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metaphysic_n now_o it_o be_v manifest_a that_o a_o right_a line_n draw_v betwixt_o the_o same_o point_n be_v always_o short_a as_o euclid_n show_v in_o his_o element_n where_o he_o demonstrate_v that_o two_o side_n of_o any_o triangle_n be_v count_v together_o be_v long_o than_o the_o three_o the_o better_a to_o understand_v the_o work_n of_o nature_n we_o shall_v observe_v in_o the_o motion_n of_o a_o heavy_a part_n to_o the_o centre_n a_o double_a scope_n or_o end_n first_o that_o the_o say_a part_n of_o a_o terrestrial_a body_n shall_v be_v move_v or_o separate_v from_o the_o place_n to_o which_o it_o be_v by_o violence_n transpose_v second_o that_o this_o body_n shall_v be_v restore_v home_o and_o unite_v to_o the_o spherical_a substance_n of_o the_o earth_n in_o which_o it_o must_v chief_o seek_v its_o preservation_n that_o these_o two_o end_n be_v best_a and_o soon_o compass_v by_o a_o right_a line_n be_v most_o manifest_a for_o
first_o a_o sepaparation_n from_o the_o place_n to_o which_o it_o be_v move_v be_v more_o quick_a &_o expedient_a by_o a_o right_a line_n forasmuch_o as_o crooked_a and_o circular_a line_n turn_v back_o as_o it_o be_v into_o themselves_o again_o also_o the_o union_n and_o conjunction_n of_o a_o part_n with_o the_o sphere_n of_o the_o earth_n be_v most_o indebt_v to_o a_o right_a motion_n because_o as_o we_o have_v declare_v the_o way_n be_v short_a second_o it_o may_v be_v allege_v that_o nature_n be_v a_o uniform_a and_o necessary_a agent_n restrain_v to_o one_o only_o bind_v or_o end_n and_o therefore_o can_v neither_o strengthen_v weaken_v remit_v or_o suspend_v the_o action_n but_o work_v always_o by_o the_o same_o mean_n the_o same_o effect_n whence_o it_o be_v that_o she_o choose_v a_o right_a line_n be_v but_o one_o betwixt_o two_o point_n whereas_o crooked_a line_n may_v be_v draw_v infinite_a and_o the_o motion_n direct_v by_o crooked_a line_n will_v prove_v various_a and_o opposite_a to_o the_o prescript_n of_o nature_n moreover_o shall_v we_o imagine_v that_o nature_n at_o any_o time_n wrought_v by_o a_o crooked_a or_o circular_a line_n it_o may_v be_v demand_v from_o what_o agent_n this_o obliquity_n shall_v arise_v not_o from_o nature_n itself_o because_o as_o we_o say_v she_o work_v always_o to_o the_o utmost_a of_o her_o strength_n have_v no_o power_n to_o remit_v or_o suspend_v her_o actioâ—s_n but_o a_o crooked_a motion_n arise_v from_o the_o remission_n or_o slack_n of_o the_o agent_n force_v and_o turn_v it_o away_o from_o the_o intend_a end_n which_o only_o find_v place_n in_o free_a and_o voluntary_a agent_n neither_o come_v this_o deflexion_n from_o the_o medium_n or_o air_n because_o it_o can_v have_v no_o such_o power_n to_o resist_v three_o if_o the_o motion_n be_v not_o perform_v in_o a_o right_a line_n it_o can_v have_v no_o opposite_a or_o contrary_n because_o as_o aristotle_n teach_v to_o a_o circular_a or_o crooked_a motion_n 4._o no_o other_o motion_n can_v be_v opposite_a or_o contrary_n in_o respect_n of_o the_o whole_a circle_n but_o only_o in_o regard_n of_o the_o diameter_n which_o be_v always_o a_o right_a line_n by_o this_o it_o be_v plain_a that_o a_o weighty_a point_n consider_v in_o itself_o abstract_o can_v but_o be_v carry_v to_o the_o centre_n in_o a_o right_a line_n which_o right_a line_n real_o and_o physical_o point_v out_o unto_o we_o a_o radius_fw-la or_o beam_n draw_v from_o the_o centre_n to_o the_o circumference_n to_o show_v that_o the_o god_n of_o nature_n in_o compose_v the_o earthly_a globe_n both_o observe_v and_o teach_v we_o the_o use_n of_o geometry_n 2_o a_o point_n move_v towards_o the_o centre_n will_v move_v swift_a in_o the_o end_n then_o in_o the_o beginning_n this_o have_v be_v plain_o observe_v by_o experience_n that_o a_o stone_n let_v fall_v from_o a_o tower_n or_o high_a place_n will_v in_o motion_n grow_v swift_a and_o swift_a till_o it_o approach_v the_o ground_n or_o place_n whereon_o it_o fall_v the_o reason_n may_v be_v give_v from_o the_o air_n which_o resist_v so_o much_o the_o less_o by_o how_o much_o the_o body_n descend_v low_a towards_o the_o earth_n or_o centre_n because_o when_o it_o be_v high_a the_o distance_n be_v great_a the_o part_n of_o the_o air_n will_v make_v more_o resistance_n the_o reason_n render_v by_o aristotle_n of_o this_o resistance_n be_v because_o in_o the_o begin_n of_o the_o motion_n the_o stone_n or_o heavy_a body_n find_v the_o air_n quiet_a and_o fix_a but_o be_v once_o set_v on_o motion_n the_o high_a part_n of_o the_o air_n successive_o move_v those_o which_o be_v under_o be_v drive_v by_o the_o violence_n of_o the_o stone_n so_o fall_v and_o prepare_v as_o it_o be_v the_o way_n for_o his_o come_n this_o reason_n may_v in_o some_o sort_n content_v a_o ingenious_a wit_n till_o a_o better_a be_v find_v out_o 10_o so_o much_o for_o the_o motion_n of_o a_o heavy_a point_n or_o centre_n it_o remain_v that_o we_o treat_v next_o of_o the_o motion_n and_o conformity_n of_o magnitude_n to_o the_o centre_n of_o the_o earth_n wherein_o we_o consider_v not_o only_o the_o centre_n or_o middle_a point_n but_o the_o whole_a mass_n of_o the_o magnitude_n who_o motion_n and_o conformity_n shall_v be_v express_v in_o this_o theorem_a 1_o the_o motion_n of_o a_o magnitude_n towards_o the_o centre_n be_v not_o mere_o natural_a but_o mix_v with_o a_o violent_a motion_n this_o may_v easy_o be_v demonstrate_v because_o no_o point_n of_o any_o magnitude_n be_v move_v to_o the_o centre_n natural_o but_o the_o middle_a point_n or_o centre_n of_o the_o magnitude_n for_o although_o the_o centre_n be_v move_v in_o a_o perpendicular_a line_n which_o make_v right_a angle_n with_o the_o horizon_n yet_o the_o extreme_a part_n be_v move_v in_o line_n parallel_v which_o can_v possible_o make_v right_a angle_n with_o the_o horizon_n or_o meet_v in_o the_o centre_n which_o may_v be_v show_v in_o this_o figure_n let_v there_o be_v a_o circle_n as_o abl_v this_o do_v we_o will_v imagine_v a_o certain_a magnitude_n hang_v in_o the_o air_n and_o tend_v to_o the_o centre_n c_o which_o be_v signify_v by_o the_o line_n pen_n it_o be_v certain_a that_o the_o centre_n of_o the_o magnitude_n e_o will_v move_v and_o conform_v itself_o downward_o towards_o the_o centre_n of_o the_o earth_n by_o the_o line_n aec_fw-la which_o motion_n will_v be_v natural_a as_o that_o which_o be_v derive_v to_o a_o centre_n from_o a_o circumference_n by_o the_o direct_a radius_fw-la which_o be_v the_o rule_n of_o all_o natural_a motion_n but_o the_o other_o part_n without_o the_o centre_n of_o this_o magnitude_n can_v move_v but_o in_o so_o many_o line_n which_o shall_v be_v parallel_v the_o one_o to_o the_o other_o as_o for_o example_n the_o point_n n_o must_v needs_o move_v in_o the_o line_n ng_z and_o the_o point_n p_o in_o the_o line_n pf_n which_o be_v of_o equal_a distance_n will_v never_o concur_v in_o the_o centre_n and_o therefore_o can_v be_v esteem_v natural_a ray_n of_o the_o circle_n whence_o we_o may_v collect_v that_o the_o motion_n of_o these_o part_n be_v not_o natural_a but_o violent_a for_o if_o any_o shall_v imagine_v the_o motion_n of_o these_o part_n to_o be_v natural_a then_o shall_v the_o point_n n_o move_v to_o the_o centre_n of_o the_o earth_n by_o the_o line_n nc_fw-fr and_o the_o point_n p._n by_o the_o line_n pc_n and_o so_o by_o how_o much_o the_o more_o any_o weighty_a body_n shall_v approach_v the_o centre_n of_o the_o earth_n by_o so_o much_o it_o shall_v be_v diminish_v and_o curtail_v in_o his_o quantity_n so_o that_o in_o the_o centre_n itself_o all_o the_o part_n shall_v concur_v in_o a_o indivisible_a point_n which_o be_v absurd_a &_o contradict_v all_o reason_n 11_o hitherto_o have_v we_o speak_v of_o the_o conformity_n of_o all_o earthly_a and_o weighty_a body_n to_o the_o terrene_a centre_n as_o they_o be_v take_v absolute_o it_o now_o remain_v that_o we_o speak_v of_o these_o body_n as_o they_o be_v take_v comparative_o be_v compare_v one_o with_o the_o other_o this_o discourse_n proper_o belong_v to_o a_o art_n which_o be_v call_v staticke_a and_o mathematical_a who_o office_n be_v to_o demonstrate_v the_o affection_n of_o heaviness_n and_o lightness_n of_o all_o body_n out_o of_o their_o cause_n the_o chief_a sensible_a instrument_n whereon_o these_o property_n be_v demonstrate_v and_o show_v be_v the_o bilanz_n or_o ballance_n but_o these_o specialty_n we_o leave_v to_o such_o as_o have_v purposely_o write_v of_o this_o subject_n among_o which_o the_o most_o ancient_a and_o chief_a be_v archimedes_n who_o heavenly_a wit_n overtake_v all_o such_o as_o go_v before_o he_o and_o outgo_v all_o such_o as_o followed_z enough_o it_o will_v seem_v in_o this_o treatise_n to_o insert_v a_o proposition_n or_o two_o staticall_a to_o show_v the_o conformity_n of_o two_o magnitude_n and_o their_o proper_a centre_n move_v downward_o towards_o the_o globe_n of_o the_o earth_n and_o its_o centre_n 1_o the_o line_n wherein_o the_o centre_n of_o two_o heavy_a body_n be_v move_v downward_o be_v continue_v will_v meet_v in_o the_o centre_n of_o the_o earth_n a_o heavy_a point_n or_o centre_n as_o we_o have_v demonstrate_v heretofore_o in_o this_o chapter_n be_v move_v towards_o the_o centre_n of_o the_o world_n in_o a_o right_a line_n which_o be_v imagine_v to_o be_v a_o ray_n of_o the_o whole_a sphere_n derive_v from_o the_o circumference_n to_o the_o centre_n &_o therefore_o it_o be_v impossible_a they_o shall_v be_v parallel_n or_o equidistant_a but_o concurrent_a line_n but_o because_o the_o whole_a distance_n betwixt_o we_o and_o the_o centre_n be_v very_o great_a it_o must_v needs_o happen_v that_o in_o a_o small_a space_n the_o concourse_n of_o
360_o by_o multiplication_n be_v produce_v have_v exact_o these_o part_n 1.2.3.4.5.6.10.12.15.20.30_o likewise_o 360_o have_v exact_o 1.2.3.4.5.6.8.9.10.12.15.18.20.24.30.36.40.46.60.72.90.120.180_o of_o all_o which_o part_v there_o be_v so_o great_a use_n in_o astronomy_n and_o many_o time_n in_o geography_n that_o without_o it_o there_o will_v be_v small_a exactness_n for_o as_o we_o see_v a_o yard_n measure_n will_v little_a steed_n the_o mercer_n or_o clothier_n except_o it_o be_v again_o divide_v into_o small_a part_n so_o fall_v it_o out_o in_o the_o account_n of_o the_o cosmographer_n 3_o of_o the_o terrestrial_a circle_n some_o be_v absolute_a some_o relative_n the_o absolute_a be_v such_o as_o be_v assign_v without_o any_o respect_n to_o our_o sight_n of_o which_o sort_n be_v the_o meridian_n and_o parallel_n 4._o the_o meridian_n be_v a_o circle_n draw_v by_o the_o pole_n of_o the_o world_n and_o the_o vertical_a point_n of_o the_o place_n the_o meridian_n circle_n be_v so_o call_v of_o astronomer_n because_o when_o the_o sun_n according_a to_o their_o supposition_n by_o the_o motion_n of_o the_o first_o movable_a come_v into_o this_o circle_n it_o make_v midday_n and_o then_o have_v be_v run_v his_o course_n from_o his_o rise_n to_o arrive_v there_o just_a so_o long_o as_o he_o shall_v be_v move_v from_o thence_o to_o the_o place_n of_o his_o set_n in_o this_o meridian_n be_v place_v the_o two_o pole_n of_o the_o equator_fw-la which_o be_v the_o same_o with_o the_o pole_n of_o the_o world_n in_o this_o also_o be_v the_o vertical_a point_n and_o the_o point_n opposite_a unto_o it_o term_v the_o pole_n of_o the_o horizon_n whereof_o we_o shall_v speak_v hereafter_o so_o that_o so_o many_o meridian_n be_v imagine_a to_o be_v in_o the_o earth_n as_o there_o be_v vertical_a point_n for_o howsoever_o we_o see_v not_o many_o meridian_n paint_v on_o the_o face_n of_o the_o artificial_a globe_n yet_o must_v there_o be_v so_o many_o imagine_v in_o the_o real_a earth_n as_o zenithes_n and_o orison_n so_o that_o it_o be_v impossible_a for_o a_o man_n to_o move_v never_o so_o little_a from_o east_n to_o west_n without_o change_v his_o meridian_n yet_o for_o more_o order_n sake_n have_v the_o cosmographer_n reduce_v the_o number_n of_o meridian_n to_o half_a the_o number_n of_o the_o degree_n in_o a_o circle_n to_o wit_n to_o 180_o that_o every_o meridian_n cut_v the_o equator_fw-la and_o other_o parallel_n in_o two_o opposite_a place_n shall_v answer_v to_o two_o degree_n in_o the_o same_o circle_n by_o which_o it_o appear_v that_o every_o meridian_n divide_v the_o terrene_a globe_n in_o two_o half_n whereof_o the_o one_o be_v respective_o term_v of_o the_o east_n the_o other_o of_o the_o west_n but_o to_o avoid_v all_o ambiguity_n of_o speech_n we_o ought_v to_o consider_v that_o a_o meridian_n be_v twofold_a either_o the_o true_a meridian_n or_o magnetical_a meridian_n the_o true_a meridian_n ordinary_o so_o call_v be_v that_o which_o direct_o pass_v by_o the_o pole_n of_o the_o world_n of_o which_o we_o here_o treat_v which_o indeed_o as_o we_o shall_v show_v be_v the_o only_a true_a magnetical_a meridian_n but_o that_o which_o some_o have_v false_o call_v the_o magnetical_a meridian_n be_v that_o which_o run_v by_o the_o pole_n of_o the_o magnetical_a variation_n and_o much_o differ_v from_o the_o true_a because_o as_o we_o have_v teach_v the_o variation_n be_v diverse_a according_a to_o the_o diversity_n of_o place_n &_o therefore_o can_v answer_v in_o any_o certain_a proportion_n to_o the_o pole_n of_o the_o terrene_a globe_n the_o true_a meridian_n circle_n as_o it_o have_v manifold_a use_n in_o astronomy_n namely_o to_o distinguish_v midday_n and_o midnight_n to_o measure_v the_o rise_n and_o set_v of_o the_o star_n etc._n etc._n matter_n not_o to_o be_v neglect_v of_o geographer_n so_o have_v it_o a_o more_o special_a use_n in_o geography_n to_o design_n the_o longitude_n and_o latitude_n of_o the_o place_n with_o their_o distance_n with_o many_o other_o matter_n treat_v of_o hereafter_o 5_o concern_v the_o meridian_n circle_v we_o be_v to_o know_v two_o thing_n the_o invention_n of_o it_o and_o the_o distinction_n the_o invention_n be_v whereby_o we_o be_v teach_v to_o find_v out_o the_o true_a meridian_n in_o any_o place_n assign_v 6_o the_o invention_n of_o the_o meridian_n be_v again_o twofold_a the_o one_o more_o accurate_a which_o be_v either_o astronomical_a or_o magnetical_a the_o other_o popular_a the_o astronomical_a way_n be_v perform_v by_o observe_v the_o celestial_a motion_n the_o meridian_n may_v be_v find_v out_o the_o astronomical_a way_n in_o diverse_a manner_n by_o instrument_n devise_v for_o this_o purpose_n by_o ingenious_a artificer_n whereof_o some_o be_v describe_v by_o gemma_fw-la frisius_n in_o his_o cosmographie_n but_o to_o avoid_v the_o cost_n of_o curious_a instrument_n i_o will_v set_v down_o our_o way_n depend_v on_o this_o theorem_a 1_o if_o two_o several_a sunne-shadowe_n be_v observe_v the_o one_o in_o the_o forenoon_n the_o other_o in_o the_o afternoon_n of_o the_o same_o day_n exact_o to_o touch_v with_o their_o end_n the_o circumference_n of_o the_o same_o circle_n describe_v in_o a_o plain_a parallel_n to_o the_o plain_a of_o the_o horizon_n the_o line_n from_o the_o centre_n equal_o divide_v the_o arch_n of_o that_o circle_n betwixt_o the_o two_o shadow_n will_v be_v the_o true_a meridian_n circle_n for_o that_o place_n this_o theorem_a howsoever_o consist_v of_o many_o part_n be_v notwithstanding_o easy_a enough_o to_o be_v understand_v be_v explayn_v by_o a_o ocular_a demonstration_n let_v there_o be_v get_v a_o platform_n of_o wood_n or_o metal_n and_o place_v even_o that_o it_o may_v lie_v parallel_n with_o the_o plain_a of_o the_o horizon_n in_o this_o plain_a let_v there_o be_v describe_v diverse_a circle_n from_o the_o same_o centre_n e._n in_o this_o centre_n let_v there_o be_v raise_v a_o gnomon_n of_o to_o right_a angle_n so_o that_o the_o top_n of_o this_o gnomon_n f_o shall_v every_o where_o be_v equal_o distant_a from_o the_o circumference_n of_o each_o circle_n describe_v in_o the_o plain_a which_o may_v easy_o be_v know_v because_o if_o it_o be_v equal_o distant_a from_o any_o three_o point_n of_o any_o circle_n circumference_n it_o will_v also_o be_v equal_o distant_a from_o all_o the_o rest_n alike_o as_o clavius_n have_v teach_v in_o the_o 4_o of_o his_o gnomonic_n this_o platform_n be_v thus_o order_v let_v the_o shadow_n of_o the_o gnomon_n be_v observe_v sometime_o before_o noon_n until_o such_o time_n as_o it_o exact_o shall_v touch_v the_o circumference_n of_o one_o of_o those_o circle_n as_o in_o eglantine_n again_o in_o the_o afternoon_n let_v the_o shadow_n be_v observe_v till_o with_o his_o end_n it_o meet_v the_o circumference_n of_o the_o same_o circle_n as_o in_o eh_n which_o will_v happen_v so_o many_o hour_n afternoon_n as_o the_o other_o before_o noon_n these_o two_o point_n g_z and_o h_z be_v diligent_o observe_v let_v the_o arch_n of_o the_o circle_n gh_o be_v divide_v into_o two_o half_n with_o a_o line_n draw_v from_o the_o centre_n e_o which_o shall_v be_v ed._n this_o line_n ed_z will_v be_v the_o true_a meridian_n for_o that_o place_n on_o which_o when_o the_o shadow_n of_o the_o gnomon_n shall_v happen_v to_o fall_v we_o may_v assure_v ourselves_o that_o it_o be_v full_a noon_n 7_o the_o magnetical_a invention_n be_v perform_v by_o the_o magnetical_a directory_n needle_n this_o way_n be_v subject_a to_o much_o error_n and_o not_o so_o certain_a as_o the_o former_a because_o as_o we_o have_v show_v before_o there_o be_v find_v very_o few_o place_n which_o admit_v not_o some_o of_o variation_n yet_o because_o it_o may_v be_v profitable_a to_o such_o who_o have_v not_o the_o command_n always_o of_o the_o sun_n or_o sight_n of_o the_o star_n i_o will_v insert_v this_o theorem_a 1_o the_o line_n wherein_o the_o directory_n needle_n be_v direct_v from_o north_n to_o south_n be_v the_o meridian_n for_o the_o place_n this_o may_v be_v show_v in_o any_o mariner_n compass_n or_o 〈◊〉_d sunne-dyall_n who_o needle_n be_v magnetical_o touch_v for_o bâ—â—ing_v set_v even_o parallel_v to_o the_o plain_n of_o the_o horizon_n it_o will_v show_v by_o the_o needle_n the_o miridian_n for_o that_o place_n in_o every_o vertical_a point_n on_o the_o earth_n for_o example_n in_o the_o sea-compasse_n in_o the_o next_o page_n experience_n will_v witness_v in_o every_o region_n of_o the_o earth_n that_o the_o one_o point_n sign_v out_o by_o the_o lily_n will_v always_o turn_v to_o the_o north_n the_o other_o opposite_a part_n will_v turn_v itself_o to_o the_o south_n which_o two_o part_n be_v join_v together_o by_o a_o right_a line_n will_v show_v the_o meridian_n foâ—â—â—at_a place_n the_o meridian_n i_o say_v not_o always_o the_o true_a for_o this_o invention_n take_v from_o
in_o longitude_n 30_o degree_n 45_o minute_n in_o latitude_n 49_o degree_n 35_o min_fw-mi then_o we_o will_v suppose_v summatra_n as_o place_v at_o c_o to_o have_v in_o longitude_n 131_o degree_n but_o no_o latitude_n the_o difference_n of_o longitude_n will_v be_v aec_fw-la of_o 100_o degree_n 15_o minute_n and_o the_o compliment_n ae_n 79_o degree_n 45_o minute_n then_o work_v according_a to_o the_o rule_n of_o trigonometry_n we_o shall_v find_v the_o sign_n of_o the_o arch_a fc_n to_o be_v 6_o degree_n 37_o ½_o minute_n which_o be_v add_v to_o fc_n be_v 90_o degree_n will_v produce_v 96_o degree_n 37_o ½_o minute_n to_o which_o arch_n there_o will_v answer_v 1449_o german-mile_n 16_o the_o second_o case_n be_v when_o both_o place_n be_v situate_a without_o the_o equatour_n this_o be_v again_o twofold_a for_o either_o the_o two_o place_n be_v understand_v to_o be_v situate_a towards_o the_o same_o pole_n or_o else_o one_o place_n towards_o the_o northern_a the_o other_o towards_o the_o southern_a pole_n both_o which_o case_n shall_v be_v teach_v in_o these_o rule_n 1_o if_o both_o place_n who_o distance_n be_v seek_v be_v situate_a towards_o the_o same_o pole_n there_o will_v arise_v a_o triangle_n who_o side_n and_o angle_n will_v be_v know_v by_o the_o four_o axiom_n of_o pitiscus_n in_o trigonometry_n the_o four_o book_n as_o for_o example_n in_o this_o present_a figure_n let_v the_o two_o place_n give_v be_v fg_v the_o triangle_n to_o be_v know_v will_v be_v fbg_n who_o acute_a angle_n will_v be_v at_o b._n let_v the_o place_n give_v be_v as_o fh_n the_o triangle_n to_o be_v resolve_v &_o know_v will_v be_v fbh_n have_v a_o right_a angle_n at_o h._n final_o if_o the_o place_n supposâ—ed_v to_o be_v give_v be_v as_o fi_n the_o triangle_n to_o be_v know_v will_v be_v fbi_n with_o a_o obtuse_a angle_n at_o i._n 2_o if_o the_o one_o place_n be_v situate_v towards_o the_o north-pole_n and_o the_o other_o towards_o the_o south-pole_n there_o will_v arise_v a_o triangle_n whereof_o the_o one_o side_n about_o the_o angle_n which_o be_v give_v will_v be_v great_a than_o a_o quadrant_a as_o in_o the_o former_a figure_n let_v the_o place_n give_v be_v as_o g_z and_o k_o also_o h_n and_o k_n also_o i_o and_o k_o there_o will_v still_o fall_v out_o a_o triangle_n who_o one_o side_n contain_v the_o angle_n give_v will_v be_v great_a than_o a_o quadrant_a as_o bk_n wherefore_o for_o the_o side_n bk_n you_o must_v take_v his_o compliment_n to_o the_o semicircle_n bf_n that_o be_v for_o the_o triangle_n gbk_n you_o must_v work_v by_o the_o triangle_n gbf_n and_o instead_o of_o the_o triangle_n hbk_n you_o must_v take_v the_o triangle_n hbf_n and_o for_o the_o triangle_n ibk_n you_o must_v work_v by_o the_o triangle_n ibf_n according_a to_o the_o four_o axiom_n of_o the_o four_o book_n of_o pitiscus_n to_o which_o i_o have_v rather_o refer_v my_o reader_n then_o intermix_v our_o geographical_a discourse_n with_o handle_v the_o principle_n of_o geometry_n which_o here_o be_v to_o be_v suppose_v so_o many_o precedent_a proposition_n which_o express_v as_o they_o ought_v will_v transcend_v the_o bound_n of_o my_o intend_a journey_n 17_o of_o the_o astractive_a way_n of_o find_v out_o the_o distance_n of_o place_n we_o have_v speak_v the_o mechanical_a depend_v on_o the_o use_n of_o instrument_n and_o mechanical_a operation_n whereof_o we_o will_v show_v one_o way_n in_o this_o theorem_a 1_o by_o the_o work_n with_o a_o semicircle_n the_o distance_n of_o two_o place_n may_v be_v find_v out_o this_o invention_n by_o mr_n blundevill_n seem_v to_o be_v ascribe_v to_o edward_n wright_n yet_o have_v it_o be_v take_v up_o of_o foreign_a writer_n as_o their_o own_o and_o use_v in_o their_o chart_n and_o map_n the_o manner_n of_o operation_n be_v thus_o first_o let_v there_o be_v draw_v a_o semicircle_n upon_o a_o right_a diameter_n sign_v out_o will_v be_v the_o letter_n abcd_v whereof_o d_o shall_v be_v the_o centre_n as_o you_o find_v it_o decipher_v in_o this_o present_a figure_n the_o great_a this_o semicircle_n be_v make_v so_o much_o the_o more_o easy_a will_v be_v the_o operation_n because_o the_o degree_n will_v be_v large_a then_o this_o semicircle_n be_v draw_v and_o according_o divide_v imagine_v that_o by_o the_o help_n of_o it_o you_o desire_v to_o find_v out_o the_o distance_n betwixt_o london_n and_o jerusalem_n which_o city_n be_v know_v to_o differ_v both_o in_o longitude_n and_o latitude_n now_o that_o the_o true_a distance_n betwixt_o these_o two_o place_n may_v be_v find_v out_o you_o must_v first_o subtract_v the_o lesser_a longitude_n out_o of_o the_o great_a so_o shall_v you_o find_v the_o difference_n of_o their_o longitude_n which_o be_v 47_o degree_n then_o reckon_v that_o difference_n upon_o the_o semicircle_n begin_v at_o a_o and_o so_o proceed_v to_o b_o and_o at_o the_o end_n of_o that_o difference_n make_v a_o mark_n with_o the_o letter_n e_o into_o which_o point_n by_o your_o ruler_n let_v a_o right_a line_n be_v draw_v from_o d_o the_o centre_n of_o the_o semicircle_n this_o be_v in_o this_o sort_n perform_v let_v the_o lesser_a latitude_n be_v seek_v out_o which_o be_v 32_o degree_n in_o the_o foresay_a semicircle_n begin_v your_o account_n from_o the_o point_n e_o and_o so_o proceed_v towards_o b_o and_o at_o the_o end_n of_o the_o lesser_a latitude_n let_v another_o point_n be_v mark_v out_o with_o the_o letter_n g_o from_o which_o point_n let_v there_o be_v draw_v a_o perpendicular_a which_o may_v fall_v with_o right_a angle_n upon_o the_o former_a line_n draw_v from_o d_o to_z e_z and_o where_o it_o chance_v to_o fall_v there_o mark_v out_o a_o point_n with_o the_o letter_n h_n this_o be_v perform_v let_v the_o great_a latitude_n which_o be_v 51_o degree_n 32_o minute_n be_v seek_v out_o in_o the_o semicircle_n begin_v to_o reckon_v from_o a_o towards_o b_o and_o at_o the_o end_n of_o that_o latitude_n set_v down_o another_o point_n sign_v out_o by_o the_o letter_n i_o from_o whence_o let_v there_o be_v draw_v another_o perpendicular_a line_n that_o may_v fall_v with_o right_a angle_n upon_o the_o diameter_n ac_fw-la and_o here_o mark_v out_o a_o point_n with_o the_o letter_n k_o this_o do_v take_v with_o your_o compass_n the_o distance_n betwixt_o k_o and_o h_n which_o distance_n you_o must_v set_v down_o upon_o the_o diameter_n ac_fw-la place_v the_o one_o foot_n of_o your_o compass_n upon_o k_o and_o the_o other_o towards_o the_o centre_n d_o and_o there_o mark_v out_o a_o point_n with_o the_o letter_n l_o then_o with_o your_o compass_n take_v the_o short_a perpendicular_a line_n gh_o and_o apply_v that_o wideness_n upon_o the_o long_a perpendicular_a line_n ik_fw-mi place_v the_o one_o foot_n of_o your_o compass_n at_o ay_o which_o be_v the_o bound_n of_o the_o great_a latitude_n and_o extend_v the_o other_o towards_o k_o and_o there_o make_v a_o point_n at_o m._n then_o with_o your_o compass_n take_v the_o distance_n betwixt_o l_o and_o m_o and_o apply_v the_o same_o to_o the_o semicircle_n place_v the_o one_o foot_n of_o your_o compass_n in_o a_o and_o the_o other_o towards_o b_o and_o there_o mark_v out_o a_o point_n with_o the_o letter_n n._n now_o the_o number_n of_o degree_n comprehend_v betwixt_o a_o and_o n_o will_v express_v the_o true_a distance_n of_o the_o two_o place_n which_o will_v be_v find_v to_o be_v 39_o degree_n which_o be_v multiply_v by_o 60_o and_o so_o convert_v into_o mile_n according_a to_o our_o former_a rule_n will_v produce_v 2340_o which_o be_v the_o distance_n of_o the_o say_a place_n 17_o the_o expression_n of_o the_o distance_n of_o two_o place_n may_v be_v perform_v either_o by_o the_o globe_n or_o map_n according_a to_o these_o rule_n 1_o the_o distance_n betwixt_o two_o place_n in_o the_o globe_n be_v observe_v by_o the_o quadrant_a of_o altitude_n and_o apply_v to_o the_o degree_n of_o the_o equatour_n or_o any_o great_a circle_n will_v show_v how_o many_o mile_n such_o place_n be_v distant_a the_o practice_n hereof_o be_v very_o easy_a as_o shall_v be_v teach_v in_o this_o example_n we_o will_v for_o instance_n take_v toledo_n in_o the_o midst_n of_o spain_n and_o the_o cape_n of_o good_a hope_n in_o the_o south_n promontory_n of_o all_o africa_n the_o space_n take_v by_o a_o quadrant_a of_o altitude_n or_o any_o thread_n apply_v to_o the_o equatour_n will_v be_v find_v to_o be_v about_o 82_o degree_n which_o be_v multiply_v by_o 60_o and_o so_o convert_v into_o mile_n will_v render_v 4920_o the_o true_a distance_n betwixt_o these_o two_o place_n 2_o the_o distance_n betwixt_o any_o two_o place_n in_o the_o chart_n observe_v by_o a_o compass_n and_o apply_v to_o the_o degree_n of_o a_o great_a circle_n will_v show_v how_o
geographie_n delineate_v forth_o in_o two_o book_n contain_v the_o spherical_a and_o topical_a part_n thereof_o by_o nathanael_n carpenter_n fellow_n of_o exeter_n college_n in_o oxford_n the_o second_o edition_n correct_v ecclesiast_n 1._o one_o generation_n come_v and_o another_o go_v but_o the_o earth_n remain_v for_o ever_o oxford_z print_v by_o john_n lichfield_n for_o henry_n cripps_n and_o be_v to_o be_v sell_v by_o henry_n curteyne_a anno_fw-la domini_fw-la m._n dc_o xxxv_o to_o the_o right_n honourable_a william_n earl_n of_o pembroke_n lord_n chamberlaine_n to_o the_o king_n most_o excellent_a majesty_n knight_n of_o the_o most_o noble_a order_n of_o the_o garter_n and_o chancellor_n of_o the_o university_n of_o oxford_n right_o honourable_a this_o poor_a infant_n of_o i_o which_o i_o now_o offer_v to_o your_o honourable_a acceptance_n be_v consecrate_v you_o in_o the_o first_o conception_n if_o the_o hasty_a desire_n i_o have_v to_o present_v it_o make_v it_o as_o a_o abortive_a brat_n seem_v unworthy_a my_o first_o wish_n and_o your_o favourable_a patronage_n impute_v it_o i_o beseech_v you_o not_o to_o self-will_a but_o duty_n which_o will_v rather_o show_v herself_o too_o officious_a then_o negligent_a what_o i_o now_o dedicate_v rather_o to_o your_o honour_n than_o my_o own_o ambition_n i_o desire_v no_o far_o to_o be_v account_v i_o than_o your_o generous_a approbation_n wish_v it_o no_o other_o fate_n then_o either_o to_o die_v with_o your_o dislike_n or_o live_v with_o your_o name_n and_o memory_n the_o general_a acclamation_n of_o the_o learned_a of_o this_o age_n acknowledge_v with_o all_o thankful_a duty_n as_o well_o your_o love_n to_o learning_n as_o zeal_n to_o religion_n have_v long_o since_o stamp_v i_o you_o this_o arrogant_a desire_n of_o i_o ground_v more_o on_o your_o heroic_a virtue_n than_o my_o private_a end_n promise_v i_o more_o in_o your_o honourable_a estimation_n than_o some_o other_o in_o your_o greatness_n the_o expression_n of_o myself_o in_o these_o faculty_n beside_o my_o profession_n indebt_v more_o to_o love_n than_o ability_n set_v my_o ambition_n a_o pinch_n high_o than_o my_o nature_n but_o such_o be_v the_o magnificent_a splendour_n of_o your_o countenance_n which_o may_v easy_o lend_v your_o poor_a servant_n so_o much_o light_n as_o to_o lead_v he_o out_o of_o darkness_n and_o as_o the_o sun_n reflect_v on_o the_o base_a earth_n at_o once_o both_o view_n and_o guild_v his_o imperfection_n my_o language_n and_o formality_n i_o owe_v not_o to_o the_o court_n but_o university_n whereof_o i_o can_v but_o expect_v your_o honour_n to_o be_v a_o impartial_a umpire_n be_v a_o most_o vigorous_a member_n of_o the_o one_o and_o the_o head_n of_o the_o other_o corporation_n if_o these_o fruit_n of_o my_o labour_n purchase_v so_o much_o as_o your_o honour_n least_o approbabation_n i_o shall_v hold_v my_o wish_n even_o accomplish_v in_o their_o end_n and_o desire_v only_a to_o be_v think_v so_o worthy_a in_o your_o honourable_a esteem_n as_o to_o live_v and_o die_v your_o honour_n in_o all_o duty_n and_o service_n to_o be_v command_v nathanael_n carpenter_n the_o analysis_n of_o the_o first_o book_n geography_n who_o object_n be_v the_o whole_a earth_n be_v either_o spherical_a which_o be_v twofold_a either_o primary_n which_o consider_v the_o terrestrial_a sphere_n either_o as_o it_o be_v natural_a wherein_o be_v to_o be_v consider_v two_o thing_n the_o principle_n whereof_o it_o consist_v to_o wit_n matter_n and_o form_n chapter_n 1._o propriety_n arise_v out_o of_o they_o which_o again_o be_v either_o real_a such_o as_o be_v assign_v in_o respect_n of_o the_o earth_n itself_o which_o be_v either_o elementary_a as_o the_o conformity_n of_o all_o the_o part_n concur_v to_o the_o constitution_n of_o the_o sphere_n chapter_n 2._o magnetical_a which_o be_v either_o partial_a as_o the_o coition_n direction_n variation_n declination_n chap._n 3._o totall_n as_o the_o verticity_n and_o revolution_n chap._n 4._o heaven_n wherein_o we_o treat_v of_o the_o site_n stability_n and_o proportion_n of_o the_o earth_n in_o respect_n of_o the_o heaven_n chap._n 5._o imaginary_a such_o as_o be_v the_o circle_n and_o lineament_n of_o the_o globe_n of_o who_o invention_n and_o expression_n chap._n 6._o artificial_a in_o the_o artificial_a sphere_n represent_v the_o natural_a unto_o we_o which_o be_v either_o common_a or_o magnetical_a chap._n 7._o secondary_a which_o handle_v such_o matter_n in_o the_o sphere_n as_o secondary_o arise_v out_o of_o the_o first_o such_o be_v measure_n of_o the_o earth_n with_o the_o diverse_a manner_n of_o invention_n chap._n 8._o distinction_n which_o be_v either_o space_n consider_v simple_o in_o themselves_o in_o which_o sort_n they_o be_v divide_v into_o zone_n climate_n and_o parallel_n chap._n 9_o in_o respect_n of_o the_o inhabitant_n which_o suffer_v manifold_a distinction_n chap._n 10._o distance_n which_o be_v either_o simple_a wherein_o be_v consider_v the_o longitude_n &_o latitude_n of_o place_n chap._n 11._o comparative_a wherein_o two_o place_n differ_v either_o in_o longitude_n or_o latitude_n or_o both_o be_v consider_v chap._n 12._o topical_a libro_fw-la 2o._o of_o the_o special_a content_n of_o each_o chapter_n of_o the_o first_o book_n according_a to_o the_o several_a theorem_n chap._n i._o of_o the_o terrestrial_a globe_n the_o matter_n and_o form_n 1_o in_o the_o terrestrial_a sphere_n be_v more_o earth_n than_o water_n pag._n 8_o 2_o the_o earth_n and_o water_n together_o make_v one_o sphere_n pag._n 10_o chap._n ii_o of_o the_o conformity_n of_o part_n in_o the_o constitution_n of_o the_o terrestrial_a sphere_n 1_o the_o part_n of_o the_o terrestrial_a sphere_n do_v natural_o conform_v and_o dispose_v themselves_o as_o well_o to_o the_o production_n and_o generation_n as_o to_o the_o continuance_n and_o preservation_n of_o it_o pag._n 14_o 2_o all_o earthly_a body_n incline_v and_o approach_v to_o the_o centre_n as_o near_o as_o they_o can_v 16_o 3_o of_o two_o heavy_a body_n strive_v for_o the_o same_o place_n that_o always_o prevail_v which_o be_v heavy_a 22_o 4_o hence_o it_o come_v to_o pass_v that_o the_o earth_n enjoy_v the_o low_a place_n the_o next_o the_o water_n and_o the_o last_o the_o air_n ibid._n 5_o the_o centre_n of_o the_o earth_n be_v not_o a_o attractive_a but_o a_o mere_a respective_a point_n 25._o 6_o the_o same_o point_n be_v the_o centre_n of_o magnitude_n and_o weight_n in_o the_o terrestrial_a sphere_n 26_o 7_o every_o point_n or_o centre_n of_o a_o weighty_a body_n be_v move_v towards_o the_o centre_n of_o the_o terrestrial_a globe_n by_o a_o right_a line_n 27_o 8_o a_o heavy_a point_n move_v towards_o the_o centre_n will_v move_v fast_o in_o the_o end_n then_o in_o the_o beginning_n 28_o 9_o the_o motion_n of_o a_o magnitude_n towards_o the_o centre_n be_v not_o mere_o natural_a but_o mix_v with_o a_o violent_a motion_n 29_o 10_o the_o line_n wherein_o the_o centre_n of_o two_o heavy_a body_n be_v move_v downeward_o be_v continue_v will_v meet_v in_o the_o centre_n of_o the_o earth_n 31_o 11_o two_o heavy_a body_n of_o the_o same_o figure_n and_o matter_n whether_o equal_a or_o unequal_a will_v in_o a_o equal_a time_n move_v in_o a_o equal_a space_n 32_o 12_o the_o terrestrial_a globe_n be_v round_o and_o spherical_a 33_o 13_o the_o rugged_a and_o unequal_a part_n of_o the_o earth_n hinder_v not_o the_o spherical_a roundness_n of_o it_o 36_o 14_o the_o water_n concur_v with_o the_o earth_n in_o the_o globe_n be_v also_o spherical_a 38_o chap._n iii_o of_o the_o partial_a magnetical_a affection_n in_o the_o sphere_n of_o the_o earth_n 1_o the_o terrestrial_a sphere_n be_v of_o a_o magnetical_a nature_n and_o disposition_n pag._n 46_o 2_o the_o magnetical_a motion_n be_v excite_v in_o a_o small_a and_o unperceivable_a difference_n of_o time_n 49_o 3_o the_o motive_n quality_n be_v spread_v spherical_o through_o every_o part_n of_o the_o magnetical_a body_n 49_o 4_o the_o motive_n quality_n of_o the_o magnetical_a body_n be_v strong_a of_o all_o in_o the_o pole_n in_o other_o part_n so_o much_o the_o strong_a by_o how_o much_o they_o be_v situate_v near_o the_o pole_n 50_o 5_o magnetical_a body_n move_v not_o uncertain_o but_o have_v their_o motion_n direct_v and_o conform_v to_o certain_a bound_n 52_o 6_o the_o magnet_n communicate_v his_o virtue_n to_o iron_n or_o steel_n if_o it_o be_v touch_v with_o it_o 55_o 7_o the_o magnetical_a coition_n be_v strong_a of_o all_o in_o the_o pole_n 56_o 8_o the_o south_n part_n of_o the_o loadstone_n turn_v to_o the_o north_n and_o the_o north_n to_o the_o south_n 57_o 9_o the_o contrary_a motion_n in_o magnet_n be_v the_o just_a confluxe_n and_o conformity_n of_o such_o body_n to_o magnetical_a union_n 59_o 10_o if_o any_o part_n southward_a of_o the_o magnetical_a body_n be_v tear_v away_o or_o diminish_v so_o much_o
retain_v in_o itself_o the_o virtue_n of_o the_o loadstone_n yet_o by_o reason_n of_o the_o liquefaction_n be_v altogether_o languish_v and_o as_o it_o be_v bury_v but_o upon_o touch_n of_o a_o loadstone_n be_v stir_v up_o to_o his_o former_a vigour_n for_o the_o magnet_n insinuat_v his_o incorporeal_a influence_n into_o the_o iron_n and_o so_o rectify_v and_o animate_v that_o force_n which_o be_v almost_o dead_a 2_o the_o magnetical_a coiton_n be_v strong_a of_o all_o in_o the_o pole_n this_o may_v easy_o be_v demonstrate_v by_o a_o experiment_n for_o if_o the_o iron_n needle_n which_o be_v propose_v to_o be_v attract_v and_o the_o pole_n and_o centre_n be_v place_v in_o the_o same_o right_a line_n then_o this_o coition_n will_v be_v to_o a_o perpendicular_a as_o in_o a_o and_o b_o to_o wit_n the_o pole_n in_o the_o diagramme_n but_o in_o the_o middle_a space_n they_o will_v oblique_o respect_v and_o point_n and_o by_o how_o much_o far_o off_o from_o the_o pole_n it_o be_v by_o so_o much_o be_v this_o virtue_n weak_a but_o in_o the_o equator_fw-la itself_o it_o become_v mere_o parallel_v without_o any_o inclination_n at_o all_o to_o know_v in_o what_o proportion_n this_o force_n be_v increase_v or_o weaken_v we_o must_v put_v another_o ground_n that_o the_o force_n of_o this_o coition_n be_v increase_v proportional_o as_o the_o chord_n of_o a_o circle_n for_o by_o how_o much_o the_o least_o chorde_v in_o a_o circle_n differ_v from_o the_o diameter_n so_o much_o the_o force_n attractive_a differ_v from_o themselves_o for_o since_o the_o attraction_n be_v a_o coition_n of_o one_o body_n with_o another_o and_o magnetical_a body_n be_v carry_v by_o a_o convertible_a nature_n it_o come_v to_o pass_v that_o a_o line_n draw_v from_o one_o pole_n to_o another_o in_o the_o diameter_n direct_o meet_v with_o the_o body_n but_o in_o other_o place_n less_o so_o that_o the_o less_o it_o be_v convert_v to_o the_o body_n the_o less_o and_o weak_a will_v be_v the_o coition_n 3_o so_o much_o be_v speak_v of_o the_o magnetical_a coition_n it_o follow_v that_o we_o speak_v of_o magnetical_a direction_n which_o be_v a_o natural_a conversion_n and_o conformity_n of_o the_o magnetical_a body_n to_o the_o pole_n of_o the_o earth_n it_o be_v manifest_a that_o a_o magnetical_a body_n so_o seat_v that_o it_o can_v move_v without_o any_o impediment_n will_v turn_v itself_o in_o such_o wise_a that_o the_o one_o pole_n of_o it_o will_v respect_v the_o north_n pole_n of_o the_o earth_n the_o other_o the_o south_n which_o motion_n we_o call_v direction_n this_o we_o may_v plain_o see_v in_o a_o mariner_n compass_v who_o lily_n always_o respect_v the_o north_n point_fw-fr if_o a_o compass_n be_v want_v the_o same_o may_v be_v show_v in_o a_o little_a corken-boate_n which_o be_v put_v in_o the_o water_n with_o a_o loadstone_n in_o it_o will_v so_o turn_v and_o convert_v itself_o that_o the_o pole_n of_o the_o loadstone_n will_v at_o length_n point_n out_o the_o pole_n of_o the_o terrestrial_a globe_n the_o manner_n how_o shall_v be_v disclose_v in_o these_o theorem_n 1_o the_o south_n part_n of_o the_o loadstone_n turn_v to_o the_o north_n and_o the_o north_n part_n to_o the_o south_n to_o confirm_v this_o assertion_n some_o have_v produce_v this_o experiment_n let_v there_o be_v cut_v out_o of_o a_o rock_n of_o loadstone_n a_o magnet_n of_o reasonable_a quantity_n let_v the_o two_o pole_n both_o north_n and_o south_n be_v mark_v out_o in_o the_o loadstone_n the_o manner_n of_o which_o we_o shall_v perhaps_o teach_v hereafter_o then_o let_v it_o be_v put_v in_o a_o corken_v little_a boat_n on_o the_o water_n so_o that_o it_o may_v free_o float_v hither_o &_o thither_o it_o will_v be_v evident_a that_o that_o part_n which_o in_o the_o rock_n or_o i_o point_v northward_o will_v respect_v the_o south_n and_o contrariwise_o the_o south_n part_n will_v respect_v the_o north_n as_o we_o may_v see_v in_o this_o figure_n let_v the_o magnet_n as_o it_o be_v continuate_v with_o the_o mine_n or_o globe_n of_o the_o earth_n be_v ab_fw-la so_o that_o a_o shall_v be_v in_o the_o north_n pole_n b_o the_o southpole_n let_v this_o loadstone_n be_v cut_v out_o of_o this_o rock_n or_o i_o &_o place_v on_o the_o water_n in_o a_o little_a timber_n boat_n which_o shall_v be_v cd_o we_o shall_v find_v that_o this_o little_a dish_n or_o boat_n will_v turn_v itself_o so_o long_o until_o the_o northpart_v a_o be_v turn_v to_o the_o southpart_n b_o and_o on_o the_o other_o part_n the_o southpart_n b_o be_v convert_v to_o the_o northpart_v a_o and_o this_o comformity_n will_v the_o whole_a rock_n of_o loadstone_n claim_n if_o it_o be_v divide_v and_o separate_v from_o the_o globe_n of_o the_o earth_n the_o reason_n why_o the_o magnet_n in_o the_o boat_n on_o the_o water_n turn_v wind_v and_o seat_v itself_o to_o a_o contrary_a motion_n to_o that_o it_o primary_o receive_v while_o it_o be_v join_v to_o the_o bowel_n of_o the_o earth_n and_o unite_v to_o the_o body_n of_o the_o great_a magnet_n be_v because_o every_o part_n of_o a_o loadstone_n be_v separate_v from_o the_o whole_a whereof_o it_o be_v a_o part_n become_v of_o itself_o a_o perfect_a complete_a magnetical_a body_n as_o we_o may_v say_v a_o little_a earth_n have_v all_o the_o property_n of_o the_o great_a globe_n as_o pole_n meridian_n aequator_n etc._n etc._n and_o therefore_o according_a to_o the_o nature_n of_o magnetical_a union_n speak_v of_o in_o our_o next_o theorem_a will_v in_o no_o wise_n endure_v to_o settle_v itself_o as_o it_o do_v before_o but_o deem_v it_o a_o thing_n more_o natural_a and_o of_o more_o perfection_n to_o turn_v his_o aspect_n a_o contrary_a way_n to_o that_o which_o he_o enjoy_v at_o his_o first_o constitution_n here_o may_v we_o note_v a_o great_a error_n of_o gemma_fw-la frisius_n who_o in_o his_o corollary_n upon_o the_o 15_o chap._n of_o his_o cosmographical_a comment_n on_o p._n appian_n affirm_v that_o the_o needle_n magnetical_o effect_v will_v on_o this_o side_n the_o aequator_fw-la respect_v the_o north-pole_n but_o be_v past_o the_o line_n will_v straightway_o turn_v about_o and_o point_n to_o the_o southpole_n a_o error_n as_o mr_n hues_n say_v unworthy_a so_o great_a a_o mathematician_n but_o gemma_fw-la frisius_n in_o some_o â—ort_n may_v be_v excuse_v for_o as_o much_o as_o the_o ground_n of_o magnetical_a philosophy_n be_v in_o his_o time_n either_o not_o discover_v or_o most_o unperfect_o know_v and_o the_o uncertain_a relation_n of_o navigator_n be_v repute_v the_o best_a argument_n and_o how_o easy_a a_o matter_n it_o be_v for_o a_o traveller_n in_o this_o sort_n to_o deceive_v a_o scholar_n who_o out_o of_o his_o read_n and_o experience_n can_v show_v nothing_o to_o the_o contrary_a let_v every_o man_n judge_v 2_o this_o contrary_a motion_n here_o speak_v of_o be_v the_o just_a confluxe_n and_o conformity_n of_o such_o body_n to_o magnetical_a union_n this_o be_v demonstrate_v by_o gilbert_n in_o this_o manner_n let_v the_o whole_a magnetical_a body_n be_v cd_o then_o c_z will_v turn_v to_o the_o north_n of_o the_o earth_n b_o and_o d_o unto_o the_o south_n part_n a._n let_v this_o magnet_n be_v cut_v in_o twain_o by_o the_o middle_a line_n or_o aequator_fw-la and_o the_o point_n e_o will_v tend_v to_o a_o and_o the_o part_n f_o will_v direct_v itself_o to_o b_o for_o as_o in_o the_o whole_a so_o in_o the_o part_n divide_v nature_n desire_v the_o union_n of_o these_o body_n the_o end_n e_z willing_o accord_v with_o f_o but_z e_z will_v not_o willing_o join_v itself_o with_o d_o nor_o f_o with_o c_o for_o than_o it_o will_v have_v c_o against_o its_o nature_n to_o move_v towards_o a_o the_o south_n or_o d_o in_o b_o which_o be_v the_o south_n separate_a the_o stone_n in_o the_o place_n of_o division_n and_o turn_v c_o to_o d_o and_o they_o will_v convenient_o agree_v and_o accord_n for_o d_o will_v turn_v itself_o to_o the_o south_n as_o before_o and_o c_o to_o the_o north_n and_o e_z and_o f_o joint_a part_n in_o the_o mineral_n or_o rock_n will_v now_o be_v most_o sunder_v for_o these_o magnetical_a part_n concur_v and_o meet_v together_o not_o by_o any_o affinity_n of_o matter_n but_o receive_v all_o their_o motion_n and_o inclination_n from_o the_o form_n so_o that_o the_o limit_n whether_o joint_n or_o divide_v be_v direct_v magnetical_o to_o the_o pole_n of_o the_o earth_n in_o the_o same_o manner_n as_o in_o the_o divide_a body_n 3_o if_o any_o part_n southward_o of_o the_o magnetical_a body_n be_v tear_v away_o or_o diminish_v so_o much_o shall_v be_v also_o diminish_v of_o the_o northpart_n and_o contrariwise_o if_o any_o part_n be_v take_v away_o in_o the_o northpart_n so_o much_o shall_v the_o virtue_n of_o the_o
yet_o may_v the_o rest_v compare_v among_o themselves_o be_v range_v in_o a_o certain_a order_n as_o the_o second_o third_z four_o five_o and_o so_o along_o till_o we_o come_v again_o to_o the_o first_o be_v in_o all_o reduce_v to_o the_o number_n of_o 180_o answer_v to_o 360_o degree_n as_o we_o have_v teach_v so_o much_o for_o the_o meridian_n 11_o the_o parallel_n be_v equidistant_a circle_n pass_v from_o the_o east_n to_o the_o west_n direct_o i_o have_v define_v the_o parallel_n circle_n in_o a_o large_a sense_n then_o former_a geographer_n usual_o have_v take_v it_o in_o as_o willing_a under_o this_o general_a name_n not_o only_o to_o include_v the_o parallel_n common_o so_o call_v but_o also_o the_o equatour_n because_o i_o see_v no_o reason_n why_o the_o equatour_n be_v every_o where_o equidistant_a from_o each_o other_o circle_n shall_v not_o suffer_v this_o acception_n the_o common_a sort_n of_o cosmographer_n under_o this_o name_n will_v only_o comprise_v the_o minor_a circle_n which_o be_v conceive_v to_o be_v equal_o distant_a and_o correspondent_a to_o the_o equinoctial_a circle_n so_o that_o all_o shall_v be_v so_o call_v in_o respect_n of_o the_o equatour_n to_o who_o they_o be_v say_v to_o answer_v not_o in_o site_n and_o position_n for_o as_o much_o as_o they_o decline_v from_o the_o middle_n of_o the_o earth_n to_o the_o north_n and_o south_n but_o in_o comparison_n and_o proportion_n for_o as_o the_o equatour_n be_v draw_v from_o east_n to_o west_n and_o divide_v the_o whole_a sphere_n of_o the_o earth_n into_o the_o north_n and_o south_n hemisphere_n so_o the_o other_o also_o divide_v the_o globe_n of_o the_o earth_n though_o not_o into_o two_o equal_a part_n as_o the_o equatour_n but_o unequal_a these_o parallel_n many_o way_n be_v distinguish_v from_o the_o meridian_n first_o because_o the_o meridian_n be_v draw_v direct_o from_o north_n to_o south_n but_o the_o parallel_n from_o east_n to_o west_n second_o the_o meridian_n how_o many_o soever_o they_o be_v imagine_v to_o be_v concur_v and_o meet_v all_o in_o the_o pole_n of_o the_o earth_n whereas_o the_o parallel_n howsoever_o draw_v out_o at_o length_n will_v never_o concur_v or_o meet_v in_o any_o point_n whence_o it_o must_v needs_o follow_v that_o all_o parallel_n and_o meridian_n in_o the_o globe_n must_v cut_v one_o the_o other_o and_o make_v right_a angle_n these_o parallel_n although_o infinite_a in_o number_n may_v be_v in_o the_o sphere_n reduce_v to_o the_o number_n of_o the_o meridian_n because_o they_o be_v draw_v through_o the_o opposite_a point_n and_o degree_n of_o the_o meridian_n semicircle_n which_o will_v make_v up_o the_o number_n of_o 180_o but_o yet_o for_o conveniency_n they_o have_v not_o paint_v so_o many_o in_o the_o face_n of_o the_o artificial_a sphere_n for_o as_o much_o as_o so_o many_o line_n and_o circle_n may_v beget_v confusion_n wherefore_o ptolemy_n and_o the_o ancient_n have_v distinguish_v the_o parallel_n on_o both_o side_n the_o equator_fw-la north_n and_o south_n with_o such_o a_o distance_n that_o where_o the_o day_n shall_v increase_v one_o quarter_n of_o a_o hour_n a_o new_a parallel_n shall_v be_v place_v so_o that_o the_o long_a day_n of_o one_o parallel_n shall_v surpass_v the_o long_a day_n of_o another_o for_o one_o quarter_n of_o a_o hour_n by_o which_o appear_v that_o the_o parallel_n be_v not_o of_o one_o greatness_n but_o by_o how_o much_o near_o the_o pole_n they_o be_v place_v so_o much_o less_o be_v they_o and_o so_o much_o great_a by_o how_o much_o far_o off_o from_o the_o pole_n and_o near_o the_o equatour_n these_o circle_n be_v of_o great_a use_n in_o geography_n as_o to_o distinguish_v the_o zone_n climate_n and_o latitude_n of_o region_n to_o show_v the_o elevation_n of_o the_o pole_n and_o to_o design_n out_o the_o length_n and_o shortness_n of_o the_o day_n in_o any_o part_n of_o the_o earth_n 12_o a_o parallel_n circle_n be_v of_o two_o sort_n either_o great_a or_o lesser_a the_o great_a be_v the_o equatour_n or_o equinoctial_a circle_n 13_o the_o equatour_n be_v the_o great_a of_o the_o parallel_n pass_v through_o the_o midst_n of_o the_o earth_n and_o exact_o divide_v they_o from_o the_o pole_n into_o two_o equal_a half_n or_o hemisphere_n whereof_o the_o one_o be_v north_n the_o other_o south_n this_o circle_n be_v call_v the_o equatour_n or_o equinoctial_a of_o astronomer_n because_o that_o when_o the_o sun_n pass_v under_o it_o as_o upon_o the_o 11_o of_o march_n and_o the_o 13_o of_o september_n it_o make_v the_o day_n and_o night_n equal_a this_o circle_n of_o astronomer_n be_v esteem_v the_o most_o notable_a be_v the_o measure_n of_o the_o diurnal_a and_o most_o regular_a motion_n the_o laâ—ines_n have_v take_v the_o name_n and_o appellation_n of_o this_o circle_n from_o the_o day_n as_o the_o greek_n from_o the_o night_n wherein_o the_o sense_n be_v no_o way_n vary_a because_o the_o equality_n of_o the_o day_n argue_v the_o like_a equality_n of_o the_o night_n the_o two_o pole_n of_o the_o circle_n be_v the_o same_o with_o the_o pole_n of_o the_o universal_a earth_n to_o wit_n the_o arctic_a or_o north-pole_n and_o the_o antarctic_a and_o southern_a pole_n whereof_o the_o former_a be_v always_o conspicuous_a in_o our_o horizon_n the_o other_o lie_v couch_v and_o hide_v from_o our_o sight_n it_o be_v call_v the_o articke-pole_n from_o the_o constellation_n of_o the_o little_a bear_n in_o the_o heaven_n near_o to_o the_o which_o it_o be_v situate_v in_o opposition_n to_o the_o which_o the_o other_o be_v call_v antarctic_a it_o have_v manifold_a use_n in_o astronomy_n copious_o by_o astronomer_n and_o no_o less_o in_o geography_n for_o without_o this_o equinoctial_a circle_n no_o description_n of_o the_o earth_n can_v be_v absolute_a &_o perfect_a neither_o any_o city_n or_o place_n in_o the_o terrestrial_a globe_n or_o map_n set_v in_o his_o due_a and_o proper_a place_n this_o equinoctial_a circle_n in_o regard_n of_o the_o earth_n pass_v through_o the_o middlemost_a part_n almost_o of_o africa_n by_o ethiopia_n america_n and_o taprobana_n so_o that_o it_o exact_o divide_v the_o globe_n of_o the_o earth_n into_o two_o half_n the_o northern_a and_o southern_a hemisphere_n so_o that_o these_o people_n which_o dwell_v under_o the_o equatour_n be_v say_v to_o inhabit_v the_o middle_n of_o the_o world_n because_o they_o incline_v neither_o to_o the_o north_n nor_o to_o the_o south_n have_v so_o much_o distance_n from_o the_o arctic_a antarticke-pole_n of_o the_o earth_n moreover_o by_o this_o circle_n as_o we_o will_v declare_v hereafter_o be_v note_v out_o unto_o we_o the_o east_n and_o west_n part_n of_o the_o sphere_n no_o way_n to_o be_v neglect_v of_o geographer_n 1_o concern_v the_o equatour_n two_o thing_n be_v to_o be_v observe_v either_o the_o invention_n or_o the_o site_n and_o position_n the_o invention_n be_v either_o astronomical_a or_o magnetical_a the_o astronomical_a according_a to_o these_o rule_n 1_o 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there_o be_v note_v all_o the_o point_n by_o which_o the_o end_n or_o top_n of_o the_o shadow_n have_v pass_v for_o all_o those_o point_n in_o the_o time_n of_o equinoctial_a be_v in_o a_o right_a line_n because_o then_o the_o end_n of_o the_o shadow_n be_v carry_v in_o a_o line_n in_o the_o time_n of_o the_o equinox_n in_o a_o herizontall_a plain_a this_o line_n will_v be_v the_o true_a equinoctiall-line_n the_o cause_n be_v give_v by_o clavius_n in_o gnomonicis_n lib._n 1._o prop._n 1._o corollar_n 2._o which_o depend_v on_o many_o geometrical_a and_o astronomical_a principle_n as_o too_o far_o from_o my_o purpose_n i_o omit_v 15_o the_o magnetical_a invention_n of_o the_o equatour_n be_v wrought_v by_o the_o magnetical_a inclinatory_a needle_n according_a to_o this_o proposition_n 1_o wheresoever_o at_o any_o place_n of_o the_o terrestrial_a
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measure_v another_o conceit_n more_o absurd_a than_o the_o former_a be_v not_o only_o the_o common_a people_n who_o condition_n may_v excuse_v their_o ignorance_n but_o of_o such_o as_o will_v be_v esteem_v learned_a who_o contend_v that_o the_o greatness_n of_o the_o earth_n can_v be_v measure_v the_o only_a reason_n they_o can_v allege_v for_o themselves_o be_v 1_o that_o a_o great_a part_n of_o the_o earth_n be_v unaccessible_a by_o reason_n of_o steep_a rock_n high_a mountain_n spacious_a and_o thick_a wood_n moorish_a fog_n and_o such_o like_a impediment_n 2_o that_o the_o part_n of_o it_o be_v for_o the_o most_o part_n uneven_a and_o subject_a to_o no_o regular_a figure_n without_o the_o which_o no_o measure_n can_v be_v exact_a the_o first_o cavil_n be_v of_o no_o moment_n because_o whereas_o we_o affirm_v that_o the_o earth_n by_o man_n may_v be_v measure_v we_o hold_v it_o not_o necessary_a that_o it_o shall_v be_v traverse_v over_o by_o journey_n or_o voyage_n for_o as_o 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league_n and_o mile_n in_o which_o we_o little_o regard_v such_o a_o needless_a curiosity_n 1_o the_o common_a measure_n by_o which_o the_o quantity_n of_o the_o earth_n be_v know_v be_v miles_n and_o furlong_n here_o be_v to_o be_v note_v that_o such_o instrument_n as_o serve_v for_o measure_v be_v of_o two_o sort_n either_o great_a or_o lesser_a the_o small_a be_v of_o diverse_a sort_n as_o a_o grain_n inch_n foot_n perch_n pole_n and_o such_o like_a some_o of_o these_o howsoever_o sometime_o useful_a in_o topographie_n can_v have_v little_a or_o no_o use_n at_o all_o in_o the_o vast_a greatness_n of_o the_o whole_a earth_n wherefore_o the_o geographer_n seldom_o descend_v so_o low_a but_o take_v notice_n of_o great_a measure_n such_o as_o be_v miles_n &_o furlong_n where_o we_o may_v observe_v by_o the_o way_n that_o the_o usual_a measure_n among_o the_o grecian_n be_v by_o stadia_fw-la or_o furlong_n among_o many_o of_o the_o latin_n by_o mile_n under_o which_o we_o also_o 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shall_v we_o seldom_o make_v use_n of_o any_o other_o than_o the_o common_a german_a mile_n or_o the_o common_a italian_a mile_n to_o which_o as_o the_o most_o know_v the_o rest_n may_v easy_o be_v reduce_v 3_o the_o object_n here_o propose_v to_o be_v measure_v be_v the_o sphere_n of_o the_o earth_n the_o dimension_n according_a to_o which_o it_o be_v measure_v be_v either_o simple_a or_o compound_v 4_o the_o simple_a be_v twofold_a either_o the_o perimeter_n or_o the_o diameter_n the_o perimeter_n otherwise_o call_v the_o circumference_n be_v a_o great_a circle_n measure_v the_o earth_n round_o about_o 5_o the_o invention_n of_o the_o perimeter_n of_o the_o earth_n depend_v on_o these_o follow_a proposition_n 1_o if_o two_o or_o more_o circle_n be_v draw_v about_o the_o same_o centre_n and_o from_o the_o centre_n to_o the_o circumference_n be_v draw_v two_o right_a line_n the_o arch_n of_o all_o the_o circle_n comprehend_v within_o the_o say_v right_a line_n will_v be_v like_a and_o 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