one_o unto_o another_o and_o cut_v the_o sphere_n into_o equal_a piece_n the_o less_o circle_n be_v in_o number_n 4._o namely_o the_o 2._o polares_fw-la and_o the_o 2._o tropick_n which_o be_v not_o all_o of_o they_o equal_a one_o unto_o another_o neither_o divide_v they_o the_o sphere_n into_o two_o equal_a piece_n of_o the_o great_a circle_n contain_v the_o measure_n of_o the_o first_o motion_n chap._n 17._o the_o whole_a heaven_n or_o universal_a frame_n turn_v round_o by_o the_o first_o motion_n do_v in_o the_o middle_a place_n between_o the_o 2._o pole_n desscribe_v a_o certain_a circular_a compass_n whereof_o we_o be_v to_o consider_v the_o name_n the_o definition_n the_o commodity_n the_o name_n thereof_o be_v diverse_a for_o it_o be_v sometime_o call_v 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d aequidialis_fw-la that_o be_v if_o we_o may_v so_o term_v it_o equidiall_n sometime_o the_o line_n or_o the_o orb_n of_o the_o equality_n or_o equation_n of_o the_o day_n sometime_o the_o equinoctial_a and_o equator_fw-la and_o sometime_o the_o girdle_n of_o the_o first_o motion_n or_o movable_a the_o definition_n thereof_o be_v that_o wherein_o the_o magnitude_n situation_n and_o equal_a conversion_n thereof_o be_v contain_v the_o magnitude_n thereof_o be_v consider_v in_o that_o it_o be_v the_o great_a circle_n &_o have_v these_o 2._o propriety_n the_o one_o that_o it_o divide_v the_o sphere_n into_o 2._o equal_a part_n the_o other_o that_o it_o have_v the_o same_o centre_n with_o the_o world_n the_o situation_n thereof_o be_v in_o the_o midst_n between_o both_o the_o pole_n of_o the_o world_n in_o which_o respect_n it_o differ_v from_o the_o rest_n of_o the_o parallel_n and_o oblique_a circle_n the_o equal_a conversion_n thereof_o be_v that_o perfect_a revolution_n which_o it_o fulfil_v within_o the_o determinate_a space_n of_o 24._o hour_n the_o commodity_n thereof_o be_v great_a &_o manifold_a and_o it_o be_v either_o astronomical_a or_o geographical_a the_o use_n thereof_o in_o astronomical_a matter_n be_v see_v chief_o in_o 4._o thing_n first_o by_o the_o help_n thereof_o we_o understand_v the_o measure_n of_o the_o first_o motion_n and_o thereby_o recon_fw-mi the_o time_n which_o be_v the_o measure_n of_o the_o first_o motion_n second_o it_o help_v we_o in_o the_o find_n out_o of_o the_o equinoctial_o and_o that_o in_o two_o respect_n the_o one_o in_o respect_n of_o the_o whole_a earth_n for_o every_o horizon_n of_o every_o country_n divide_v the_o equator_fw-la only_o of_o all_o the_o parallel_n into_o 2._o equal_a piece_n whereby_o it_o come_v to_o pass_v that_o when_o the_o ☉_o be_v in_o the_o equinoctial_a the_o day_n &_o the_o night_n throughout_o the_o whole_a world_n be_v equal_a the_o other_o in_o respect_n of_o certain_a region_n for_o those_o that_o dwell_v under_o the_o equator_fw-la in_o what_o part_n of_o the_o heaven_n soever_o the_o ☉_o be_v have_v always_o the_o aequinoctium_n or_o the_o day_n and_o the_o night_n equal_a three_o thereby_o we_o find_v out_o both_o the_o situation_n of_o the_o star_n either_o towards_o the_o north_n or_o towards_o the_o south_n because_o it_o distinguish_v the_o north_n part_n of_o the_o world_n from_o the_o south_n as_o also_o their_o declination_n either_o septentrional_a or_o meridional_a fourthlye_a through_o the_o help_n thereof_o we_o search_v the_o length_n of_o the_o artificial_a day_n the_o utility_n thereof_o in_o geographie_n be_v see_v in_o 3._o thing_n 1_o thereby_o we_o set_v every_o town_n in_o his_o due_a place_n in_o the_o terrestrial_a globe_n 2_o it_o bring_v we_o unto_o the_o knowledge_n of_o all_o the_o parallel_n aswell_o celestial_a as_o terrestrial_a 3_o by_o the_o aid_n thereof_o we_o finish_v the_o description_n of_o the_o earth_n of_o the_o great_a circle_n measure_v the_o second_o motion_n chap._n 18._o the_o star_n of_o heaven_n which_o be_v move_v round_o about_o from_o the_o west_n toward_o the_o east_n do_v describe_v in_o the_o midst_n between_o their_o pole_n a_o certain_a circular_a surface_n common_a to_o all_o the_o planet_n and_o a_o certain_a circular_a line_n proper_a unto_o the_o ☉_o only_a concern_v the_o circular_a surface_n there_o be_v deliver_v by_o the_o astronomer_n to_o be_v consider_v the_o name_n the_o definition_n the_o measure_n and_o the_o use_n thereof_o the_o name_n be_v diverse_a draw_v either_o from_o the_o greek_n or_o from_o the_o latin_n the_o greek_n call_v it_o the_o zodiac_n either_o of_o 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d life_n for_o that_o it_o be_v the_o path_n wherein_o the_o ☉_o take_v to_o be_v the_o author_n of_o life_n do_v walk_v or_o else_o of_o 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d a_o live_a creature_n for_o that_o the_o ancient_a astronomer_n have_v beautify_v this_o circle_n with_o the_o figure_n of_o certain_a live_a creature_n the_o latin_n term_v it_o signifer_fw-la as_o carry_v the_o sign_n they_o call_v it_o also_o the_o oblique_a circle_n or_o the_o circle_n lean_v a_o side_n the_o definition_n contain_v the_o magnitude_n the_o oblique_a situation_n and_o the_o limit_n thereof_o concern_v the_o magnitude_n thereof_o this_o be_v only_o to_o be_v consider_v that_o it_o be_v one_o of_o the_o great_a circle_n the_o oblique_a situation_n thereof_o be_v either_o in_o respect_n of_o the_o parallel_n which_o it_o cut_v at_o inequal_a angle_n or_o of_o the_o irregulare_fw-la ascension_n and_o descension_n or_o of_o the_o pole_n of_o the_o world_n from_o the_o which_o it_o be_v not_o equidistant_a the_o limit_n thereof_o be_v the_o 2_o tropick_n which_o it_o touch_v and_o divide_v the_o equator_fw-la into_o two_o equal_a part_n decline_v therefrom_o by_o little_a &_o little_a unto_o the_o distance_n of_o 31._o gr_n 28._o mi._n the_o measure_n thereof_o be_v either_o in_o regard_n of_o the_o length_n that_o it_o have_v or_o of_o the_o breadth_n the_o length_n thereof_o be_v 360._o gr_n and_o be_v divide_v into_o 6._o northern_a sign_n as_o ♈_o ♉_o ♊_o ♋_o ♌_o â™_o &_o into_o 6._o southren_n sign_n as_o ♎_o â™_o â™_o ♑_o â™’_o ♓_o the_o breadth_n thereof_o be_v 16._o gr_n as_o well_o in_o regard_n of_o the_o roam_a of_o the_o planet_n from_o the_o cliptrck_n and_o special_o of_o ♀_o &_o ♂_o as_o also_o in_o respect_n of_o the_o principal_a consfellation_n whereof_o the_o great_a part_n decline_v from_o the_o midst_n of_o the_o zodiac_n the_o use_n be_v chief_o see_v in_o the_o obliquity_n thereof_o for_o thereby_o it_o fall_v out_o that_o the_o part_n of_o heaven_n do_v with_o the_o more_o ease_n maintain_v their_o course_n against_o the_o first_o and_o universal_a motion_n as_o also_o that_o the_o star_n may_v sometime_o be_v in_o the_o south_n and_o sometime_o in_o the_o north_n for_o the_o great_a benefit_n of_o the_o inhabitant_n of_o the_o earth_n the_o circular_a line_n proper_a unto_o the_o ☉_o only_o have_v diverse_a name_n with_o the_o definition_n &_o commodity_n peculiar_o appertain_v thereunto_o it_o be_v call_v the_o wheel_a the_o way_n the_o course_n the_o place_n of_o the_o ☉_o the_o ecliptic_a line_n also_o the_o burn_a line_n and_o the_o division_n of_o the_o zodiac_n the_o definition_n thereof_o be_v that_o whereby_o it_o be_v call_v a_o great_a circle_n divide_v the_o breadth_n of_o the_o zodiac_n into_o 2._o equal_a part_n the_o commodity_n thereof_o be_v note_v as_o well_o in_o design_v the_o eclipse_n of_o the_o ☉_o &_o ☽_o which_o never_o happen_v but_o when_o both_o of_o they_o be_v under_o or_o very_o near_o the_o ecliptic_a line_n as_o also_o in_o distinguish_v of_o the_o 4._o quarter_n or_o season_n of_o the_o year_n of_o certain_a term_n whereby_o the_o star_n have_v relation_n unto_o the_o aforesaid_a circle_n chap._n 19_o the_o whole_a number_n aswell_o of_o the_o sixed_a star_n as_o also_o of_o the_o planet_n have_v relation_n both_o to_o the_o equator_fw-la and_o to_o the_o zodiac_n they_o have_v a_o twofold_a relation_n unto_o the_o equator_fw-la either_o in_o regard_n of_o the_o orbiculare_a longitude_n of_o the_o equator_fw-la or_o of_o the_o lateral_a position_n thereof_o in_o the_o orbiculare_a longitude_n of_o the_o equator_fw-la we_o be_v to_o note_v the_o name_n and_o the_o definition_n it_o be_v sometime_o call_v the_o longitude_n of_o a_o star_n and_o sometime_o the_o right_a ascension_n it_o be_v define_v the_o ask_v of_o the_o equator_fw-la comprehend_v between_o the_o head_n of_o ♈_o and_o the_o section_n of_o a_o great_a circle_n pass_v through_o the_o pole_n of_o the_o world_n and_o the_o true_a place_n of_o the_o star_n the_o lateral_a position_n have_v also_o name_n definition_n and_o division_n it_o be_v call_v the_o declination_n of_o a_o start_n it_o be_v define_v to_o be_v the_o ark_n of_o a_o great_a circle_n pass_v through_o the_o pole_n of_o the_o world_n and_o the_o true_a place_n of_o the_o star_n the_o say_a ark_n be_v intercept_v between_o the_o
equator_fw-la and_o true_a place_n of_o the_o starie_n it_o be_v divide_v into_o the_o septentrional_a and_o meridional_a declination_n the_o relation_n that_o the_o star_n have_v unto_o the_o zodiac_n be_v also_o two_o fold_n either_o according_a to_o the_o longitude_n of_o the_o zodrake_n or_o else_o according_a to_o the_o transuerse_a distance_n toward_o either_o of_o the_o pole_n in_o the_o longitude_n of_o the_o zodiac_n we_o be_v to_o consider_v the_o name_n and_o the_o definition_n it_o be_v call_v longitude_n for_o that_o it_o be_v recove_v longwaies_o on_o the_o circumference_n of_o the_o ecliptic_a it_o be_v also_o call_v the_o true_a motion_n of_o the_o star_n it_o be_v define_v to_o be_v the_o ark_n of_o the_o zodiac_n intercept_v between_o the_o head_n of_o ♈_o and_o the_o section_n of_o a_o great_a circle_n pass_v through_o the_o pole_n of_o the_o zodiac_n and_o the_o true_a place_n of_o the_o star_n in_o the_o transuerse_a distance_n we_o be_v to_o note_v the_o name_n the_o definition_n and_o the_o division_n it_o be_v call_v latitude_n because_o it_o be_v reckon_v according_a to_o the_o position_n that_o it_o have_v from_o some_o one_o side_n of_o the_o ecliptic_a it_o be_v define_v to_o be_v the_o ark_n of_o a_o great_a circle_n draw_v through_o the_o pole_n of_o the_o zodiac_n and_o the_o true_a place_n of_o the_o star_n the_o say_a ark_n be_v intercept_v between_o the_o zodiac_n and_o the_o centre_n of_o the_o star_n it_o be_v divide_v into_o the_o septentrional_a latitude_n when_o the_o star_n be_v under_o the_o northerly_a sign_n and_o into_o the_o meridional_a latitude_n when_o they_o be_v in_o the_o southerly_a sign_n of_o the_o propertion_n and_o supputation_n of_o the_o declination_n of_o every_o point_n of_o the_o ecliptic_a or_o the_o regard_n of_o the_o part_n of_o the_o zodtake_n unto_o the_o equator_fw-la chap._n 20._o in_o the_o declination_n of_o any_o point_n of_o the_o ecliptic_a 2._o thing_n be_v to_o be_v observe_v the_o proportion_n and_o the_o supputation_n in_o the_o proportion_n we_o may_v note_v also_o 2._o thing_n for_o either_o they_o have_v none_o obliquation_n or_o else_o their_o obliquation_n be_v equal_a those_o that_o have_v none_o obliquation_n be_v the_o head_n of_o ♈_o and_o ♎_o as_o be_v the_o common_a intersection_n of_o the_o equator_fw-la and_o the_o zodiac_n those_o that_o have_v equal_a obliquation_n be_v such_o as_o be_v equal_o distant_a from_o the_o equator_fw-la and_o they_o be_v either_o great_a obliquation_n or_o else_o the_o great_a the_o great_a obliquation_n be_v those_o that_o have_v any_o distance_n less_o than_o the_o great_a from_o either_o of_o the_o section_n and_o of_o that_o sort_n there_o be_v always_o four_o the_o great_a obliquation_n be_v those_o that_o have_v the_o great_a distance_n from_o the_o equator_fw-la as_o the_o head_n of_o ♋_o that_o s_o the_o summer_n solstice_n and_o the_o head_n of_o ♑_o that_o be_v the_o winter_n solstice_n the_o supputation_n be_v make_v either_o by_o the_o table_n of_o declination_n or_o of_o sines_n the_o table_n of_o declination_n be_v calculate_v in_o sundry_a place_n by_o astronomer_n and_o they_o consist_v of_o the_o 2._o side_n the_o area_n and_o of_o the_o two_o extremity_n or_o end_n the_o side_n be_v either_o at_o the_o right_a hand_n or_o at_o the_o left_a that_o at_o the_o left_a hand_n to_o be_v enter_v into_o when_o you_o have_v the_o sign_n in_o the_o top_n of_o the_o table_n and_o that_o on_o the_o right_a hand_n when_o the_o sign_n be_v in_o the_o foot_n thereof_o the_o area_n be_v that_o wherein_o at_o the_o common_a angle_n the_o declination_n be_v find_v the_o 2._o extremity_n be_v those_o that_o contain_v the_o sign_n of_o which_o extremity_n the_o one_o be_v call_v the_o top_n or_o upper_a part_n the_o other_o the_o foot_n or_o the_o nether_a patte_n of_o the_o table_n the_o supputation_n that_o be_v make_v by_o the_o table_n of_o sines_n be_v perform_v by_o the_o help_n of_o the_o rule_n of_o 4._o proportion_n all_o number_n wherein_o 3._o number_n be_v give_v and_o four_o be_v to_o be_v seek_v out_o the_o 3._o number_n give_v must_v contain_v the_o right_n sine_fw-la of_o the_o whole_a quadrant_a or_o of_o the_o semidiameter_n the_o right_a sine_fw-la of_o the_o great_a declination_n of_o the_o ☉_o and_o the_o right_a sine_fw-la of_o the_o distance_n of_o the_o point_n of_o the_o ecliptic_a give_v from_o the_o first_o section_n of_o the_o zodiac_n and_o the_o equator_fw-la the_o four_o number_n produce_v by_o multiplitation_n and_o division_n be_v the_o right_a sine_fw-la of_o the_o declination_n seek_v who_o subtended_a ark_n declare_v the_o number_n of_o degree_n of_o the_o 2._o circle_n call_v the_o colour_n distinguish_v the_o equinoctial_a and_o solstitial_a point_n chap._n 21._o forasmuch_o as_o there_o be_v certain_a point_n of_o the_o zodiac_n and_o the_o equator_fw-la more_o notable_a than_o the_o rest_n therefore_o the_o astronomer_n have_v think_v good_a to_o fit_v unto_o those_o point_n 2._o circle_n whereof_o we_o may_v consider_v the_o reason_n of_o their_o name_n their_o definition_n their_o number_n their_o figuration_n or_o description_n and_o their_o use_n they_o be_v terméd_v colour_n that_o be_v imperfect_a in_o 3._o respect_n 1._o because_o they_o appear_v always_o incomplete_a or_o maim_v the_o which_o thing_n notwithstanding_o seem_v to_o be_v common_a with_o diverse_a other_o circle_n 2._o because_o they_o have_v some_o part_n that_o do_v never_o arise_v 3._o because_o they_o be_v carry_v about_o after_o a_o imperfect_a manner_n &_o not_o according_a to_o the_o position_n of_o longitude_n as_o the_o motion_n of_o the_o heaven_n be_v the_o definition_n contain_v their_o magnitude_n their_o intersection_n and_o their_o motion_n as_o touch_v their_o magnitude_n they_o be_v of_o the_o number_n of_o the_o great_a circle_n as_o touch_v their_o intersection_n they_o cut_v one_o another_o in_o both_o the_o pole_n of_o the_o world_n at_o spherical_a right_a angle_n in_o their_o motion_n they_o be_v move_v together_o with_o the_o sphere_n their_o number_n be_v two_o whereof_o the_o one_o pass_v through_o the_o equinoctial_a point_n and_o the_o pole_n of_o the_o world_n and_o be_v call_v either_o the_o equinoctial_a colour_n or_o the_o distinguisher_n of_o the_o equinoctial_o the_o other_o pass_v through_o the_o solstitial_a point_n and_o the_o pole_n both_o of_o ecliptic_a and_o of_o the_o world_n and_o be_v call_v both_o the_o solstitial_a colour_n the_o distinguisher_n of_o the_o solstice_n and_o also_o the_o circle_n of_o the_o great_a declination_n their_o figuration_n be_v describe_v by_o the_o semidiameter_n of_o the_o world_n who_o revolution_n be_v ful_o perform_v through_o the_o pole_n of_o the_o world_n and_o the_o equinoctial_a point_n make_v the_o equinoctial_a colour_n but_o pass_v through_o the_o pole_n of_o the_o world_n and_o the_o solstitial_a point_n it_o make_v the_o solstitial_a colour_n their_o use_n be_v manifold_a but_o principal_o in_o 3._o thing_n 1._o in_o distinguish_v the_o equinoctial_a and_o solstitial_a point_n 2._o in_o reckon_n aswell_o the_o quantity_n of_o the_o great_a declination_n of_o the_o ☉_o by_o the_o ark_n intercept_v between_o the_o equator_fw-la and_o the_o ecliptic_a as_o the_o space_n comprehend_v between_o the_o pole_n of_o the_o world_n and_o the_o pole_n of_o the_o ecliptic_a which_o be_v always_o equal_a unto_o the_o ark_n of_o the_o great_a declination_n 3._o for_o better_a understanding_n of_o the_o ascension_n and_o descension_n of_o the_o sign_n of_o the_o meridian_n chap._n 22._o the_o ☉_o carry_v about_o by_o the_o first_o motion_n when_o it_o be_v at_o the_o high_a design_v a_o point_n of_o a_o circle_n who_o definition_n variety_n and_o office_n we_o be_v to_o consider_v the_o definition_n take_v hold_n both_o of_o the_o name_n thereof_o and_o of_o the_o matter_n itself_o it_o be_v call_v the_o circle_n meridian_n meridional_a and_o merinoctiall_a the_o circle_n of_o the_o midday_n and_o midnight_n either_o because_o it_o divide_v both_o the_o day_n and_o the_o night_n into_o 2._o equal_a part_n the_o one_o ascend_v the_o other_o descend_v or_o else_o because_o so_o often_o as_o the_o ☉_o according_a to_o the_o first_o motion_n be_v under_o the_o meridian_n it_o be_v then_o either_o midday_n or_o else_o midnight_n the_o matter_n itself_o be_v that_o according_a whereto_o it_o be_v define_v to_o be_v one_o of_o the_o great_a circle_n draw_v through_o the_o pole_n of_o the_o world_n and_o the_o vertical_a point_n of_o any_o place_n give_v and_o stand_v still_o when_o the_o sphere_n be_v move_v the_o variety_n of_o the_o meridian_n by_o reason_n of_o the_o round_a figure_n of_o the_o earth_n be_v either_o none_o at_o all_o or_o manifold_a it_o be_v none_o at_o all_o either_o in_o regard_n of_o reason_n or_o of_o sense_n it_o be_v
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 orâ—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 â—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 à ll_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 â—nor_n set_v of_o the_o antarcticke_a circle_n the_o conâ—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
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 mà de_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 giuâ—_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 aâ—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
compass_n thereof_o do_v cover_v all_o thing_n like_o a_o thing_n without_o measure_n and_o end_n but_o the_o elemental_a part_n be_v cover_v within_o the_o compass_n of_o the_o heaven_n the_o diameter_n thereof_o contain_v the_o diameter_n of_o the_o earth_n 23._o time_n their_o distinction_n according_a to_o their_o motion_n be_v in_o that_o the_o celestial_a part_n have_v a_o circular_a and_o a_o spherical_a motion_n the_o elemental_a a_o right_a motion_n more_o imperfect_a than_o the_o circular_a final_o they_o be_v distinguish_v according_a to_o their_o office_n for_o of_o those_o thing_n that_o be_v engender_v in_o the_o elemental_a part_n the_o heaven_n work_v by_o a_o continual_a motion_n be_v as_o it_o be_v the_o formal_a and_o efficient_a cause_n from_o whence_o life_n be_v derive_v and_o the_o elemental_a part_n which_o be_v subject_a unto_o passion_n and_o alteration_n be_v as_o it_o be_v the_o material_a cause_n from_o whence_o nourishment_n do_v proceed_v the_o reason_n of_o the_o sublunare_n or_o elemental_a region_n chap._n 9_o the_o elemental_a region_n which_o the_o heaven_n encompass_v comprehend_v within_o it_o the_o element_n wherein_o we_o be_v to_o consider_v the_o definition_n the_o number_n and_o the_o situation_n or_o order_n the_o element_n be_v simple_a body_n aswell_o in_o respect_n of_o the_o mix_a body_n which_o be_v understand_v to_o be_v compound_v of_o they_o as_o of_o the_o simple_a and_o least_o part_n as_o also_o in_o respect_n of_o the_o division_n for_o that_o they_o can_v be_v divide_v into_o body_n of_o diverse_a kind_n if_o they_o be_v give_v pure_a and_o without_o mixture_n for_o the_o use_n of_o live_a creature_n and_o thing_n grow_v do_v make_v they_o impure_a the_o element_n be_v 4._o in_o number_n find_v so_o to_o be_v by_o sense_n and_o by_o reason_n the_o element_n be_v find_v to_o be_v sour_a by_o sense_n which_o the_o physician_n do_v sollow_v first_o for_o that_o more_o simple_a body_n can_v be_v show_v 2_o nature_n have_v allot_v unto_o they_o certain_a place_n to_o the_o end_n that_o other_o thing_n may_v by_o they_o be_v breed_v and_o nourish_v 3_o nothing_o else_o can_v evident_o be_v show_v whereof_o other_o thing_n may_v be_v make_v 4_o in_o live_a creture_n there_o be_v certain_a part_n agreeable_a unto_o the_o nature_n of_o the_o several_a element_n the_o element_n be_v find_v to_o be_v four_o by_o two_o reason_n the_o former_a whereof_o be_v draw_v from_o the_o number_n of_o the_o four_o prime_a quality_n and_o the_o four_o fold_n possible_a knit_n together_o of_o they_o for_o heat_n may_v be_v join_v either_o with_o dryness_n which_o two_o make_v fire_n or_o else_o with_o moisture_n which_o two_o do_v make_v up_o aer_fw-la and_o cold_a may_v be_v join_v with_o moisture_n as_o it_o come_v to_o pass_v in_o the_o water_n or_o with_o dryness_n as_o in_o earth_n the_o late_a reason_n be_v take_v from_o the_o four_o fold_v difference_n of_o the_o right_a motion_n for_o the_o element_n be_v direct_o move_v either_o upwarde_a or_o downward_o such_o thing_n as_o move_v upward_o as_o light_v thing_n do_v be_v say_v so_o to_o do_v either_o simple_o as_o the_o fire_n which_o be_v the_o light_a of_o the_o rest_n or_o respectivelie_o as_o the_o aer_fw-la which_o be_v light_a than_o the_o water_n or_o the_o earth_n such_o thing_n as_o move_v downward_o as_o heanye_a thing_n do_v be_v say_v so_o to_o do_v either_o respectivelie_a as_o the_o water_n compare_v unto_o the_o fire_n and_o aer_fw-la or_o simple_o as_o the_o earth_n which_o be_v the_o heavy_a of_o all_o the_o rest_n the_o situation_n and_o order_n of_o the_o element_n be_v find_v either_o by_o their_o motion_n or_o else_o by_o the_o communication_n of_o their_o quality_n and_o first_o by_o the_o motion_n for_o inasmuch_o as_o the_o fire_n and_o the_o aer_fw-la do_v natural_o move_v upward_o the_o fire_n shall_v occupy_v the_o high_a place_n the_o aer_fw-la a_o upper_a place_n and_o for_o that_o the_o water_n and_o the_o earth_n do_v natural_o move_v downward_o the_o water_n shall_v possess_v a_o low_a place_n and_o the_o earth_n the_o low_a again_o the_o order_n of_o the_o element_n be_v find_v out_o by_o the_o communication_n of_o their_o quality_n for_o it_o be_v unfit_a that_o such_o thing_n as_o be_v mere_o contrary_a but_o such_o as_o in_o some_o sort_n can_v agree_v together_o shall_v be_v nigh_o one_o another_o the_o fire_n therefore_o shall_v be_v join_v unto_o the_o aer_fw-la by_o reason_n of_o the_o heat_n common_a unto_o they_o both_o the_o aer_fw-la unto_o the_o water_n by_o reason_n of_o the_o common_a moisture_n and_o the_o earth_n unto_o the_o water_n by_o reason_n of_o coldness_n common_a to_o they_o both_o the_o two_o fold_n difference_n of_o the_o celestial_a motion_n chap._n 10._o the_o whole_a frame_n of_o the_o world_n be_v carry_v round_o about_o with_o 2._o motion_n each_o of_o they_o be_v distinguish_v from_o the_o other_o in_o name_n and_o in_o reason_n the_o one_o of_o they_o be_v call_v the_o first_o and_o universal_a motion_n likewise_o the_o diurnal_a or_o worldly_a motion_n because_o it_o bring_v the_o day_n unto_o the_o world_n for_o in_o this_o motion_n the_o ☉_o and_z all_z the_o celestial_a body_n do_v every_o day_n arise_v and_o set_v they_o call_v it_o also_o the_o violent_a and_o rapt_a motion_n because_o by_o the_o violent_a swiftness_n thereof_o it_o carry_v with_o it_o the_o rest_n of_o the_o sphere_n the_o other_o be_v call_v the_o second_o and_o particular_a motion_n altogether_o contrary_a unto_o the_o former_a as_o by_o which_o all_o the_o particular_a orb_n do_v resist_v the_o universal_a motion_n they_o call_v it_o also_o sinister_a motus_fw-la the_o motion_n to_o the_o left_a hand_n as_o the_o former_a be_v in_o like_a sort_n call_v dexter_a that_o be_v the_o motion_n to_o the_o right_a hand_n the_o 2._o motion_n be_v also_o distinguish_v according_a to_o the_o reason_n or_o the_o substance_n in_o the_o which_o they_o be_v inherent_a for_o they_o differ_v the_o one_o from_o the_o other_o three_o way_n the_o first_o difference_n be_v in_o respect_n either_o of_o the_o whole_a for_o the_o diurnal_a motion_n be_v common_a unto_o all_o the_o celestial_a body_n or_o else_o of_o the_o part_n or_o star_n either_o fix_v or_o wander_a which_o have_v a_o motion_n peculiar_a and_o proper_a unto_o themselves_o the_o second_o difference_n be_v either_o in_o regard_n of_o the_o situation_n of_o the_o axe_n for_o the_o diurnal_a motion_n be_v make_v upon_o the_o axe_n and_o pole_n of_o the_o world_n and_o therefore_o the_o equator_fw-la divide_v it_o in_o the_o middle_n but_o the_o proper_a motion_n be_v make_v upon_o the_o axe_n and_o pole_n of_o the_o zodiac_n and_o therefore_o the_o zodiac_n do_v cut_v it_o in_o the_o middle_n or_o else_o it_o be_v in_o regard_n of_o the_o position_n of_o the_o term_n inasmuch_o as_o the_o diurnal_a revolution_n be_v make_v from_o the_o east_n unto_o the_o west_n or_o as_o plinte_n 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
diameter_n or_o else_o be_v compare_v but_o with_o the_o orb_n of_o the_o ☉_o which_o be_v prove_v by_o the_o equal_a space_n of_o the_o day_n and_o night_n the_o measure_n of_o the_o compass_n of_o the_o earth_n chap._n 14._o the_o circumference_n of_o the_o globe_n of_o the_o earth_n and_o water_n be_v find_v out_o by_o the_o rule_n of_o four_o proportional_a number_n in_o which_o rule_n 3._o number_n be_v give_v and_o the_o four_o be_v unknown_a the_o three_o number_n give_v which_o contain_v the_o proportion_n of_o a_o segment_n of_o a_o celestial_a circle_n unto_o the_o like_a space_n on_o the_o earth_n be_v 1._o the_o difference_n of_o latitude_n 2_o the_o viatorie_a distance_n 3._o the_o circumference_n of_o the_o whole_a heaven_n by_o the_o difference_n of_o latitude_n be_v understand_v so_o many_o celestial_a degree_n as_o any_o terrestrial_a place_n be_v distant_a asunder_o the_o viatorie_a distance_n be_v that_o terrestrial_a space_n of_o way_n that_o be_v answerable_a unto_o one_o degree_n or_o any_o other_o difference_n of_o latitude_n and_o it_o be_v find_v out_o 3_o manner_n of_o way_n first_o by_o the_o distance_n of_o any_o two_o place_n upon_o the_o earth_n situate_v under_o one_o meridian_n the_o say_a distance_n be_v precise_o try_v second_o by_o the_o latitude_n of_o both_o place_n either_o observe_v by_o instrument_n or_o take_v out_o of_o table_n thirdlye_o by_o subduct_v the_o less_o out_o of_o the_o great_a for_o so_o the_o difference_n of_o latitude_n shall_v appear_v whereunto_o the_o space_n of_o way_n know_v between_o the_o place_n give_v shall_v be_v answerable_a whereby_o unto_o each_o degree_n of_o a_o great_a circle_n in_o the_o heaven_n there_o be_v answerable_a upon_o the_o earth_n after_o ptolemee_n furlong_n 500_o pass_n 62500._o great_a league_n 15._o after_o eratosthenes_n surl_n 700._o pass_n 87500_o leag_n 21._o â…ž_n the_o circumference_n of_o the_o whole_a heaven_n contain_v 360._o gr_n be_v the_o 3._o number_n in_o the_o proportion_n 1_o for_o that_o of_o a_o little_a and_o of_o a_o great_a globe_n there_o be_v the_o like_a reason_n 2._o because_o the_o terrestrial_a meridian_n have_v the_o same_o centre_n with_o the_o celestial_a the_o four_o number_n of_o the_o proportion_n that_o be_v the_o circuit_n of_o the_o great_a circle_n in_o the_o earth_n have_v 2._o consideration_n the_o first_o be_v the_o manner_n of_o the_o search_v thereof_o and_o that_o be_v first_o by_o multiply_v the_o three_o number_n that_o be_v the_o circumference_n of_o the_o heaven_n by_o the_o second_o which_o contain_v the_o space_n of_o way_n upon_o earth_n and_o then_o by_o divide_v the_o product_n by_o the_o first_o which_o be_v the_o difference_n of_o latitude_n the_o second_o consideration_n be_v of_o the_o quotient_a or_o manifestation_n of_o the_o content_n which_o according_a to_o prolemee_n be_v mile_n 22550._o furl_n 180000._o pas_fw-fr 22500000._o great_a league_n 5400._o according_a to_o eratosthenes_n mile_n 61250._o furl_n 252000._o pass_n 61250000._o great_a league_n 7875._o the_o measure_n of_o the_o diameter_n and_o semidiameter_n of_o the_o earth_n as_o also_o of_o the_o area_n and_o surface_n thereof_o chap._n 15._o in_o measure_v the_o terrestrial_a globe_n we_o conder_n either_o the_o diameter_n or_o the_o semidiameter_n or_o the_o area_n or_o the_o connex_v surface_n thereof_o the_o diameter_n be_v measure_v by_o the_o proportion_n thereof_o unto_o the_o whole_a circumference_n by_o the_o rule_n of_o four_o proportional_a number_n wherein_o again_o three_o be_v give_v and_o the_o four_o be_v unknowen_a the_o three_o number_n give_v be_v thorough_o know_v and_o understand_v must_v be_v due_o place_v and_o they_o must_v contain_v two_o thing_n the_o first_o be_v the_o proportion_n of_o the_o circumference_n of_o a_o circle_n unto_o the_o diameter_n thereof_o which_o be_v tripla_fw-la sesquiseptima_fw-la that_o be_v to_o say_v the_o circumference_n be_v unto_o the_o diameter_n as_o 22._o be_v unto_o 7._o the_o second_o be_v the_o great_a circuit_n of_o the_o earth_n in_o any_o measure_n which_o be_v set_v down_o in_o the_o 14._o chapter_n the_o four_o number_n of_o the_o proportion_n be_v unknowen_a be_v the_o diameter_n which_o be_v seek_v first_o by_o multiply_v the_o third_o by_o the_o second_o which_o be_v 7._o &_o divide_v the_o product_n by_o the_o first_o which_o be_v 22._o then_o by_o subduct_v the_o 22._o part_n which_o come_v forth_o of_o the_o division_n of_o the_o circumference_n by_o 22._o out_o of_o the_o circumference_n &_o divide_v the_o remainder_n by_o 3._o whereupon_o arise_v the_o content_a of_o the_o diameter_n after_o ptolemee_n contain_v mile_n 7159_o 〈◊〉_d furl_n 57272_o 〈◊〉_d pass_v 7159090_o 10_o 11_o great_a leag_v 1718_o 〈◊〉_d after_o eratosih_n mâ—es_n 19488_o 7_o 11_o fur_n 80181_o 〈◊〉_d pass_v 1948863_o 〈◊〉_d great_a leag_n 2505_o 〈◊〉_d the_o semidiameter_n be_v the_o distance_n between_o the_o convex_n surface_n of_o the_o earth_n and_o he_o centre_n thereof_o which_o some_o do_v imagine_v to_o be_v the_o place_n of_o helly_a the_o say_a distance_n be_v find_v two_o waâ—es_n 1_o by_o the_o proportion_n of_o the_o circle_n unto_o the_o semidiameter_n which_o be_v sâ—â—tuple_v over_o and_o beside_o 1_o 14_o or_o as_o 44_o be_v unto_o 7._o 2_o by_o divide_v the_o diameter_n into_o two_o part_n by_o which_o mean_v it_o shall_v be_v find_v to_o contain_v after_o ptolemec_n mile_n 3579_o ½_n furl_n 28636_o pass_n 3579545_o great_a leag_n 859_o 1_o 11_o after_o eratosthenes_n mile_n 9744._o furl_n 40090_o ½_n pass_v 974431._o great_a leag_n 12â—2_n ½_n the_o area_n or_o plane_n be_v find_v by_o multiply_v half_o the_o circuit_n of_o the_o earth_n take_v in_o any_o know_a measure_n by_o the_o semidiameter_n thereof_o the_o convex_n surface_n that_o cover_v the_o whole_a earth_n be_v find_v by_o multiply_v the_o terrestrial_a area_n or_o plane_n by_o 4._o the_o general_a definition_n and_o division_n of_o the_o circle_n chap._n 16._o in_o as_o much_o as_o the_o surface_n of_o the_o heaven_n be_v spherical_a and_o their_o motion_n circular_a therefore_o for_o the_o better_a conceive_v of_o the_o reason_n of_o the_o celestial_a motion_n they_o be_v distinguish_v into_o certain_a circle_n as_o part_n whereof_o we_o be_v to_o show_v the_o name_n &_o the_o division_n in_o the_o name_n we_o be_v to_o consider_v their_o acception_n and_o their_o diversity_n be_v notwithstanding_o all_o one_o in_o signification_n the_o acception_n of_o the_o name_n circle_n be_v of_o two_o sort_n geometrical_a and_o astronomical_a the_o geometrical_a acception_n be_v when_o a_o circle_n be_v take_v for_o a_o plane_n figure_n which_o one_o line_n equal_o distant_a from_o the_o centre_n do_v encompass_v the_o astronomical_a acception_n be_v other_o as_o it_o signify_v a_o circular_a line_n or_o a_o circumference_n want_v breadth_n or_o else_o a_o circular_a surface_n which_o have_v breadth_n thereunto_o adjoin_v the_o diversity_n of_o name_n all_o one_o in_o meaning_n be_v when_o circle_n be_v call_v amongst_o diverse_a author_n thread_n compass_n orb_n segment_n ring_n parallel_n &_o equidistant_a line_n the_o division_n of_o circle_n be_v diverslye_o deliver_v by_o the_o greek_n and_o latin_n in_o three_o respect_n first_o in_o respect_n of_o the_o material_a sphere_n within_o the_o which_o some_o of_o the_o circle_n be_v not_o place_v &_o be_v therefore_o call_v extrinsical_a fix_v and_o manisold_a as_o the_o orison_n and_o the_o meridian_n other_o be_v place_v within_o the_o sphere_n &_o be_v therefore_o call_v intrinsical_v movable_a and_o singular_a as_o be_v the_o two_o polares_fw-la the_o equator_fw-la the_o zodiac_n the_o two_o colour_n and_o the_o two_o tropicke_n second_o in_o respect_n of_o the_o pole_n of_o the_o world_n or_o the_o twofolde_a motion_n of_o the_o heaven_n and_o in_o this_o case_n the_o greek_n distinguish_v they_o again_o into_o three_o sort_n the_o first_o be_v parallel_n in_o number_n 5._o namely_o the_o 2._o polares_fw-la the_o 2._o tropick_n and_o the_o equator_fw-la all_o which_o have_v the_o same_o pole_n with_o the_o world_n be_v equidistant_a on_o all_o side_n and_o serve_v the_o first_o or_o universal_a motion_n the_o second_o be_v oblique_a circle_n in_o number_n 3._o namely_o the_o zodiac_n serve_v the_o second_o motion_n the_o horizon_n the_o milk_n way_n all_o the_o which_o lie_v oblique_a between_o the_o pole_n the_o third_o be_v those_o circle_n that_o be_v draw_v through_o the_o pole_n and_o they_o be_v also_o 3._o in_o number_n namely_o the_o equinoctial_a and_o solstitial_a colour_n and_o the_o meridian_n the_o third_o division_n of_o circle_n be_v in_o respect_n of_o their_o quantity_n according_a whereunto_o some_o circle_n be_v call_v great_a and_o some_o less_o the_o great_a circle_n be_v in_o number_n 6._o name_o the_o equator_fw-la the_o zodiac_n theâ—_n colour_n the_o horizon_n and_o the_o meridian_n all_o which_o be_v equal_a
none_o at_o all_o in_o regard_n of_o reason_n when_o one_o place_n be_v distant_a from_o another_o in_o latitude_n only_o that_o be_v from_o the_o north_n to_o the_o south_n or_o contrariwise_o it_o be_v none_o at_o all_o in_o sense_n when_o one_o place_n be_v distant_a from_o another_o according_a unto_o longitude_n which_o be_v from_o the_o east_n unto_o the_o west_n or_o contrariwise_o 36._o scrup_n that_o be_v about_o 300._o furlong_n the_o variety_n be_v manifold_a in_o regard_n also_o of_o reason_n and_o of_o sense_n the_o manifold_a variety_n in_o regard_n of_o reason_n be_v when_o examine_v the_o least_o distance_n toward_o the_o east_n or_o west_n we_o conclude_v another_o meridian_n and_o by_o this_o mean_v we_o may_v have_v so_o many_o meriridian_n as_o there_o shall_v be_v place_n at_o every_o small_a distance_n towards_o the_o east_n the_o manifold_a variety_n according_a unto_o sense_n be_v as_o often_o as_o any_o two_o place_n shall_v be_v distant_a one_o from_o another_o between_o east_n and_o west_n more_fw-mi they_o half_o a_o degree_n and_o by_o this_o mean_v we_o may_v have_v so_o many_o meridians_fw-la as_o there_o be_v half_a degree_n of_o the_o equinoctial_a circle_n the_o office_n of_o the_o meridiane_a be_v twofolde_a either_o astronomical_a or_o geographical_a the_o astronomical_a office_n thereof_o be_v execute_v two_o manner_n of_o way_n 1._o in_o point_v out_o the_o noon_n tide_n or_o midday_n either_o natural_a or_o artificial_a 2._o the_o diverse_a habitude_n and_o position_n of_o the_o star_n follow_v the_o motion_n of_o the_o heaven_n itself_o be_v ascribe_v unto_o the_o meridian_n the_o geographical_a office_n thereof_o be_v also_o of_o two_o sort_n 1._o by_o the_o help_n thereof_o the_o longitude_n of_o all_o place_n be_v calculate_v and_o what_o place_n be_v more_o oriental_a and_o which_o more_o occidental_a 2._o by_o the_o aid_n thereof_o we_o describe_v in_o the_o terrestrial_a plane_n a_o correspondent_a merdiane_fw-la line_n for_o diverse_a use_n of_o astronomicalli_n instrument_n of_o the_o horizon_n chap._n 23._o there_o be_v also_o another_o circle_n which_o the_o ☉_o by_o the_o first_o motion_n do_v point_n out_o in_o the_o east_n and_o west_n point_n who_o definition_n division_n and_o dignity_n be_v to_o be_v consider_v the_o definition_n stretch_v itself_o both_o to_o the_o name_n thereof_o and_o to_o the_o matter_n it_o have_v diverse_a appellation_n and_o be_v sometime_o call_v the_o horizon_n finitor_n finiens_fw-la as_o limit_v our_o sight_n and_o sometime_o the_o compass_n or_o circle_n of_o the_o hemisphere_n of_o diverse_a region_n the_o matter_n itself_o attend_v the_o description_n of_o the_o centre_n or_o pole_n thereof_o the_o circumference_n and_o the_o magnitude_n the_o centre_n or_o pole_n of_o the_o horizon_n be_v the_o vertical_a point_n of_o each_o place_n distant_a from_o the_o equator_fw-la so_o much_o as_o the_o pole_n of_o the_o world_n be_v distant_a from_o the_o horizon_n the_o circumference_n of_o the_o horizon_n be_v that_o which_o the_o semidiameter_n of_o the_o world_n in_o his_o full_a revolution_n through_o the_o point_n of_o the_o east_n and_o west_n and_o the_o rest_n of_o the_o brim_a of_o heaven_n describe_v the_o magnitude_n of_o the_o horizon_n be_v consider_v in_o that_o it_o be_v one_o of_o the_o great_a circle_n divide_v the_o world_n in_o regard_n of_o sense_n into_o 2._o equal_a segmente_n whereof_o the_o one_o be_v call_v the_o upper_a the_o see_v or_o the_o diurnal_a segment_n the_o other_o the_o low_a the_o hide_a or_o the_o nocturnal_a segment_n the_o division_n of_o the_o horizon_n be_v consider_v in_o respect_n of_o the_o equator_fw-la as_o it_o be_v either_o a_o right_n or_o a_o oblique_a horizon_n the_o right_a or_o orthogonall_a horrizon_n have_v 3._o propriety_n 1_o with_o the_o equator_fw-la it_o have_v equal_a angle_n 2_o it_o have_v the_o pole_n or_o the_o vertical_a point_n in_o the_o equator_fw-la 3_o it_o have_v the_o pole_n of_o the_o world_n in_o his_o circumference_n the_o oblique_a bend_a or_o incline_v horizon_n be_v in_o all_o thing_n contrary_a unto_o the_o right_n the_o dignity_n of_o the_o horizon_n by_o reason_n of_o the_o manifold_a use_n thereof_o be_v great_a for_o by_o the_o help_n thereof_o we_o learn_v 6._o thing_n 1_o the_o quantity_n of_o the_o artificial_a day_n and_o night_n and_o consequent_o the_o time_n of_o the_o rise_n and_o set_v of_o the_o ☉_o 2_o the_o equal_a hour_n of_o the_o day_n the_o ☉_o shine_v 3_o the_o degree_n of_o the_o zodiac_n wherewith_o any_o star_n give_v do_v arise_v and_o set_v 4_o what_o star_n do_v always_o appear_v or_o be_v always_o hide_v 5_o the_o rising_z and_o set_v of_o the_o star_n 6_o the_o eclipse_n of_o the_o ☉_o &_o ☽_o either_o see_v or_o not_o see_v the_o division_n of_o the_o horizon_n according_a to_o proclus_n chap._n 24._o moreover_o the_o greek_n deliver_v unto_o we_o a_o more_o subtle_a division_n of_o the_o horizon_n and_o it_o be_v twofold_a the_o one_o to_o be_v conceive_v in_o mind_n only_o the_o other_o fall_v within_o the_o compass_n of_o our_o sense_n or_o our_o sight_n concern_v the_o horizon_n to_o be_v conceive_v in_o mind_n only_o we_o be_v to_o note_v the_o name_n the_o description_n the_o cause_n it_o be_v diverf_o name_v as_o either_o rational_a or_o conceive_v by_o reason_n by_o the_o greek_n call_v 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d and_o also_o natural_a the_o description_n thereof_o be_v absolve_v by_o a_o semidiameter_n and_o a_o circumference_n and_o the_o area_n thereof_o the_o semidiameter_n be_v that_o line_n whereof_o the_o one_o extremity_n be_v in_o the_o eye_n of_o the_o inhabitant_n of_o the_o world_n the_o other_o extremity_n be_v in_o the_o or_o be_v of_o the_o fix_a star_n the_o circumference_n and_o the_o area_n be_v the_o space_n and_o compass_n which_o the_o semidiameter_n make_v be_v carry_v about_o by_o the_o brim_n of_o that_o part_n of_o the_o heaven_n that_o be_v extant_a above_o the_o horizon_n the_o cause_n allege_v be_v that_o our_o sight_n be_v inhable_a to_o pierce_v unto_o the_o behold_n of_o all_o the_o fix_a star_n do_v conclude_v that_o there_o be_v a_o certain_a circle_n in_o the_o heaven_n that_o limit_v the_o thing_n see_v from_o the_o thing_n not_o see_v in_o the_o horrizon_n apprehend_v by_o our_o sense_n we_o be_v to_o note_v the_o name_n the_o description_n the_o variety_n it_o be_v call_v the_o horizon_n sensible_a or_o perceive_v by_o our_o sense_n also_o the_o apparent_a and_o artificial_a horizon_n the_o description_n be_v perform_v by_o a_o semidiameter_n a_o circumference_n and_o a_o plane_n the_o semidiameter_n be_v that_o line_n whereof_o the_o one_o limit_n be_v in_o our_o eye_n the_o other_o be_v in_o the_o end_n of_o our_o sight_n upon_o the_o surface_n of_o the_o earth_n consist_v of_o a_o thousand_o furlong_n which_o end_n we_o imagine_v in_o a_o free_a prospect_n to_o join_v the_o heaven_n and_o the_o earth_n together_o the_o circumference_n and_o plane_n be_v that_o space_n &_o compass_n which_o the_o aforesaid_a semidiameter_n turn_v about_o do_v describe_v the_o variety_n be_v common_a aswell_o unto_o the_o rational_a as_o the_o sensible_a horizon_n &_o it_o be_v either_o none_o at_o all_o or_o else_o manifold_a the_o variety_n of_o the_o sensible_a horizon_n be_v say_v to_o be_v none_o at_o all_o when_o the_o horizon_n do_v continue_v all_o one_o and_o the_o same_o and_o it_o be_v either_o in_o reason_n or_o in_o sense_n the_o sensible_a horizon_n be_v not_o vary_v in_o reason_n when_o the_o place_n be_v not_o any_o whit_n nor_o any_o way_n change_v the_o sensible_a horizon_n be_v say_v not_o to_o be_v vary_v in_o sense_n when_o the_o place_n distant_a about_o 400._o furlonge_v one_o from_o another_o that_o be_v 48_o mi._n do_v not_o alter_v either_o the_o climate_n or_o the_o length_n of_o the_o day_n or_o the_o apparence_n of_o the_o heaven_n the_o variety_n of_o the_o sensible_a horizon_n be_v manifold_a when_o the_o place_n be_v vary_v more_o than_o 400._o furlonge_v and_o be_v situate_v either_o toward_o the_o east_n or_o west_n in_o which_o variety_n neither_o the_o climate_n nor_o the_o length_n of_o the_o day_n nor_o the_o apparence_n of_o the_o heaven_n be_v change_v with_o the_o horizon_n or_o else_o they_o be_v situate_v towards_o the_o north_n or_o south_n wherein_o together_o with_o the_o horizon_n both_o the_o climate_n and_o the_o length_n of_o the_o day_n &_o the_o apparence_n of_o the_o heaven_n be_v alter_v of_o the_o two_o tropicke_n chap._n 25._o the_o ☉_o carry_v about_o by_o the_o second_o motion_n in_o his_o great_a declination_n from_o the_o equator_fw-la by_o the_o violence_n of_o the_o first_o motion_n describe_v certain_a parallel_n whereof_o the_o general_a reason_n the_o number_n &_o the_o office_n be_v to_o be_v consider_v the_o