o ecliptic_a and_o then_o move_v to_o the_o line_n of_o 12._o as_o if_o the_o place_n of_o the_o sun_n give_fw-mi be_v the_o four_o of_o ♊_o the_o bead_n be_v lay_v to_o this_o degree_n and_o then_o move_v to_o the_o hour_n of_o 12_o in_o the_o summer_n the_o thread_n will_v fall_v on_o the_o 15_o day_n of_o may_n and_o the_o 9_o of_o july_n or_o if_o it_o be_v move_v to_o the_o hour_n of_o 12_o in_o the_o winter_n the_o thread_n will_v shall_v on_o the_o 6_o of_o january_n and_o the_o 16_o of_o november_n which_o of_o these_o be_v the_o day_n of_o the_o month_n require_v may_v appear_v by_o the_o quarter_n of_o the_o year_n in_o this_o and_o the_o former_a proposition_n you_o have_v two_o way_n to_o rectify_v the_o bead_n by_o the_o place_n of_o the_o sun_n and_o by_o the_o day_n of_o the_o month_n the_o better_a way_n be_v by_o the_o place_n of_o the_o sun_n for_o in_o the_o other_o the_o leap-yeare_n may_v breed_v some_o small_a difference_n there_o be_v yet_o a_o three_o way_n for_o the_o seaman_n have_v a_o table_n for_o the_o declination_n on_o each_o day_n of_o the_o year_n may_v set_v the_o bead_n thereto_o in_o the_o line_n of_o declination_n 3_o the_o hour_n of_o the_o day_n be_v give_v to_o find_v the_o altitude_n of_o the_o sun_n above_o the_o horizon_n the_o bead_n be_v set_v for_o the_o time_n by_o either_o of_o the_o three_o way_n let_v the_o thread_n be_v move_v from_o the_o hour_n of_o 12_o towards_o the_o line_n of_o declination_n till_o the_o bead_n fall_v on_o the_o hour_n give_v and_o the_o degree_n which_o it_o cut_v in_o the_o quadrant_n shall_v show_v the_o altitude_n of_o the_o sun_n at_o that_o time_n as_o if_o the_o time_n give_fw-mi be_v the_o ten_o of_o april_n the_o sun_n be_v then_o in_o the_o begin_n of_o ♉_o the_o bead_n be_v rectify_v you_o shall_v find_v the_o height_n at_o noon_n 50_o gr_n 0_o m._n at_o 11_o in_o the_o morning_n 48_o gr_n 12_o m._n at_o 10_o but_o 43_o gr_n 12_o m._n at_o 9_o but_o 36_o gr_n at_o 8_o but_o 27_o gr_n 30_o m._n at_o 7_o but_o 18_o gr_n 18_o m._n at_o 6_o but_o 9_o gr_n at_z 5_o it_o meet_v with_o the_o line_n of_o declination_n and_o have_v no_o altitude_n at_o all_o and_o therefore_o you_o may_v think_v it_o do_v rise_v much_o about_o that_o hour_n then_o if_o you_o move_v the_o thread_n again_o from_o the_o line_n of_o declination_n towards_o the_o hour_n of_o 12_o you_o shall_v find_v that_o the_o sun_n be_v 8_o gr_n 33_o m._n below_o the_o horizon_n at_o 4_o in_o the_o morning_n &_o near_o 16_o gr_n at_o 3_o and_o 21_o gr_n 51_o m._n at_o 2_o and_o 25_o gr_n 40_o m._n at_o 1_o and_o 27_o gr_n at_o midnight_n 4_o the_o altitude_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 the_o altitude_n be_v observe_v as_o before_o let_v the_o bead_n be_v set_v for_o the_o time_n then_o bring_v the_o thread_n to_o the_o altitude_n so_o the_o bead_n shall_v show_v the_o hour_n of_o the_o day_n as_o if_o the_o 10_o of_o april_n have_v set_v the_o bead_n for_o the_o time_n you_o shall_v find_v by_o the_o quadrant_a the_o altitude_n to_o be_v 36_o gr_n the_o bead_n at_o the_o same_o time_n will_v fall_v upon_o the_o houre-line_n of_o 9_o and_o 3_o wherefore_o the_o hour_n be_v 9_o in_o the_o forenoon_n or_o 3_o in_o the_o afternoon_n if_o the_o altitude_n be_v near_o 40_o gr_n you_o shall_v find_v the_o bead_n at_o the_o same_o time_n to_o fall_v half_a way_n between_o the_o houre-line_n of_o 9_o and_o 3_o and_o the_o houre-line_n of_o 10_o and_o 2_o wherefore_o it_o must_v be_v either_o half_a a_o hour_n past_o 9_o in_o the_o morning_n or_o half_o a_o