in_o the_o northern_a sign_n that_o be_v from_o the_o 10_o of_o march_n to_o the_o 13_o of_o september_n therefore_o lay_v the_o index_n to_o the_o east_n or_o aequinoctial_a point_n note_v with_o e._n or_o 40._o &_o 50._o in_o the_o limb_n so_o have_v you_o instant_o at_o once_o without_o far_a rectification_n both_o the_o altitude_n and_o hour_n of_o the_o sun_n come_v east_n or_o west_n above_o the_o horizon_n for_o all_o or_o any_o of_o the_o day_n above_o specify_v so_o the_o parallel_n of_o any_o day_n of_o the_o month_n meet_v with_o the_o edge_n of_o the_o index_n give_v the_o sun_n altitude_n in_o the_o index_n and_o the_o meridian_n meet_v therewith_o show_v the_o hour_n exam._n so_o if_o it_o be_v the_o second_o of_o may_n or_o the_o 22._o of_o july_n the_o parallel_n belong_v to_o those_o day_n meet_v with_o the_o index_n near_o about_o 23._o gr_n 17._o m_o and_o there_o also_o meet_v with_o that_o point_n the_o hour_n line_n of_o 7_o and_o 5._o which_o show_v that_o when_o the_o sun_n be_v 23._o gr_n 17._o m_o high_a either_o upon_o the_o second_o of_o may_n or_o the_o 22._o of_o july_n then_o the_o sun_n will_v be_v due_a east_n or_o west_n and_o that_o will_v happen_v to_o be_v at_o 7_o of_o the_o clock_n in_o the_o forenoon_n and_o 5._o of_o the_o clock_n in_o the_o afternoon_n pro._n 8_o eight_o to_o find_v the_o distance_n of_o the_o sun_n rise_v or_o set_v any_o day_n of_o the_o year_n from_o the_o east_n or_o west_n call_v the_o sun_n amplitude_n constru_n ¦_o ctio_fw-la 12_o lay_v the_o index_n to_o the_o day_n of_o the_o month_n for_o the_o time_n give_v &_o the_o edge_n of_o it_o in_o the_o limb_n of_o the_o instrument_n shall_v show_v the_o amplitude_n require_v so_o if_o the_o day_n be_v the_o 13_o exam._n of_o october_n the_o number_n of_o degree_n from_o the_o point_n of_o east_n note_v with_o 40._o 50._o unto_o the_o index_n be_v 18._o gr_n 40._o m._n which_o be_v the_o sun_n amplitude_n for_o the_o give_v day_n viz._n the_o 13_o day_n of_o october_n nine_o to_o know_v the_o sun_n meridional_a pro._n 9_o altitude_n or_o the_o sun_n depression_n under_o the_o horizon_n at_o midnight_n here_o or_o in_o any_o latitude_n for_o any_o day_n in_o the_o year_n lay_v the_o index_n unto_o the_o hour_n of_o 12_o and_o where_o constru_n ¦_o ctio_fw-la 11_o the_o parallel_n of_o the_o day_n of_o the_o month_n meet_v that_o therewith_o shall_v be_v the_o sun_n meridional_a altitude_n so_o if_o it_o be_v the_o 13_o day_n of_o october_n as_o before_o exam._n the_o parallel_n for_o that_o day_n be_v 11._o gr_n and_o a_o half_a from_o the_o equator_fw-la south_n this_o cross_v the_o index_n in_o 27._o gr_n which_o be_v the_o sun_n meridional_a altitude_n that_o day_n now_o for_o the_o sun_n depression_n at_o midnight_n here_o be_v to_o be_v note_v that_o any_o degree_n of_o the_o ecliptic_a be_v at_o any_o time_n so_o much_o below_o the_o horizon_n as_o his_o opposite_a degree_n in_o the_o ecliptic_a be_v above_o the_o horizon_n at_o the_o same_o time_n constru_n ¦_o ctio_fw-la 12_o therefore_o where_o the_o contrary_a parallel_n of_o the_o sun_n viz._n 11._o gr_n and_o a_o half_a north_n meet_v with_o the_o index_n in_o the_o hour_n of_o 12._o that_o shall_v be_v the_o sun_n meridional_a depression_n at_o midnight_n the_o say_v 13_o day_n of_o october_n pro._n 10_o ten_o to_o find_v the_o time_n of_o daybreak_a and_o end_n of_o twilight_n with_o the_o position_n of_o the_o sun_n under_o the_o horizon_n for_o any_o time_n this_o proposition_n have_v reference_n to_o the_o sun_n depression_n under_o the_o horizon_n for_o it_o be_v say_v to_o be_v day_n break_v or_o twilight_n to_o end_n when_o the_o sun_n be_v 18._o gr_n under_o the_o horizon_n therefore_o the_o construction_n in_o this_o will_v be_v thus_o constru_n ¦_o ctio_fw-la 13_o account_v 18._o gr_n on_o the_o index_n then_o move_v the_o index_n until_o that_o degree_n meet_v with_o the_o contrary_a parallel_n of_o declination_n for_o the_o day_n give_v so_o the_o meridian_n or_o houreline_n that_o meet_v therewith_o shall_v be_v the_o hour_n of_o day_n break_v require_v exam._n so_o if_o the_o day_n be_v the_o 10._o of_o april_n the_o parallel_n of_o declination_n for_o that_o day_n be_v north_n ii_o gr_n and_o a_o half_n which_o i_o seek_v out_o one_o the_o other_o side_n of_o the_o aequator_fw-la viz._n ii_o gr_n and_o a_o half_a south_n declination_n and_o mark_v where_o the_o 18_o gr_n of_o the_o index_n meet_v therewith_o for_o there_o also_o be_v the_o hour_n of_o day_n break_v viz._n with_o in_o 20._o m._n of_o 3._o in_o the_o morning_n and_o 20._o m._n past_o 9_o for_o the_o end_n of_o twilight_n the_o say_v 10_o of_o april_n also_o the_o index_n in_o the_o horizon_n at_o that_o instant_a show_v the_o position_n of_o the_o sun_n under_o the_o horizon_n viz._n near_o 48_o gr_n 10._o m._n to_o the_o north_n of_o the_o east_n but_o if_o the_o day_n have_v be_v the_o 13_o of_o october_n the_o hour_n of_o daybreake_n have_v be_v 2_o minute_n before_o 5._o and_o twilight_n will_v have_v end_v 2._o m._n after_o 7._o eleven_o to_o find_v the_o inequallitie_n pro._n 11_o of_o time_n between_o day_n break_v and_o sun_n rise_v for_o any_o day_n of_o the_o year_n assign_v by_o the_o first_o construction_n for_o the_o day_n give_v constructio_fw-la 14_o find_v the_o time_n of_o sun_n rise_v and_o by_o the_o former_a 13_o construction_n the_o hour_n and_o time_n of_o day_n break_v belong_v to_o those_o day_n then_o compare_v the_o time_n between_o the_o sun_n rise_v and_o day_n break_v of_o the_o one_o with_o that_o of_o the_o other_o so_o the_o difference_n of_o those_o two_o shall_v be_v the_o difference_n of_o time_n require_v example_n  _fw-fr  _fw-fr  _fw-fr h._n m._n  _fw-fr h._n m._n  _fw-fr so_n on_o the_o ten_o of_o march_n the_o sun_n rise_v be_v at_o 6._o 00_o the_o time_n between_o day_n break_v and_o sun_n rise_v be_v 2._o 0_o the_o difference_n be_v 12._o m._n day_n break_n be_v at_o 4._o 00_o docemb_v the_o sun_n rise_v it_o at_o 8._o 12_o 2._o 12_o day_n break_v be_v at_o 6._o 00_o the_o difference_n be_v 1._o ho._n 22._o m._n may_v the_o sun_n rise_v be_v at_o 4._o 11_o 3._o 34_o day_n break_v at_o 12_o 37_o so_o the_o difference_n of_o time_n between_o day_n break_v and_o sun_n rise_v the_o 10_o of_o december_n be_v near_o a_o quarter_n of_o a_o hour_n long_o than_o that_o of_o the_o 10_o of_o march_n but_o more_o than_o a_o hour_n and_o half_o long_a between_o day_n break_v and_o sun_n rise_v the_o 10_o of_o may_n than_o the_o 10_o of_o march_n pro._n 12_o twelfe_o to_o find_v the_o hour_n and_o altitude_n of_o the_o sun_n come_v upon_o a_o decline_a wall_n any_o day_n of_o the_o year_n ☞_o ☞_o see_v the_o declination_n of_o plain_n or_o wall_n be_v account_v from_o the_o point_n of_o east_n or_o west_n in_o the_o horizon_n as_o the_o sun_n amplitude_n be_v the_o number_v of_o they_o therefore_o shall_v be_v alike_o in_o the_o limb_n of_o the_o instrument_n now_o admit_v the_o declination_n of_o a_o plain_a or_o wall_n to_o be_v 22._o gr_n the_o operation_n constru_n ¦_o ctio_fw-la 15_o will_v be_v thus_o the_o index_n be_v set_v thereto_o you_o may_v instant_o see_v at_o what_o hour_n the_o sun_n will_v come_v upon_o the_o plain_a for_o any_o day_n in_o the_o year_n for_o where_o the_o parallel_n of_o the_o day_n of_o the_o month_n cross_v the_o index_n among_o the_o houreline_n which_o index_n represent_v the_o plain_a that_o be_v the_o hour_n of_o the_o sun_n come_v upon_o the_o plain_a and_o the_o degree_n in_o the_o index_n give_v the_o sun_n altitude_n examp._n so_o if_o the_o sun_n be_v in_o the_o tropic_n of_o ♋_o the_o tropic_n meet_v with_o the_o index_n almost_o within_o 5_o m._n of_o 9_o in_o the_o morning_n and_o at_o that_o time_n the_o sun_n come_v upon_o the_o plain_a and_o there_o the_o tropic_n cut_v also_o the_o index_n in_o 45._o gr_n 40._o m._n which_o be_v the_o sun_n altitude_n at_o that_o time_n that_o the_o sun_n will_v glance_v or_o begin_v to_o shine_v upon_o the_o plain_a as_o for_o the_o time_n of_o the_o sun_n continuance_n on_o the_o plain_a as_o be_v specify_v in_o the_o index_n or_o table_n account_v the_o declination_n on_o the_o other_o side_n of_o the_o east_n point_n and_o lay_v the_o index_n thereto_o so_o the_o edge_n of_o it_o in_o the_o tropic_n of_o ♋_o will_n point_n out_o at_o what_o hour_n the_o sun_n go_v of_o the_o plain_a viz._n at_o 6._o of_o the_o clock_n &_o 38._o m_o near_o if_o the_o declination_n be_v west_n as_o here_o it_o
the_o south_n pole_n under_o the_o horizon_n which_o be_v always_o equal_a to_o the_o elevation_n of_o the_o north_n pole_n above_o the_o horizon_n so_o if_o upon_o the_o ten_o of_o april_n exam._n the_o meridian_n altitude_n shall_v be_v find_v to_o be_v 50._o gr_n the_o declination_n belong_v to_o that_o day_n by_o the_o 3._o pro._n be_v 11._o gr_n and_o a_o half_a north_n which_o be_v subtract_v according_a to_o the_o former_a direction_n leave_v 38._o gr_n 30._o m_o the_o height_n of_o the_o aequinoctial_a above_o the_o horizon_n &_o that_o take_v from_o 90._o leaf_n 51._o gr_n 30._o m_o the_o depression_n of_o the_o south_n pole_n under_o the_o horizon_n or_o the_o elevation_n of_o the_o north_n pole_n above_o the_o horizon_n for_o the_o height_n of_o the_o aequinoctial_a know_v the_o compliment_n thereof_o be_v always_o the_o latitude_n of_o the_o place_n or_o height_n of_o the_o pole_n and_o here_o note_v general_o that_o the_o height_n of_o the_o pole_n and_o aequinoctial_a together_o do_v always_o make_v a_o quadrant_n or_o 90._o gr_n therefore_o the_o height_n of_o one_o of_o they_o be_v know_v the_o height_n of_o the_o other_o be_v also_o know_v and_o further_a here_o note_v that_o if_o the_o sun_n have_v north_n declination_n the_o sun_n be_v so_o much_o high_a than_o the_o aequinoctial_a at_o none_o that_o day_n by_o so_o much_o as_o his_o declination_n come_v to_o but_o if_o the_o sun_n have_v south_n declination_n than_o the_o sun_n be_v low_a than_o the_o aequinoctial_a that_o day_n at_o noon_n by_o so_o much_o as_o his_o declination_n come_v to_o by_o which_o you_o may_v easy_o gether_o when_o to_o add_v or_o subtract_v the_o sun_n declination_n to_o or_o from_o the_o sun_n meridianall_a altitude_n to_o get_v the_o height_n of_o aequator_fw-la which_o know_v the_o pole_n height_n can_v be_v unknown_a pro._n 34_o eight_o to_o find_v the_o sun_n azimuth_n and_o altitude_n for_o any_o hour_n constru_n ¦_o ctio_fw-la 44_o mark_n where_o the_o parallel_n for_o the_o day_n of_o the_o month_n meet_v with_o the_o give_v hour_n and_o bring_v the_o edge_n of_o the_o index_n thereto_o so_o the_o degree_n that_o the_o edge_n of_o the_o index_n cut_v in_o the_o limb_n of_o the_o instrument_n that_o shall_v be_v the_o sun_n azimuth_n and_o the_o degree_n that_o the_o hour_n cut_v in_o the_o index_n that_o shall_v be_v the_o sun_n altitude_n require_v so_o if_o upon_o the_o ten_o of_o december_n at_o nine_o of_o the_o clock_n in_o the_o morning_n exam._n the_o sun_n azimuth_n and_o altitude_n be_v require_v mark_v first_o where_o the_o tropic_a of_o capricorn_n which_o be_v the_o parallel_n for_o that_o day_n give_v meet_v with_o the_o give_v hour_n of_o nine_o and_o bring_v the_o index_n thereto_o so_o the_o edge_n of_o it_o in_o the_o limb_n point_v out_o near_o 40._o gr_n and_o a_o half_a &_o so_o much_o be_v the_o sun_n azimuth_n from_o the_o south_n at_o nine_o of_o the_o clock_n in_o the_o forenoon_n the_o say_v ten_o of_o december_n and_o the_o hour_n line_n meet_v with_o the_o index_n show_v near_o 5._o gr_n 25._o m._n so_o much_o be_v the_o sun_n altitude_n at_o that_o time_n now_o if_o you_o move_v the_o index_n soft_o along_o as_o the_o edge_n of_o it_o pass_v by_o any_o hour_n for_o any_o day_n of_o the_o year_n so_o the_o edge_n of_o the_o index_n in_o the_o limb_n of_o the_o instrument_n show_v the_o sun_n azimuth_n and_o the_o intersection_n of_o the_o parallel_n with_o the_o index_n shall_v show_v the_o sun_n altitude_n belong_v to_o that_o hour_n nine_o to_o show_v the_o uncertainty_n pro._n 35_o of_o time_n by_o note_v the_o shadow_n of_o thing_n it_o be_v usual_o note_v by_o some_o that_o when_o the_o shadow_n of_o the_o edge_n of_o a_o window_n door_n wall_n or_o such_o like_a shall_v touch_v such_o or_o such_o mark_n that_o it_o shall_v be_v then_o such_o or_o such_o a_o hour_n of_o the_o day_n and_o so_o constant_o to_o hold_v for_o all_o the_o year_n this_o observation_n be_v far_o from_o truth_n and_o the_o principal_n of_o astronomy_n and_o may_v be_v easy_o contradict_v by_o such_o which_o have_v but_o indifferent_a judgement_n in_o the_o nature_n of_o shadow_n and_o the_o sun_n passage_n by_o the_o meridian_n and_o vertical_a circle_n of_o the_o heaven_n for_o by_o how_o much_o great_a the_o propinquity_n of_o the_o sun_n approachment_n be_v unto_o the_o zenith_n or_o vertical_a point_n by_o so_o much_o the_o more_o shall_v the_o hour_n or_o time_n be_v various_a in_o one_o and_o the_o same_o azimuth_n so_o in_o the_o last_o pro._n the_o azimuth_n of_o the_o sun_n the_o ten_o of_o december_n at_o nine_o of_o the_o clock_n in_o the_o forenoon_n be_v find_v to_o be_v 40._o gr_n and_o a_o half_a exam_n and_o the_o sun_n distance_n from_o the_o zenith_n at_o that_o time_n be_v near_o 84._o gr_n 35._o m_o now_o admit_v the_o sun_n distance_n from_o the_o zenith_n the_o ten_o of_o june_n be_v but_o 32._o gr_n 35._o m_o the_o sun_n be_v in_o the_o same_o azimuth_n the_o hour_n will_v be_v half_a a_o hour_n past_o 10._o for_o the_o index_n be_v lay_v to_o the_o hour_n of_o 9_o in_o the_o tropic_n of_o ♑_o which_o be_v the_o sun_n parallel_n for_o the_o say_v ten_o of_o december_n and_o it_o cut_v the_o constru_n ¦_o ctio_fw-la 45_o parallel_n of_o the_o sun_n motion_n in_o the_o inequality_n of_o time_n and_o so_o the_o compliment_n of_o the_o former_a 32._o gr_n 35._o m_o in_o the_o index_n meet_v with_o the_o tropic_n of_o ♋_o which_o be_v the_o sun_n parallel_n for_o the_o ten_o of_o june_n in_o half_a a_o hour_n past_o 10._o so_o that_o it_o evident_o appear_v that_o the_o shadow_n of_o a_o perpendicular_a thing_n on_o the_o ten_o of_o december_n denote_v the_o hour_n of_o the_o day_n to_o be_v 9_o of_o the_o clock_n the_o same_o shadow_n the_o ten_o of_o june_n shall_v represent_v half_o a_o hour_n past_o 10._o so_o the_o error_n shall_v be_v a_o hour_n and_o a_o half_a but_o if_o you_o move_v the_o index_n unto_o the_o hour_n of_o 9_o belong_v to_o the_o ten_o of_o june_n the_o index_n shall_v point_v you_o out_o in_o the_o limb_n near_o 68_o gr_n of_o azimuth_n for_o that_o hour_n which_o at_o 9_o of_o the_o clock_n the_o ten_o of_o december_n be_v but_o 40._o gr_n &_o a_o half_a so_o the_o difference_n of_o azimuth_n in_o one_o and_o the_o same_o hour_n shall_v be_v 27._o gr_n and_o a_o half_a &_o the_o time_n as_o before_o a_o hour_n and_o a_o half_a which_o difference_n be_v sufficient_a to_o confirm_v the_o point_n ten_o to_o find_v the_o quarter_n of_o pro._n 36_o the_o year_n and_o day_n of_o the_o month_n if_o it_o be_v forget_v constru_n ¦_o ctio_fw-la 46_o at_o any_o appearance_n of_o the_o sun_n by_o the_o 27._o pro._n take_v the_o sun_n altitude_n then_o place_v the_o north_n and_o south_n edge_n of_o the_o instrument_n unto_o the_o meridian_n line_n former_o draw_v if_o in_o the_o forenoon_n otherwise_o place_v the_o east_n and_o west_n edge_n of_o instrument_n to_o the_o meridian-line_n and_o erect_v the_o prependicular_a at_o the_o end_n of_o the_o index_n then_o move_v the_o index_n to_o and_o fro_o until_o the_o shadow_n of_o the_o prependicular_a fall_n by_o the_o side_n of_o the_o index_n so_o the_o parallel_n that_o meet_v with_o the_o degree_n of_o the_o sun_n observe_v altitude_n in_o the_o edge_n of_o the_o index_n parallel_n in_o the_o calendar_n that_o shall_v show_v the_o day_n of_o the_o month_n require_v so_o if_o exam._n upon_o a_o certain_a day_n in_o the_o year_n the_o sun_n altitude_n be_v observe_v and_o find_v to_o be_v 36._o gr_n have_v place_v the_o edge_n of_o the_o instrument_n to_o the_o meridian_n line_n and_o rectify_v the_o index_n then_o move_v the_o index_n until_o the_o shadow_n of_o the_o prependicular_a fall_n by_o the_o edge_n of_o the_o instrument_n let_v the_o instrument_n rest_n at_o this_o position_n and_o account_v the_o former_a 36._o gr_n upon_o the_o index_n which_o degree_n meet_v with_o the_o hour_n in_o the_o aequator_fw-la and_o also_o that_o intersect_v the_o calendar_n in_o the_o ten_o of_o march_n &_o the_o thirteen_o of_o september_n but_o which_o of_o these_o day_n be_v the_o day_n of_o the_o month_n the_o next_o day_n observation_n of_o the_o sun_n upon_o the_o same_o hour_n will_v help_v you_o for_o if_o the_o sun_n altitude_n besound_v to_o be_v great_a than_o the_o day_n of_o the_o month_n inquire_v after_o it_o be_v the_o ten_o of_o march_z because_o the_o sun_n from_o the_o ten_o of_o december_n unto_o the_o eleven_o of_o june_n do_v every_o day_n at_o one_o &_o the_o same_o hour_n ascend_v but_o if_o the_o sun_n altitude_n be_v find_v to_o be_v
less_o than_o the_o former_a day_n observation_n specify_v be_v than_o the_o day_n require_v be_v the_o thirteen_o of_o september_n because_o that_o from_o the_o eleven_o of_o june_n unto_o the_o ten_o of_o december_n the_o sun_n altitude_n every_o day_n do_v sensible_o diminish_v at_o one_o and_o the_o same_o hour_n ☞_o ☞_o but_o here_o be_v to_o be_v note_v that_o if_o there_o be_v no_o meridional_a line_n than_o the_o prependicular_a over_o the_o constru_n ¦_o ctio_fw-la 47_o centre_n and_o the_o axis_n of_o the_o index_n be_v erect_v place_v down_o the_o back_n of_o the_o instrument_n upon_o a_o horizontall_a plain_a and_o move_v the_o instrument_n to_o and_o fro_o until_o the_o shadow_n of_o the_o axis_n meet_v with_o the_o same_o hour_n below_o the_o tropic_n among_o the_o common_a hour_n that_o the_o shadow_n of_o the_o prependicular_a over_o the_o centre_n of_o the_o instrument_n meet_v with_o on_o the_o face_n of_o the_o instrument_n for_o then_o the_o parallel_n that_o 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subdive_v into_o ten_o other_o equal_a part_n which_o thing_n so_o divide_v shall_v represent_v a_o common_a scale_n then_o measure_v the_o shadow_n with_o the_o scale_n and_o mark_v how_o often_o the_o shadow_n be_v long_o than_o the_o scale_n and_o the_o decimall_n part_n if_o there_o be_v any_o so_o have_v you_o the_o proportion_n between_o the_o shadow_n and_o that_o which_o do_v cast_v the_o shadow_n and_o then_o be_v it_o resolve_v accor_v to_o the_o converse_n of_o the_o fifteen_o pro._n exam._n admit_v some_o one_o upon_o the_o 12._o of_o february_n or_o on_o the_o nine_o of_o october_n hold_v a_o staff_n prependicular_a as_o a_o b_o or_o suppose_v it_o to_o be_v part_n of_o the_o coin_n of_o a_o house_n or_o edge_n of_o a_o window_n or_o such_o like_a shall_v cast_v a_o shadow_n as_o b_o c_o which_o be_v note_v or_o draw_v and_o have_v divide_v the_o staff_n or_o thing_n as_o before_o and_o shall_v then_o measure_v the_o shadow_n as_o b_o c_o by_o the_o say_a staff_n or_o scale_n and_o find_v it_o to_o be_v contain_v therein_o three_o time_n and_o 6_o parts_z or_o 6_o decimal_n the_o porportion_n of_o the_o gnomon_n or_o scale_v a_o b_o to_o the_o shadow_n b_o c_o will_v be_v as_o 1_o to_o 3._o and_o 6_o 10._o construc_fw-fr ¦_o tio_fw-la 50_o move_v therefore_o the_o index_n to_o and_o fro_o until_o the_o edge_n of_o it_o mere_a with_o 3._o and_o 6_o 10_o in_o the_o line_n of_o shadow_n so_o have_v you_o the_o degree_n of_o the_o sun_n altitude_n at_o that_o instant_n in_o the_o index_n viz._n 15._o gr_n and_o ½_n then_o seek_v out_o the_o parallel_n for_o the_o 12._o of_o february_n or_o the_o nine_o of_o october_n the_o day_n give_v which_o be_v near_o the_o ten_o degree_n from_o the_o aequator_fw-la south_n move_v the_o index_n until_o the_o former_a 15._o gr_n and_o ½_n in_o the_o index_n meet_v with_o the_o say_a parallel_n for_o the_o day_n so_o have_v you_o the_o hour_n belong_v to_o that_o time_n which_o will_v be_v near_o 42_o m_o past_o 8._o in_o the_o morning_n or_o 18._o m_o past_o 3_o in_o the_o after_o noon_n and_o the_o edge_n of_o the_o index_n in_o the_o limb_n of_o the_o instrument_n show_v the_o sun_n azimuth_n also_o at_o that_o instant_n viz_o near_o 39_o gr_n 12._o m_o from_o the_o east_n towards_o the_o south_n now_o for_o the_o meridional_a line_n this_o may_v be_v do_v constru_n ¦_o ctio_fw-la 51_o at_o any_o time_n after_o if_o the_o azimuth_n be_v not_o forget_v for_o if_o the_o centre_n of_o the_o instrument_n be_v lay_v down_o upon_o any_o part_n of_o the_o shadow_n b_o c_o and_o so_o the_o instrument_n to_o be_v move_v upon_o his_o centre_n until_o the_o say_a shadow_n b_o c_o former_o draw_v cut_v the_o edge_n of_o the_o limb_n in_o the_o aforesaid_a azimuth_n of_o 39_o gr_n 30._o m_o than_o the_o meridian_n of_o the_o instrument_n shall_v be_v in_o the_o meridian_n of_o the_o world_n and_o if_o that_o shadow_n be_v from_o a_o window_n or_o building_n the_o position_n of_o the_o instrument_n shall_v denote_v the_o position_n of_o the_o window_n or_o building_n twelve_o to_o find_v the_o declination_n pro._n 38_o of_o a_o wall_n by_o see_v the_o sun_n beginning_n to_o shine_v thereon_o or_o go_v from_o it_o by_o the_o 27._o pro._n take_v the_o height_n of_o the_o sun_n and_o constru_n ¦_o ctio_fw-la 52_o by_o the_o 28._o pro._n find_v the_o sun_n azimuth_n for_o the_o altitude_n so_o the_o azimuth_n thus_o find_v shall_v be_v the_o declination_n of_o the_o plain_a require_v for_o the_o declination_n of_o any_o perpendicular_a plain_n be_v account_v from_o the_o point_n of_o east_n west_n north_n or_o south_n in_o the_o horizon_n as_o the_o sun_n azimuth_n be_v therefore_o whatsoever_o plain_n be_v in_o the_o plain_a of_o any_o virticall_a circle_n that_o plain_o be_v as_o far_o from_o any_o of_o the_o cardinal_n point_v of_o the_o horizon_n as_o the_o sun_n be_v at_o that_o time_n &_o so_o the_o sun_n be_v in_o that_o virticall_a circle_n shall_v necessary_o glance_v upon_o the_o plain_a and_o therefore_o look_v what_o the_o sun_n azimuth_n be_v at_o that_o instant_n such_o shall_v be_v the_o declination_n of_o the_o plain_a require_v thirteen_o to_o find_v the_o declination_n pro._n 39_o of_o a_o plain_a upon_o any_o appearance_n of_o the_o sun_n thus_o for_o the_o construction_n of_o the_o aforesaid_a 13._o use_n which_o do_v depend_v upon_o the_o sun_n observation_n the_o 48._o 49._o 50._o 9_o 13._o 14._o and_o 15_o use_n of_o the_o index_n or_o table_n against_o page_n the_o first_o shall_v have_v follow_v but_o before_o i_o speak_v of_o they_o it_o will_v not_o be_v inconvenient_a that_o i_o apply_v the_o instrument_n unto_o the_o resolution_n of_o the_o 44._o 45._o 46._o &_o 47._o use_n of_o the_o aforesaid_a index_n or_o table_n which_o have_v reference_n to_o night_n observation_n upon_o such_o star_n which_o be_v or_o may_v be_v place_v on_o the_o face_n of_o the_o instrument_n between_o the_o two_o tropicke_n or_o under_o the_o tropic_n of_o cancer_n according_a to_o there_o declination_n and_o right_a ascension_n which_o be_v these_o follow_v the_o name_n of_o the_o star_n decli_n rec_n the_o name_n of_o the_o star_n decli_n rec._n g._n m._n h._n m._n g.m._n g.m._n h._n m_o g._n m._n exit_fw-la alae_fw-la pegasi_fw-la 13.9_o n._n 23.54_o 1._o 30._o coâ—_n hydrae_fw-la 7.5_o a_o 9_o 10._o 42.45_o pri_fw-la ♈_o â—1_n 40_o n._n 1.46_o 26._o 30._o cor_fw-la leonis_fw-la 13.45_o b._n 9_o 48._o 33.00_o oculus_fw-la ♉_o 15.42_o n._n 4.15_o 63.45_o cauda_fw-la ♌_o 16.38_o b_o 11.30_o 7.26_o pri_fw-la singuli_fw-la ori._n 0._o 17._o s._n 5._o 13._o 78.15_o spica_fw-la â™_o 9_o â—0_n m._n 13._o 5._o 16.15_o canis_fw-la maior_fw-la 16_o 1â—_n s._n 6._o 30._o 82.15_o
the_o column_n m._n 5294._o which_o i_o take_v from_o the_o scale_n b._n and_o protract_v it_o from_o t._n to_o 30._o in_o the_o line_n 2._o 10._o now_o place_v one_o foot_n of_o the_o compass_n in_o 30._o next_o 10._o and_o extend_v the_o other_o foot_n to_o p._n the_o ecliptic_a may_v be_v intersect_v in_o the_o point_n of_o ♉_o and_o ♓_o and_o place_v in_o 30._o towards_o 2._o the_o same_o extent_n will_v intersect_v the_o ecliptic_a in_fw-la â™_o and_o â™_o in_o like_a manner_n may_v the_o centre_n of_o the_o rest_n of_o the_o degree_n of_o the_o ecliptic_a be_v protract_v in_o the_o line_n 2._o 10._o from_o t._n out_o of_o the_o colume_n m._n and_o p._n and_o so_o all_o the_o ecliptic_a divide_v from_o degree_n to_o degree_n but_o this_o may_v be_v otherwise_o do_v beside_o that_o which_o be_v deliver_v touch_v the_o draw_n of_o the_o parallel_n ecliptic_a and_o hour_n line_n there_o remain_v yet_o how_o to_o put_v on_o the_o calendar_n to_o graduate_v the_o index_n and_o to_o draw_v and_o divide_v the_o line_n of_o shadow_n this_o may_v be_v easy_o do_v from_o the_o table_n r._n calculate_v and_o accommodate_v to_o that_o purpose_n for_o the_o year_n 1640_o and_o may_v sufficient_o serve_v for_o many_o year_n after_o without_o any_o sensible_a error_n have_v divide_v the_o quadrant_n constru_n ∣_o ction_n e.s._n and_o e.n._n as_o before_o into_o the_o usual_a degree_n of_o a_o quadrant_n lay_v a_o ruler_n upon_o the_o centre_n z._n and_o account_v the_o degree_n from_o the_o point_n e._n in_o the_o quadrant_n towards_o n._n and_o s._n out_o of_o the_o table_n r._n according_a to_o the_o several_a colume_n of_o the_o table_n r._n and_o intersect_v the_o quadrant_n calendar_n how_o to_o inscribe_v the_o calendar_n with_o small_a short_a line_n so_o shall_v the_o ark_n of_o the_o horizon_n of_o the_o instrument_n from_o e._n be_v divide_v into_o the_o usual_a day_n of_o the_o month_n which_o be_v the_o calendar_n and_o the_o beginning_n of_o these_o division_n may_v be_v at_o the_o 10._o of_o march_n and_o so_o go_v on_o to_o the_o 11._o of_o june_n and_o then_o again_o to_o begin_v from_o the_o 10._o of_o march_n and_o go_v on_o unto_o the_o 10._o of_o december_n and_o these_o day_n may_v be_v note_v upon_o the_o inside_n of_o the_o horizontall_a ark_n with_o short_a line_n from_o e._n as_o before_o and_o at_o every_o month_n may_v be_v place_v a_o representative_a letter_n for_o that_o month_n and_o every_o 10._o and_o 5._o day_n of_o every_o month_n may_v be_v note_v with_o a_o small_a stroke_n somewhat_o long_o than_o the_o rest_n to_o help_v the_o memory_n the_o ready_a to_o number_v in_o like_a manner_n may_v the_o rest_n of_o the_o day_n of_o the_o calendar_n be_v intersect_v in_o the_o out_o side_n of_o the_o horizontall_a ark_n towards_o the_o limb_n begin_v at_o the_o 13._o of_o september_n and_o so_o go_v on_o to_o the_o 11._o of_o june_n than_o again_o from_o the_o 13._o of_o september_n and_o go_v on_o unto_o the_o 10._o of_o december_n and_o these_o month_n may_v be_v also_o note_v with_o significant_a letter_n appropriate_a to_o each_o month_n and_o each_o 10._o and_o 15._o day_n of_o the_o month_n may_v be_v also_o denote_v as_o before_o with_o a_o stroke_n somewhat_o long_o than_o the_o rest_n according_a to_o the_o scheme_n against_o page_n the_o 1._o how_o to_o graduate_v the_o index_n for_o the_o instrument_n let_v the_o index_n be_v equal_a to_o the_o semidiameter_n z._n e._n and_o then_o may_v it_o be_v divide_v out_o of_o the_o table_n q._n by_o the_o help_n of_o the_o scale_n a._n beginning_n at_o the_o centre_n the_o index_n be_v divide_v and_o place_v on_o the_o centre_n of_o the_o instrument_n at_o z._n it_o shall_v help_v to_o put_v on_o and_o divide_v the_o line_n of_o shadow_n as_o follow_v lay_v the_o edge_n of_o the_o index_n to_o a._n in_o the_o limb_n which_o be_v near_o the_o 10._o of_o december_n and_o move_v it_o to_o any_o degree_n in_o the_o table_n s._n and_o account_v the_o 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these_o part_n for_o radius_fw-la and_o on_o z._n describe_v the_o obscure_a ark_n a._n e._n b._n and_o upon_o z._n erect_v a_o perpendicular_a to_o the_o line_n m._n n._n to_o cut_v the_o ark_n a._n b._n in_o e._n now_o from_o e._n to_o a._n protract_v 40._o gr_n and_o from_o e._n to_o b._n protract_v 50._o gr_n so_o the_o angle_n e._n z._n m._n shall_v be_v 90._o and_o also_o a.z.b._n shall_v be_v 90._o now_o have_v make_v a_o scale_n of_o z.e._n like_v to_o the_o scale_n a._n according_a to_o the_o former_a direction_n then_o out_o of_o the_o column_n c._n and_o by_o help_n of_o the_o say_a scale_n a._n from_o z._n you_o may_v protract_v z._n ♋_o 2493._o z.q._n 4823._o and_o z._n ♑_o 7673._o and_o from_o the_o column_n f._n y_fw-fr u._fw-mi may_v protract_v the_o distance_n of_o the_o centre_n of_o those_o intersection_n from_o z._n viz._n z._n 1.5269_o z._n 2.7949_o and_o z._n 3.16217_o and_o so_o place_v the_o compass_n in_o these_o centre_n you_o may_v describe_v the_o equator_fw-la and_o both_o tropic_n but_o if_o z._n m_o and_o z._n n._n be_v divide_v according_a to_o the_o scale_n a._n then_o from_o z._n you_o may_v account_v the_o intersection_n of_o the_o parallel_n and_o distance_n of_o the_o centre_n and_o so_o describe_v the_o parallel_n with_o great_a expedition_n and_o so_o shall_v you_o have_v the_o scheme_n or_o trapeziall_a form_n of_o the_o instrument_n b._n a._n ♑_o ♋_o and_o may_v be_v finish_v according_a to_o that_o against_o page_n the_o 1._o by_o the_o table_n and_o direction_n here_o calculate_v and_o deliver_v to_o that_o end_n now_o to_o augment_v the_o instrument_n to_o any_o proportion_n assign_v as_o if_o between_o the_o tropicke_n be_v suppose_v to_o be_v 10._o inch_n the_o radius_fw-la may_v be_v find_v out_o or_o if_o the_o radius_fw-la be_v 4._o foot_n which_o be_v according_a to_o my_o own_o instrument_n what_o distance_n may_v there_o be_v between_o the_o tropicke_n the_o proportion_n will_v be_v as_o 516._o to_o 1000_o so_o the_o breadth_n to_o the_o scale_n or_o as_o 1000_o to_o 516._o so_o the_o scale_n to_o the_o breadth_n therefore_o by_o the_o ring_n bring_v 516._o in_o the_o movable_a to_o 1000_o in_o the_o fix_a so_o right_a against_o any_o radius_fw-la in_o the_o fix_a be_v the_o distance_n between_o the_o tropicke_n in_o the_o movable_a or_o against_o the_o distance_n assign_v for_o the_o tropicke_n in_o the_o movable_a be_v the_o measure_n of_o the_o radius_fw-la or_o scale_n in_o the_o fix_a so_o if_o ♑_o ♋_o be_v allot_v to_o be_v 10._o inch_n for_o the_o distance_n between_o the_o tropicke_n the_o scale_n or_o radius_fw-la of_o the_o instrument_n shall_v be_v 19_o 4_o 10._o fere_n but_o if_o the_o scale_n or_o radius_fw-la be_v 4._o foot_n or_o 48._o inch_n than_o the_o distance_n between_o the_o tropicke_n of_o ♑_o and_o ♋_o will_v be_v near_o 24_o 77_o 100_o inches_n thus_o for_o the_o make_n of_o the_o instrument_n the_o description_n of_o which_o follow_v the_o description_n of_o the_o horizontall_a quadrant_n the_o form_n of_o this_o instrument_n be_v like_o a_o mix_a trapezia_n as_o appear_v against_o page_n 1._o where_o of_o two_o side_n be_v right_a and_o the_o other_o two_o side_n be_v circular_a which_o fall_v out_o to_o be_v so_o from_o the_o nature_n of_o the_o projection_n and_o that_o part_n which_o i_o have_v think_v most_o convenient_a for_o use_v and_o be_v full_o sufficient_a for_o that_o which_o i_o have_v deliver_v upon_o it_o and_o may_v be_v make_v of_o any_o plain_a material_a but_o fit_a in_o brass_n or_o silver_n the_o several_a part_n of_o which_o instrument_n be_v five_o viz._n the_o back_n the_o face_n the_o
21._o 19_o 25._o 24._o 35._o 2._o 38._o 37._o 20._o 41._o and_o 42._o as_o follow_v the_o day_n of_o the_o month_n know_v to_o find_v 1._o the_o hour_n of_o sun_n rise_v set_v and_o length_n of_o the_o day_n 2._o the_o sun_n difference_n of_o ascention_n 3._o the_o sun_n declination_n 4._o what_o day_n be_v alike_o in_o length_n and_o what_o day_n the_o sun_n rise_v in_o the_o one_o shall_v be_v the_o sun_n set_v in_o the_o other_o 5._o the_o sun_n place_n or_o degree_n in_o the_o ecliptic_a 6._o the_o sun_n right_a ascension_n and_o oblique_a ascension_n 7._o the_o hour_n and_o altitude_n of_o the_o sun_n come_v east_n or_o west_n 8._o the_o distance_n of_o the_o sun_n rise_v or_o set_v from_o the_o east_n or_o west_n 9_o the_o height_n or_o depression_n of_o the_o sun_n in_o the_o meridian_n here_o or_o for_o any_o latitude_n 10._o the_o time_n of_o day_n break_v and_o end_n of_o twilight_n 11._o the_o inequality_n of_o time_n between_o day_n break_v and_o sun_n rise_v 12._o the_o hour_n and_o altitude_n of_o the_o sun_n come_v upon_o any_o decline_a wall_n 13._o at_o what_o hour_n and_o altitude_n the_o sun_n must_v have_v to_o be_v opposite_a or_o perpendicular_a to_o a_o decline_a wall_n first_o to_o find_v the_o time_n of_o sun_n pro._n 1_o rise_v or_o set_v and_o length_n of_o the_o day_n for_o any_o day_n of_o the_o year_n seek_v the_o day_n of_o the_o month_n in_o the_o calendar_n constru_n ¦_o ctio_fw-la 1_o and_o the_o hour_n line_n that_o meet_v therewith_o show_v the_o time_n of_o sun_n rise_v or_o set_v so_o if_o the_o day_n of_o the_o month_n be_v the_o 13._o exam._n of_o october_n the_o parallel_n that_o meet_v therewith_o be_v the_o hour_n viz._n 7._o of_o the_o clock_n at_o which_o time_n the_o sun_n rise_v the_o same_o hour_n be_v note_v also_o with_o 5._o which_o be_v the_o time_n of_o sun_n set_v that_o day_n this_o double_a make_n 10._o the_o length_n of_o the_o day_n require_v second_o to_o find_v the_o difference_n pro._n 2_o of_o ascention_n for_o any_o day_n of_o the_o year_n mark_v what_o meridian_n meet_v with_o the_o day_n constru_n ¦_o ctio_fw-la 2_o of_o the_o month_n in_o the_o calendar_n as_o suppose_v the_o day_n to_o be_v the_o former_a 13._o of_o october_n which_o be_v the_o hour_n line_n of_o 7._o and_o 5._o as_o before_o and_o account_v the_o number_n of_o meridian_n to_o the_o hour_n of_o 6._o so_o have_v you_o 15._o gr_n or_o a_o hour_n which_o be_v the_o difference_n of_o ascension_n for_o the_o 13._o day_n of_o october_n require_v pro._n 3_o three_o to_o find_v the_o sun_n declination_n for_o any_o day_n constru_n ¦_o ctio_fw-la 3_o mark_v what_o parallel_n of_o declination_n meet_v with_o the_o day_n of_o the_o month_n in_o the_o calendar_n and_o account_v how_o many_o degree_n it_o be_v from_o the_o equinoctial_a so_o have_v you_o the_o sun_n declination_n for_o that_o day_n exam._n so_o if_o the_o day_n be_v the_o last_o of_o august_n the_o parallel_n that_o meet_v therewith_o be_v the_o 5_o from_o the_o equator_fw-la and_o somuch_o be_v the_o sun_n declination_n that_o day_n viz._n 5._o gr_n north_n declination_n pro._n 4_o four_o to_o find_v what_o day_n in_o the_o year_n be_v alike_o in_o length_n and_o what_o day_n the_o sun_n rise_v in_o the_o one_o shall_v be_v the_o sun_n set_v in_o the_o other_o constru_n ¦_o ctio_fw-la 4_o for_o the_o first_o note_z that_o the_o day_n between_o the_o 10_o of_o december_n and_o the_o 11_o of_o june_n be_v day_n of_o increase_n and_o the_o rest_n be_v day_n of_o decrease_v now_o right_a against_o any_o day_n of_o decrease_n in_o the_o calendar_n be_v the_o day_n of_o increase_n which_o day_n be_v equal_a one_o to_o the_o other_o exam._n so_o the_o 19_o day_n of_o may_n be_v against_o the_o 4._o of_o july_n at_o which_o time_n the_o sun_n rise_v and_o set_v alike_o without_o sensible_a error_n viz._n 4._o of_o the_o clock_n and_o therefore_o those_o day_n be_v of_o equal_a length_n and_o so_o of_o other_o for_o the_o second_o to_o 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the_o former_a parallel_n of_o the_o 13_o of_o october_n meet_v with_o the_o ecliptic_a in_o the_o begin_n of_o â™_o and_o ♓_o but_o which_o of_o these_o be_v the_o sun_n place_n the_o quarter_n of_o the_o year_n may_v easy_o tell_v you_o viz._n â™_o which_o be_v the_o sun_n place_n or_o the_o degree_n in_o the_o ecliptic_a for_o that_o day_n pro._n 6_o six_o to_o find_v the_o sun_n right_a ascension_n and_o oblique_a ascension_n at_o any_o time_n constru_n ¦_o ctio_fw-la 7_o consider_v what_o meridean_a meet_v with_o the_o sun_n place_n in_o the_o ecliptic_a for_o the_o day_n give_v and_o mark_v the_o number_n of_o meridian_n in_o the_o equator_fw-la for_o the_o meridian_n be_v number_v in_o the_o equator_fw-la as_o be_v say_v before_o in_o the_o description_n so_o have_v you_o the_o sun_n right_a ascension_n but_o here_o note_n that_o the_o degree_n in_o the_o ecliptic_a be_v number_v forward_o and_o backward_o in_o the_o ecliptic_a unto_o 360._o gr_n upon_o this_o instrument_n so_o be_v the_o right_a ascension_n of_o those_o degree_n also_o number_v forward_o and_o backward_o in_o the_o aequator_fw-la for_o the_o right_a ascension_n of_o any_o degree_n in_o the_o ecliptic_a be_v that_o degree_n of_o the_o aequator_fw-la which_o be_v opposite_a unto_o it_o the_o succession_n of_o the_o sign_n consider_v so_o if_o the_o sun_n be_v in_o the_o begin_n of_o â™_o the_o right_a ascension_n be_v near_o 208._o degree_n for_o the_o meridian_n that_o pass_v by_o the_o begin_n of_o â™_o be_v account_v in_o the_o equator_fw-la from_z ♈_o and_o be_v within_o 6._o m_o of_o 28._o gr_n now_o the_o right_a ascension_n of_o ♋_o be_v 90._o gr_n and_o the_o beginning_n the_o of_o ♎_o be_v 180._o gr_n and_o from_o the_o begin_n of_o ♎_o to_o the_o beginning_n â™_o be_v within_o 6._o m_o of_o 28._o gr_n as_o before_o all_o be_v which_o put_v together_o make_v near_o 208._o gr_n the_o right_a ascension_n of_o the_o sun_n the_o 13_o day_n of_o october_n to_o find_v the_o sun_n oblique_a ascension_n at_o any_o time_n note_v that_o the_o difference_n of_o ascension_n be_v the_o constru_n ¦_o ctio_fw-la 8_o difference_n always_o between_o the_o right_a ascension_n of_o the_o sun_n and_o the_o oblique_a ascension_n thereof_o therefore_o the_o right_a ascension_n know_v by_o the_o last_o direction_n &_o the_o difference_n of_o ascension_n by_o the_o second_o direction_n the_o oblique_a ascension_n be_v easy_o have_v by_o addition_n or_o substraction_n thus_o if_o the_o sun_n be_v in_o a_o southern_a sign_n than_o the_o oblique_a ascension_n be_v great_a than_o the_o right_a ascension_n by_o so_o much_o as_o the_o difference_n of_o ascention_n come_v to_o but_o if_o the_o sun_n be_v in_o a_o northern_a sign_n the_o oblique_a ascension_n be_v so_o much_o less_o which_o difference_n of_o ascension_n as_o before_o by_o the_o 2_o pro_fw-la for_o the_o say_v 13_o of_o october_n be_v 15._o gr_n this_o ad_fw-la unto_o the_o right_a ascension_n of_o the_o begin_n of_o â™_o viz._n 208._o gr_n make_v 223._o gr_n the_o sun_n oblique_a ascension_n for_o the_o begin_n of_o â™_o on_o the_o 13_o day_n of_o october_n but_o if_o the_o sun_n have_v be_v in_o the_o begin_n of_o ♉_o the_o oblique_a ascension_n will_v have_v be_v only_o near_o 13._o gr_n viz._n 12._o gr_n 54._o m._n seven_o to_o find_v the_o sun_n altitude_n pro._n 7_o and_o hour_n of_o the_o sun_n come_v east_n or_o west_n any_o day_n of_o the_o year_n above_o the_o horizon_n here_o note_v that_o this_o proposition_n hold_v in_o use_n constru_n ¦_o ctio_fw-la 9_o only_o for_o that_o time_n of_o the_o sun_n be_v
the_o meridian_n construc_n ¦_o tio_fw-la 27_o from_o the_o give_v day_n in_o the_o calendar_n and_o note_v the_o day_n of_o the_o month_n against_o it_o than_o number_n the_o day_n between_o that_o day_n and_o the_o give_v day_n and_o you_o have_v the_o answer_n so_o if_o the_o day_n be_v the_o last_o of_o february_n exam._n or_o the_o first_o of_o march_n consider_v the_o sun_n set_v that_o day_n by_o the_o instrument_n which_o be_v 40._o m_o past_o 5._o this_o double_v make_v the_o length_n of_o the_o day_n 11._o hour_n 20._o m_o then_o from_o the_o last_o of_o february_n account_n 7._o gr_n and_o a_o half_a and_o it_o will_v point_v out_o the_o fifteen_o of_o march_n at_o which_o time_n the_o sun_n seat_v at_o 10._o m_o past_o 6_o which_o double_v make_v 12_o hour_n 20._o m_o so_o the_o fifteen_o of_o march_n the_o length_n of_o the_o day_n be_v a_o hour_n long_o than_o it_o be_v the_o first_o of_o march_n and_o the_o difference_n of_o time_n only_o but_o 15._o day_n but_o if_o the_o number_n of_o day_n be_v account_v to_o or_o from_o the_o sun_n enter_v into_o the_o tropical_a point_n it_o will_v be_v more_o than_o 35._o day_n before_o the_o day_n will_v be_v a_o hour_n long_o or_o short_a exam._n so_o if_o from_o the_o ten_o of_o june_n we_o shall_v account_v 7._o gr_n and_o a_o half_a among_o the_o meridian_n from_o that_o meridian_n that_o meet_v with_o the_o ten_o of_o june_n it_o will_v fall_v out_o at_o the_o 16_o day_n of_o july_n at_o which_o time_n the_o day_n will_v be_v a_o hour_n short_a than_o it_o be_v the_o ten_o of_o june_n and_o the_o interval_n of_o time_n more_o than_o twice_o as_o much_o as_o the_o former_a viz._n 39_o day_n pro._n 21_o eight_o to_o find_v the_o inequality_n of_o time_n in_o equal_a mounthes_n or_o equal_a number_n of_o day_n this_o proposition_n at_o the_o first_o seem_v as_o a_o paradox_n yet_o by_o this_o instrument_n may_v easy_o be_v resolve_v and_o so_o consequent_o from_o mathematical_a principle_n demonstrate_v not_o only_o the_o inequality_n of_o equal_a month_n but_o also_o the_o inequality_n of_o natural_a day_n now_o a_o day_n natural_a according_a to_o the_o general_a definition_n be_v one_o revolution_n of_o the_o aequator_fw-la or_o primum_fw-la mobile_a that_o be_v from_o sun_n rise_v to_o sun_n rise_v or_o it_o be_v the_o time_n wherein_o the_o sun_n pass_v by_o the_o meridian_n and_o come_v to_o the_o meridian_n again_o common_o take_v for_o 24._o hour_n but_o be_v cause_n that_o in_o that_o intervale_n of_o time_n the_o sun_n pass_v from_o the_o meridian_n and_o come_v to_o the_o meridian_n again_o the_o sun_n move_v according_a to_o his_o natural_a motion_n secundum_fw-la antiquiorum_fw-la traditionem_fw-la near_o a_o degree_n more_o or_o less_o therefore_o the_o natural_a day_n shall_v be_v some_o what_o long_o or_o short_a than_o 24._o hour_n viz._n by_o so_o much_o as_o the_o difference_n of_o right_a ascension_n of_o that_o degree_n of_o the_o ecliptic_a come_v to_o that_o the_o sun_n be_v in_o and_o see_v the_o degree_n of_o the_o ecliptic_a among_o themselves_o have_v not_o the_o same_o difference_n of_o right_a ascension_n that_o the_o other_o degree_n have_v notwithstanding_o the_o degree_n of_o the_o ecliptic_a among_o themselves_o be_v equal_a the_o one_o to_o the_o other_o the_o sun_n motion_n ender_v those_o degree_n be_v sometime_o quick_a and_o sometime_o slow_a it_o will_v necessary_o follow_v that_o the_o sun_n will_v move_v more_o or_o less_o until_o the_o sun_n can_v touch_v the_o meridian_n which_o be_v the_o limit_n or_o term_v of_o the_o sun_n diurnal_a revolution_n as_o before_o this_o difference_n and_o inequality_n of_o time_n in_o natural_a day_n may_v by_o calculation_n be_v give_v from_o day_n to_o day_n but_o because_o it_o be_v so_o insensible_a little_a in_o a_o day_n hardly_o by_o a_o instrument_n of_o this_o nature_n can_v be_v see_v but_o by_o a_o number_n of_o day_n compare_v with_o another_o number_n of_o day_n it_o will_v evident_o appear_v so_o exam._n if_o it_o be_v require_v how_o much_o the_o month_n of_o december_n be_v long_o than_o the_o month_n of_o march_n in_o the_o first_o of_o which_o month_n the_o sun_n motion_n be_v quick_a be_v about_o the_o perigeum_n then_o at_o other_o constru_n ¦_o ctio_fw-la 28_o time_n now_o both_o of_o which_o month_n have_v equal_a number_n of_o day_n viz._n 31._o find_v the_o right_a ascension_n for_o the_o beginning_n and_o end_v of_o mar._n viz._n 350.0_o the_o difer_n of_o right_a ascension_n for_o the_o month_n of_o mar._n be_v 29.30_o the_o difference_n between_o these_o be_v 5._o gr_n 19_o 30._o begin_v and_o end_v of_o dece_fw-la viz._n 257._o ¾_n the_o difer_n of_o right_a ascension_n for_o the_o month_n of_o dece_fw-la be_v 34._o 30._o 292._o ¼_n which_o 5._o gr_n be_v convert_v into_o time_n by_o allow_v 4_o minute_n to_o a_o degree_n make_v about_o 20._o m_o and_o so_o much_o be_v the_o month_n of_o december_n long_a than_o the_o month_n of_o march_n 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