have_v the_o great_a latitude_n be_v and_o say_v as_o the_o tang_n of_o the_o compl_a of_o the_o lesser_a distance_n from_o the_o pole_n be_v to_o the_o radius_fw-la so_o be_v the_o sine_fw-la of_o the_o compl_a or_o excess_n of_o the_o difference_n of_o longitude_n to_o the_o tang_n of_o the_o first_o base_a take_v this_o first_o base_a out_o of_o the_o great_a distance_n from_o the_o pole_n and_o the_o remain_v shall_v be_v the_o second_o base_a then_o say_v as_o the_o sine_fw-la of_o the_o compl_a of_o the_o first_o base_a be_v to_o the_o sine_fw-la of_o the_o compl_a of_o the_o second_o base_a so_o be_v the_o sine_fw-la of_o the_o compl_a of_o the_o lesser_a distance_n from_o the_o pole_n to_o the_o sine_fw-la of_o the_o compl_a of_o the_o distance_n of_o the_o two_o star_n if_o any_o man_n will_v take_v pain_n to_o calculate_v by_o this_o last_o rule_n the_o distance_n of_o some_o note_a star_n of_o the_o first_o second_o and_o three_o magnitude_n round_o about_o the_o heaven_n which_o be_v not_o above_o 5_o or_o 6_o degree_n at_o the_o most_o one_o from_o the_o other_o and_o shall_v keep_v they_o write_v in_o his_o book_n they_o may_v serve_v as_o a_o rule_n or_o instrument_n whereby_o he_o may_v reasonable_o estimate_v with_o his_o eye_n the_o distance_n of_o any_o planet_n or_o comet_n or_o other_o apparition_n from_o a_o know_a fix_a star_n not_o very_o far_o remote_a by_o compare_v the_o distance_n which_o he_o will_v know_v with_o some_o of_o those_o know_a distance_n which_o he_o shall_v find_v either_o to_o be_v equal_a or_o else_o to_o have_v some_o proportion_n thereto_o 42._o the_o longitude_n and_o latitude_n of_o any_o two_o city_n be_v give_v to_o find_v their_o distance_n the_o manner_n of_o the_o operation_n be_v the_o very_a same_o with_o the_o former_a unto_o which_o therefore_o i_o refer_v the_o reader_n only_o will_v note_v that_o in_o the_o heaven_n the_o longitude_n and_o latitude_n be_v take_v in_o respect_n of_o the_o ecliptic_a which_o be_v the_o way_n of_o the_o sun_n all_o the_o star_n in_o their_o proper_a motion_n have_v reference_n unto_o it_o as_o unto_o their_o measure_n and_o rule_v but_o in_o the_o earth_n the_o principal_a circle_n be_v the_o equinoctial_a divide_v it_o into_o the_o northern_a and_o southern_a he_o misphaere_n and_o therefore_o in_o the_o earth_n the_o longitude_n and_o latitude_n be_v reckon_v by_o the_o aequinoctial_a the_o distance_n of_o two_o place_n upon_o the_o earth_n be_v find_v in_o degree_n may_v be_v convert_v into_o english_a mile_n by_o take_v 60_o mile_n for_o every_o degree_n and_o one_o mile_n for_o every_o minute_n 43._o to_o find_v at_o what_o hour_n a_o fix_a star_n come_v into_o the_o meridian_n any_o day_n seek_v the_o right_a ascension_n of_o the_o sun_n for_o that_o day_n by_o sect_n 〈◊〉_d and_o subduct_v it_o out_o of_o the_o right_a ascension_n of_o the_o star_n and_o reduct_v the_o degree_n remain_v into_o hour_n by_o sect_n 1._o the_o same_o shall_v show_v how_o long_a time_n from_o the_o noon_n before_o the_o same_o star_n shall_v come_v into_o the_o meridian_n wherefore_o if_o at_o any_o time_n of_o the_o night_n a_o star_n who_o right_a ascension_n be_v know_v be_v in_o the_o meridian_n the_o hour_n of_o the_o night_n be_v easy_o find_v 44._o the_o height_n of_o any_o know_a star_n above_o the_o horizon_n be_v by_o any_o mean_v give_v to_o find_v the_o hour_n of_o the_o night_n first_o seek_v out_o the_o hour_n of_o that_o star_n come_v into_o the_o meridian_n the_o same_o day_n by_o sect._n 43._o again_o seek_v out_o the_o horary_a distance_n of_o that_o star_n from_o the_o meridian_n according_a to_o sect_n 19_o and_o then_o if_o the_o star_n be_v on_o the_o east_n side_n not_o yet_o come_v to_o the_o meridian_n take_v the_o difference_n of_o those_o two_o number_n but_o if_o the_o star_n be_v past_o the_o meridian_n take_v the_o sum_n of_o they_o for_o the_o hour_n of_o the_o night_n 45._o the_o height_n of_o the_o pole_n be_v give_v to_o find_v the_o come_n of_o any_o fix_a star_n in_o the_o due_a east_n or_o west_n say_v as_o the_o radius_fw-la be_v to_o the_o tang_n of_o the_o star_n declination_n so_o be_v the_o tang_n of_o the_o compl_a of_o the_o pole_n to_o the_o sine_fw-la of_o the_o compl_a of_o the_o star_n horary_a distance_n from_o the_o meridian_n 46._o the_o height_n of_o the_o pole_n be_v give_v to_o find_v the_o altitude_n of_o any_o fix_a star_n above_o the_o horizon_n be_v due_a east_n or_o west_n say_v as_o the_o sine_fw-la of_o the_o height_n of_o the_o pole_n be_v to_o the_o radius_fw-la so_o be_v the_o sine_fw-la of_o the_o star_n declination_n to_o the_o sine_fw-la of_o the_o altitude_n at_o due_a east_n or_o west_n 47._o by_o the_o altitude_n of_o any_o two_o know_a fix_a star_n take_v when_o they_o be_v both_o in_o the_o same_o azumith_n to_o find_v the_o height_n of_o the_o pole_n first_o say_v as_o the_o sine_fw-la of_o the_o difference_n of_o the_o star_n altitude_n be_v to_o the_o sine_fw-la of_o the_o difference_n of_o their_o right_a ascension_n so_o be_v the_o sine_fw-la of_o the_o near_a star_n distance_n from_o the_o apparent_a pole_n to_o the_o sine_fw-la of_o a_o angle_n to_o be_v keep_v again_o compare_v the_o further_a star_n distance_n from_o the_o pole_n with_o the_o distance_n from_o the_o zenith_n and_o say_v as_o the_o radius_fw-la be_v to_o the_o sine_fw-la of_o the_o compl_a of_o the_o angle_n keep_v so_o be_v the_o tang_n of_o the_o lesser_a of_o the_o compare_v arch_n to_o the_o tang_n of_o the_o first_o base_a subduct_v the_o first_o base_a out_o of_o the_o great_a of_o the_o two_o compare_v arch_n and_o the_o remain_v shall_v be_v the_o second_o base_a then_o last_o say_v as_o the_o sine_fw-la of_o the_o compliment_n of_o the_o first_o base_a be_v to_o the_o sine_fw-la of_o the_o compl_a of_o the_o second_o base_a so_o be_v the_o sine_fw-la of_o the_o compl_a of_o the_o lesser_a of_o the_o two_o compare_v arch_n to_o the_o sine_fw-la of_o the_o height_n of_o the_o pole_n 48._o to_o find_v out_o the_o horizontall_a parallax_n of_o the_o moon_n first_o the_o distance_n of_o the_o moon_n from_o the_o centre_n of_o the_o earth_n must_v be_v know_v in_o semidiameter_n of_o the_o earth_n which_o unto_o they_o that_o be_v acquaint_v with_o the_o theory_n of_o the_o planet_n be_v not_o very_o difficult_a and_o whereof_o peradventure_o i_o may_v hereafter_o teach_v the_o practice_n by_o most_o easy_a and_o exact_a instrument_n which_o i_o have_v long_o since_o frame_v say_v as_o the_o distance_n of_o the_o moon_n from_o the_o centre_n of_o the_o earth_n be_v to_o the_o semidiameter_n of_o the_o earth_n so_o be_v the_o radius_fw-la to_o the_o sine_fw-la of_o the_o moon_n horizontall_a parallax_n in_o that_o distance_n 49._o the_o horizontall_a parallax_n of_o the_o moon_n be_v give_v to_o find_v her_o parallax_n in_o any_o apparent_a altitude_n as_o the_o radius_fw-la be_v to_o the_o sine_fw-la of_o the_o altitude_n of_o the_o moon_n so_o be_v the_o sine_fw-la of_o the_o horizontall_a parallax_n to_o the_o sine_fw-la of_o the_o parallax_n in_o that_o altitude_n 50._o the_o place_n of_o the_o moon_n in_o the_o ecliptic_a have_v little_a or_o no_o latitude_n as_o in_o the_o eclipse_n of_o the_o sun_n together_o with_o her_o parallax_n of_o altitude_n be_v give_v to_o find_v the_o parallax_n of_o her_o longitude_n and_o latitude_n if_o the_o moon_n be_v in_o the_o 90_o degree_n of_o the_o ecliptic_a she_o have_v no_o parallax_n of_o longitude_n and_o the_o parallax_n of_o latitude_n be_v the_o very_a parallax_n in_o that_o altitude_n but_o if_o the_o moon_n be_v not_o in_o the_o 90_o deg_fw-la say_v as_o the_o radius_fw-la be_v to_o the_o tang_n of_o the_o angle_n of_o the_o ecliptic_a with_o the_o horizon_n so_o be_v the_o sine_fw-la of_o the_o compl_a of_o the_o distance_n of_o the_o moon_n from_o the_o ascendent_n or_o descendent_a degree_n of_o the_o ecliptic_a to_o the_o tang_n of_o the_o compl_a of_o the_o angle_n of_o the_o ecliptic_a with_o the_o azumith_n of_o the_o moon_n again_o say_v as_o the_o radius_fw-la be_v to_o the_o sine_fw-la of_o that_o angle_n so_o be_v the_o parallax_n of_o the_o moon_n altitude_n to_o the_o parallax_n of_o her_o latitude_n last_o say_v as_o the_o radius_fw-la be_v to_o the_o sine_fw-la of_o the_o compl_a of_o that_o former_a angle_n so_o be_v the_o parallax_n of_o the_o moon_n altitude_n to_o the_o parallax_n of_o her_o longitude_n which_o be_v to_o be_v add_v to_o the_o true_a motion_n of_o the_o moon_n if_o she_o be_v on_o the_o east_n part_n of_o the_o 90_o degree_n of_o the_o ecliptic_a or_o to_o be_v subduct_v out_o of_o it_o if_o she_o be_v on_o the_o west_n
that_o imaginary_a parallel_n do_v the_o manifold_a use_n of_o this_o instrument_n especial_o rely_v because_o the_o true_a place_n of_o the_o sun_n all_o that_o day_n be_v in_o some_o part_n or_o point_n of_o that_o circle_n wherefore_o for_o the_o better_a conceive_v and_o bear_v in_o mind_n thereof_o every_o five_o parallel_n be_v herein_o make_v a_o little_o grosser_n than_o the_o rest_n i_o use_v and_o thus_o by_o the_o eye_n and_o view_v only_o to_o behold_v and_o comprehend_v the_o course_n of_o the_o sun_n both_o for_o his_o annual_a and_o diurnal_a motion_n may_v be_v the_o first_o use_n of_o this_o instrument_n two_o use_n to_o take_v the_o height_n of_o the_o sun_n above_o the_o horizon_n set_a up_o the_o pin_n which_o be_v therefore_o make_v fit_a for_o the_o hole_n at_o the_o centre_n perpendicular_a in_o the_o centre_n and_o put_v the_o indices_fw-la on_o both_o side_n down_o upon_o the_o meridian_n that_o they_o with_o their_o weight_n may_v not_o sway_v the_o instrument_n any_o way_n as_o it_o hang_v then_o with_o a_o thread_n put_v into_o the_o hole_n above_o in_o the_o handle_n hang_v it_o perpendicular_o bear_v the_o edge_n towards_o the_o sun_n that_o the_o pin_n may_v cast_v a_o shadow_n upon_o the_o degree_n in_o the_o limb_n for_o that_o degree_n which_o the_o shadow_n of_o the_o pin_n cut_v in_o the_o limb_n be_v the_o height_n of_o the_o sun_n above_o the_o horizon_n at_o that_o present_a iii_o use_n to_o find_v the_o declination_n of_o the_o sun_n every_o day_n look_v the_o day_n of_o the_o month_n propose_v in_o the_o ecliptic_a and_o mark_v how_o many_o degree_n the_o prick_n show_v that_o day_n be_v distant_a from_o the_o equinoctial_a either_o on_o the_o summer_n or_o winter_n side_n viz_o north_n or_o south_n example_n i._o what_o will_v the_o declination_n of_o the_o sun_n be_v upon_o the_o 11_o day_n of_o august_n look_v the_o 11_o day_n of_o august_n and_o you_o shall_v find_v it_o in_o the_o sixth_o circle_n above_o the_o aequinoctial_a now_o because_o each_o parallel_n stand_v as_o have_v be_v say_v before_o for_o 2_o degree_n the_o sun_n shall_v that_o day_n decline_v north-ward_n 12_o degree_n example_n ii_o what_o declination_n have_v the_o sun_n upon_o the_o 24_o day_n of_o march_n look_v the_o 24_o day_n of_o march_n and_o you_o shall_v find_v it_o between_o the_o second_o and_o three_o northern_a parallel_n as_o it_o be_v a_o half_a and_o one_o five_o part_n more_o of_o that_o distance_n from_o the_o second_o reckon_v therefore_o 4_o degree_n for_o the_o two_o circle_n and_o one_o degree_n for_o the_o half_a space_n so_o shall_v the_o sun_n declination_n be_v 5_o degree_n and_o about_o one_o five_o part_n of_o a_o degree_n northward_o that_o same_o day_n example_n iii_o what_o declination_n have_v the_o sun_n upon_o the_o 13_o day_n of_o november_n look_v the_o 13_o day_n of_o november_n and_o you_o shall_v find_v it_o below_o the_o equinoctial_a ten_o parallel_n and_o about_o one_o quarter_n which_o be_v 20_o degree_n and_o a_o half_a southward_o so_o much_o be_v the_o declination_n and_o according_a to_o these_o example_n judge_v of_o all_o the_o rest_n four_o use_n to_o find_v the_o right_a ascension_n of_o the_o sun_n every_o day_n imagine_v a_o hour_n line_n through_o the_o day_n of_o the_o month_n give_v and_o mark_v in_o what_o point_n it_o will_v crâ—sse_v the_o aequinoctial_a then_o lay_v a_o ruler_n or_o a_o straight_a scroll_n of_o paper_n to_o the_o pole_n of_o the_o world_n note_v in_o the_o instrument_n with_o p_o w_n and_o that_o same_o point_n for_o the_o ruler_n shall_v in_o the_o innermost_a circle_n of_o the_o limb_n of_o the_o south_n side_n cut_v the_o right_a ascension_n of_o the_o sun_n for_o that_o day_n to_o be_v reckon_v from_o the_o west_n to_o the_o point_n of_o intersection_n for_o the_o first_o or_o upper_a semicircle_n of_o the_o ecliptic_a or_o from_o the_o east_n together_o with_o 180_o for_o the_o second_o or_o low_a semicircle_n of_o the_o ecliptic_a v._o use_v to_o find_v the_o longitude_n of_o the_o sun_n or_o in_o what_o degree_n of_o the_o sign_n he_o be_v every_o day_n the_o pole_n of_o the_o first_o semicircle_n of_o the_o ecliptic_a be_v note_v p_o i._n and_o the_o pole_n of_o the_o second_o semicircle_n be_v note_v p_o i_o i._o lie_v a_o ruler_n or_o a_o straight_a scroll_n of_o paper_n to_o the_o day_n of_o the_o month_n and_o the_o proper_a pole_n of_o the_o semicircle_n of_o the_o ecliptic_a in_o which_o it_o be_v for_o the_o ruler_n shall_v in_o the_o innermost_a circle_n of_o the_o limb_n on_o the_o south_n side_n cut_v the_o degree_n of_o the_o sun_n place_n in_o the_o ecliptic_a reckon_v it_o in_o the_o same_o manner_n as_o you_o do_v in_o find_v the_o sun_n right_a ascension_n and_o the_o arch_n thus_o find_v be_v call_v the_o longitude_n of_o the_o sun_n which_o may_v be_v expanse_v into_o sign_n by_o reckon_v on_o the_o limb_n from_o the_o west_n to_o south_n ♈_o ♉_o ♊_o and_o from_o south_n to_o east_n ♋_o ♌_o â™_o then_o back_o again_o from_o east_n to_o south_n â™’_o â™_o â™_o and_o last_o from_o south_n to_o west_n ♑_o â™’_o ♓_o allow_v 30_o degree_n for_o each_o of_o those_o twelve_o sign_n vi_o use_n to_o find_v the_o diurnal_a arch_n or_o circle_n of_o the_o sun_n course_n every_o day_n the_o sun_n every_o day_n by_o his_o motion_n as_o have_v be_v say_v describe_v a_o circle_n parallel_v to_o the_o aequinoctial_a which_o be_v either_o one_o of_o the_o circle_n in_o the_o instrument_n or_o somewhere_o between_o two_o of_o they_o first_o then_o seek_v 〈◊〉_d of_o the_o month_n and_o if_o it_o fall_v upon_o one_o of_o those_o 〈◊〉_d that_o be_v the_o circle_n of_o the_o sun_n course_n that_o same_o day_n but_o if_o it_o fall_v between_o any_o two_o of_o those_o parallel_n imagine_v in_o your_o mind_n and_o estimate_n with_o your_o eye_n another_o parallel_n through_o that_o point_n between_o those_o two_o parallel_n keep_v still_o the_o same_o distance_n from_o each_o of_o they_o as_o in_o the_o first_o of_o the_o three_o former_a example_n the_o circle_n of_o the_o sun_n course_n upon_o the_o 11_o day_n of_o august_n shall_v be_v the_o very_a sixth_o parallel_n above_o the_o aequinoctial_a towards_o the_o centre_n in_o example_n ii_o the_o circle_n of_o the_o sun_n course_n upon_o the_o 24_o day_n of_o march_n shall_v be_v a_o imaginary_a circle_n between_o the_o second_o and_o three_o parallel_n still_o keep_v a_o half_a of_o that_o space_n and_o one_o five_o part_n more_o of_o the_o rest_n from_o the_o second_o in_o example_n iii_o the_o circle_n of_o the_o sun_n course_n upon_o the_o 13_o day_n of_o november_n shall_v be_v a_o imaginary_a circle_n between_o the_o ten_o and_o eleaventh_o parallel_n below_o the_o aequinoctial_a still_o keep_v one_o quarter_n of_o that_o space_n from_o the_o ten_o vii_o use_v to_o find_v the_o rise_n and_o set_v of_o the_o sun_n every_o day_n seek_v out_o as_o be_v last_o show_v the_o imaginary_a circle_n or_o parallel_v of_o the_o sun_n course_n for_o that_o day_n and_o mark_v the_o point_n where_o it_o meet_v with_o the_o horizon_n both_o on_o the_o east_n and_o west_n side_n thereof_o for_o that_o be_v the_o very_a point_n of_o the_o sun_n rise_v and_o set_v that_o same_o day_n and_o the_o hour_n line_n which_o be_v on_o both_o side_n of_o it_o by_o proportion_v the_o distance_n reasonable_o according_a to_o 15_o minute_n for_o the_o quarter_n of_o the_o hour_n will_v show_v the_o hour_n of_o the_o sun_n rise_v on_o the_o east_n side_n and_o the_o sun_n set_v on_o the_o west_n side_n viii_o use_v to_o know_v the_o reason_n and_o manner_n of_o the_o increase_v and_o decrease_v of_o the_o day_n and_o night_n throughout_o the_o whole_a year_n when_o the_o sun_n be_v in_o the_o aequinoctial_a it_o rise_v and_o set_v at_o 6_o a_o clock_n for_o in_o the_o instrument_n the_o intersection_n of_o the_o aequinoctial_a and_o the_o ecliptic_a with_o the_o horizon_n be_v in_o the_o 6_o a_o clock_n circle_n on_o 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the_o day_n set_a the_o edge_n of_o the_o label_n to_o the_o azumith_n give_v and_o mark_v in_o what_o point_n the_o same_o edge_n cross_v the_o parallel_n of_o the_o sun_n for_o that_o day_n that_o point_n of_o intersection_n show_v the_o height_n of_o the_o sun_n above_o the_o horizon_n upon_o the_o label_n and_o also_o it_o show_v the_o hour_n of_o the_o day_n among_o the_o hour_n line_n xvii_o use_v to_o find_v at_o what_o hour_n the_o sun_n come_v to_o be_v full_a east_n or_o west_n every_o day_n in_o summer_n apply_v the_o edge_n of_o the_o label_n unto_o the_o east_n or_o west_n point_v of_o the_o limb_n and_o mark_v in_o what_o point_n the_o say_a edge_n cut_v the_o parallel_n of_o the_o sun_n for_o that_o day_n for_o that_o same_o point_n among_o the_o hour_n line_n shall_v show_v the_o time_n of_o the_o sun_n come_v to_o be_v full_a east_n or_o west_n in_o that_o day_n and_o likewise_o of_o what_o altitude_n the_o sun_n will_v be_v above_o the_o horizon_n at_o that_o time_n 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shadow_n or_o by_o the_o shadow_n of_o any_o gnomon_n set_v up_o perpendicular_a to_o the_o horizon_n or_o else_o parallel_v to_o it_o xix_o use_v to_o find_v out_o the_o meridian_n line_n and_o the_o point_n of_o the_o compass_n without_o a_o magnetical_a needle_n yea_o more_fw-it exact_o then_o with_o a_o needle_n take_v the_o height_n of_o the_o sun_n by_o the_o shadow_n of_o the_o pin_n and_o apply_v the_o same_o height_n reckon_v on_o the_o index_n or_o label_n to_o the_o parallel_n of_o the_o sun_n for_o that_o day_n whereby_o you_o have_v the_o true_a place_n of_o the_o sun_n in_o the_o instrument_n as_o have_v be_v show_v in_o the_o xiii_o use_v then_o keep_v both_o the_o label_n
plain_a perpendicular_a to_o the_o meridian_n be_v that_o which_o stand_v direct_o north_n or_o south_n which_o if_o it_o be_v also_o perpendicular_a to_o the_o horizon_n be_v call_v north_n or_o south_n direct_v upright_o but_o if_o it_o stoop_v from_o the_o zenith_n forward_o it_o be_v call_v north_n or_o south_n incline_v if_o backward_o it_o be_v call_v north_n or_o south_n recline_v and_o note_v that_o in_o a_o stoop_a plain_n that_o side_n which_o be_v towards_o the_o horizon_n be_v incline_v and_o that_o which_o be_v towards_o the_o zenith_n be_v recline_v the_o plain_a oblique_a to_o the_o meridian_n be_v that_o which_o stand_v not_o direct_o north_n or_o south_n but_o decline_v one_o side_n into_o the_o east_n and_o the_o other_o into_o the_o west_n and_o be_v therefore_o call_v decline_a eastward_o or_o westward_o according_a as_o either_o side_n of_o the_o plain_n look_v as_o if_o a_o upright_a wall_n be_v southern_a decline_v from_o the_o south_n into_o the_o east_n it_o be_v call_v south_n decline_v eastward_n upright_o but_o if_o it_o be_v not_o upright_o it_o be_v call_v south_n decline_v eastward_o and_o incline_v or_o recline_v the_o plain_a parallel_n to_o the_o meridian_n be_v that_o which_o look_v direct_o east_n or_o west_n and_o according_o have_v his_o denomination_n whether_o it_o be_v upright_o incline_v or_o recline_v the_o plain_a parallel_n to_o the_o horizon_n be_v call_v horizontall_a and_o be_v represent_v by_o the_o instrument_n itself_o or_o at_o least_o by_o the_o inner_a most_o circle_n of_o the_o limb_n thereof_o and_o note_v that_o the_o arch_n of_o declination_n be_v reckon_v from_o the_o next_o east_n or_o west_n point_n and_o that_o the_o arch_n of_o inclination_n or_o reclination_n be_v reckon_v from_o the_o zenith_n or_o the_o compliment_n of_o it_o from_o the_o horizon_n so_o that_o every_o upright_o plain_a be_v understand_v to_o pass_v through_o the_o zenith_n which_o in_o the_o instrument_n be_v the_o centre_n and_o thus_o have_v show_v the_o several_a affection_n of_o plain_n we_o will_v now_o proceed_v to_o show_v the_o manner_n how_o to_o set_v they_o upon_o the_o instrument_n a_o direct_a north_n or_o south_n upright_o plain_a be_v represent_v in_o the_o instrument_n by_o a_o line_n draw_v through_o the_o centre_n from_o the_o east_n point_n to_o the_o west_n which_o be_v also_o the_o horizontall_a intersection_n of_o the_o plaâ—ne_n and_o by_o it_o you_o shall_v see_v that_o the_o southern_a side_n or_o face_n of_o the_o plain_n be_v open_a to_o all_o the_o hour_n between_o six_o in_o the_o morning_n and_o six_o in_o the_o evening_n and_o that_o about_o london_n the_o northern_a side_n only_o in_o the_o summer_n enjoy_v the_o sun_n from_o his_o rise_n till_o after_o seven_o in_o the_o morning_n and_o from_o before_o 5_o a_o clock_n in_o the_o afternoon_n till_o his_o set_n a_o direct_a east_n or_o west_n upright_o plain_a be_v represent_v in_o the_o instrument_n by_o the_o meridian_n which_o be_v also_o the_o horizontall_a intersection_n of_o the_o plain_a and_o in_o it_o you_o shall_v see_v that_o all_o the_o forenoon_n hour_n be_v open_a to_o the_o east_n side_n and_o all_o the_o afternoon_n hour_n to_o the_o west_n side_n a_o decline_a plain_n be_v thus_o set_v upon_o the_o instrument_n reckon_v on_o the_o horizon_n the_o arch_n of_o declination_n from_o the_o east_n or_o west_n point_n and_o at_o the_o end_n draw_v a_o line_n through_o the_o centre_n unto_o the_o opposite_a point_n of_o the_o horizon_n so_o that_o each_o side_n thereof_o may_v be_v open_a to_o that_o point_n either_o east_n or_o west_n into_o which_o the_o declination_n be_v suppose_v that_o line_n so_o draw_v bring_v the_o centre_n be_v the_o horizontall_a intersection_n of_o the_o plain_a and_o represent_v the_o plain_n itself_o if_o it_o be_v upright_o for_o example_n there_o be_v about_o london_n a_o upright_a wall_n decline_v eastward_n 35_o degree_n which_o i_o will_v set_v upon_o the_o instrument_n hold_v the_o southern_a part_n of_o the_o instrument_n to_o you_o and_o reckon_v from_o the_o east_n backward_o into_o the_o north_n upon_o the_o horizon_n 35_o degree_n there_o draw_v a_o line_n through_o the_o centre_n this_o line_n shall_v not_o only_o upon_o the_o south_n side_n represent_v a_o southern_a plain_a decline_a eastward_o 35_o degree_n but_o also_o upon_o the_o north_n side_n shall_v represent_v a_o northern_a plain_a decline_a westward_o 35_o deg_fw-la and_o moreover_o it_o will_v appear_v that_o on_o the_o southern_a side_n shall_v be_v draw_v the_o hour_n from_o almost_o 4_o a_o clock_n in_o the_o morning_n till_o 3_o in_o the_o afternoon_n and_o that_o in_o the_o northern_a side_n shall_v be_v draw_v upon_o one_o side_n 4_o a_o clock_n in_o the_o morning_n only_o and_o upon_o the_o other_o side_n all_o the_o hour_n from_o 3_o in_o the_o afternoon_n till_o sun_n set_v and_o â—o_o consequent_o the_o declination_n of_o a_o upright_a wall_n or_o window_n be_v give_v it_o may_v be_v find_v at_o what_o hour_n the_o sun_n upon_o any_o day_n in_o the_o year_n will_v come_v to_o that_o wall_n or_o window_n and_o when_o it_o will_v go_v from_o it_o as_o in_o the_o former_a example_n there_o be_v about_o london_n a_o northern_a wall_n decline_v westward_o 35_o deg_fw-la i_o will_v know_v at_o what_o time_n of_o the_o day_n the_o sun_n will_v begin_v to_o shine_v upon_o it_o on_o the_o 24_o day_n of_o march._n set_v the_o index_n at_o 35_o deg_fw-la from_o west_n towards_o south_n and_o because_o that_o day_n the_o sun_n declination_n be_v 6_o degree_n northward_o look_v at_o what_o hour_n the_o sixth_o parallel_n above_o the_o aequinoctial_a towards_o the_o centre_n meet_v with_o the_o index_n so_o place_v and_o you_o shall_v find_v it_o at_o 3_o â—_o clock_n in_o the_o afternoon_n wherefore_o at_o that_o time_n the_o sun_n will_v begin_v to_o shine_v upon_o the_o wall_n that_o same_o day_n the_o pole_n of_o every_o upright_a wall_n be_v in_o the_o horizon_n 90_o deg_fw-la that_o be_v a_o quarter_n of_o a_o circle_n distant_a from_o the_o line_n represent_v the_o plain_a wherefore_o if_o upon_o that_o line_n in_o the_o centre_n you_o erect_v a_o perpendicular_a the_o end_n thereof_o in_o the_o horizon_n shall_v be_v the_o pole_n of_o that_o plain_a and_o be_v so_o far_o distant_a from_o the_o north_n and_o south_n point_n as_o the_o plain_n itself_o be_v from_o the_o east_n and_o west_n xxvi_o use_v to_o set_v a_o incline_v and_o recline_a wall_n or_o plain_a upon_o the_o instrument_n and_o to_o find_v how_o many_o hour_n the_o sun_n shall_v shine_v thereon_o at_o some_o time_n of_o the_o year_n when_o you_o have_v a_o incline_v or_o recline_v plain_o to_o be_v describe_v on_o the_o instrument_n first_o the_o horizontall_a intersection_n be_v to_o be_v set_v thereon_o as_o if_o it_o be_v upright_o together_o with_o the_o line_n perpendicular_a thereto_o in_o which_o be_v the_o pole_n of_o the_o plain_a according_a as_o be_v teach_v in_o the_o xxv_o use_v then_o upon_o the_o scale_n of_o degree_n in_o your_o paper_n reckon_v the_o arch_n of_o inclination_n or_o reclination_n and_o with_o your_o compass_n take_v &_o set_v it_o in_o your_o instrument_n upon_o the_o line_n perpendicular_a to_o the_o horizontall_a intersection_n of_o your_o plain_n from_o the_o centre_n that_o way_n into_o which_o the_o inclination_n or_o reclination_n tend_v the_o same_o shall_v be_v the_o uppermost_a point_n of_o your_o plain_n again_o with_o your_o compass_n take_v the_o compliment_n of_o inclination_n or_o reclination_n both_o upon_o the_o scale_n of_o degree_n and_o also_o upon_o the_o scale_n of_o centre_n of_o arch_n in_o your_o paper_n and_o set_v both_o space_n upon_o the_o same_o perpendicular_a line_n but_o on_o the_o other_o side_n of_o the_o centre_n extend_v if_o need_v be_v at_o the_o short_a of_o those_o space_n shall_v be_v the_o pole_n of_o your_o plain_n and_o at_o the_o long_o of_o they_o shall_v be_v the_o centre_n of_o it_o last_o set_v one_o foot_n of_o your_o compass_n in_o the_o centre_n of_o your_o plain_n and_o extend_v the_o other_o foot_n to_o the_o uppermost_a point_n describe_v in_o your_o instrument_n a_o arch_n of_o a_o circle_n which_o if_o you_o have_v do_v well_o will_v exact_o fall_v upon_o the_o end_n of_o the_o horizontal_n intersection_n of_o your_o plain_n that_o arch_n shall_v represent_v your_o plain_n incline_v upon_o the_o low_a side_n which_o be_v towards_o the_o horizon_n or_o limb_n but_o recline_v upon_o the_o upperside_n which_o be_v towards_o the_o zenith_n or_o centre_n and_o so_o either_o side_n shall_v show_v in_o what_o hour_n line_n the_o sun_n at_o some_o time_n of_o the_o year_n will_v shine_v upon_o it_o that_o in_o delineat_v a_o dial_n thereon_o it_o may_v not_o be_v cumber_v
and_o then_o add_v together_o the_o product_n in_o the_o first_o multiplication_n 1_o ·_o 47_o ∷_o 240_o ·_o 11280_o ·_o for_o set_v the_o arm_n of_o the_o index_n at_o 1_o and_o 47_o in_o the_o four_o circle_n and_o then_o bring_v the_o antecedent_n arm_n which_o stand_v at_o 1_o unto_o 240_o and_o the_o consequent_a arm_n will_v show_v 11280._o again_o in_o the_o second_o multiplication_n 1_o ·_o 9_o ∷_o 12_o ·_o 108_o ·_o for_o set_v the_o two_o arm_n of_o the_o index_n at_o 1_o and_o 9_o in_o the_o four_o circle_n and_o bring_v the_o antecedent_n arm_n unto_o 12_o and_o the_o consequent_a arm_n will_v show_v 108._o last_o add_v together_o 11280_o and_o 108_o and_o the_o sum_n 11388_o will_v be_v the_o number_n of_o penny_n contain_v in_o the_o say_a sum_n of_o 47_o li_n 9sh._o 9_o a_o example_n of_o division_n how_o many_o pound_n and_o shilling_n be_v in_o 11388_o penny_n divide_v 11388_o by_o 240_o the_o division_n be_v thus_o 240_o ·_o 1_o ∷_o 11388_o ·_o 47_o ⌊_o 5_o for_o set_v the_o two_o arm_n of_o the_o index_n at_o 240_o and_o 1_o in_o the_o four_o circle_n and_o then_o bring_v the_o antecedent_n arm_n which_o stand_v at_o 240_o unto_o 11388_o and_o the_o consequent_a arm_n will_v show_v 47_o and_o almost_o a_o half_a but_o how_o many_o shilling_n that_o excess_n do_v contain_v will_v appear_v if_o first_o you_o find_v by_o multiplication_n that_o 11280_o penny_n be_v contain_v in_o 47_o li_n which_o subduct_v from_o 11388_o there_o will_v remain_v for_o the_o excess_n 108_o penny_n afterward_o by_o division_n you_o may_v seek_v how_o many_o shilling_n be_v in_o 108_o penny_n the_o division_n be_v thus_o 12_o ·_o 1_o ∷_o 108_o ·_o 9_o for_o set_v the_o arm_n of_o the_o index_n at_o 12_o and_o 1_o then_o bring_v the_o antecedent_n arm_n which_o stand_v at_o 12_o unto_o 108_o and_o the_o consequent_a arm_n will_v show_v 9_o 9_o any_o fraction_n give_v may_v be_v reduce_v into_o decimal_a part_n thus_o set_a the_o antecedent_n arm_n of_o the_o index_n at_o the_o denominator_fw-la of_o the_o fraction_n give_v in_o the_o four_o circle_n and_o the_o consequent_a arm_n at_o the_o numerator_n then_o keep_v the_o same_o distance_n bring_v the_o antecedent_n arm_n unto_o 1_o and_o the_o consequent_a arm_n will_v show_v the_o decimal_a part_n so_o â—40_n â—â—â—_o be_v 0_o ⌊_o 75._o and_o 19_o 48_o be_v 0_o ⌊_o 396_o chap._n iii_o now_o follow_v certain_a example_n of_o proportion_n example_n i._n if_o 54_o elnes_n of_o holland_n be_v sell_v for_o 96_o shilling_n for_o how_o many_o shilling_n be_v 9_o elnes_n sell_v the_o term_n give_v be_v 54_o ·_o 96_o ∷_o 9_o ·_o according_a to_o the_o 2_o chap._n 3_o sect._n set_v one_o of_o the_o arm_n of_o the_o index_n at_o the_o antecedent_n term_v 54_o in_o the_o four_o circle_n and_o the_o other_o arm_n at_o the_o consequent_a term_n 96_o then_o keep_v that_o distance_n bring_v the_o antecedent_n arm_n unto_o 9_o and_o the_o consequent_a arm_n beyond_o the_o line_n of_o the_o radius_fw-la will_v show_v 16_o for_o the_o four_o proportional_a according_a to_o the_o consideration_n in_o the_o 2_o chap._n sect._n 3_o therefore_o 54_o ·_o 96_o ∷_o 9_o ·_o 16_o ·_o be_v proportional_o and_o 16_o shilling_n be_v the_o price_n of_o 9_o elnes_n example_n ii_o if_o 108_o bushel_n of_o corn_n be_v sufficient_a for_o a_o company_n of_o soldier_n keep_v a_o fort_n for_o 36_o day_n how_o many_o day_n will_v 12_o bushel_n suffice_v that_o same_o number_n of_o soldier_n the_o term_n give_v be_v 108_o ·_o 36_o ∷_o 12_o ·_o set_a one_o arm_v of_o the_o index_n at_o the_o antecedent_n term_v 108_o in_o the_o four_o circle_n and_o the_o other_o arm_n at_o the_o consequent_a term_n 12_o be_v mindful_a of_o the_o consideration_n in_o the_o 2_o chap._n 3_o sect._n then_o keep_v that_o same_o distance_n bring_v the_o antecedent_n arm_n unto_o 36_o and_o the_o consequent_a arm_n will_v show_v 4._o therefore_o 108_o ·_o 36_o ∷_o 12_o ·_o 4_o ·_o shall_v be_v proportional_n and_o 4_o be_v the_o number_n of_o day_n seek_v for_o example_n iii_o there_o be_v lay_v up_o in_o a_o fort_n so_o much_o corn_n as_o will_v suffice_v for_o 756_o soldier_n which_o keep_v that_o fort_n for_o 196_o day_n how_o many_o soldier_n will_n that_o same_o corn_n suffice_v for_o 364_o day_n the_o proportion_n be_v reciprocal_a therefore_o the_o term_n give_v be_v 364_o ∶_o 756_o ∷_o 196_o ·_o set_a one_o arm_v of_o the_o index_n at_o the_o antecedent_n term_v 364_o and_o the_o other_o arm_n at_o the_o consequent_a 196_o and_o keep_v the_o same_o distance_n bring_v the_o antecedent_n arm_n unto_o 756_o and_o the_o consequent_a arm_n will_v show_v 407+_n and_o therefore_o for_o so_o many_o soldier_n will_v the_o corn_n lay_v up_o suffice_v for_o 364_o day_n or_o 13_o month_n example_n four_o there_o be_v a_o tower_n who_o height_n i_o will_v measure_v with_o a_o quadrant_n i_o take_v two_o station_n in_o the_o same_o right_a line_n from_o the_o tower_n and_o at_o either_o station_n have_v observe_v the_o height_n through_o the_o sight_n i_o find_v that_o the_o perpendicular_a cut_v in_o the_o near_a station_n 28_o degree_n 7_o minute_n almost_o and_o in_o the_o further_a station_n 21_o degr_n 58_o min._n almost_o and_o between_o both_o the_o station_n the_o distance_n be_v 76_o foot_n the_o rule_n of_o measure_v height_n by_o two_o station_n be_v contain_v in_o these_o theorem_n theor._n as_o the_o difference_n of_o the_o tangent_n of_o the_o arch_n cut_v in_o either_o station_n be_v to_o the_o distance_n between_o the_o station_n so_o be_v the_o tangent_fw-la of_o the_o lesser_a arch_n to_o the_o near_a distance_n from_o the_o tower_n again_o theor._n as_o the_o radius_fw-la be_v to_o the_o tangent_fw-la of_o the_o great_a arch_n so_o be_v the_o near_a distance_n find_v to_o the_o height_n and_o therefore_o because_o by_o the_o 1_o chap._n 6_o sect._n the_o tangent_n of_o the_o arch_n 28°_n 7′_n and_o 21°_n 58′_n be_v 5342_o and_o 4032_o who_o difference_n be_v 1310_o the_o proportion_n will_v be_v first_o 1310_o ·_o 76_o ∷_o tang_n 21°_n 58′_n ·_o 234_o ·_o wherefore_o 234_o foot_n be_v the_o near_a distance_n second_o radius_fw-la ·_o tang_n 28°_n 7′_n ∷_o 234_o ·_o 125_o ·_o wherefore_o 125_o foot_n be_v the_o height_n seek_v for_o example_n v._o to_o find_v the_o declination_n of_o the_o sun_n the_o 9_o day_n of_o may._n the_o place_n of_o the_o sun_n for_o every_o day_n may_v be_v have_v never_o enough_o out_o of_o this_o table_n by_o add_v unto_o the_o place_n of_o the_o sun_n in_o the_o begin_n of_o that_o month_n so_o many_o degree_n as_o there_o be_v day_n pass_v in_o that_o month_n but_o if_o the_o number_n of_o degree_n exceed_v 30_o the_o excess_n be_v to_o be_v account_v in_o the_o sign_n next_o follow_v wherefore_o the_o 9_o of_o may_v the_o place_n of_o the_o sun_n be_v ♉_o 20+9_n that_o be_v ♉_o 29_o which_o be_v 59_o degr_n distant_a from_o the_o next_o aequinoctial_a point_n the_o place_n of_o the_o sun_n in_o the_o begin_n of_o every_o month_n january_n ♑_o 21_o february_n â™’_o 22_o march_n ♓_o 20_o april_n ♈_o 21_o may_n ♉_o 20_o june_n ♊_o 19_o july_n ♋_o 18_o august_n ♌_o 13_o septemb_n â™_o 18_o october_n ♎_o 17_o novemb_v â™_o 18_o decemb_v â™_o 19_o these_o thing_n be_v know_v the_o rule_n be_v deliver_v in_o this_o theorem_a theor._n as_o the_o radius_fw-la be_v to_o the_o sine_fw-la of_o the_o sun_n distance_n from_o the_o next_o aequinoctial_a point_n so_o be_v the_o sine_fw-la of_o the_o sun_n great_a declination_n to_o the_o sine_fw-la of_o the_o declination_n seek_v for_o the_o proportion_n will_v be_v radius_fw-la ·_o sine_fw-la 59°_n ∷_o sine_z 2â—°_n 30′_n ·_o sine_fw-la 19°_n â—9′·_fw-la and_o so_o much_o be_v the_o declination_n seek_v for_o example_n vi_o to_o find_v the_o right_a ascension_n of_o the_o sun_n the_o 9_o day_n of_o may._n seek_v the_o place_n of_o the_o sun_n for_o the_o day_n propose_v in_o the_o former_a table_n and_o the_o sun_n distance_n from_o the_o next_o aequinoctial_a point_n as_o in_o the_o former_a example_n these_o thing_n be_v know_v the_o rule_n be_v by_o one_o of_o these_o two_o theorem_n theor._n as_o the_o radius_fw-la be_v to_o the_o sine_fw-la of_o the_o compliment_n of_o the_o sun_n great_a declination_n so_o be_v the_o the_o tangent_fw-la of_o the_o sun_n distance_n from_o the_o next_o aequinoctial_a point_n to_o the_o tangent_fw-la of_o the_o distance_n of_o the_o right_a ascension_n of_o the_o sun_n from_o the_o same_o aequinoctial_a point_n or_o theor._n as_o the_o tangent_fw-la of_o the_o great_a declination_n of_o the_o sun_n be_v to_o the_o radius_fw-la so_o be_v the_o tangent_fw-la of_o
then_o go_v back_o again_o to_o your_o first_o pole_n look_v what_o know_a star_n be_v direct_o over_o your_o last_o pole_n for_o that_o star_n be_v in_o the_o meridian_n you_o may_v therefore_o instant_o go_v to_o some_o convenient_a place_n and_o take_v a_o mark_n whereby_o you_o may_v at_o all_o time_n know_v the_o meridian_n as_o be_v afore_o teach_v when_o therefore_o at_o any_o time_n of_o the_o night_n you_o will_v know_v what_o a_o clock_n it_o be_v go_v to_o that_o place_n where_o you_o stand_v and_o look_v direct_o over_o your_o mark_n see_v if_o any_o of_o the_o 12_o fix_a star_n be_v in_o the_o meridian_n or_o if_o none_o of_o they_o be_v therein_o observe_v which_o two_o of_o they_o be_v on_o either_o side_n thereof_o and_o what_o part_n of_o that_o space_n be_v in_o the_o meridian_n then_o go_v into_o the_o light_n and_o take_v your_o instrument_n and_o set_v the_o index_n to_o that_o star_n or_o point_v which_o you_o see_v in_o the_o meridian_n mark_v what_o hour_n it_o cut_v for_o that_o same_o hour_n be_v add_v to_o the_o hour_n which_o the_o day_n of_o the_o month_n show_v shall_v give_v you_o the_o true_a hour_n of_o the_o night_n so_o that_o you_o cast_v out_o 12_o hour_n from_o the_o say_a sum_n if_o it_o shall_v chance_v to_o be_v more_o example_n suppose_v the_o five_o of_o december_n that_o the_o middle_a point_n of_o the_o space_n between_o the_o bright_a star_n in_o the_o head_n of_o aries_n and_o the_o bull_n eye_n be_v in_o the_o meridian_n set_a the_o index_n to_o the_o middle_a point_n of_o the_o space_n between_o those_o two_o star_n in_o the_o instrument_n and_o it_o will_v cut_v in_o the_o hour_n circle_v 2_o and_o a_o half_a then_o again_o set_v the_o index_n to_o the_o five_o of_o december_n and_o in_o the_o hour_n circle_v it_o will_v cut_v 7_o which_o add_v unto_o 2_o and_o a_o half_a give_v 9_o and_o a_o half_a for_o the_o true_a hour_n of_o the_o night_n another_o example_n suppose_v the_o 19_o of_o december_n that_o one_o three_o part_n of_o the_o space_n between_o the_o bull_n eye_n and_o the_o right_a shoulder_n of_o orion_n be_v in_o the_o meridian_n set_a the_o index_n to_o one_o three_o part_n of_o that_o space_n in_o the_o instrument_n and_o it_o will_v cut_v in_o the_o hour_n circle_v 4_o and_o half_a a_o quarter_n almost_o again_o set_v the_o index_n to_o the_o 19_o of_o december_n and_o in_o the_o hour_n circle_v it_o will_v cut_v 6_o which_o be_v add_v unto_o 4_o and_o half_o a_o quarter_n almost_o give_v 10_o and_o almost_o half_a a_o quarter_n for_o the_o hour_n of_o the_o night_n the_o second_o part_n of_o this_o book_n show_v the_o use_n of_o the_o second_o side_n of_o the_o instrument_n for_o the_o work_n of_o most_o question_n which_o may_v be_v perform_v by_o the_o globe_n and_o the_o declination_n of_o dial_n upon_o any_o kind_n of_o plain_a upon_o the_o second_o side_n of_o the_o instrument_n be_v delineate_v the_o projection_n of_o the_o upper_a hemisphere_n upon_o the_o plain_a of_o the_o horizon_n the_o horizon_n itself_o be_v understand_v to_o be_v the_o innermost_a circle_n of_o the_o limb_n and_o be_v divide_v on_o both_o side_n from_o the_o point_n of_o east_n and_o west_n into_o degree_n note_v with_o 10_o 20_o 30_o etc._n etc._n unto_o 90._o and_o the_o centre_n of_o the_o instrument_n be_v the_o zenith_n or_o vertical_a point_n within_o the_o horizon_n the_o middle_a straight_a line_n or_o diameter_n point_v north_n and_o south_n be_v the_o meridian_n or_o 12_o a_o clock_n line_n and_o the_o other_o shortarch_v line_n on_o both_o side_n of_o it_o be_v the_o hour_n line_n distinguish_v according_o by_o their_o figure_n these_o hour_n line_n shall_v indeed_o be_v draw_v through_o the_o whole_a plain_n cross_v one_o another_o in_o the_o pole_n of_o the_o world_n but_o that_o the_o instrument_n may_v be_v more_o fair_a they_o be_v only_o draw_v short_a and_o because_o diverse_a excellent_a use_n do_v require_v the_o total_a delineation_n of_o the_o hour_n circle_n i_o have_v in_o a_o several_a paper_n inscribe_v entire_o both_o the_o hour_n line_n and_o also_o two_o other_o circle_n between_o they_o contain_v every_o one_o five_o degree_n but_o if_o the_o instrument_n be_v large_a enough_o to_o receive_v they_o it_o be_v best_o if_o every_o degree_n have_v his_o circle_n and_o so_o every_o 15_o circle_n shall_v be_v a_o hour_n line_n and_o of_o the_o parallel_n there_o need_v no_o more_o but_o the_o aequinoctial_a and_o both_o the_o tropic_n for_o as_o much_o as_o there_o will_v be_v great_a use_n of_o this_o paper_n instrument_n i_o have_v in_o the_o 24_o use_v show_v the_o manner_n of_o make_v it_o so_o that_o any_o that_o 1â—_n ingenuous_a and_o ready_a hand_a may_n himself_o delineate_v one_o sufficient_a enough_o to_o serve_v his_o turn_n for_o any_o elevation_n the_o two_o arch_n which_o across_o the_o hour_n line_n meet_v on_o both_o side_n in_o the_o point_n of_o intersection_n of_o the_o six_o a_o clock_n line_n with_o the_o horizon_n be_v the_o two_o semicircle_n of_o the_o ecliptic_a or_o annual_a circle_n of_o the_o sun_n the_o upper_a of_o which_o arch_n serve_v for_o the_o summer_n half_a year_n and_o the_o low_a for_o the_o winter_n half_a year_n and_o be_v therefore_o divide_v in_o 365_o day_n which_o be_v also_o distinguish_v into_o 12_o month_n with_o long_a line_n have_v their_o name_n set_v down_o and_o into_o tenthes_o and_o fifthe_n with_o short_a line_n and_o the_o rest_n of_o the_o day_n with_o prick_n as_o may_v plain_o be_v see_v in_o the_o instrument_n and_o this_o be_v for_o the_o ready_a find_v out_o of_o the_o place_n of_o the_o sun_n every_o day_n and_o also_o for_o show_v of_o the_o sun_n yearly_a motion_n because_o by_o this_o motion_n the_o sun_n go_v round_o about_o the_o heaven_n in_o the_o compass_n of_o a_o year_n make_v the_o four_o part_n or_o season_n thereof_o namely_o the_o spring_n in_o that_o quarter_n of_o the_o ecliptic_a which_o begin_v at_o the_o intersection_n on_o the_o west_n side_n of_o the_o instrument_n and_o be_v therefore_o call_v the_o vernal_a intersection_n then_o the_o summer_n in_o that_o quarter_n of_o the_o ecliptic_a which_o begin_v with_o the_o intersection_n of_o the_o meridian_n in_o the_o high_a point_n next_o the_o zenith_n and_o after_o that_o autumn_n in_o that_o quarter_n of_o the_o ecliptic_a which_o begin_v at_o the_o intersection_n on_o the_o east_n side_n of_o the_o instrument_n and_o be_v therefore_o call_v the_o autumnal_a intersection_n and_o last_o the_o winter_n in_o that_o quarter_n of_o the_o ecliptic_a which_o begin_v at_o the_o intersection_n with_o the_o meridian_n in_o the_o low_a point_n next_o the_o horizon_n but_o beside_o this_o yearly_a motion_n the_o sun_n have_v a_o diurnal_a or_o daily_a motion_n whereby_o it_o make_v day_n and_o night_n with_o all_o the_o diversity_n and_o inequality_n thereof_o which_o be_v express_v by_o those_o other_o circle_v draw_v across_o the_o hour_n line_n the_o middlemost_a whereof_o be_v grosser_n than_o the_o rest_n meet_v with_o the_o ecliptic_a in_o the_o point_n of_o the_o vernal_a and_o autumnal_a intersection_n be_v the_o aequinoctial_a and_o the_o rest_n on_o both_o side_n of_o it_o be_v call_v the_o parallel_n or_o diurnal_a arch_n of_o the_o sun_n the_o two_o outermost_a whereof_o be_v the_o tropic_n because_o in_o they_o the_o sun_n have_v his_o further_a digression_n or_o declination_n from_o the_o aequinoctial_a which_o be_v degree_n 23½_n and_o thence_o begin_v again_o to_o return_v to_o the_o aequinoctial_a the_o upper_a of_o the_o two_o tropic_n next_o the_o centre_n in_o this_o our_o northern_a hemisphere_n be_v the_o tropic_a of_o cancer_n and_o the_o sun_n be_v in_o it_o be_v high_a into_o the_o north_n make_v the_o long_a day_n of_o summer_n and_o the_o low_a next_o the_o horizon_n be_v call_v the_o tropic_a of_o capricorn_n and_o the_o sun_n be_v in_o it_o be_v low_a into_o the_o south_n make_v the_o short_a day_n of_o winter_n between_o the_o two_o tropic_n and_o the_o aequinoctial_a infinite_a such_o parallel_n circle_n be_v understand_v to_o be_v contain_v for_o the_o sun_n be_v what_o point_n soever_o of_o the_o ecliptic_a it_o be_v carry_v describe_v by_o his_o lation_n a_o circle_n parallel_n to_o the_o aequinoctial_a yet_o those_o parallel_n which_o be_v in_o the_o instrument_n though_o draw_v but_o to_o every_o second_o degree_n of_o declination_n may_v be_v sufficient_a to_o direct_v the_o eye_n in_o imagine_v and_o trace_v out_o through_o every_o day_n of_o the_o whole_a year_n in_o the_o ecliptic_a a_o proper_a circle_n which_o may_v be_v the_o diurnal_a arch_n of_o the_o sun_n for_o that_o day_n for_o upon_o the_o right_a estimation_n of_o