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cause_n celestial_a heaven_n zone_n 36 3 13.6746 5 false
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ID Title Author Corrected Date of Publication (TCP Date of Publication) STC Words Pages
A29742 An account of the rotula arithmetica invented by Mr. George Brown. Brown, George, 1650-1730.; Dary, Michael. Dary's Miscellanies.; Cooke, Francis, fl. 1669. Principles of geometrie.; Georgius, Henisschius. Tables of the astronomical institutions. 1700 (1700) Wing B5019; ESTC R4627 82,687 247

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breadth_n and_o in_o colour_n the_o cause_n be_v diverse_a and_o those_o either_o fabulous_a or_o natural_a the_o fabulous_a cause_n be_v in_o number_n 4._o the_o first_o be_v take_v from_o the_o scorch_n of_o the_o ☉_o as_o if_o the_o ☉_o have_v sometime_o make_v his_o motion_n there_o and_o by_o his_o scorch_n have_v cause_v that_o place_n to_o be_v white_a the_o second_o be_v draw_v from_o the_o milk_n of_o juno_n that_o run_v plentiful_o out_o of_o her_o pap_n paint_v this_o circle_n of_o that_o colour_n the_o three_o be_v fetch_v from_o the_o seat_n and_o habitation_n of_o strong_a and_o valiant_a man_n who_o the_o poet_n have_v place_v in_o this_o circle_n the_o four_o be_v derive_v out_o of_o the_o way_n of_o the_o god_n as_o if_o they_o pass_v thereby_o unto_o the_o palace_n of_o jupiter_n the_o natural_a cause_n allege_v although_o they_o be_v many_o yet_o be_v principal_o but_o 3._o the_o first_o by_o theophrastus_n who_o say_v that_o it_o be_v that_o join_v together_o 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term_v it_o from_o the_o right_n toward_o the_o left_a hand_n but_o the_o proper_a revolution_n be_v from_o the_o west_n unto_o the_o east_n or_o from_o the_o left_a towards_o the_o right_a hand_n the_o three_o difference_n be_v in_o consideration_n of_o the_o swiftness_n for_o the_o diurnal_a motion_n fulfil_v his_o course_n within_o the_o space_n of_o 24._o common_a hour_n but_o the_o proper_a motion_n in_o diverse_a distance_n of_o time_n according_a to_o the_o largeness_n of_o the_o orb_n namely_o the_o orb_n of_o the_o fix_a star_n perform_v his_o circle_n in_o 36000._o year_n of_o ♄_o in_o 30_o of_o ♃_o in_o 12_o of_o ♂_o in_o 2._o year_n of_o the_o ☉_o in_o 365._o day_n and_o about_o 6._o hour_n of_o ♀_o in_o 384._o day_n after_o pliny_n the_o orb_n of_o ☿_o in_o as_o many_o day_n as_o the_o ☉_o and_o the_o orb_n of_o the_o ☽_o in_o 27._o day_n &_o 8._o hour_n the_o circular_a form_n and_o circular_a motion_n of_o the_o heaven_n chap._n 11._o the_o heaven_n be_v circular_a in_o motion_n and_o in_o figure_n the_o circular_a motion_n of_o the_o heaven_n be_v prove_v as_o well_o by_o 2._o experiment_n as_o by_o 2._o argument_n the_o one_o experiment_n be_v take_v from_o the_o star_n of_o the_o 8._o orb_n which_o both_o in_o their_o rise_n &_o set_v do_v always_o keep_v one_o &_o the_o same_o habitude_n both_o in_o regard_n of_o the_o earth_n and_o one_o to_o another_o which_o thing_n can_v agree_v with_o none_o other_o than_o a_o circular_a motion_n about_o the_o centre_n the_o other_o experiment_n be_v also_o take_v from_o the_o star_n of_o the_o 8._o orb_n always_o appear_v and_o retain_v in_o diverse_a place_n the_o same_o distance_n from_o the_o pole_n and_o onestom_n another_o which_o also_o agree_v with_o the_o circular_a motion_n only_o the_o first_o
on_o the_o one_o side_n long_o from_z whence_o be_v derive_v figure_n long_o and_o broad_a as_o pillar_n or_o cylinder_n or_o else_o they_o be_v of_o other_o sort_n which_o be_v infinite_a from_o whence_o diverse_a form_n and_o kind_n of_o body_n be_v draw_v the_o regular_fw-la body_n contain_v under_o surface_n fold_v one_o towards_o another_o be_v only_o these_o 5._o the_o tetraedrons_n the_o hexaedrons_n the_o octaedrons_n the_o dodecaedrons_n and_o the_o lcosaedron_n irregulare_fw-la body_n be_v such_o as_o inequal_a surface_n do_v limit_n and_o describe_v the_o which_o surface_n be_v either_o turn_v round_o or_o fold_a one_o towards_o another_o the_o surface_v turn_v round_o and_o make_v irregulare_fw-la bodies_z be_v either_o the_o section_n of_o circle_n or_o else_o they_o be_v inequal_a right_n line_v figure_n the_o section_n of_o circle_n be_v either_o great_a than_o a_o semicircle_n whereof_o the_o lenticulare_a body_n be_v make_v or_o else_o they_o be_v less_o than_o a_o semicircle_n and_o thereby_o be_v the_o onalle_n make_v the_o inequal_a right_n line_v figure_n by_o who_o conversion_n the_o irregulare_fw-la body_n be_v make_v may_v be_v of_o what_o sort_n soever_o whereby_o diverse_a kind_n of_o vessel_n be_v frame_v either_o want_v or_o exceed_v the_o regular_fw-la form_n the_o irregulare_fw-la body_n màde_v of_o inequal_a surface_n fold_v one_o towards_o another_o may_v differ_v infinite_o of_o the_o name_n and_o definition_n of_o the_o sphere_n chap._n 6._o in_o as_o much_o as_o we_o make_v often_o mention_v of_o the_o sphere_n and_o thereafter_o do_v entitle_v this_o present_a treatise_n the_o doctrine_n of_o the_o sphere_n it_o shall_v not_o be_v amiss_o to_o declare_v the_o name_n and_o the_o definition_n thereof_o the_o name_n be_v use_v in_o diverse_a signification_n 1._o it_o signify_v sometime_o any_o solid_a regular_fw-la body_n limit_v with_o one_o surface_n only_o 2._o sometime_o it_o signify_v a_o instrument_n that_o do_v instisie_n the_o apparence_n of_o heaven_n and_o contain_v the_o celestial_a circle_n and_o be_v otherwise_o term_v a_o ring_n or_o material_a sphere_n 3._o sometime_o it_o signify_v the_o whole_a world_n whereunto_o all_o the_o condition_n of_o the_o sphere_n may_v be_v apply_v for_o it_o be_v a_o solid_a body_n wherein_o nature_n abhor_v that_o any_o emptiness_n shall_v be_v giu●_fw-la it_o have_v a_o spherical_a form_n run_v daily_o about_o his_o own_o axis_n without_o intermission_n it_o have_v a_o point_n place_v in_o the_o midst_n thereof_o namely_o the_o earth_n the_o definition_n thereof_o as_o it_o signify_v any_o body_n be_v by_o io._n desacro_fw-la baseo_fw-la set_v down_o two_o way_n the_o one_o after_o encl._n 11._o elem._n the_o other_o out_o of_o theodosius_n the_o definition_n thereof_o take_v out_o of_o euclid_n contain_v the_o geometrical_a description_n of_o the_o sphere_n for_o the_o sphere_n be_v describe_v by_o the_o fix_a and_o unmoved_a diameter_n and_o by_o the_o a●ke_n of_o the_o semicircle_n which_o must_v be_v full_o bring_v about_o the_o definition_n of_o a_o sphere_n according_a to_o theodosius_n determine_v first_o the_o orbiculate_a form_n every_o part_n whereof_o be_v equal_o distant_a from_o the_o centre_n second_o the_o principal_a part_n as_o the_o convexe_n surface_n which_o be_v but_o one_o and_o the_o centre_n that_o be_v the_o point_n in_o the_o midst_n equidistant_a from_o every_o part_n of_o the_o surface_n and_o the_o axis_n about_o which_o the_o sphere_n be_v turn_v and_o which_o be_v limit_v by_o the_o 2_o pole_n viz._n the_o north_n pole_n or_o pole_n arctic_a and_o the_o south_n pole_n or_o pole_n antarcticke_a and_o three_o the_o solidity_n for_o it_o be_v a_o complete_a body_n have_v all_o the_o dimension_n the_o division_n of_o the_o celestial_a sphere_n chap._n 7._o the_o celestial_a sphere_n according_a to_o io._n de_fw-fr sacro_fw-la bosco_fw-la admit_v a_o double_a division_n according_a to_o substance_n and_o according_a to_o accident_n the_o celestial_a sphere_n consider_v according_a to_o the_o substance_n be_v divide_v into_o several_a orb_n in_o the_o which_o we_o be_v to_o note_v the_o number_n and_o the_o cause_n the_o number_n be_v diverse_o set_v down_o for_o the_o ancients_n content_v themselves_o with_o 8._o orb_n only_o do_v distinguish_v they_o into_o the_o orb_n of_o the_o 7._o planet_n viz_o of_o ♄_o ♃_o ♂_o ☉_o ♀_o ☿_o and_o ☽_o and_o the_o firmament_n of_o the_o fix_a star_n and_o the_o late_a astronomer_n unto_o the_o time_n of_o alphonsus_n into_o 9_o orb_n but_o the_o modern_a among_o who_o purbachius_n be_v the_o first_o add_v the_o ten_o the_o cause_n be_v consider_v either_o in_o the_o diversity_n of_o their_o number_n note_v both_o by_o the_o former_a and_o late_a astronomer_n or_o in_o their_o order_n the_o ancient_a astronomer_n note_v their_o diverse_a number_n either_o by_o the_o brightness_n of_o the_o star_n reckon_n so_o many_o orb_n as_o they_o perceive_v to_o contain_v any_o star_n or_o by_o the_o peculiar_a motion_n of_o each_o several_a orb_n reckon_n so_o many_o orb_n as_o they_o find_v simple_a motion_n belong_v thereunto_o the_o late_a astronomer_n for_o instruction_n and_o the_o better_a reconing_n sake_n add_v the_o nine_o and_o the_o ten_o as_o circle_n necessary_a for_o the_o understanding_n of_o the_o motion_n of_o the_o 8._o sphere_n unknown_a unto_o the_o ancient_a astronomer_n the_o order_n be_v prove_v 1._o by_o the_o slow_a motion_n of_o the_o high_a and_o the_o swift_a motion_n of_o the_o low_a orb_n 2._o by_o the_o occultation_n or_o hide_v of_o the_o high_a star_n by_o the_o low_a 3._o by_o the_o diversity_n of_o apect_n either_o great_a or_o little_a or_o insensible_a the_o celestial_a sphere_n consider_v according_a unto_o accident_n that_o be_v according_a to_o the_o situation_n of_o the_o heaven_n or_o the_o course_n of_o the_o star_n be_v distinguish_v into_o a_o right_n or_o a_o oblique_a sphere_n the_o right_a sphere_n belong_v unto_o those_o that_o dwell_v under_o the_o equinoctial_a who_o by_o reason_n that_o the_o pole_n of_o the_o world_n about_o the_o which_o the_o star_n be_v carry_v by_o the_o first_o movable_a have_v none_o elevation_n as_o also_o for_o that_o the_o horizon_n cut_v all_o the_o parallel_n under_o which_o the_o star_n do_v go_v at_o right_a angle_n perceive_v no_o reflection_n in_o the_o diurnal_a motion_n of_o the_o star_n the_o sphere_n be_v say_v to_o be_v oblique_a wherein_o the_o o_o and_o the_o rest_n of_o the_o star_n be_v carry_v from_o the_o east_n into_o the_o west_n by_o a_o oblique_a motion_n and_o it_o be_v septentrional_a unto_o those_o that_o have_v the_o north_n pole_n elevate_v and_o meridional_a unto_o those_o under_o the_o southern_a elevation_n the_o partition_n of_o the_o whole_a world_n and_o the_o comparison_n of_o the_o celestial_a with_o the_o elemental_a sphere_n chap._n 8._o the_o whole_a frame_n of_o the_o world_n be_v make_v of_o some_o certain_a and_o those_o more_o principal_a and_o notable_a part_n whereof_o there_o be_v first_o the_o number_n and_o the_o name_n and_o then_o the_o difference_n to_o be_v consider_v the_o number_n and_o name_n be_v double_a for_o the_o part_n be_v either_o ethereal_a or_o sublunare_v the_o aethereal_a that_o be_v the_o celestial_a part_n without_o the_o which_o philosophy_n admit_v nothing_o to_o be_v although_o the_o divine_n do_v add_v the_o three_o which_o they_o call_v angelical_a and_o the_o platonic_n intellectual_a be_v that_o whereof_o we_o entreat_v in_o the_o 7._o chapter_n the_o sublunare_n be_v that_o which_o contain_v the_o elemental_a body_n and_o those_o either_o simple_a as_o the_o fire_n the_o aer_fw-la the_o water_n the_o earth_n or_o else_o mix_v which_o be_v diverse_a and_o innumerable_a engender_v of_o the_o 4._o element_n either_o perfect_a or_o imperfect_a the_o difference_n or_o dissimilitude_n of_o the_o part_n of_o the_o world_n be_v that_o whereby_o they_o be_v distinguish_v one_o from_o another_o either_o in_o respect_n of_o their_o situation_n or_o of_o their_o dignity_n magnitude_n motion_n or_o their_o office_n they_o be_v distinguish_v according_a to_o their_o situation_n for_o the_o celestial_a part_n have_v obtain_v the_o high_a place_n the_o elemental_a the_o low_a their_o distinction_n according_a to_o dignity_n be_v note_v in_o the_o part_n contain_v by_o the_o celestial_a region_n which_o part_n be_v bright_a and_o immortal_a and_o by_o the_o elemental_a region_n those_o part_n be_v of_o their_o own_o nature_n obscure_a and_o decay_a or_o else_o it_o be_v note_v in_o the_o part_n contain_v whereof_o the_o one_o be_v altogether_o with_o out_o alteration_n neither_o increase_v nor_o diminish_v the_o other_o be_v continual_o subject_a unto_o generation_n and_o corruption_n and_o be_v increase_v and_o diminish_v their_o distinction_n according_a to_o their_o magnitude_n be_v consider_v in_o that_o the_o celestial_a part_n with_o the_o great_a
general_a reason_n be_v either_o in_o respect_n of_o their_o name_n or_o their_o definition_n they_o be_v name_v by_o the_o greek_n 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d tropicke_n by_o the_o latin_v versiles_n conversius_fw-la vertentes_fw-la tourn_v and_o the_o solstitial_a parallel_n their_o definition_n contain_v their_o quantity_n and_o their_o circumference_n their_o quantity_n be_v note_v either_o in_o respect_n of_o the_o other_o circle_n these_o be_v count_v in_o the_o number_n of_o the_o less_o circle_n or_o in_o regard_n of_o themselves_o whereby_o they_o be_v count_v equal_a in_o asmuch_o as_o they_o be_v equal_o distant_a from_o the_o centre_n of_o the_o world_n be_v separate_v the_o one_o from_o the_o other_o by_o the_o double_a distance_n of_o the_o ☉_o great_a declination_n their_o circumference_n be_v that_o round_a compass_n which_o the_o ☉_o pass_v through_o the_o 2_o solstitial_a point_n do_v describe_v they_o be_v in_o number_n 2._o the_o one_o septentrional_a the_o other_o meridional_a the_o septentrional_a tropic_n be_v on_o this_o side_n of_o the_o equator_fw-la in_o respect_n of_o we_o which_o we_o call_v either_o the_o summer_n tropic_n for_o that_o it_o pass_v through_o the_o point_n of_o the_o summer_n solstice_n or●ls_v the_o tropic_n of_o ♋_o because_o it_o be_v describe_v through_o the_o end_n of_o ♊_o &_o the_o beginning_n of_o ♋_o the_o meridional_a tropic_n be_v situate_v on_o the_o other_o side_n of_o the_o equator_fw-la and_o be_v call_v either_o the_o winter_n tropic_n as_o pass_v through_o the_o point_n of_o the_o winter_n solstice_n or_o the_o tropic_n of_o ♑_o because_o it_o be_v draw_v through_o the_o head_n of_o ♑_o the_o office_n and_o commodity_n of_o they_o be_v in_o number_n 4._o 1_o they_o show_v the_o trope_n that_o be_v the_o conversion_n or_o tourning_n of_o the_o ☉_o aswell_o in_o summer_n happen_v in_o our_o age_n the_o 3._o and_o 2._o of_o the_o ides_n of_o june_n as_o also_o in_o winter_n the_o 3._o &_o 2._o of_o the_o ides_n of_o december_n 2_o they_o show_v in_o every_o situation_n of_o the_o sphere_n both_o the_o long_a day_n which_o be_v as_o long_o as_o the_o diurnal_a ark_n of_o the_o tropic_n of_o ♋_o contain_v hour_n and_o the_o short_a day_n which_o be_v as_o long_o as_o the_o space_n of_o hour_n contain_v within_o the_o diurnal_a ark_n of_o the_o tropic_n of_o ♑_o 3_o they_o point_n out_o the_o limit_n of_o the_o course_n of_o the_o ☉_o and_o his_o great_a declination_n which_o be_v 23._o gr_n 52._o mi._n as_o in_o the_o time_n of_o aristarchus_n &_o ptolemee_n or_o 23._o gr_n 28._o mi._n as_o it_o be_v now_o in_o our_o time_n 4_o they_o show_v the_o burn_a zone_n which_o they_o separate_v from_o the_o temperate_a and_o the_o midst_n of_o the_o second_o climate_n which_o they_o call_v dia-syenes_a and_o anti-dia-syenes_a of_o the_o 2._o polare_fw-la circle_n chap._n 26._o the_o two_o pole_n of_o the_o zodiac_n carry_v about_o by_o the_o regular_fw-la revolution_n of_o the_o universal_a frame_n describe_v about_o the_o pole_n of_o the_o world_n two_o circle_n whereof_o the_o general_a reason_n the_o number_n and_o the_o use_n be_v to_o be_v note_v the_o general_a reason_n offer_v to_o our_o consideration_n their_o name_n their_o definition_n and_o their_o accident_n they_o be_v call_v the_o polare_fw-la circle_n either_o because_o they_o be_v describe_v about_o the_o pole_n or_o by_o the_o pole_n their_o definition_n by_o the_o latin_n it_o be_v make_v by_o their_o quantity_n and_o their_o circumference_n and_o plane_n touch_v their_o quantity_n they_o be_v in_o the_o number_n of_o the_o less_o circle_n equal_a in_o all_o place_n their_o circumference_n and_o plane_n be_v describe_v either_o by_o line_n draw_v from_o the_o pole_n of_o the_o zodiac_n unto_o the_o axe_n of_o the_o world_n at_o right_a angle_n and_o have_v by_o the_o daily_a motion_n a_o perfect_a revolution_n or_o else_o they_o be_v describe_v by_o certain_a semidiameter_n draw_v from_o the_o centre_n of_o the_o earth_n unto_o the_o pole_n of_o the_o zodiac_n and_o turn_v about_o by_o the_o diurnal_a and_o nocturnal_a motion_n the_o accident_n of_o the_o polare_fw-la circle_n do_v determine_v either_o their_o equality_n for_o they_o be_v parallel_n compare_v either_o one_o with_o another_o in_o asmuch_o as_o they_o be_v equidistant_a from_o the_o centre_n or_o compare_v with_o the_o tropick_n &_o the_o equator_fw-la or_o else_o they_o determine_v their_o distance_n either_o from_o the_o next_o tropic_n which_o be_v 43._o gr_n or_o from_o the_o pole_n of_o the_o world_n which_o be_v equal_a unto_o the_o ☉_o great_a declination_n they_o be_v two_o in_o number_n the_o one_o septentrional_a the_o other_o meridional_a the_o septentrional_a polare_fw-la circle_n be_v describe_v by_o the_o north_n pole_n of_o the_o ecliptic_a the_o meridional_a by_o the_o south_n pole_n thereof_o the_o septentrional_a polare_fw-la circle_n be_v call_v boreall_n north_n of_o the_o north_n wind_v call_v boreas_n and_o arctic_a and_o septentrional_a because_o of_o the_o 2._o constellation_n the_o one_o of_o the_o great_a bear_v call_v arctos_n the_o other_o of_o the_o less_o bear_v call_v septentriones_fw-la which_o be_v nigh_o thereunto_o the_o meridional_a polare_fw-la circle_n be_v call_v australl_a or_o southern_a of_o the_o south_n wind_v call_v auster_n and_o antarcticke_a ●s_a opposite_a unto_o the_o arctic_a and_o meridional_a of_o the_o south_n part_n of_o heaven_n call_v meridy_n their_o use_n be_v note_v in_o that_o they_o comprehend_v the_o cold_a and_o freeze_a zone_n and_o the_o inhabitant_n of_o the_o earth_n call_v perison_n who_o shadow_n go_v round_o about_o they_o and_o on_o either_o side_n limit_v the_o the_o distance_n of_o the_o pole_n the_o polare_fw-la circle_n otherwise_o describe_v according_a to_o the_o grecian_n chap._n 27._o the_o polare_fw-la circle_n be_v describe_v either_o according_a to_o the_o great_a declination_n of_o the_o ☉_o or_o the_o altitude_n of_o the_o pole_n above_o the_o horizon_n the_o great_a declination_n of_o the_o ☉_o by_o mean_n of_o the_o motion_n of_o inclination_n of_o the_o eight_o sphere_n be_v diverse_a for_o it_o be_v one_o in_o time_n past_a and_o be_v find_v to_o be_v another_o now_o and_o of_o such_o circle_n the_o reason_n be_v declare_v in_o the_o chapter_n before_o the_o polare_fw-la circle_n describe_v according_a to_o the_o altitude_n of_o the_o pole_n require_v the_o consideration_n of_o their_o definition_n their_o variety_n their_o office_n and_o the_o manner_n of_o their_o description_n in_o define_v the_o arctic_a polate_a circle_n we_o say_v 1._o that_o it_o be_v the_o great_a of_o those_o circle_n which_o be_v always_o in_o our_o sight_n that_o be_v of_o those_o which_o we_o may_v see_v at_o the_o same_o instant_n 2._o that_o it_o touch_v the_o horizon_n in_o one_o point_n 3._o that_o it_o be_v altogether_o above_o the_o earth_n in_o define_v the_o antarctick_a polare_fw-la circle_n we_o say_v 1._o that_o it_o be_v equal_a and_o parallel_v unto_o the_o arctic_a 2._o that_o it_o touch_v the_o horizon_n in_o one_o point_n 3._o that_o it_o be_v altogether_o hide_a under_o the_o earth_n the_o variety_n be_v manifold_a according_a to_o the_o didiversitie_n of_o the_o climate_n for_o either_o they_o be_v not_o at_o àll_a as_o in_o a_o right_a sphere_n it_o happen_v where_o exclude_v altogether_o the_o polare_fw-la circle_n the_o greek_n recon_fw-mi 3._o parallel_n only_o or_o else_o they_o be_v and_o those_o sometime_o either_o less_o equal_a or_o great_a than_o the_o tropicke_n or_o else_o they_o be_v equal_a unto_o the_o equator_fw-la and_o the_o horizon_n for_o by_o how_o much_o the_o pole_n shall_v be_v high_o by_o so_o much_o shall_v these_o circle_n be_v great_a the_o office_n and_o use_n of_o the_o arctic_a circle_n be_v in_o that_o it_o show_v the_o star_n that_o never_o arise_v ●nor_n set_v of_o the_o antarcticke_a circle_n the_o con●trary_a be_v to_o be_v conceive_v the_o mean_n of_o their_o description_n be_v by_o those_o star_n that_o in_o any_o region_n do_v touch_v the_o horizon_n of_o the_o milky_a circle_n chap._n 28._o of_o all_o the_o circle_n there_o be_v none_o to_o be_v see_v beside_o the_o milky_a circle_n which_o for_o that_o the_o greek_n do_v recon_fw-mi among_o the_o other_o circle_n we_o will_v express_v the_o name_n the_o definition_n the_o cause_n thereof_o and_o the_o distinct_a star_n which_o make_v the_o same_o the_o name_n be_v diverse_a as_o galaxia_fw-la the_o milky_a orb_n or_o circle_n the_o milky_a zone_n or_o milky_a way_n the_o arabian_n dal_n it_o matarati_n as_o it_o be_v a_o broad_a space_n or_o ark_n that_o move_v it_o be_v define_v to_o be_v one_o of_o the_o great_a circle_n oblique_a draw_v or_o stretch_v towards_o both_o the_o pole_n most_o bright_o shine_v apparent_a unto_o the_o sense_n inequal_a both_o in_o