exact_o smooth_a and_o lie_v very_o flat_a without_o any_o manner_n of_o lean_v or_o decline_v which_o you_o must_v wary_o and_o diligent_o try_v by_o your_o level_n and_o your_o plumbe_v line_n take_v the_o centre_n a_o upon_o which_o describe_v a_o circle_n b_o c_o d_o e_o represent_v the_o horizon_n who_o circumference_n you_o may_v divide_v or_o imagine_v only_o to_o be_v divide_v into_o degree_n and_o from_o a_o the_o centre_n thereof_o erect_v a_o steel_n or_o wire_n standing_z plumbe_v upright_o or_o perpendicular_a to_o the_o flat_a of_o the_o circle_n a_o b_o c_o d_o by_o trial_n of_o your_o plumbe_v rule_n then_o take_v a_o board_n make_v precise_a square_n have_v the_o side_n somewhat_o long_o than_o the_o semidiameter_n of_o the_o circle_n b_o c_o d_o e_o and_o set_v one_o corner_n thereof_o in_o the_o centre_n a_o so_o that_o one_o of_o the_o side_n contain_v it_o may_v agree_v just_a with_o the_o steel_n or_o wire_n and_o the_o other_o with_o the_o circle_n plain_a then_o look_v along_o the_o upper_a edge_n or_o through_o two_o sight_n set_v upon_o the_o edge_n and_o continual_o lift_v it_o up_o without_o swerve_v till_o the_o side_n that_o lie_v upon_o the_o flat_a of_o the_o circle_n agree_v with_o the_o steel_n the_o line_n of_o your_o sight_n or_o the_o line_n draw_v from_o the_o centre_n for_o in_o respect_n of_o the_o heaven_n mighty_a distance_n the_o difference_n between_o they_o be_v not_o sensible_a shall_v howsoever_o the_o square_n be_v place_v describe_v a_o azimute_v and_o if_o stay_v the_o edge_n of_o the_o square_n at_o one_o height_n the_o corner_n be_v continual_o keep_v in_o the_o centre_n without_o drip_v by_o turn_v it_o round_o about_o the_o steel_n you_o shall_v describe_v a_o almicantar_n parallel_n to_o the_o horizon_n in_o this_o manner_n carry_v the_o square_a about_o &_o lift_v it_o up_o &_o down_o till_o you_o see_v the_o pole_n star_n or_o if_o you_o can_v aim_v at_o it_o the_o often_o speak_v of_o immovable_a point_n stay_v it_o fast_o in_o that_o situation_n either_o of_o the_o edge_n without_o sensible_a error_n may_v be_v take_v for_o the_o axis_n of_o the_o world_n which_o extend_v fall_v on_o both_o the_o pole_n that_o which_o be_v see_v be_v the_o arctic_a pole_n and_o the_o antarctick_a that_n which_o be_v under_o the_o horizon_n in_o lift_v it_o up_o and_o down_o you_o shall_v in_o the_o heaven_n point_n out_o the_o meridian_n circle_n and_o bring_v it_o just_a to_o the_o flat_a of_o the_o circle_n b_o c_o d_o e_o the_o edge_n will_v there_o show_v the_o right_a line_n b_o d_o which_o be_v the_o meridian_n line_n the_o line_n c_o e_o in_o a_o cross_v the_o line_n b_o d_o be_v the_o line_n of_o right_a east_n and_o right_a west_n the_o azimute_v stand_v upon_o c_o e_z be_v the_o vertical_a circle_n or_o the_o circle_n of_o the_o east_n the_o azimute_v stand_v upon_o g_o f_o be_v sometime_o say_v to_o be_v of_o so_o many_o degree_n as_o be_v between_o b_o the_o north_n point_n of_o the_o horizon_n and_o g_o where_o the_o azimute_v stand_v upon_o g_o f_o cut_v the_o horizon_n uz._n the_o circumference_n b_o g_o denominate_v the_o azimute_v stand_v upon_o g_o f_o and_o sometime_o that_o circumference_n g_o e_o which_o contain_v the_o number_n of_o the_o degree_n betweéene_v the_o same_o point_n and_o the_o line_n of_o east_n and_o west_n e_o c_o which_o be_v the_o very_a pole_n of_o the_o meridian_n work_v by_o the_o pole_n star_n these_o thing_n will_v somewhat_o vary_v from_o exactness_n which_o some_o help_n by_o await_v the_o time_n when_o the_o star_n next_o the_o wheel_n of_o charles_n wain_n common_o call_v the_o filler_z or_o hill_n horse_n be_v direct_o over_o or_o under_o the_o pole_n star_n so_o that_o the_o square_a be_v lift_v up_o and_o down_o close_o by_o the_o steel_n pass_v by_o they_o both_o but_o howsoever_o this_o may_v suffice_v for_o some_o conceit_n of_o these_o term_n hereafter_o shall_v be_v teach_v other_o most_o precise_a way_n to_o describe_v and_o take_v they_o most_o exact_o to_o return_v again_o therefore_o to_o our_o principal_a purpose_n in_o behold_v of_o the_o star_n how_o they_o continual_o rise_v in_o the_o east_n side_n of_o the_o horizon_n ascend_v unto_o the_o meridian_n and_o so_o from_o thence_o descend_v unto_o the_o west_n side_n you_o shall_v observe_v that_o always_o they_o keep_v their_o distance_n from_o the_o pole_n star_n or_o the_o true_a pole_n unchaunged_a as_o if_o you_o mark_v the_o two_o hinder_v wheel_n of_o charles_n wain_n you_o shall_v find_v howsoever_o they_o be_v situate_v in_o the_o heaven_n that_o their_o distance_n from_o the_o pole_n star_n be_v always_o one_o and_o the_o same_o not_o near_o or_o further_o of_o at_o one_o time_n then_o a_o other_o and_o therefore_o every_o star_n or_o point_n by_o such_o motion_n in_o a_o globe_n or_o sphere_n his_o superficies_n describe_v the_o circumference_n of_o a_o circle_n so_o that_o the_o whole_a heaven_n must_v seem_v to_o turn_v upon_o the_o pole_n and_o make_v a_o circular_a motion_n or_o revolution_n this_o motion_n in_o diverse_a respect_n have_v diverse_a name_n call_v sometime_o the_o diurnal_a motion_n sometime_o the_o motion_n of_o the_o first_o movable_a heaven_n sometime_o notus_fw-la captus_fw-la again_o every_o star_n or_o peynt_a by_o this_o conversion_n describe_v a_o circle_n if_o you_o take_v some_o star_n or_o point_n which_o lie_v between_o the_o pole_n just_a 90._o degree_n from_o either_o of_o they_o that_o will_v describe_v a_o circle_n pass_v by_o the_o point_n of_o east_n and_o west_n which_o for_o some_o reason_n hereafter_o to_o be_v express_v be_v call_v the_o equinoctial_a the_o other_o point_n or_o star_n describe_v circle_n parallel_v to_o the_o equinoctial_a circle_n which_o be_v call_v circle_n of_o declination_n because_o if_o from_o the_o pole_n of_o the_o world_n by_o any_o point_n take_v in_o any_o of_o the_o parallel_n a_o great_a circle_n be_v draw_v to_o the_o equinoctial_a that_o portion_n of_o it_o which_o lie_v between_o the_o equinoctial_a and_o the_o parallel_n be_v call_v the_o declination_n of_o the_o point_n so_o take_v some_o of_o these_o parallel_n towards_o the_o north_n describe_v by_o revolution_n of_o the_o point_n or_o star_n that_o never_o set_v be_v whole_a above_o the_o horizon_n and_o one_o of_o they_o which_o some_o name_n the_o arctic_a circle_n touch_v it_o only_o about_o the_o antarcticke_a pole_n there_o be_v some_o whole_o under_o the_o horizon_n and_o one_o which_o some_o call_v the_o antarcticke_a circle_n only_o touch_v it_o in_o the_o south_n point_n other_o between_o these_o two_o touch_v parallel_n which_o arise_v and_o set_v or_o go_v down_o cut_v the_o horizon_n who_o portion_n lie_v between_o that_o point_n and_o the_o true_a east_n or_o west_n be_v call_v the_o amplitude_n or_o latitude_n of_o the_o rise_n or_o the_o set_n of_o the_o point_n describe_v the_o parallel_n these_o thing_n hitherto_o rehearse_v traveller_n may_v every_o where_o and_o in_o all_o country_n observe_v and_o beside_o in_o their_o journey_n southward_n or_o northward_o they_o shall_v see_v sometime_o more_o and_o sometime_o few_o star_n never_o to_o go_v down_o more_o in_o go_v northward_o few_o in_o go_v southward_o yet_o always_o without_o alteration_n keep_v one_o and_o the_o same_o distance_n one_o from_o another_o mary_n the_o pole_n star_n or_o the_o true_a pole_n proportionable_o to_o the_o length_n of_o the_o way_n travel_v alter_v his_o distance_n from_o the_o horizon_n and_o the_o zenith_n appear_v the_o further_a you_o go_v northward_o the_o high_a &_o the_o further_a you_o go_v southward_o the_o low_a and_o so_o according_o that_o portion_n of_o the_o meridian_n between_o the_o equinoctial_a and_o the_o zenith_n which_o be_v call_v the_o latitude_n of_o the_o country_n be_v always_o equal_a to_o that_o which_o be_v between_o the_o horizon_n and_o the_o pole_n call_v his_o height_n or_o elevation_n be_v of_o necessity_n great_a or_o lesser_a so_o that_o your_o situation_n be_v apparent_o change_v in_o respect_n of_o the_o heaven_n but_o yet_o still_o you_o keep_v the_o same_o distance_n from_o it_o whereby_o you_o may_v easy_o infer_v the_o figure_n or_o shape_n of_o the_o earth_n to_o be_v like_a and_o answerable_a to_o the_o celestial_a sphere_n and_o that_o how_o vast_a and_o huge_a soever_o it_o be_v in_o itself_o yet_o in_o comparison_n of_o the_o large_a compass_n of_o the_o heaven_n it_o be_v just_o count_v for_o no_o more_o but_o a_o small_a point_n or_o prick_v for_o it_o never_o hinder_v you_o from_o see_v the_o precise_a half_n of_o the_o celestial_a sphere_n which_o be_v the_o bigness_n thereof_o any_o thing_n of_o account_n it_o will_v of_o necessity_n do_v for_o better_a understanding_n of_o these_o
matter_n imagine_v the_o circle_n b_o c_o d_o e_o describe_v on_o the_o centre_n a_o to_o represent_v the_o meridian_n and_o upon_o the_o line_n e_o c_o a_o semicircle_n erect_v perpendicular_o to_o represent_v the_o horizon_n who_o pole_n or_o the_o zenith_n the_o point_n b_o be_v and_o let_v h_n be_v the_o north_n pole_n from_o h_n to_o a_o the_o place_n of_o your_o stand_n be_v the_o centre_n of_o the_o horizon_n and_o the_o whole_a sphere_n and_o so_o consequent_o of_o all_o the_o great_a circle_n in_o the_o same_o sphere_n describe_v from_o the_o pole_n h_n to_o the_o centre_n a_o draw_v a_o right_a line_n and_o extend_v it_o unto_o ay_o the_o line_n h_n i_o be_v the_o axis_n of_o the_o world_n the_o pole_n be_v h_n the_o north_n and_o i_o the_o south_n or_o antarcticke_a pole_n let_v the_o point_n g_o take_v in_o the_o meridian_n be_v just_a 90._o degree_n from_o either_o pole_n so_o that_o the_o circumference_n g_o h_n g_o i_o be_v just_a quadrant_n by_o the_o revolution_n of_o the_o sphere_n upon_o the_o pole_n h_n ay_o which_o be_v the_o diurnal_a motion_n the_o line_n g_o a_o shall_v describe_v a_o circle_n pass_v by_o the_o centre_n of_o the_o sphere_n and_o perpendicular_a to_o the_o meridian_n therefore_o it_o must_v pass_v by_o the_o pole_n thereof_o which_o be_v in_o the_o horizon_n the_o point_n of_o east_n and_o west_n as_o the_o circle_n set_v plumbe_v upon_o the_o diameter_n f_o g_o will_v do_v other_o point_n as_o s_n n_o v_o describe_v circle_n parallel_v to_o that_o stand_n upon_o g_o f_o of_o which_o that_o which_o stand_v upon_o c_o s_n do_v only_o touch_v the_o horizon_n and_o be_v whole_o above_o it_o the_o other_o beyond_o it_o to_o the_o pole-ward_n as_o v._o w_o be_v whole_o above_o it_o and_o come_v not_o near_o so_o likewise_o e_z t_o be_v always_o under_o the_o horizon_n and_o only_o touch_v it_o the_o other_o beyond_o it_o towards_o ay_o be_v under_o it_o and_o never_o come_v near_o it_o now_o if_o in_o go_v northward_o the_o pole_n h_n grow_v high_o the_o equinoctial_a must_v go_v further_o from_o the_o zenith_n for_o see_v b_o c_z and_o g_o h_n be_v equal_a that_o be_v the_o just_a quarter_n of_o the_o same_o circle_n if_o you_o take_v away_o the_o circumference_n b_o h_n common_a to_o they_o both_o the_o residue_n g_o b_o the_o distance_n of_o the_o equinoctial_a from_o the_o meridian_n which_o be_v the_o latitude_n of_o the_o country_n who_o zenith_n be_v b_o be_v equal_a to_o h_n c_o the_o height_n of_o the_o pole_n above_o the_o horizon_n or_o the_o elevation_n of_o the_o pole_n and_o as_o the_o pole_n rise_v high_a so_o be_v the_o circle_n s_o cremoved_a from_o the_o horizon_n further_o and_o further_o whereby_o you_o see_v that_o by_o that_o mean_v more_o star_n never_o set_v the_o circumference_n of_o the_o meridian_n g_o n_n g_o s_o g_o v_o be_v call_v the_o declination_n of_o the_o point_n n_o s_o v_o take_v in_o the_o parallel_n n_o z_o s_o c_o v_o w_n and_o the_o portion_n of_o the_o horizon_n between_o the_o point_n of_o true_a east_n and_o the_o point_n where_o the_o parallel_n stand_v upon_o n_n z_o cuâ—teth_v the_o horizon_n be_v the_o amplitude_n or_o latitude_n of_o rise_v of_o the_o point_n l_o or_o any_o other_o take_v in_o the_o parallel_n stand_v upon_o the_o diameter_n n_o z._n these_o thing_n be_v well_o conceive_v let_v we_o consider_v again_o that_o as_o apparent_o as_o any_o star_n the_o sun_n make_v his_o revolution_n arise_v on_o the_o east_n side_n of_o the_o horizon_n and_o mount_v up_o unto_o the_o meridian_n at_o which_o time_n it_o be_v high_a noon_n descend_v again_o unto_o the_o west_n side_n which_o time_n of_o his_o continuance_n above_o the_o horizon_n be_v call_v the_o artificial_a day_n then_o be_v hide_v from_o our_o sight_n the_o night_n begin_v which_o continue_v till_o the_o sun_n pass_v by_o that_o part_n of_o the_o meridian_n which_o be_v under_o the_o earth_n when_o it_o be_v midnight_n with_o we_o return_v again_o unto_o the_o east_n side_n make_v up_o the_o natural_a day_n which_o be_v the_o space_n of_o time_n from_o the_o sun_n rise_v to_o the_o sun_n rise_v again_o and_o may_v be_v indifferent_o reckon_v from_o sun_n set_v to_o sun_n set_v as_o the_o jew_n do_v or_o from_o midnight_n to_o midnight_n which_o be_v our_o common_a account_n the_o obscure_a light_n before_o the_o sun_n rise_v be_v call_v the_o dawn_n and_o break_v of_o the_o day_n after_o his_o set_n be_v call_v the_o twilight_n crepusculum_fw-la in_o latin_a be_v a_o common_a name_n to_o both_o time_n although_o in_o the_o sun_n daily_a revolution_n we_o observe_v all_o this_o yet_o be_v it_o not_o without_o much_o variety_n and_o change_n his_o rise_n and_o set_v be_v not_o always_o in_o one_o place_n of_o the_o horizon_n nor_o his_o height_n in_o the_o meridian_n always_o the_o same_o at_o noon_n in_o the_o midst_n of_o winter_n about_o the_o 12._o of_o our_o december_n when_o the_o day_n be_v short_a and_o the_o night_n long_o it_o rise_v &_o set_v most_o southerly_a and_o be_v low_a in_o the_o meridian_n at_o noon_n towards_o the_o spring_n as_o the_o day_n wax_v long_o and_o long_o in_o rising_z and_o set_v it_o continual_o grow_v from_o the_o south_n and_o mount_v high_a and_o high_o in_o the_o meridian_n till_o about_o the_o 11._o of_o our_o march_n make_v the_o day_n and_o night_n equal_a it_o rise_v and_o set_v just_a east_n and_o west_n come_v at_o noon_n to_o the_o common_a section_n of_o the_o equinoctial_a and_o the_o meridian_n then_o as_o summer_n come_v on_o the_o day_n increase_n it_o rise_v and_o set_v more_o northerly_a mount_v still_o high_a and_o high_o in_o the_o meridian_n at_o noon_n till_o in_o the_o midst_n of_o summer_n the_o day_n be_v at_o the_o long_a about_o the_o 12._o of_o our_o june_n it_o be_v at_o the_o high_a in_o the_o meridian_n at_o noon_n and_o rise_v and_o set_v further_a north_n then_o as_o the_o day_n shorten_v it_o return_v back_o again_o grow_v continual_o lower_v at_o noon_n and_o rise_v and_o set_v less_o northerly_a till_o the_o day_n and_o night_n become_v equal_a again_o about_o the_o 13._o of_o our_o september_n when_o it_o rise_v and_o set_v precise_o east_n and_o west_n again_o and_o at_o noon_n will_v be_v in_o the_o common_a section_n of_o the_o equinoctial_a and_o the_o meridian_n from_o that_o point_n it_o grow_v low_a and_o low_a at_o noon_n rise_v &_o set_v more_o and_o more_o southerly_a as_o the_o night_n increase_n till_o about_o the_o 12._o of_o our_o december_n the_o day_n be_v at_o the_o short_a it_o become_v low_a again_o at_o noon_n and_o in_o rise_v and_o set_v most_o southerly_a as_o it_o be_v before_o of_o this_o return_v from_o the_o high_a in_o summer_n and_o the_o low_a in_o winter_n the_o two_o parallel_n which_o it_o then_o describe_v by_o the_o diurnal_a revolution_n be_v call_v tropicke_n and_o the_o equinoctial_a be_v so_o name_v because_o in_o march_n and_o september_n the_o sun_n come_v to_o it_o the_o day_n be_v make_v equal_a to_o the_o night_n by_o these_o variety_n it_o be_v easy_o gather_v that_o the_o sun_n make_v a_o peculiar_a course_n beside_o his_o diurnal_a revolution_n in_o a_o great_a circle_n touch_v the_o two_o tropic_n and_o decline_v from_o the_o equinoctial_a which_o it_o divide_v as_o all_o great_a circle_n do_v one_o another_o into_o two_o equal_a part_n or_o semicircle_n this_o decline_a circle_n because_o when_o the_o sun_n and_o moon_n either_o meet_v or_o be_v opposite_a in_o it_o there_o happen_v a_o eclipse_n be_v call_v the_o ecliptic_a and_o sometime_o the_o zodiac_n but_o the_o zodiac_n proper_o be_v a_o superficies_n like_o a_o fillet_n or_o a_o girdle_n lay_v upon_o this_o circle_n circumference_n comprehend_v on_o either_o side_n of_o it_o six_o or_o as_o some_o say_v eight_o degree_n the_o pole_n of_o this_o circle_n which_o decline_v from_o the_o pole_n of_o the_o world_n as_o the_o circle_n itself_o decline_v from_o the_o equinoctial_a describe_v by_o the_o diurnal_a revolution_n two_o parallel_n which_o some_o in_o stead_n of_o they_o afore_o describe_v take_v for_o the_o arctic_a and_o antarcticke_a circle_n that_o section_n of_o the_o equinoctial_a and_o the_o ecliptic_a which_o the_o sun_n come_v to_o in_o the_o spring_n time_n be_v call_v the_o vernal_a section_n that_o which_o be_v opposite_a to_o it_o by_o which_o the_o sun_n pass_v in_o the_o end_n of_o harvest_n be_v the_o autumnal_a section_n the_o point_n which_o touch_v the_o tropicke_n be_v common_o call_v solstitial_a point_n the_o great_a circle_n pass_v by_o the_o equinoctial_a section_n and_o the_o pole_n of_o the_o world_n be_v the_o
equinoctial_a colour_n that_o which_o pass_v by_o the_o pole_n of_o the_o world_n and_o the_o solstitial_a point_n be_v call_v the_o solstitial_a or_o tropical_a colour_n the_o portion_n thereof_o lie_v between_o the_o two_o tropicke_n be_v the_o distance_n of_o the_o tropicke_n who_o half_a be_v the_o sun_n great_a declination_n otherwise_o call_v the_o obliquity_n of_o the_o zodiac_n which_o by_o observation_n make_v with_o large_a instrument_n be_v in_o this_o our_o age_n find_v by_o great_a artesman_n to_o be_v 23._o degree_n and_o 30._o minute_n who_o report_n it_o shall_v be_v sufficient_a to_o accept_v of_o and_o commit_v to_o memory_n without_o take_v or_o try_v it_o by_o any_o small_a instrument_n though_o some_o writer_n of_o the_o use_n of_o the_o astrolabe_n have_v make_v that_o one_o of_o their_o special_a conclusion_n the_o equinoctial_a and_o the_o ecliptic_a be_v circle_n of_o chief_a account_n the_o first_o be_v the_o rule_n and_o measure_n of_o the_o first_o motion_n or_o the_o motion_n of_o primum_fw-la mobile_a otherwise_o call_v the_o diurnal_a revolution_n and_o the_o other_o as_o it_o be_v the_o standard_n whereby_o all_o secondary_a motion_n be_v examine_v therefore_o the_o degree_n of_o these_o circle_n have_v peculiar_a name_n call_v in_o the_o equinoctial_a tempora_fw-la time_n because_o they_o be_v the_o first_o measure_n of_o time_n every_o 15._o degree_n ascend_v make_v a_o hour_n and_o so_o the_o whole_a revolution_n of_o 360._o which_o be_v perform_v every_o natural_a day_n make_v 24._o hour_n astronomer_n begin_v to_o account_v the_o part_n or_o degree_n as_o well_o in_o the_o equinoctial_a as_o in_o the_o ecliptic_a from_o that_o point_n common_a to_o they_o both_o which_o be_v call_v the_o vernal_a section_n and_o though_o in_o the_o equinoctial_a there_o be_v no_o change_n of_o name_n yet_o in_o the_o ecliptic_a or_o zodiac_n every_o thirty_o degree_n be_v call_v a_o sign_n and_o have_v a_o peculiar_a name_n the_o first_o 30._o immedtat_o follow_v the_o vernal_a section_n be_v call_v aries_n the_o next_o 30._o taurus_n the_o three_o 30._o gemini_fw-la the_o four_o 30._o who_o first_o point_n begin_v a_o new_a quadrant_a and_o touch_v the_o summer_n tropic_n be_v term_v cancer_n the_o five_o 30._o leo_n the_o sixth_o virgo_fw-la these_o six_o sign_n make_v up_o the_o semicircle_n of_o the_o zodiac_n which_o lean_v or_o decline_v from_o the_o equinoctial_a towards_o the_o north_n pole_n the_o first_o 30._o after_o this_o semicircle_n begin_v at_o the_o autumnal_a section_n make_v the_o seven_o sign_n name_v libra_n the_o next_o or_o eight_o 30._o be_v the_o sign_n scorpio_n the_o nine_o 30._o be_v sagittarius_fw-la the_o ten_o 30._o beginning_n a_o new_a quadrant_a with_o the_o first_o point_n which_o touch_v the_o winter_n tropic_n be_v capricornus_fw-la the_o eleven_o 30._o be_v aquarius_n and_o the_o twelve_o 30._o be_v pisces_fw-la there_o be_v character_n use_v to_o express_v every_o sign_n with_o which_o be_v find_v in_o every_o almanac_n the_o sun_n pass_v in_o the_o ecliptic_a from_o point_n to_o point_n make_v his_o continual_a revolution_n in_o it_o without_o swerve_v to_o the_o one_o side_n or_o the_o other_o other_o star_n for_o the_o most_o part_n decline_v from_o it_o but_o yet_o have_v their_o place_n determine_v by_o longitude_n and_o latitude_n in_o respect_n thereof_o thus_o by_o any_o point_n or_o star_n a_o great_a circle_n be_v draw_v from_o the_o pole_n of_o the_o ecliptic_a to_o his_o circumference_n the_o section_n there_o make_v or_o the_o portion_n of_o the_o ecliptic_a between_o that_o section_n and_o the_o vernal_a section_n be_v the_o longitude_n of_o the_o point_n or_o star_n by_o which_o the_o great_a circle_n be_v draw_v his_o latitude_n be_v that_o portion_n of_o the_o same_o great_a circle_n lie_v between_o the_o star_n and_o the_o ecliptic_a the_o sun_n be_v in_o any_o point_n of_o the_o ecliptic_a and_o the_o point_n itself_o with_o all_o other_o star_n wheresoever_o place_v beside_o be_v in_o like_a manner_n compare_v to_o the_o equinoctial_a and_o in_o respect_n thereof_o not_o only_o their_o declination_n which_o have_v be_v touch_v before_o but_o also_o their_o right_a ascension_n be_v consider_v a_o great_a circle_n be_v draw_v from_o the_o pole_n of_o the_o world_n to_o the_o equinoctial_a by_o any_o point_n or_o star_n his_o right_a ascension_n be_v that_o portion_n of_o the_o equinoctial_a take_v between_o that_o point_n where_o the_o great_a circle_n cut_v and_o the_o vernal_a section_n the_o declination_n be_v the_o portion_n of_o the_o great_a circle_n so_o draw_v which_o lie_v between_o the_o equinoctial_a and_o the_o star_n which_o as_o before_o be_v note_v be_v also_o determine_v by_o a_o parallel_n to_o the_o equinoctial_a pass_v by_o the_o star_n the_o right_a ascension_n be_v so_o call_v because_o under_o the_o equinoctial_a that_o be_v in_o a_o situation_n where_o the_o equinoctial_a pass_v by_o the_o zenith_n and_o the_o horizon_n by_o the_o pole_n of_o the_o world_n the_o horizon_n by_o which_o once_o in_o 24._o hour_n every_o point_n ascend_v do_v the_o office_n of_o any_o great_a circle_n so_o draw_v as_o be_v appoint_v and_o agree_v with_o it_o most_o exact_o this_o situation_n be_v call_v sphaera_fw-la recta_fw-la the_o right_a sphere_n and_o the_o horizon_n in_o that_o situation_n horizon_n rectus_fw-la the_o right_a horizon_n but_o when_o the_o equinoctial_a decline_v from_o the_o zenith_n and_o the_o pole_n be_v one_o above_o the_o other_o beneath_o the_o horizon_n that_o situation_n be_v call_v the_o oblique_a or_o decline_a sphere_n and_o the_o horizon_n the_o oblique_a horizon_n which_o never_o agree_v with_o the_o foresay_a great_a circle_n draw_v by_o the_o pole_n of_o the_o world_n and_o therefore_o with_o the_o star_n there_o be_v another_o point_n of_o the_o equinoctial_a in_o the_o horizon_n between_o which_o and_o the_o vernal_a section_n be_v contain_v that_o portion_n of_o the_o equinoctial_a that_o be_v call_v the_o star_n oblique_a ascension_n and_o the_o portion_n of_o the_o equinoctial_a between_o the_o end_n of_o the_o right_n and_o oblique_a ascension_n be_v call_v the_o difference_n ascensionall_n but_o for_o help_v the_o conceit_n of_o these_o thing_n i_o will_v use_v a_o linearie_a example_n take_v the_o former_a figure_n where_o e_z c_z be_v the_o meridian_n line_n and_o the_o diameter_n on_o which_o the_o horizon_n stand_v now_o in_o the_o midst_n of_o winter_n the_o sun_n be_v low_a in_o the_o meridian_n in_o the_o point_n k_o by_o the_o diurnal_a revolution_n describe_v a_o parallel_n stand_v upon_o the_o diameter_n k_o m_o which_o cut_v the_o horizon_n from_o the_o east_n towards_o the_o south_n it_o continual_o grow_v high_a and_o high_o in_o the_o meridian_n pan_n &_o rise_v in_o the_o horizon_n near_o and_o near_o the_o east_n till_o about_o the_o 11._o of_o march_n at_o noon_n it_o come_v to_o g_o the_o section_n of_o the_o equinoctial_a and_o the_o meridian_n and_o then_o by_o the_o diurnal_a revolution_n describe_v a_o circle_n just_a answer_v the_o equinoctial_a which_o pass_v by_o the_o point_n of_o east_n and_o west_n in_o the_o horizon_n stand_v upon_o the_o diameter_n g_o f_o from_o thence_o aâ—_n summer_n come_v on_o it_o ascend_v in_o the_o meridian_n and_o rise_v more_o northerly_a upon_o the_o horizon_n till_o about_o the_o 12._o of_o our_o june_n be_v at_o the_o high_a in_o n_n it_o describe_v a_o parallel_n stand_v upon_o the_o diameter_n n_o z_o in_o which_o it_o rise_v upon_o the_o horizon_n further_a from_o the_o east_n to_o the_o northward_o from_o thence_o it_o descend_v again_o by_o g_z to_o k_o and_o pass_v in_o the_o horizon_n by_o the_o true_a east_n to_o the_o further_a southward_n than_o it_o ascend_v again_o till_o it_o come_v to_o n_n continual_o return_v from_o the_o high_a to_o the_o low_a &_o from_o the_o low_a to_o the_o high_a whereof_o the_o two_o parallel_n stand_v upon_o the_o diameter_n k_o m_o l_o n_o be_v call_v tropicke_n by_o these_o change_v it_o be_v easy_o gather_v that_o the_o sun_n beside_o the_o diurnal_a revolution_n make_v another_o proper_a to_o itself_o in_o a_o circle_n stand_v upon_o the_o diameter_n k_o l_o draw_fw-mi from_o tropic_n to_o tropic_n by_o a_o the_o centre_n of_o the_o sphere_n by_o reason_n whereof_o this_o circle_n call_v the_o ecliptic_a and_o the_o equinoctial_a divide_v the_o one_o the_o other_o into_o two_o semicircle_n the_o ecliptic_a be_v sometime_o call_v the_o zodiac_n though_o proper_o the_o zodiac_n be_v a_o superficies_n lie_v on_o either_o side_n of_o it_o as_o you_o see_v the_o superficies_n o_o p_o q_o r_o part_v by_o the_o line_n z_o k._n the_o common_a diameter_n of_o the_o equinoctial_a and_o the_o ecliptic_a stand_n in_o a_o perpendicular_a to_o the_o plain_a of_o the_o circle_n b_o c_o d_o e_o
many_o exquisite_a argument_n which_o i_o mean_v not_o to_o prosecute_v but_o hope_v from_o the_o testimony_n of_o sense_n in_o such_o manner_n to_o deduce_v the_o position_n that_o any_o mean_a capacity_n may_v have_v so_o reasonable_a a_o conceit_n of_o they_o that_o with_o probability_n they_o may_v easy_o be_v admit_v i_o will_v refer_v their_o exact_a and_o more_o subtle_a demonstration_n with_o the_o reproof_n of_o such_o as_o impugn_v they_o to_o some_o other_o handle_v or_o to_o some_o other_o place_n therefore_o require_v first_o the_o reader_n not_o to_o cast_v untimely_a doubt_n nor_o hasty_o to_o judge_v of_o any_o part_n by_o itself_o before_o he_o have_v consider_v and_o in_o some_o manner_n understand_v the_o whole_a discourse_n i_o will_v according_a to_o hypocrates_n his_o counsel_n begin_v with_o the_o notable_a and_o easy_a thing_n whosoever_o do_v but_o cast_v up_o his_o eye_n unto_o heaven_n present_o perceive_v that_o it_o compass_v he_o round_o about_o in_o manner_n of_o half_a a_o globe_n or_o a_o hemisphere_n and_o if_o he_o stand_v upon_o some_o high_a place_n or_o be_v at_o sea_n far_o from_o land_n where_o nothing_o can_v be_v see_v but_o water_n and_o the_o sky_n his_o eye_n if_o he_o turn_v himself_o about_o will_v represent_v unto_o he_o at_o the_o low_a bound_n or_o limit_n which_o he_o see_v the_o fashion_n of_o a_o circle_n upon_o who_o plain_a as_o upon_o a_o base_a this_o visible_a hemisphere_n seem_v to_o be_v place_v therefore_o that_o circle_n be_v first_o in_o greek_a and_o be_v now_o common_o in_o english_a call_v the_o horizon_n that_o be_v to_o say_v bound_a or_o limit_v uz._n the_o compass_n of_o your_o sight_n the_o largeness_n of_o this_o circle_n even_o as_o it_o fall_v under_o view_n be_v of_o so_o great_a a_o compass_n as_o you_o need_v not_o restrain_v the_o centre_n thereof_o according_a to_o the_o precise_a mathematical_a definition_n to_o one_o determinate_a exquisite_a indivisible_a and_o very_a point_n or_o prick_v but_o without_o sensible_a error_n as_o your_o eye_n will_v plain_o testify_v any_o one_o at_o pleasure_n may_v be_v take_v in_o the_o place_n where_o you_o stand_v from_o a_o centre_n so_o take_v if_o there_o be_v or_o be_v imagine_v a_o plumbe_v line_n or_o line_n perpendicular_a to_o the_o plain_a of_o the_o horizon_n extend_v unto_o the_o heaven_n the_o place_n which_o there_o it_o touch_v be_v common_o call_v by_o a_o arabian_a name_n the_o zenith_n be_v in_o truth_n the_o pole_n of_o the_o horizon_n and_o the_o line_n itself_o his_o axis_n by_o this_o axis_n and_o any_o line_n cross_v it_o if_o plainness_n be_v every_o way_n extend_v reach_v unto_o heaven_n they_o mark_v out_o their_o circumference_n or_o semicircle_n cut_v one_o another_o in_o the_o zenith_n but_o in_o the_o horizon_n their_o section_n be_v right_a line_n cut_v one_o another_o in_o his_o centre_n those_o circle_n be_v name_v azimute_n and_o be_v imagine_v by_o astronomer_n to_o be_v cut_v by_o other_o circle_n parallel_n to_o the_o horizon_n which_o they_o term_v alinicantars_n and_o circle_v of_o altitude_n because_o the_o portion_n of_o the_o azimute_v which_o be_v between_o the_o horizon_n and_o the_o parallel_n show_v how_o his_o above_o the_o horizon_n that_o point_n of_o the_o parallel_n be_v by_o which_o the_o azimute_v pass_v furthermore_o in_o a_o clear_a night_n behold_v the_o bright_a shine_a star_n you_o shall_v evident_o perceive_v how_o they_o change_v their_o place_n continual_o some_o to_o rise_v and_o show_v themselves_o other_o to_o go_v down_o under_o the_o horizon_n and_o to_o be_v hide_v from_o your_o sight_n only_o if_o you_o place_v yourself_o so_o that_o your_o right_a hand_n be_v towards_o their_o rise_n and_o your_o left_a hand_n towards_o their_o go_v down_o look_v right_a forth_o and_o somewhat_o upward_o you_o shall_v behold_v certain_a star_n which_o be_v all_o time_n of_o the_o night_n to_o be_v see_v and_o never_o charles_n wayne_n pole_n star_n little_o bear_v go_v down_o among_o some_o of_o which_o place_v after_o this_o fashion_n there_o be_v one_o common_o call_v the_o pole_n star_n which_o be_v the_o last_o in_o the_o tail_n of_o the_o constellation_n call_v the_o little_a bear_n lie_v in_o manner_n direct_o as_o it_o be_v in_o a_o right_a line_n with_o those_o two_o in_o the_o hindermost_a wheel_n of_o charles_n his_o wain_n this_o star_n seem_v little_a or_o nothing_o to_o remove_v out_o of_o his_o place_n and_o indeed_o not_o far_o from_o it_o there_o be_v a_o point_n or_o prick_v which_o remain_v in_o one_o and_o the_o same_o place_n always_o immovable_a the_o azimute_v pass_v by_o the_o orison_n axis_n and_o a_o right_a line_n draw_v from_o this_o immovable_a point_n or_o the_o pole_n star_n be_v proper_o call_v the_o meridian_n circle_n the_o common_a section_n of_o it_o and_o the_o horizon_n be_v a_o right_a line_n be_v the_o meridian_n line_n or_o the_o line_n of_o north_n and_o south_n the_o right_a line_n which_o cross_v this_o meridian_n line_n at_o right_a angle_n in_o the_o centre_n of_o the_o horizon_n be_v call_v the_o line_n of_o true_a east_n and_o true_a west_n or_o simple_o the_o line_n of_o east_n and_o west_n which_o point_v the_o end_n thereof_o extend_v direct_o fall_v upon_o the_o arimute_v stand_v upon_o this_o line_n joannes_n de_fw-fr roias_n &_o other_o special_o such_o as_o write_v of_o dyall_v as_o it_o be_v for_o dignity_n and_o pre-eminence_n do_v call_v the_o vertical_a circle_n which_o name_n be_v common_a to_o all_o azimute_n because_o they_o pass_v by_o the_o zenith_n in_o latin_a call_v vertex_fw-la or_o punctum_fw-la eregione_fw-la verticis_fw-la for_o a_o distinction_n gemma_fw-la frosius_n have_v name_v it_o the_o circle_n of_o the_o east_n the_o other_o azimute_n have_v no_o proper_a name_n but_o be_v measure_v or_o determine_v in_o the_o orison_n circumference_n that_o and_o so_o likewise_o all_o other_o circle_n astronomer_n do_v imagine_v to_o be_v divide_v into_o 360._o equal_a part_n which_o they_o name_v degree_n that_o be_v to_o say_v every_o quarter_n or_o quadrant_a into_o 90._o degree_n every_o degree_n they_o further_o divide_v into_o 60._o minute_n every_o minute_n into_o 60._o second_n every_o second_o into_o 60._o three_o and_o so_o continue_v sometime_o unto_o ten_o and_o may_v go_v further_o if_o they_o will_n by_o these_o degree_n minute_n etc._n etc._n which_o be_v between_o that_o point_n where_o any_o azimute_v cut_v the_o horizon_n and_o the_o meridian_n line_n or_o the_o line_n of_o east_n and_o west_n the_o azimute_v be_v determine_v assign_v or_o say_v to_o be_v give_v upon_o the_o point_n where_o the_o vertical_a circle_n cut_v the_o horizon_n which_o point_n be_v the_o true_a pole_n of_o the_o meridian_n and_o the_o precise_a east_n and_o west_n if_o by_o often_o and_o diligent_a view_v you_o shall_v see_v two_o star_n the_o one_o in_o the_o east_n and_o the_o other_o at_o the_o same_o time_n right_a against_o it_o in_o the_o west_n in_o winter_n time_n even_o in_o one_o night_n you_o may_v behold_v that_o which_o be_v in_o the_o east_n first_o ascend_v and_o then_o again_o descend_v at_o length_n to_o come_v into_o the_o west_n and_o that_o which_o be_v in_o the_o west_n be_v till_o that_o time_n hide_v from_o your_o sight_n then_o to_o appear_v again_o rise_v in_o the_o east_n all_o this_o while_n continual_o the_o like_a shape_n of_o a_o hemisphere_n be_v still_o represent_v to_o your_o eye_n without_o any_o change_n or_o alteration_n whereby_o you_o may_v gather_v the_o heaven_n to_o be_v a_o perfect_a globe_n or_o sphere_n have_v that_o part_n under_o the_o horizon_n equal_a and_o like_a to_o that_o which_o you_o see_v above_o it_o and_o that_o the_o place_n where_o you_o stand_v be_v the_o very_a centre_n thereof_o a_o line_n draw_v from_o the_o pole_n star_n or_o rather_o from_o the_o point_n immovable_a before_o mention_v call_v the_o arctic_a or_o north_n pole_n a_o line_n i_o say_v draw_v or_o imagine_v to_o be_v draw_v from_o that_o point_n to_o the_o place_n of_o your_o stand_n be_v call_v the_o aris_n of_o the_o world_n and_o extend_v to_o the_o other_o side_n of_o the_o celestial_a sphere_n which_o be_v under_o we_o fall_v there_o upon_o the_o south_n or_o antarcticke_a pole_n which_o in_o these_o our_o country_n never_o appear_v these_o thing_n be_v but_o a_o little_a héedy_o consider_v be_v so_o manifest_a and_o apparent_a that_o neither_o example_n nor_o figure_n be_v great_o requisite_a for_o the_o perfect_a understanding_n of_o they_o yet_o in_o this_o beginning_n to_o remove_v all_o difficulty_n and_o to_o make_v every_o thing_n as_o plain_a as_o may_v be_v do_v thus_o much_o in_o some_o plain_a ground_n or_o rather_o upon_o a_o post_n or_o stone_n or_o some_o such_o like_a thing_n make_v
the_o point_n k_o and_o l_o be_v the_o solstitial_a point_n the_o circle_n b_o c_o d_o e_o be_v the_o solstitial_a colour_n the_o circle_n stand_v upon_o ay_o h_n and_o pass_v by_o the_o perpendicular_a diameter_n or_o the_o equinoctial_a section_n be_v the_o equinoctial_a colour_n the_o circumference_n k_n n_n be_v the_o distance_n of_o the_o tropic_n the_o one_o half_a thereof_o g_z k_o or_o g_o n_n be_v the_o obliquity_n of_o the_o zodiac_n or_o the_o sun_n great_a declination_n for_o it_o grow_v less_o &_o less_o as_o it_o come_v near_o the_o equinoctial_a section_n where_o it_o have_v no_o declination_n at_o all_o it_o never_o decline_v from_o the_o ecliptic_a or_o circle_n stand_v upon_o k_o z_o but_o make_v his_o motion_n in_o it_o his_o place_n be_v name_v of_o the_o point_n wherein_o it_o be_v other_o star_n or_o point_n without_o the_o ecliptic_a as_o for_o example_n s_n have_v their_o place_n determine_v by_o a_o great_a circle_n b_o c_o d_o e_o draw_fw-mi from_o x_o the_o pole_n of_o the_o zodiac_n by_o sâ—o_n â—o_z k_o a_o point_n in_o the_o ecliptic_a circumference_n the_o portion_n of_o the_o ecliptic_a between_o the_o vernal_a section_n and_o k_o or_o the_o point_n k_o be_v the_o longitude_n of_o s_n and_o the_o circumference_n s_o k_n be_v his_o latitude_n in_o like_a manner_n if_o by_o any_o star_n or_o point_n y_o and_o the_o pole_n of_o the_o world_n h_n i_o there_o be_v draw_v a_o great_a circle_n b_o c_o d_o e_o cut_v the_o equinoctial_a in_o g_z the_o portion_n of_o the_o equinoctial_a between_o the_o vernal_a section_n and_o g_o be_v the_o right_a ascension_n of_o you_o and_o the_o circumference_n g_o y_fw-fr be_v his_o declination_n now_o if_o g_z the_o section_n of_o the_o meridian_n and_o the_o equinoctial_a be_v the_o zenith_n of_o any_o place_n the_o horizon_n must_v stand_v on_o i_o h_n and_o pass_v by_o the_o pole_n of_o the_o world_n which_o situation_n be_v call_v the_o right_a sphere_n and_o the_o horizon_n the_o right_a horizon_n wherein_o by_o the_o diurnal_a revolution_n twice_o in_o 24._o hour_n the_o circle_n b_o c_o d_o e_o must_v join_v close_o with_o it_o but_o if_o g_z the_o section_n of_o the_o equinoctial_a and_o the_o meridian_n decline_v from_o b_o the_o zenith_n which_o situation_n be_v call_v the_o oblique_a sphere_n and_o the_o horizon_n then_o stand_v on_o e_z c_z be_v a_o oblique_a horizon_n by_o the_o diurnal_a motion_n make_v upon_o the_o pole_n h_o i_o the_o circle_n b_o c_o d_o e_o can_v never_o agréene_a or_o match_n even_o with_o the_o horizon_n therefore_o of_o force_n some_o other_o point_n of_o the_o equinoctial_a and_o not_o g_z must_v be_v in_o the_o horizon_n with_o you_o the_o circumference_n of_o the_o equinoctial_a between_o that_o point_n in_o the_o horizon_n and_o the_o vernal_a section_n be_v the_o oblique_a ascension_n of_o you_o but_o the_o portion_n that_o lie_v between_o that_o point_n and_o g_o be_v the_o difference_n ascensionall_n that_o point_n of_o the_o zodiac_n where_o it_o be_v cut_v off_o the_o meridian_n be_v call_v medium_fw-la coeli_fw-la mid_a heaven_n culmen_fw-la and_o cor_fw-la coeli_fw-la above_o the_o horizon_n &_o imum_fw-la coeli_fw-la under_o the_o horizon_n the_o lesser_a angle_n make_v by_o that_o section_n be_v call_v the_o meridian_n angle_n the_o point_n of_o the_o ecliptic_a that_o be_v in_o the_o east_n side_n of_o the_o horizon_n be_v call_v the_o ascendent_n and_o the_o horoscope_n the_o section_n there_o make_v the_o angle_n of_o which_o the_o lesser_a be_v call_v the_o horizontall_a angle_n the_o quantity_n thereof_o be_v equal_a to_o the_o nonagesimus_fw-la gradus_fw-la of_o the_o ecliptic_a which_o be_v peculiar_o give_v to_o that_o point_n of_o it_o which_o be_v just_a 90._o degree_n from_o the_o ascendent_n there_o be_v moreover_o other_o great_a circle_n to_o be_v consider_v which_o be_v call_v circle_n of_o position_n or_o circle_n of_o station_n six_o of_o they_o divide_v the_o heaven_n in_o twelve_o portion_n which_o be_v call_v house_n or_o station_n though_o many_o time_n those_o name_n be_v restrain_v only_o to_o such_o part_n of_o the_o zodiac_n as_o be_v intercept_v by_o those_o circle_n though_o the_o horizon_n be_v always_o take_v for_o one_o and_o the_o beginning_n of_o the_o first_o house_n yet_o be_v the_o rest_n by_o diverse_a diverse_o draw_v some_o will_v have_v they_o all_o to_o have_v the_o meridian_n line_n for_o their_o common_a diameter_n and_o yet_o agree_v in_o this_o make_v difference_n in_o place_v they_o campanus_n and_o gazulus_fw-la divide_v the_o vertical_a circle_n into_o twelve_o equal_a part_n and_o by_o every_o two_o opposite_a section_n draw_v a_o circle_n of_o position_n regiomontanus_n divide_v the_o equinoctial_a into_o twelve_o equal_a part_n and_o will_v have_v every_o circle_n of_o position_n pass_v by_o two_o of_o those_o opposite_a section_n both_o these_o way_n keep_v the_o horizon_n and_o the_o meridian_n for_o circle_n of_o position_n other_o divide_v the_o zodiac_n into_o twelve_o equal_a part_n begin_v at_o the_o ascendent_n and_o two_o of_o those_o opposite_a section_n draw_v from_o the_o pole_n of_o the_o zodiac_n their_o circle_n of_o position_n these_o keep_v the_o same_o ascendent_n that_o the_o former_a do_v but_o must_v differ_v many_o time_n in_o the_o ten_o house_n or_o the_o cardo_n medij_fw-la coeli_fw-la though_o gemma_fw-la write_v that_o all_o agree_v about_o the_o foru_a cardines_fw-la that_o be_v the_o horoscope_n seven_o house_n culmen_fw-la and_o imum_fw-la coeli_fw-la for_o they_o can_v have_v always_o the_o meridian_n &_o the_o horizon_n for_o circle_n of_o position_n other_o draw_v these_o circle_n from_o the_o pole_n of_o the_o world_n and_o that_o diverse_o but_o the_o three_o former_a way_n be_v in_o great_a estimation_n a_o circle_n of_o position_n differ_v from_o a_o angle_n of_o position_n which_o after_o prolomey_n be_v a_o angle_n at_o the_o zenith_n subtend_v of_o that_o portion_n of_o the_o horizon_n which_o lie_v between_o the_o meridian_n and_o the_o azimute_v pass_v by_o the_o zenith_n of_o the_o other_o place_n unto_o which_o the_o position_n belong_v gemma_fw-la frisius_n make_v it_o a_o right_n line_v angle_n in_o the_o centre_n of_o the_o horizon_n subtend_v of_o the_o same_o circumference_n by_o it_o topographicall_a description_n be_v make_v wherein_o sometime_o the_o distance_n of_o two_o place_n be_v measure_v by_o a_o right_a line_n lie_v between_o they_o but_o in_o a_o spherical_a superficies_n by_o the_o portion_n of_o a_o great_a circle_n because_o that_o be_v the_o short_a that_o can_v be_v draw_v in_o it_o these_o thing_n may_v be_v easy_o conceive_v without_o linearie_a explication_n if_o the_o former_a matter_n be_v well_o understand_v therefore_o as_o it_o be_v beside_o the_o principal_a purpose_n set_v down_o how_o by_o supputation_n you_o may_v ready_o guess_v somewhat_o near_o the_o sun_n place_n be_v a_o thing_n for_o many_o purpose_n to_o be_v have_v in_o a_o readiness_n i_o will_v end_v this_o first_o section_n the_o thing_n be_v take_v out_o of_o clavius_n but_o fit_v to_o our_o common_a or_o the_o julian_n year_n parergon_fw-la primum_fw-la what_o month_n and_o what_o day_n of_o it_o the_o sun_n enter_v every_o sign_n of_o the_o zodiac_n first_o tell_v the_o month_n upon_o your_o finger_n seek_v innuarie_n on_o your_o thumb_n february_n on_o your_o forefinger_n and_o so_o the_o other_o in_o order_n till_o you_o come_v to_o your_o month_n which_o mark_v on_o which_o finger_n it_o fall_v in_o like_a manner_n tell_v the_o sign_n begin_v with_o aquarius_n on_o your_o thumb_n pisces_fw-la on_o your_o forefinger_n and_o so_o the_o rest_n in_o order_n till_o you_o come_v to_o the_o finger_n on_o which_o your_o month_n fall_v the_o sign_n which_o fall_v on_o that_o finger_n the_o sun_n enter_v that_o month_n then_o learn_v these_o two_o verse_n by_o heart_n inclyta_fw-la laus_fw-la justis_fw-la impenditur_fw-la haeresis_fw-la horret_fw-la garrula_fw-la grex_n gratus_fw-la faustos_fw-la gratatur_fw-la honour_n in_o like_a manner_n set_v inclyta_fw-la on_o your_o thumb_n and_o word_n by_o word_n in_o order_n till_o you_o come_v to_o the_o finger_n on_o which_o your_o month_n fall_v then_o tell_v from_o a_o in_o the_o cross_a row_n till_o you_o come_v to_o the_o first_o letter_n of_o your_o word_n take_v that_o number_n and_o subtract_v it_o from_o 20._o the_o residue_n be_v the_o day_n of_o the_o month_n when_o the_o sun_n enter_v the_o sign_n for_o example_n i_o will_v know_v what_o sign_n the_o sun_n enter_v in_o october_n and_o what_o day_n it_o enter_v tell_v from_o januarie_n upon_o my_o finger_n the_o month_n in_o order_n at_o the_o second_o go_v over_o i_o find_v october_n on_o my_o little_a finger_n then_o take_v the_o sign_n and_o tell_v from_o aquarius_n at_o the_o second_o go_v over_o
it_o exceed_v the_o latitude_n draw_v the_o line_n h_o i._n again_o let_v either_o of_o the_o circumference_n e_o f_o c_o g_o be_v equal_a to_o the_o declination_n give_v a_o ruler_n lay_v upon_o f_o and_o g_o will_n cut_v h_n i_o in_o k_o again_o a_o ruler_n lay_v on_o a_o and_o l_o will_v cut_v it_o in_o m_o with_o your_o compass_n take_v the_o distance_n m_o k_n &_o in_o the_o semicircle_n 6_o n_z a_o which_o be_v the_o synicall_a arch_n for_o the_o line_n h_n i_o from_o 6_o apply_v at_o n_o a_o distance_n equal_a to_o m_o k_n a_o ruler_n lay_v upon_o the_o points_z a_o n_z will_v cut_v the_o limb_n in_o o_o a_o distance_n equal_a to_o e_z o_o apply_v in_o the_o quadrant_a c_o d_o to_o which_o i_o suppose_v the_o declination_n belong_v from_o c_o the_o equinoctial_a section_n unto_o p_o show_v in_o the_o zodiac_n from_o e_z by_z b_o to_o p_o the_o place_n of_o the_o star_n the_o 25._o conclusion_n the_o declination_n of_o any_o star_n be_v give_v with_o his_o latitude_n which_o never_o alter_v to_o find_v the_o right_a ascension_n thereof_o as_o before_o let_v l_o be_v the_o pole_n of_o the_o zodiac_n b_o the_o pole_n of_o the_o world_n l_o i_o l_o h_n the_o compliment_n of_o the_o star_n latitude_n e_o f_o cg_n equal_a to_o the_o declination_n draw_v the_o line_n h_n i_o and_o lay_v a_o ruler_n on_o f_o and_o g_o which_o will_v cut_v a_o b_o in_o q_o and_o h_n i_o in_o k_o let_v the_o semicircle_n a_o r_o s_o be_v the_o cynical_a arch_n for_o the_o distance_n f_o g_o and_o from_o s_n in_o the_o semicircle_n a_o r_o s_o apply_v at_o r_n a_o distance_n equal_a to_o the_o distance_n q_o k_n a_o ruler_n lay_v on_o r_n &_o a_o will_v cut_v the_o limb_n in_o t_o the_o distance_n c_o t_o in_o the_o quadrant_a to_o which_o the_o declination_n belong_v apply_v from_o the_o equinoctial_a section_n show_v in_o the_o equinoctial_a the_o right_a ascension_n seek_v for_o the_o 26._o conclusion_n the_o longitude_n and_o latitude_n of_o any_o star_n be_v give_v to_o find_v the_o declination_n and_o right_a ascension_n thereof_o let_v the_o pole_n &_o latitude_n be_v as_o before_o &_o let_v e_o o_fw-fr be_v equal_a to_o the_o distance_n of_o the_o star_n place_n from_o the_o near_a equinoctial_a section_n a_o ruler_n lay_v on_o a_o and_o o_o will_v cut_v the_o circumference_n 6_o n_z a_o which_o be_v the_o synical_a arch_n to_o the_o line_n h_n i_o in_o the_o point_n n_n again_o a_o ruler_n lay_v on_o a_o &_o i_o will_v cut_v h_n i_o in_o m_o take_v the_o distance_n 6_o n_z &_o set_v one_o foot_n in_o m_n with_o the_o other_o towards_o i_o if_o the_o place_n be_v near_o the_o pole_n b_o or_o towards_o h_n if_o near_a d_o but_o here_o suppose_v it_o near_a b_o in_o m_o i_o mark_v k_o upon_o a_o and_o k_n lay_v a_o ruler_n it_o will_v cut_v the_o limb_n in_o five_o make_v the_o circumference_n b_o w_n equal_a to_o b_o v_n and_o draw_v the_o line_n a_o w_n and_o in_o it_o make_v a_o x_o equal_a to_o the_o distance_n a_o k_o a_o ruler_n lay_v on_o x_o and_o k_o will_v cut_v the_o limb_n in_o f_o and_o g_o and_o the_o line_n a_o b_o in_o q_n either_o of_o the_o circumference_n e_o f_o c_o g_o be_v equal_a to_o the_o declination_n now_o in_o the_o semicircle_n s_o r_o a_o which_o be_v the_o cynical_a arch_n for_o the_o distance_n f_o g_o apply_v a_o distance_n equal_a to_o queen_n k_o from_o s_n to_o r_n upon_o a_o and_z r_z lay_v a_o ruler_n it_o will_v cut_v the_o limb_n in_o t_o the_o circumference_n c_o t_o be_v the_o distance_n of_o the_o right_a ascension_n from_o the_o equinoctial_a section_n take_v in_o the_o quadrant_a to_o which_o the_o longitude_n belong_v the_o 27._o conclusion_n the_o declination_n and_o right_a ascension_n of_o any_o star_n be_v give_v to_o find_v the_o longitude_n and_o latitude_n thereof_o this_o differ_v not_o in_o work_v from_o the_o former_a only_o change_v the_o name_n let_v l_o be_v the_o pole_n of_o the_o world_n b_o the_o pole_n of_o the_o zodiac_n h_n i_o join_v the_o compliment_n of_o the_o declination_n give_v e_o o_n be_v equal_a to_o the_o distance_n of_o the_o right_a ascension_n from_o the_o near_a equinoctial_a section_n 6_o n_z a_o the_o synicall_a arch_n for_o h_n i_o be_v cut_v in_o n_n by_o a_o ruler_n lay_v on_o o_o and_o a_o make_v m_o k_n equal_a to_o 6_o n_n upon_o a_o and_o k_n a_o ruler_n lay_v cut_v the_o limb_n in_o five_o the_o circumference_n b_o v_n b_o w_n be_v equal_a and_o the_o live_v a_o with_o draw_v a_o x_o must_v be_v make_v equal_a to_o a_o k_o a_o ruler_n lie_v on_o x_o and_o k_o cut_v the_o limb_n in_o f_o and_o g_o so_o either_o of_o the_o circumference_n e_o f_o c_o g_o be_v equal_a to_o the_o latitude_n seek_v for_o in_o the_o synicall_a arch_n of_o f_o g_o which_o be_v a_o r_o s_o a_o distance_n equal_a to_o m_o k_n apply_v from_o s_n to_o r_n and_o then_o a_o ruler_n lay_v on_o a_o and_o r_n cut_v the_o limb_n in_o t_o so_o be_v c_o t_o the_o distance_n of_o the_o longitude_n from_o the_o near_a equinoctial_a section_n take_v in_o the_o quadrant_a to_o which_o the_o right_a ascension_n belong_v the_o 28._o conclusion_n the_o longitude_n and_o latitude_n of_o any_o two_o star_n or_o any_o two_o place_n in_o the_o earth_n be_v give_v to_o find_v the_o distance_n of_o the_o one_o from_o the_o other_o if_o they_o be_v both_o on_o one_o side_n of_o the_o equinoctial_a or_o of_o the_o ecliptic_a what_o case_n soever_o fall_v out_o you_o shall_v take_v their_o latitude_n as_o height_n above_o the_o horizon_n and_o the_o difference_n of_o their_o longitude_n as_o the_o distance_n of_o their_o azimute_n by_o which_o work_v after_o the_o 5._o conclusion_n you_o shall_v find_v their_o distance_n but_o if_o one_o be_v on_o the_o one_o side_n of_o the_o equinoctial_a and_o the_o other_o on_o the_o other_o or_o of_o the_o ecliptic_a then_o if_o they_o differ_v not_o in_o longitude_n from_o e_z towards_o b_o take_v one_o latitude_n e_o l_o and_o make_v l_o k_n equal_a to_o the_o other_o latitude_n the_o circumference_n e_o k_o in_o the_o equinoctial_a show_v their_o distance_n if_o they_o differ_v in_o longitude_n a_o whole_a semicircle_n from_o e_z towards_z d_o take_v e_o m_o one_o latitude_n and_o lay_v a_o ruler_n on_o m_n and_o a_o it_o will_v cut_v the_o limb_n on_o the_o other_o side_n in_o 6_o take_v 61_o the_o other_o latitude_n and_o from_o e_z to_z 1_o in_o the_o equinoctial_a you_o shall_v find_v the_o distance_n but_o let_v the_o difference_n of_o the_o longitude_n be_v e_o h_n and_o draw_v the_o line_n a_o h_n let_v the_o circumference_n f_o e_z be_v equal_a to_o the_o great_a latitude_n h_n i_o to_o the_o less_o then_o making_z e_z g_z equal_a to_o e_o f_o and_o h_n k_o equal_a to_o h_n i_o upon_o f_o and_o g_o a_o ruler_n lay_v will_v cut_v a_o e_o in_o n_n likewise_o lay_v on_o i_o k_o it_o will_v cut_v h_n a_o in_o p._n in_o the_o line_n a_o b_o take_v a_o qui_fw-fr equal_a to_o the_o distance_n n_o p_o and_o in_o a_o c_o make_v a_o s_n equal_a to_o f_o n_n and_z s_o w_n equal_a to_o i_o p_o in_o the_o quadrant_a c_o d_o from_z c_z unto_o 3_o apply_v a_o distance_n equal_a to_o q_o w_n the_o circumference_n c_o 3_o be_v the_o distance_n seek_v for_o the_o 29._o conclusion_n the_o latitude_n and_o distance_n of_o any_o two_o star_n or_o any_o two_o place_n in_o the_o earth_n be_v give_v to_o find_v the_o difference_n of_o their_o longitude_n let_v the_o place_n first_o be_v on_o the_o one_o side_n of_o the_o ecliptic_n or_o the_o equinoctial_a and_o let_v the_o distance_n give_v be_v c_z 4_o let_v the_o great_a latitude_n be_v e_o f_o the_o lesser_a e_o l_o make_v the_o circumference_n e_o g_o equal_a to_o of_o and_o e_o m_o equal_a to_z e_o l_o then_o lay_v a_o ruler_n on_o f_o and_o g_o it_o will_v cut_v a_o e_o in_o n_n and_o lay_v upon_o l_o and_o m_o it_o will_v cut_v it_o in_o o_o make_v a_o s_n equal_a to_o n_n f_o and_o s_o v_o equal_a to_o l_o o_fw-fr then_o open_v your_o compass_n to_o the_o distance_n c_o 4_o set_v one_o foot_n in_o five_o and_o with_o the_o other_o mark_n q_n in_o the_o line_n a_o b_o take_v the_o distance_n a_o qui_fw-fr set_v one_o foot_n in_o n_n and_o with_o the_o other_o describe_v a_o arch_n at_o p_o then_o open_v your_o compass_n to_o the_o distance_n a_o o_o and_o keep_v one_o foot_n in_o a_o with_o the_o other_o across_o the_o arch_n at_o p_o a_o ruler_n lay_v on_o a_o