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
argument_n be_v derive_v from_o the_o consutation_n of_o 2._o opinion_n whereof_o the_o one_o suppose_v thà t_v the_o motion_n of_o the_o heaven_n be_v direct_a and_o instnite_a which_o if_o it_o be_v the_o star_n shall_v vanish_v out_o of_o our_o sight_n the_o other_o that_o the_o star_n in_o their_o set_n be_v quench_v and_o in_o their_o rise_n be_v light_v again_o as_o heraclitus_n affirm_v which_o be_v absurd_a both_o in_o respect_n of_o the_o motion_n which_o be_v perpetual_a and_o constant_a in_o itself_o and_o of_o the_o contrary_a power_n which_o can_v be_v in_o the_o earth_n as_o also_o in_o regard_n of_o our_o antipode_n who_o west_n be_v our_o east_n the_o second_o argument_n be_v draw_v from_o the_o dignity_n thereof_o for_o the_o circular_a motion_n be_v the_o most_o worthy_a and_o more_o perfect_a than_o the_o right_a motion_n inasmuch_o as_o it_o breed_v no_o scission_n or_o cut_n and_o be_v make_v about_o the_o midst_n of_o the_o whole_a not_o by_o displace_v the_o whole_a body_n but_o by_o the_o only_o unchangeable_a succession_n of_o the_o situation_n of_o the_o part_n the_o criculare_a figure_n of_o the_o heaven_n be_v prove_v partly_o by_o similitude_n and_o partly_o by_o reason_n the_o similitude_n be_v this_o namely_o that_o this_o sensible_a world_n be_v the_o image_n of_o the_o first_o archetype_n or_o pattern_n of_o the_o world_n who_o be_v without_o beginning_n or_o end_n the_o reason_n do_v contain_v either_o the_o commodity_n of_o the_o circular_a figure_n or_o the_o necessity_n the_o commodity_n consist_v either_o in_o the_o capacity_n or_o else_o in_o the_o swistnes_n or_o aptness_n unto_o motion_n the_o capacity_n be_v sit_v for_o the_o heaven_n in_o that_o they_o be_v to_o comprehend_v all_o other_o thing_n fot_o the_o circular_a figure_n be_v the_o grate_a of_o alother_n circumscribe_v with_o equal_a conneâ—ities_n the_o sâ—â—stâ—es_n or_o aptness_n unto_o 〈◊〉_d be_v either_o belong_v unto_o the_o diurnal_a motion_n call_v also_o the_o right_a hand_n monon_o nature_n all_o unto_o the_o 〈◊〉_d storel_n unto_o the_o second_o motion_n which_o resist_v the_o former_a their_o ason_n draw_v from_o the_o necessity_n of_o the_o circular_a figure_n be_v either_o in_o respect_n of_o the_o whole_a world_n for_o if_o the_o 〈◊〉_d be_v of_o any_o other_o figure_n there_o must_v needs_o be_v some_o empty_a place_n and_o a_o body_n without_o a_o place_n for_o elsan_n regard_n of_o the_o celestial_a orb_n which_o gather_v can_v not_o be_v tarn_v about_o by_o diverse_a motion_n or_o else_o they_o shall_v suffer_v a_o scission_n or_o cut_v in_o sunder_o not_o without_o their_o great_a hurt_n there_o be_v one_o sarface_n of_o the_o earth_n and_o water_n and_o that_o be_v round_o chap._n 12._o the_o earth_n and_o the_o water_n make_v one_o globe_n and_o it_o be_v prove_v by_o cause_n either_o general_a or_o special_a the_o general_a cause_n belong_v unto_o both_o the_o element_n make_v up_o in_o one_o form_n and_o be_v derive_v from_o 3._o head_n first_o from_o the_o signification_n of_o the_o worder_n for_o both_o in_o common_a speech_n and_o in_o the_o scripture_n it_o be_v call_v orbis_n terra_fw-la the_o globe_n of_o the_o earth_n or_o the_o round_a world_n second_o from_o the_o spherical_a form_n aswell_o of_o the_o heaven_n into_o who_o round_a compass_n inasmuch_o as_o it_o be_v include_v it_o can_v be_v but_o it_o must_v also_o be_v round_o as_o also_o of_o the_o shadow_n that_o this_o globe_n do_v cast_v forth_o for_o the_o master_n of_o perspective_n do_v teach_v we_o that_o such_o be_v the_o dark_a body_n as_o be_v the_o shadow_n thereof_o thirdlye_o from_o the_o natural_a descend_v of_o the_o portion_n either_o of_o the_o earth_n the_o say_a portion_n covet_v the_o centre_n of_o the_o globe_n and_o fall_v upon_o the_o surface_n of_o the_o earth_n at_o right_a angle_n or_o else_o of_o the_o water_n sink_v also_o into_o the_o centre_n of_o the_o world_n for_o the_o which_o their_o descend_a they_o gather_v themselves_o into_o a_o round_a form_n and_o can_v abide_v upon_o a_o plane_n surrace_n the_o special_a cause_n be_v such_o as_o decern_v the_o roundness_n of_o the_o earth_n and_o of_o the_o water_n particulare_o the_o roundness_n of_o the_o earth_n be_v decern_v two_o way_n the_o one_o be_v according_a unto_o longitude_n from_o the_o last_o towards_o the_o west_n or_o contrariwise_o and_o that_o either_o by_o all_o the_o star_n which_o in_o diverse_a place_n do_v not_o appear_v at_o the_o same_o instant_n or_o else_o cheâ—sely_o by_o the_o ☽_o who_o eclipse_n fall_v out_o at_o one_o and_o the_o same_o time_n but_o by_o those_o in_o the_o east_n reckon_v one_o way_n by_o those_o in_o the_o west_n another_o the_o other_o be_v according_a unto_o latitude_n from_o the_o equator_fw-la toward_o each_o pole_n gather_v by_o the_o unlike_a elevation_n of_o the_o pole_n and_o inequal_a quantity_n of_o the_o day_n both_o which_o increase_n unto_o those_o that_o go_v from_o the_o equator_fw-la towards_o the_o north_n or_o south_n the_o roundness_n of_o the_o water_n be_v decern_v by_o token_n derive_v from_o the_o swell_n of_o the_o drop_n either_o hang_v or_o throw_v upon_o the_o dust_n or_o lay_v upon_o the_o moss_n of_o bough_n as_o also_o from_o the_o swell_n of_o the_o sea_n by_o mean_n whereof_o the_o land_n can_v be_v see_v from_o the_o ship_n below_o although_o from_o the_o main_a top_n it_o may_v and_o again_o if_o any_o shine_a thing_n be_v sasten_v to_o the_o top_n of_o a_o ship_n say_v fair_a from_o the_o shore_n it_o deseend_v by_o little_a and_o little_a according_a as_o the_o ship_n run_v further_o off_o and_o at_o the_o last_o be_v hide_v from_o the_o sight_n the_o situation_n immobilitie_n and_o magnitude_n of_o the_o terrestrial_a globe_n chap._n 13._o the_o earth_n or_o globe_n of_o the_o earth_n and_o water_n have_v situation_n rest_n and_o magnitude_n the_o situation_n as_o be_v in_o the_o centre_n or_o the_o place_n of_o the_o world_n far_a distant_a from_o the_o extremity_n thereof_o be_v prove_v by_o argument_n either_o direct_a or_o indirect_a the_o direct_a be_v derive_v from_o the_o nature_n of_o the_o break_a part_n express_v either_o physicallye_n or_o astronomical_o physical_o because_o wheresoever_o they_o be_v about_o the_o earth_n we_o alwate_v observe_v they_o that_o of_o their_o own_o inclination_n they_o tend_v downward_o but_o the_o centre_n be_v the_o low_a place_n astronomical_o inasmuch_o as_o all_o the_o semidiameter_n of_o the_o world_n by_o which_o heavy_a thing_n descend_v be_v continue_v through_o the_o centre_n of_o the_o world_n and_o there_o they_o cut_v one_o another_o so_o that_o where_o the_o section_n be_v make_v there_o must_v needs_o be_v the_o place_n of_o the_o earth_n the_o indirect_a argument_n consist_v in_o two_o supposition_n the_o one_o that_o the_o earth_n be_v in_o the_o axis_n of_o the_o motion_n of_o the_o heaven_n towardé_v one_o side_n &_o then_o shall_v be_v take_v away_o the_o apparent_a reason_n of_o the_o middle_a heaven_n the_o reason_n of_o the_o shadow_n equinoctial_a solstitial_a and_o plagall_a and_o the_o reason_n of_o the_o universal_a equinoctialle_n the_o other_o supposition_n that_o the_o earth_n be_v without_o the_o axis_n remove_v from_o the_o pole_n either_o to_o the_o east_n or_o to_o the_o westward_n and_o then_o shall_v be_v take_v away_o both_o in_o the_o rise_n and_o set_v the_o equal_a quantity_n both_o of_o the_o dare_v shadow_n and_o star_n the_o rest_n of_o the_o earth_n exclude_v all_o local_a motion_n either_o right_a or_o circulate_v the_o right_a motion_n be_v that_o which_o be_v make_v from_o the_o midst_n and_o it_o be_v either_o natural_a and_o peculiar_a unto_o the_o earth_n for_o otherwise_o it_o shall_v come_v to_o pass_v that_o heavy_a thing_n shall_v ascend_v or_o else_o it_o be_v violent_a some_o outward_a thing_n insorce_v it_o for_o otherwise_o it_o shall_v come_v to_o pass_v that_o the_o earth_n shall_v forsake_v the_o centre_n of_o the_o world_n the_o earth_n have_v no_o circular_a motion_n neither_o from_o the_o west_n to_o the_o eastward_o as_o some_o have_v think_v for_o if_o it_o have_v all_o thing_n that_o be_v move_v in_o the_o aer_fw-la shall_v always_o be_v move_v to_o the_o westward_o neither_o from_o the_o last_o to_o the_o westward_n by_o the_o dâ—â—n_a awl_n motion_n for_o than_o it_o shall_v be_v a_o hard_a matter_n to_o travail_v towards_o the_o east_n then_o towards_o the_o west_n the_o magnitude_n of_o the_o earth_n be_v nothing_o be_v compare_v either_o with_o the_o whole_a world_n whereof_o it_o be_v the_o centre_n which_o be_v prove_v by_o mathematical_a instrument_n that_o agree_v with_o the_o centre_n of_o the_o world_n for_o they_o at_o one_o time_n and_o through_o the_o same_o sight_n hole_n show_v two_o star_n opposite_a in_o the_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