Selected quad for the lemma: end_n

Word A Word B Word C Word D Occurrence Frequency Band MI MI Band Prominent
end_n draw_v line_n perpendicular_a 3,095 5 14.0786 5 true
View all documents for the selected quad

Text snippets containing the quad

ID Title Author Corrected Date of Publication (TCP Date of Publication) STC Words Pages
A18028 Geographie delineated forth in two bookes Containing the sphericall and topicall parts thereof, by Nathanael Carpenter, Fellow of Exceter Colledge in Oxford. Carpenter, Nathanael, 1589-1628? 1635 (1635) STC 4677; ESTC S107604 387,148 599

There are 7 snippets containing the selected quad. | View original text

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 suppos●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
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 actio●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
believe_v no_o less_o and_o can_v speak_v no_o more_o except_o i_o shall_v urge_v the_o beat_n of_o the_o great_a atlantic_a ocean_n upon_o our_o western_a shore_n which_o may_v in_o some_o sort_n qualify_v the_o excess_n of_o heat_n incident_a to_o the_o eastern_a tract_n which_o may_v produce_v some_o degree_n of_o temperature_n but_o here_o also_o we_o shall_v perhaps_o meet_v with_o cross_a instance_n which_o will_v stir_v up_o more_o doubt_v th●n_a satisfaction_n chap._n iu._n of_o the_o manner_n of_o expression_n and_o description_n of_o region_n 1_o have_v treat_v of_o the_o general_a adjunct_n of_o place_n we_o be_v next_o to_o handle_v the_o manner_n of_o describe_v a_o region_n which_o propose_v unto_o we_o two_o point_n ●_o the_o find_v out_o the_o position_n of_o two_o place_n one_o in_o regard_n of_o the_o other_o 2_o the_o translation_n of_o such_o place_n so_o find_v out_o into_o the_o globe_n or_o chart_fw-la 2_o the_o former_a depend_v on_o the_o invention_n of_o the_o angle_n of_o position_n by_o some_o dioptricke_a instrument_n this_o manner_n of_o description_n of_o a_o particular_a region_n seem_v very_o necessary_a for_o a_o geographer_n which_o every_o mechanician_a may_v soon_o learn_v and_o practice_n many_o instrument_n have_v be_v devise_v by_o curious_a artificer_n for_o this_o purpose_n who_o use_n have_v be_v set_v out_o large_o by_o late_a writer_n as_o by_o gemma_fw-la frisius_n diggs_n hopton_n and_o other_o to_o who_o my_o reader_n may_v have_v recourse_n because_o i_o hold_v it_o not_o my_o task_n in_o this_o subject_n to_o describe_v the_o instrument_n themselves_o but_o brief_o to_o show_v the_o ground_n and_o use_v of_o they_o which_o these_o proposition_n shall_v express_v 1_o diverse_a place_n observe_v at_o two_o or_o more_o station_n by_o some_o dioptricke_a instrument_n the_o situation_n of_o two_o place_n one_o in_o regard_n of_o the_o other_o may_v be_v find_v out_o and_o express_v in_o a_o plain_a this_o may_v sensible_o be_v show_v in_o the_o figure_n follow_v to_o express_v which_o the_o more_o plain_o we_o will_v set_v down_o these_o rule_n 1_o let_v there_o be_v draw_v in_o some_o chart_n or_o plain_a platform_n a_o right_a line_n which_o we_o must_v account_v to_o be_v our_o meridian_n because_o it_o shall_v afterward_o serve_v for_o that_o purpose_n this_o right_a line_n shall_v be_v ab_fw-la who_o two_o end_n a_o and_o b_o shall_v be_v take_v for_o the_o north_n and_o south_n 2_o you_o must_v choose_v out_o of_o some_o high_a place_n as_o a_o tower_n or_o mountain_n from_o whence_o you_o may_v behold_v such_o city_n town_n castle_n and_o other_o such_o notable_a place_n whereof_o you_o desire_v to_o know_v the_o situation_n and_o bear_n of_o the_o one_o to_o the_o other_o this_o high_a place_n be_v call_v the_o first_o station_n where_o you_o must_v place_v the_o plain_a before_o prepare_v in_o such_o sort_n as_o it_o may_v astronomical_o and_o true_o agree_v with_o the_o true_a meridian_n of_o the_o place_n who_o invention_n we_o have_v teach_v in_o the_o first_o book_n and_o so_o respect_v the_o four_o cardinal_n coast_n to_o wit_n east_n west_n north_n and_o south_n upon_o this_o place_n seat_v in_o such_o a_o manner_n of_o situation_n fasten_v your_o dioptricke_a instrument_n that_o it_o may_v be_v turn_v about_o the_o point_n a_o on_o every_o side_n at_o pleasure_n in_o such_o sort_n as_o the_o sight_n may_v be_v direct_v to_o every_o one_o of_o the_o adjacent_a place_n first_o then_o remove_v it_o from_o a_o direct_v your_o sight_n to_o f_o and_o draw_v the_o line_n of_o of_o indefinite_a length_n likewise_o your_o instrument_n be_v direct_v to_o g_o draw_v the_o line_n agnostus_n infinite_o which_o by_o this_o mean_n will_v also_o hit_v the_o place_n e_o let_v b_o also_o be_v imagine_v a_o certain_a place_n as_o a_o city_n or_o castle_n situate_v in_o the_o very_a meridian_n itself_o which_o we_o find_v already_o draw_v to_o our_o hand_n in_o like_a sort_n ought_v we_o to_o proceed_v with_o the_o other_o place_n c_o and_o d_o and_o as_o many_o as_o we_o please_v this_o perform_v you_o must_v remove_v yourself_o with_o your_o instrument_n and_o plain_a to_o some_o one_o of_o these_o place_n thus_o fore-marked_n out_o as_o for_o example_n unto_o d_o which_o be_v call_v the_o second_o station_n and_o there_o as_o in_o the_o former_a ascend_v up_o some_o high_a place_n the_o plain_a be_v first_o fit_v and_o place_v astronomical_o take_v the_o distance_n ad_fw-la of_o any_o length_n whatsoever_o for_o to_o the_o greatness_n of_o this_o distance_n shall_v all_o the_o rest_n be_v proportional_a hence_o so_o place_v your_o dioptricke_a instrument_n at_o the_o place_n d_o that_o it_o may_v be_v turn_v round_o and_o direct_v to_o all_o those_o place_n former_o observe_v in_o this_o sort_n level_v your_o sight_n to_o the_o place_n or_o castle_n f_o draw_v the_o line_n df_n so_o direct_v your_o sight_n to_o the_o rest_n you_o may_v draw_v the_o line_n dcg_n dedb_n etc._n etc._n now_o by_o the_o point_n of_o intersection_n of_o these_o line_n as_o in_o f_o g_o e_o c_o b_o etc._n etc._n be_v to_o be_v describe_v and_o delineate_v out_o the_o say_v notable_a landmark_n as_o town_n castle_n promontory_n and_o such_o like_a betwixt_o these_o place_n if_o any_o man_n desire_v to_o know_v the_o distance_n in_o mile_n he_o may_v know_v it_o by_o find_v out_o any_o one_o of_o these_o distance_n for_o one_o be_v know_v the_o rest_n will_v also_o be_v exact_o know_v as_o for_o example_n we_o will_v imagine_v the_o distance_n ad_fw-la to_o contain_v 10_o mile_n wherefore_o let_v the_o line_n ad_fw-la be_v divide_v into_o 10_o equal_a part_n then_o with_o your_o compass_n examine_v how_o many_o such_o part_n be_v contain_v in_o the_o distance_n of_o for_o so_o many_o mile_n will_v be_v likewise_o in_o it_o contain_v as_o for_o example_n according_a to_o this_o supposition_n we_o shall_v find_v it_o 5_o part_n wherefore_o the_o castle_n or_o city_n f_o will_v be_v 5_o mile_n distant_a from_o the_o city_n a._n he_o that_o desire_v more_o particular_o to_o acquaint_v himself_o with_o the_o use_n and_o diverse_a manner_n of_o description_n of_o region_n derive_v from_o this_o one_o ground_n let_v he_o have_v recourse_n to_o diverse_a author_n who_o have_v particular_o labour_v in_o this_o subject_n among_o which_o our_o two_o englishman_n digges_n and_o hopton_n deserve_v not_o the_o least_o praise_n whereof_o the_o late_a out_o of_o these_o principle_n have_v frame_v a_o curious_a instrument_n which_o he_o call_v his_o topographicall-glasse_n who_o use_n he_o have_v perspicuous_o and_o exact_o teach_v in_o diverse_a pleasant_a conclusion_n too_o large_a for_o the_o scope_n of_o my_o method_n to_o insert_v 2_o at_o one_o station_n by_o opticall_a observation_n the_o situation_n of_o one_o place_n in_o respect_n of_o the_o other_o may_v be_v find_v out_o this_o may_v be_v show_v out_o of_o a_o opticall_a experiment_n both_o pleasant_a and_o admirable_a the_o ground_n be_v express_v in_o this_o proposition_n the_o light_n traiect_v by_o a_o narrow_a hole_n into_o a_o dark_a place_n will_v represent_v in_o any_o table_n or_o white_a paper_n within_o whatsoever_o be_v without_o direct_o oppose_v unto_o it_o for_o demonstration_n of_o which_o proposition_n we_o must_v take_v as_o grant_v of_o the_o perspective_n author_n that_o the_o visual_a image_n or_o species_n will_v pass_v by_o a_o right_a line_n through_o any_o little_a hole_n and_o will_v be_v terminate_v in_o any_o point_n of_o the_o medium_fw-la now_o that_o it_o shall_v more_o perspicuous_o be_v see_v in_o a_o dark_a place_n then_o in_o the_o light_n the_o cause_n be_v assign_v to_o be_v because_o the_o light_n of_o the_o sun_n be_v take_v away_o or_o much_o diminish_v which_o otherwise_o will_v hide_v and_o shadow_v the_o species_n of_o the_o thing_n which_o be_v present_v to_o the_o sight_n as_o we_o see_v by_o experience_n the_o great_a light_n of_o the_o sun_n to_o obscure_v the_o star_n which_o nevertheless_o from_o the_o dark_a bottom_n of_o a_o deep_a well_o or_o i_o will_v show_v themselves_o at_o midday_n nevertheless_o we_o must_v observe_v by_o the_o way_n that_o this_o representation_n of_o any_o thing_n to_o the_o sight_n by_o this_o image_n impress_v in_o this_o sort_n in_o a_o wall_n or_o paper_n will_v show_v itself_o so_o as_o the_o part_n will_v be_v see_v inverse_v or_o as_o we_o may_v say_v turn_v on_o the_o contrary_a side_n as_o the_o high_a low_a the_o low_a high_a the_o rightside_n to_o the_o left_a and_o the_o left_a to_o the_o right_n which_o we_o may_v declare_v by_o a_o ocular_a demonstration_n in_o this_o figure_n here_o insert_v let_v we_o imagine_v a_o triangular_a platform_n of_o land_n whereof_o we_o desire_v to_o know_v the_o situation_n
to_o be_v abc_n from_o the_o extreme_a angle_n of_o this_o triangle_n we_o will_v suppose_v certain_a ray_n to_o be_v draw_v through_o the_o hole_n d_o into_o a_o dark_a place_n wherein_o shall_v be_v oppose_v to_o the_o hole_n d_o a_o white_a table_n or_o paper_n which_o shall_v be_v nm_n here_o will_v a_o ray_n from_o the_o point_n design_v out_o the_o angle_n at_o a_o be_v carry_v through_o the_o hole_n that_o it_o will_v point_v out_o in_o the_o table_n k_o because_o all_o such_o beam_n according_a to_o the_o optic_n be_v right_a line_n likewise_o the_o angle_n b_o will_n in_o the_o table_n design_n out_o the_o point_n i_o also_o c_o will_v fall_v into_o the_o point_n h_n let_v kh_n ik_fw-mi he_o be_v join_v together_o by_o right_a line_n there_o will_v appear_v the_o triangle_n ikh_n wherein_o the_o top_n of_o the_o triangle_n a_o will_v be_v see_v in_o the_o low_a place_n k_o likewise_o the_o angle_n of_o the_o basis_n b_o and_o c_o will_v appear_v in_o the_o point_n of_o the_o high_a place_n he_o and_o the_o right_a side_n a_o c_o will_v show_v itself_o in_o the_o left_a hk_n as_o the_o left_a side_n will_v be_v the_o right_n in_o ih_o wherefore_o the_o side_n of_o the_o whole_a triangle_n abc_n will_v show_v itself_o in_o the_o table_n nm_n although_o inverse_o place_v according_a to_o the_o side_n and_o angle_n and_o of_o a_o various_a greatness_n in_o respect_n of_o the_o distance_n of_o the_o table_n from_o the_o hole_n the_o invention_n have_v great_a use_n in_o astronomy_n in_o observe_v eclipse_n the_o beginning_n and_o continuance_n without_o any_o hurt_n at_o all_o to_o the_o sight_n no_o less_o use_n may_v it_o challenge_v in_o topography_n in_o describe_v of_o territory_n city_n borrow_v castle_n and_o such_o like_a in_o their_o due_a symmetry_n and_o proportion_n to_o practice_v which_o the_o better_a reusner_n will_v have_v a_o little_a house_n build_v of_o light_a timber_n with_o a_o muliangle_n basis_n in_o every_o one_o of_o who_o side_n a_o hole_n shall_v be_v make_v look_v inward_o at_o the_o vertex_fw-la or_o top_n but_o outward_o at_o the_o basis_n through_o which_o the_o species_n or_o image_n of_o all_o such_o thing_n a●_n be_v visible_a may_v have_v free_a passage_n 2_o the_o manner_n of_o translation_n of_o a_o region_n into_o the_o chart_n depend_v from_o the_o knowledge_n of_o the_o longitude_n and_o latitude_n 3_o the_o part_n to_o be_v describe_v whereof_o the_o chart_n consist_v be_v either_o essential_a or_o accidental_a the_o essential_a be_v either_o the_o line_n as_o be_v the_o meridian_n and_o parallel_n or_o the_o place_n to_o be_v delineate_v out_o by_o picture_n the_o declination_n of_o both_o which_o shall_v be_v teach_v in_o these_o rule_n 1_o to_o set_v down_o the_o meridian_n and_o parallel_n in_o a_o particular_a chart_n to_o show_v the_o practice_n hereof_o we_o will_v take_v for_o instance_n the_o region_n of_o france_n a_o example_n familiar_a with_o our_o late_a topographer_n and_o therefore_o can_v better_o warrant_v the_o description_n france_n be_v suppose_v to_o have_v in_o latitude_n 10._o degree_n in_o longitude_n 16_o this_o know_v you_o must_v proceed_v in_o this_o manner_n first_o through_o the_o middle_n of_o your_o table_n from_o head_n to_o foot_n let_v there_o be_v draw_v a_o perpendicular_a line_n express_v the_o meridian_n of_o the_o world_n which_o shall_v be_v mark_v with_o the_o letter_n of_o let_v this_o line_n be_v divide_v into_o 10._o equal_a part_n then_o draw_v two_o parallel_n line_n whereof_o the_o one_o must_v cross_v the_o say_a line_n about_o the_o point_n e_o with_o right_a angle_n and_o the_o other_o parallel_n must_v cross_v it_o again_o beneath_o in_o the_o point_n f_o with_o like_a angle_n let_v the_o uppermost_a parallel_n be_v express_v by_o ab_fw-la the_o neathermost_a with_o cd_o then_o with_o your_o compass_n take_v one_o of_o the_o 10_o part_n of_o the_o line_n of_o which_o be_v one_o degree_n and_o set_v that_o down_o apart_o by_o itself_o divide_v the_o same_o into_o 60_o minute_n as_o the_o short_a line_n gh_o in_o the_o table_n here_o insert_v will_v show_v on_o the_o right_a hand_n now_o you_o may_v learn_v by_o some_o table_n or_o map_n that_o the_o far_a part_n of_o france_n towards_o the_o north_n through_o which_o be_v draw_v the_o parallel_n ab_fw-la be_v 52._o degree_n distant_a from_o the_o equatour_n and_o that_o the_o south_n parallel_n cd_o be_v distant_a 42_o degree_n also_o certain_a table_n in_o our_o former_a book_n will_v inform_v you_o that_o to_o every_o degree_n of_o the_o parallel_n 42._o delineate_v by_o ab_fw-la do_v answer_v 37_o mile_n and_o that_o to_o every_o degree_n of_o the_o parallel_n cd_o answer_v 45_o mile_n wherefore_o with_o your_o compass_n take_v from_o the_o short_a line_n gh_o 37_o part_n or_o minute_n and_o with_o your_o compass_n keep_v at_o the_o same_o largeness_n let_v the_o parallel_n ab_fw-la be_v divide_v into_o 16_o equal_a space_n correspondent_a to_o that_o wideness_n that_o be_v to_o say_v on_o each_o side_n of_o the_o meridian_n 8_o part_n at_o which_o meridian_n of_o you_o must_v begin_v your_o measure_n towards_o either_o hand_n both_o right_a and_o left_a mark_v the_o end_n of_o every_o such_o space_n with_o a_o certain_a point_n moreover_o for_o the_o south_n parallel_n cd_o let_v 45_o part_n likewise_o be_v take_v from_o the_o short_a line_n gh_o and_o let_v that_o parallel_n be_v divide_v into_o 16_o space_n correspondent_a to_o that_o wideness_n of_o the_o compass_n eight_o space_n be_v set_v down_o on_o each_o side_n of_o the_o meridian_n of_o so_o that_o we_o must_v begin_v from_o the_o meridian_n of_o and_o mark_v the_o end_n of_o every_o such_o space_n with_o a_o point_n then_o from_o those_o point_n wherewith_o each_o of_o those_o two_o parallel_n ab_fw-la and_o cd_o be_v mark_v let_v there_o be_v draw_v a_o right_a line_n from_o point_n to_o point_n and_o those_o shall_v serve_v for_o meridian_n express_v as_o well_o the_o longitude_n of_o the_o whole_a region_n as_o of_o every_o particular_a place_n therein_o seat_v in_o like_a sort_n as_o you_o have_v divide_v the_o meridian_n of_o into_o 10_o equal_a part_n so_o again_o into_o the_o like_a number_n of_o equal_a part_n must_v be_v divide_v each_o of_o the_o two_o uttermost_a meridian_n on_o the_o left_a hand_n and_o the_o right_n mark_v with_o a_o point_n the_o end_n of_o every_o such_o space_n and_o so_o from_o point_n to_o point_n let_v there_o be_v draw_v right_a line_n cut_v all_o the_o meridian_n and_o those_o shall_v serve_v for_o parallel_n and_o in_o the_o uttermost_a space_n let_v there_o be_v write_v the_o number_n of_o longîtude_n and_o latitude_n the_o longitude_n be_v suppose_v to_o begin_v at_o the_o uttermost_a meridian_n at_o the_o left_a hand_n which_o in_o both_o parallel_n be_v the_o far_a meridian_n westward_o now_o for_o as_o much_o as_o the_o most_o westerly_a meridian_n be_v fourteen_o degree_n distant_a from_o the_o meridian_n pass_v by_o the_o canary_n land_n from_o which_o as_o the_o first_o meridian_n the_o ancient_n begin_v their_o account_n you_o must_v set_v down_o in_o the_o first_o place_n on_o the_o left_a hand_n as_o well_o over_o as_o under_o in_o the_o first_o space_n 15_o in_o the_o second_o 16_o in_o the_o three_o 17_o and_o so_o orderly_o proceed_v through_o all_o the_o space_n till_o you_o come_v to_o 30_o for_o the_o difference_n betwixt_o 14_o and_o 30_o be_v 16_o so_o you_o have_v the_o whole_a longitude_n of_o france_n express_v in_o your_o table_n which_o be_v 16_o degree_n in_o the_o like_a sort_n to_o express_v the_o latitude_n have_v the_o degree_n of_o latitude_n mark_v out_o you_o must_v begin_v at_o each_o end_n of_o the_o south_n parallel_n cd_o and_o so_o proceed_v upward_o in_o the_o two_o uttermost_a meridian_n write_v down_o in_o the_o first_o space_n at_o the_o foot_n of_o the_o table_n 43_o degree_n on_o the_o right_a hand_n and_o the_o left_a in_o the_o second_o space_n 44_o in_o the_o three_o 45_o and_o so_o upward_o along_o to_o 52_o so_o have_v you_o express_v the_o whole_a latitude_n of_o france_n from_o north_n to_o south_n for_o betwixt_o 42_o and_o 52_o be_v comprehend_v just_a 10_o degree_n these_o degree_n may_v again_o be_v divide_v at_o pleasure_n into_o lesser_a part_n as_o minute_n according_a to_o the_o largeness_n of_o your_o chart_n 2_o to_o set_v down_o city_n castle_n mountain_n river_n and_o such_o like_a special_a place_n in_o the_o chart_n the_o platform_n of_o your_o chart_n be_v once_o draw_v out_o as_o we_o have_v former_o teach_v in_o the_o precedent_a rule_n you_o may_v very_o easy_o set_v down_o special_a place_n by_o observation_n of_o the_o longitude_n or_o latitude_n of_o such_o place_n either_o by_o
the_o motive_n be_v that_o by_o which_o all_o magnetical_a body_n be_v incline_v and_o stir_v up_o to_o the_o motion_n in_o the_o reasonable_a soul_n of_o a_o man_n we_o have_v two_o faculty_n which_o show_v themselves_o a_o motive_n and_o a_o directive_a or_o disponent_fw-la power_n whereof_o the_o one_o stir_n up_o the_o motion_n the_o other_o regulate_v conform_v and_o direct_v it_o the_o former_a be_v the_o will_n the_o late_a the_o discourse_n and_o judgement_n this_o distinction_n of_o faculty_n howsoever_o more_o evident_a in_o the_o soul_n find_v place_n in_o all_o natural_a agent_n in_o which_o a_o philosopher_n ought_v to_o distinguish_v betwixt_o that_o which_o give_v they_o a_o power_n to_o move_v and_o that_o which_o limit_n determine_v and_o as_o the_o schoolman_n be_v wont_a to_o speak_v modificate_v the_o action_n among_o other_o the_o magnet-stone_n seem_v most_o to_o partake_v of_o these_o two_o power_n as_o that_o which_o among_o all_o natural_a agent_n in_o gilbert_n opinion_n seem_v most_o to_o have_v resemblance_n with_o the_o soul_n of_o a_o man_n so_o that_o by_o a_o apt_a trope_n it_o have_v be_v call_v of_o many_o the_o magnetical_a soul_n of_o the_o earth_n for_o hence_o we_o may_v well_o perceive_v one_o virtue_n or_o inclination_n which_o ●●useth_v the_o magnetical_a needle_n to_o move_v out_o of_o its_o place_n another_o by_o which_o it_o be_v apt_a to_o conform_v itself_o north_n and_o south_n as_o also_o to_o observe_v certain_a angle_n correspondent_a to_o the_o latitude_n of_o the_o place_n as_o shall_v be_v demonstrate_v in_o due_a place_n of_o the_o motive_n power_n we_o will_v produce_v these_o theorem_n 1_o the_o magnetical_a motion_n be_v excite_v in_o a_o small_a &_o unperceivable_a difference_n of_o time_n this_o proposition_n may_v be_v show_v out_o of_o evident_a experiment_n wherein_o every_o man_n sight_n may_v be_v a_o witness_n for_o if_o a_o iron-needle_n touch_v with_o the_o loadstone_n be_v place_v within_o the_o sphere_n of_o the_o magnetical_a virtue_n of_o the_o stone_n it_o will_v present_o move_v itself_o notwithstanding_o the_o interposition_n of_o solid_a body_n which_o make_v gilbert_n to_o imagine_v this_o motion_n to_o be_v effect_v by_o a_o mere_a spiritual_a and_o immaterial_a effluxe_n which_o may_v well_o be_v compare_v to_o the_o light_n which_o nevertheless_o it_o surpass_v in_o subtlety_n for_o the_o light_n be_v move_v from_o east_n to_o west_n so_o quick_o that_o many_o have_v think_v this_o motion_n to_o have_v be_v in_o a_o moment_n or_o instant_n of_o time_n but_o this_o quickness_n of_o motion_n may_v much_o more_o be_v imagine_v in_o the_o magnetical_a virtue_n be_v of_o a_o more_o subtle_a and_o pierce_a nature_n as_o may_v be_v gather_v from_o this_o reason_n to_o wit_n that_o the_o light_n be_v always_o hinder_v by_o the_o interposition_n of_o a_o thick_a and_o opacous_a body_n but_o the_o virtue_n magnetical_a find_v a_o passage_n through_o all_o solid_a body_n whatsoever_o and_o meet_v with_o no_o impediment_n 2_o this_o motive_n quality_n be_v spherical_o spread_v through_o every_o part_n of_o the_o magnetical_a body_n here_o again_o may_v we_o find_v a_o great_a resemblance_n betwixt_o the_o magnetical_a virtue_n and_o the_o light_n for_o as_o all_o light_a body_n as_o the_o sun_n moon_n and_o star_n cast_v their_o beam_n every_o way_n into_o a_o orbicular_a form_n so_o this_o magnetical_a vigour_n cast_v itself_o abroad_o not_o only_o from_o the_o centre_n towards_o the_o superficies_n but_o from_o the_o superficies_n outward_a into_o the_o air_n or_o water_n where_o this_o magnetical_a body_n be_v place_v and_o so_o make_v up_o a_o sphere_n but_o yet_o with_o this_o difference_n that_o if_o the_o body_n be_v mere_a and_o perfect_o spherical_a the_o orb_n of_o the_o magnetical_a virtue_n will_v end_v in_o a_o perfect_a sphere_n as_o we_o see_v the_o magnet_n g_z to_o confine_v his_o virtue_n within_o the_o circle_n bf_n but_o if_o it_o be_v a_o square_a or_o any_o other_o figure_n not_o spherical_a it_o imitate_v a_o sphere_n as_o near_o as_o the_o body_n will_v suffer_v in_o that_o it_o spread_v itself_o everywhere_a from_o the_o centre_n by_o right_a line_n yet_o will_v it_o be_v confine_v in_o a_o square_a figure_n correspondent_a to_o the_o body_n whence_o it_o proceed_v as_o we_o see_v the_o virtue_n of_o the_o square_a magnet_n a_o to_o cast_v his_o beam_n into_o the_o square_a figure_n ld_n 3_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 by_o so_o much_o the_o strong_a by_o how_o much_o these_o part_n be_v situate_v near_o the_o pole_n we_o suppose_v out_o of_o the_o principle_n of_o magnetical_a philosophy_n that_o a_o magnet_n have_v two_o pole_n who_o use_n we_o shall_v show_v hereafter_o these_o pole_n be_v find_v by_o experiment_n to_o have_v more_o force_n and_o vigour_n in_o they_o then_o other_o part_n and_o all_o other_o part_n to_o enjoy_v more_o or_o less_o force_n by_o how_o much_o near_o or_o far_o off_o they_o be_v situate_v to_o their_o pole_n the_o reason_n be_v ascribe_v by_o these_o writer_n to_o the_o disposition_n of_o the_o magnetical_a vigour_n in_o the_o body_n of_o the_o load_n stone_n as_o shall_v appear_v by_o this_o figure_n follow_v in_o gilbert_n express_v the_o great_a magnetical_a body_n of_o the_o earth_n let_v the_o spherical_a superficies_n of_o it_o be_v hqe_a the_o pole_n e_o the_o centre_n m_o hq_n the_o plain_a of_o the_o equinoctial_a from_o every_o point_n of_o this_o equinoctial_a plain_n the_o vigour_n magnetical_a be_v convey_v and_o extend_v to_o cfne_v and_o to_o every_o point_n from_o c_o to_o e_z the_o pole_n but_o not_o towards_o the_o point_n b_o so_o neither_o from_o g_z towards_z c._n the_o vigour_n be_v not_o strengthen_v in_o the_o part_n fhg_v from_o that_o which_o be_v gmfe_n but_o fgh_n do_v increase_v the_o virtue_n in_o h_n so_o that_o there_o can_v arise_v no_o vigour_n so_o far_o from_o the_o parallel_n to_o the_o axel_n tree_n above_o the_o say_a parallel_n but_o internal_o from_o the_o parallel_n to_o the_o pole_n so_o we_o see_v that_o from_o every_o point_n of_o the_o equinoctial_a plain_n the_o force_n be_v derive_v to_o the_o pole_n e._n but_o the_o point_n f_o have_v only_o the_o vigour_n from_o gh_a and_o the_o point_n n_o from_o oh_o but_o the_o pole_n e_z be_v corroborate_v and_o strengthen_v from_o the_o whole_a plain_a of_o the_o equinoctial_a hq_n wherefore_o the_o vigour_n magnetical_a in_o this_o pole_n be_v most_o eminent_a and_o remarkable_a but_o in_o the_o middle_a space_n as_o for_o example_n in_o f_o the_o magnetical_a quality_n be_v so_o far_o strengthen_v as_o the_o portion_n of_o the_o equinoctial_a plain_a h_n can_v give_v but_o dr_n ridley_n in_o his_o late_a magnetical_a treatise_n in_o the_o 6._o chapt._n seem_v to_o oppose_v this_o demonstration_n for_o although_o he_o acknowledge_v that_o the_o vigour_n be_v strong_a of_o all_o in_o the_o pole_n yet_o say_v he_o if_o trial_n be_v make_v what_o the_o pole_n will_v take_v perpendicular_o and_o also_o what_o the_o part_n above_o 34_o degree_n will_v lift_v up_o it_o will_v appear_v to_o be_v half_a asmuch_o perpendicular_o so_o that_o the_o pole_n do_v not_o take_v up_o as_o much_o as_o this_o and_o the_o other_o part_n do_v on_o the_o other_o side_n but_o the_o decision_n of_o these_o difference_n i_o leave_v to_o such_o as_o be_v more_o experimental_a than_o myself_o be_v destitute_a of_o those_o help_n and_o instrument_n which_o they_o enjoy_v 4_o it_o behoove_v we_o in_o the_o second_o place_n to_o speak_v of_o the_o disponent_fw-la vigour_n of_o magnetical_a body_n the_o disponent_fw-la force_n we_o call_v that_o faculty_n by_o which_o magnetical_a body_n be_v dispose_v or_o direct_v to_o a_o certain_a site_n or_o position_n 1_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 this_o proposition_n be_v confirm_v by_o manifold_a experiment_n for_o magnetical_a body_n be_v never_o find_v to_o move_v uncertain_o and_o at_o all_o adventure_n but_o conform_v themselves_o to_o certain_a pole_n and_o make_v certain_a angle_n proportional_a to_o the_o latitude_n as_o we_o shall_v show_v hereafter_o in_o particular_a the_o reason_n of_o which_o experiment_n we_o can_v draw_v from_o no_o other_o cause_n than_o the_o first_o institution_n of_o nature_n in_o all_o natural_a agent_n which_o we_o will_v have_v direct_v to_o certain_a end_n that_o nothing_o in_o her_o commonwealth_n may_v seem_v idle_a or_o unnecessary_a wherefore_o she_o give_v all_o agent_n not_o only_o a_o power_n to_o work_v their_o end_n but_o also_o show_v they_o the_o way_n square_n and_o regulate_v the_o mean_n which_o direct_v unto_o the_o end_n nowhere_a be_v this_o
other_o a_o less_o and_o yet_o in_o the_o same_o period_n of_o time_n as_o we_o may_v see_v in_o this_o figure_n follow_v let_v the_o sun_n be_v in_o the_o point_n of_o the_o ecliptic_a a_o it_o be_v manifest_a that_o he_o will_v sensible_o move_v for_o that_o day_n in_o the_o parallel_n ap._n then_o let_v he_o be_v move_v by_o his_o periodicke_a motion_n into_o the_o point_n of_o the_o ecliptic_a b_o it_o will_v for_o that_o moment_n move_v in_o the_o parallel_n ibo._n last_o of_o all_o let_v it_o be_v in_o the_o point_n of_o the_o aequator_fw-la c._n his_o parallel_n will_v be_v hcl._n it_o be_v manifest_a out_o of_o our_o former_a ground_n that_o he_o will_v be_v move_v slow_a in_o ap._n fast_a in_o io._n fast_o of_o all_o in_o hcl._n which_o swiftness_n and_o slowness_n in_o the_o sun_n motion_n make_v it_o irregular_a some_o have_v think_v to_o salve_v this_o by_o say_v that_o this_o motion_n be_v regular_a because_o in_o equal_a time_n the_o sun_n go_v proportional_a not_o equal_a space_n which_o aguillonius_fw-la hold_v in_o his_o optics_n but_o this_o shift_n be_v frivolous_a because_o it_o take_v not_o away_o the_o objection_n why_o the_o sun_n shall_v move_v fast_o and_o slow_o for_o the_o heaven_n be_v a_o natural_a not_o a_o voluntary_a agent_n and_o according_a to_o these_o ground_n find_v no_o hindrance_n or_o impediment_n must_v always_o work_v to_o his_o utmost_a power_n and_o so_o can_v slack_v or_o increase_v his_o action_n or_o motion_n that_o it_o shall_v move_v fast_o or_o slow_a hitherto_o have_v we_o show_v that_o this_o diurnal_a motion_n can_v without_o some_o absurdity_n be_v grant_v to_o the_o heaven_n in_o the_o next_o place_n we_o be_v to_o show_v that_o it_o no_o way_n can_v cross_v the_o natural_a disposition_n of_o the_o earth_n itself_o which_o we_o shall_v demonstrate_v in_o this_o manner_n if_o this_o circular_a motion_n shall_v cross_v the_o disposition_n of_o the_o earthly_a globe_n it_o will_v happen_v either_o immediate_o in_o respect_n of_o the_o mere_a nature_n which_o the_o logician_n call_v à_fw-la priore_fw-la or_o else_o in_o regard_n of_o certain_a property_n which_o follow_v necessary_o the_o nature_n of_o it_o which_o they_o term_v à_fw-fr posteriori_fw-la if_o they_o say_v it_o happen_v à_fw-la priori_fw-la in_o regard_n of_o the_o mere_a nature_n they_o must_v necessary_o have_v recourse_n to_o the_o propriety_n and_o accident_n for_o a_o demonstration_n for_o the_o internal_a form_n of_o all_o thing_n be_v in_o themselves_o insensible_a can_v be_v discover_v unto_o we_o but_o by_o their_o external_a propriety_n but_o if_o probable_a conjecture_n may_v here_o find_v any_o place_n i_o see_v no_o reason_n why_o the_o earth_n be_v find_v to_o be_v of_o a_o magnetical_a temper_n shall_v not_o challenge_v the_o same_o which_o other_o magnetical_a globe_n far_o great_a than_o the_o earth_n possess_v to_o wit_n a_o circular_a revolution_n about_o her_o own_o pole_n which_o kepler_n and_o galileus_n have_v observe_v aswell_o in_o the_o sun_n as_o jupiter_n and_o in_o like_a matter_n to_o judge_v alike_o seem_v more_o warrantable_a then_o to_o feign_v a_o disparity_n which_o nature_n never_o ground_v or_o observation_n find_v but_o this_o as_o a_o matter_n of_o small_a note_n i_o easy_o pass_v over_o follow_v the_o footstep_n of_o our_o adversary_n which_o seek_v to_o demonstrate_v the_o earth_n stability_n out_o of_o the_o external_a effect_n and_o propriety_n if_o then_o this_o revolution_n contradict_v any_o propriety_n it_o must_v be_v of_o necessity_n either_o in_o regard_n of_o the_o quantity_n and_o magnitude_n or_o else_o in_o respect_n of_o the_o figure_n and_o quality_n or_o of_o some_o motion_n or_o of_o the_o si●e_n and_o position_n for_o i_o find_v no_o other_o propriety_n of_o any_o moment_n which_o can_v enter_v into_o this_o consideration_n first_o that_o the_o quantity_n can_v no_o way_n thwart_o this_o circular_a revolution_n be_v manifest_a because_o it_o will_v happen_v either_o in_o that_o it_o be_v too_o great_a or_o too_o little_a it_o can_v be_v by_o reason_n of_o the_o greatness_n because_o the_o great_a globe_n of_o the_o sun_n and_o jupiter_n manifold_o great_a than_o the_o globe_n of_o the_o earth_n be_v by_o late_a experiment_n of_o the_o trunk-spectacle_n find_v to_o move_v about_o their_o own_o axle_n in_o a_o small_a portion_n of_o time_n the_o like_a have_v other_o deliver_v of_o the_o mo●n●_n and_o venus_n it_o be_v not_o then_o the_o mass_n or_o quantity_n which_o can_v hinder_v it_o in_o the_o earth_n neither_o on_o the_o other_o side_n can_v it_o be_v the_o smallness_n for_o body_n small_a be_v find_v as_o apt_a or_o rather_o apt_a to_o receive_v a_o circular_a motion_n which_o they_o will_v not_o deny_v i_o and_o therefore_o can_v this_o be_v prejudicial_a to_o the_o motion_n of_o the_o earth_n in_o the_o next_o place_n the_o figure_n of_o the_o earthly_a globe_n can_v hinder_v this_o motion_n because_o by_o all_o sound_a philosopher_n be_v acknowledge_v to_o be_v spherical_a it_o can_v but_o be_v deem_v most_o apt_a to_o receive_v revolution_n in_o so_o much_o as_o some_o have_v hence_o labour_v to_o draw_v a_o argument_n for_o the_o earth_n circular_a motion_n as_o deem_v this_o figure_n to_o be_v give_v to_o the_o earth_n for_o no_o other_o end_n or_o use_v three_o no_o quality_n in_o the_o earth_n can_v resist_v this_o circular_a motion_n for_o this_o quality_n by_o the_o consent_n of_o all_o will_v be_v the_o natural_a heaviness_n or_o weight_n of_o the_o earth_n but_o this_o heaviness_n take_v not_o away_o the_o natural_a revolution_n 1_o because_o gravity_n or_o heaviness_n be_v nothing_o else_o but_o the_o inclination_n of_o the_o part_n of_o the_o earth_n return_v to_o their_o natural_a place_n have_v be_v sequester_v from_o it_o but_o these_o part_n have_v once_o regain_v their_o proper_a place_n move_v no_o far_o nor_o be_v in_o those_o place_n esteem_v heavy_a or_o weighty_a whence_o it_o be_v common_o say_v among_o the_o peripatetic_n nihil_fw-la gravitat_fw-la in_o svo_fw-la loco_fw-la nothing_o be_v heavy_a in_o his_o own_o place_n which_o may_v easy_o be_v demonstrate_v out_o of_o staticke_a principle_n whereby_o we_o find_v heaviness_n and_o lightness_n to_o be_v give_v to_o the_o body_n according_a to_o the_o medium_n and_o their_o massiness_n and_o solidity_n in_o respect_n of_o one_o to_o the_o other_o 2_o if_o this_o heaviness_n be_v oppose_v to_o the_o circular_a motion_n then_o either_o immediate_o by_o itself_o or_o secondary_o by_o some_o concomitant_a accident_n it_o can_v be_v the_o first_o because_o gravity_n be_v a_o quality_n but_o motion_n a_o action_n which_o for_o aught_o my_o philosophy_n have_v teach_v i_o be_v not_o opposite_a if_o by_o reason_n of_o some_o accident_n then_o no_o question_n because_o it_o be_v contrary_a to_o lightness_n or_o levity_n which_o seem_v requisite_a to_o such_o a_o motion_n we_o willing_o yield_v this_o natural_a gravity_n of_o the_o part_n of_o the_o earth_n to_o stand_v opposite_a to_o the_o motion_n of_o ascent_n or_o move_v upward_o from_o the_o centre_n but_o nevertheless_o it_o be_v not_o any_o way_n contrary_a to_o the_o circular_a motion_n 1_o because_o contrary_n be_v always_o suppose_v to_o be_v in_o eodem_fw-la genere_fw-la in_o the_o same_o kind_n but_o the_o motion_n of_o heavy_a body_n to_o the_o centre_n and_o of_o the_o earth_n about_o the_o centre_n be_v not_o in_o the_o same_o kind_n the_o one_o be_v a_o right_a motion_n the_o other_o circular_a neither_o can_v the_o weight_n of_o the_o terrestrial_a mass_n add_v or_o diminish_v any_o thing_n in_o regard_n of_o the_o circular_a motion_n because_o a_o spherical_a and_o a_o right_a motion_n can_v either_o direct_o concur_v or_o direct_o oppose_v one_o the_o other_o 2_o we_o may_v urge_v out_o of_o the_o 4_o chap._n of_o aristotle_n 1_o book_n de_fw-fr calo_n that_o no_o circular_a motion_n can_v admit_v of_o contrariety_n which_o he_o confirm_v by_o a_o demonstration_n which_o we_o forbear_v here_o to_o insert_v be_v loath_a to_o rove_v too_o far_o from_o our_o present_a matter_n at_o length_n we_o will_v prove_v that_o this_o orbicular_a motion_n give_v unto_o the_o earth_n can_v overthrow_v or_o thwart_v any_o other_o motion_n of_o the_o earth_n for_o if_o this_o be_v so_o it_o will_v happen_v for_o one_o of_o these_o two_o respect_n either_o because_o the_o earth_n have_v some_o motion_n or_o other_o contrary_n to_o this_o or_o else_o because_o diverse_a motion_n can_v be_v in_o the_o earth_n the_o first_o can_v be_v true_a for_o that_o we_o have_v speak_v before_o because_o the_o right_a motion_n they_o find_v in_o the_o earth_n can_v be_v judge_v contrary_a to_o the_o spherical_a neither_o can_v the_o late_a be_v admit_v as_o a_o undoubted_a truth_n for_o howsoever_o aristotle_n set_v it_o
and_o compass_n dare_v not_o adventure_v into_o the_o ocean_n so_o far_o out_o of_o sight_n of_o land_n but_o to_o give_v the_o opposite_a part_n all_o reasonable_a advantage_n admit_v the_o strait_n divide_v asia_n and_o america_n be_v very_o narrow_a and_o within_o ken_n be_v it_o likely_a that_o from_o hence_o th●y_o can_v by_o ship_n transport_v so_o many_o knde_n of_o creature_n can_v we_o believe_v any_o man_n to_o be_v so_o mad_a as_o to_o carry_v over_o with_o he_o lion_n bear_n tiger_n fox_n and_o other_o innumerable_a sort_n of_o ravenous_a and_o unprofitable_a beast_n as_o pernicious_a to_o mankind_n as_o other_o creature_n serve_v for_o his_o use_n if_o any_o be_v find_v so_o foolish_a or_o malicious_a yet_o be_v it_o very_o unlikely_a he_o shall_v transport_v so_o many_o kind_n this_o argument_n seem_v no_o more_o to_o concern_v america_n than_o most_o land_n of_o the_o world_n wherein_o we_o find_v diverse_a creature_n not_o only_o serve_v for_o the_o use_n of_o man_n but_o many_o unprofitable_a &_o hateful_a to_o the_o inhabitant_n the_o mean_n of_o this_o transportation_n be_v very_o difficult_a to_o find_v st_n augustine_n with_o some_o other_o divine_n have_v be_v drive_v to_o a_o supernatural_a cause_n as_o if_o almighty_a god_n shall_v perform_v this_o matter_n by_o the_o ministry_n of_o angel_n which_o answer_v we_o dare_v not_o utter_o reject_v be_v support_v by_o the_o authority_n of_o so_o great_a a_o pillar_n of_o the_o church_n yet_o i_o can_v so_o easy_o imagine_v that_o god_n who_o use_v natural_a mean_n for_o the_o preservation_n of_o all_o live_a creature_n in_o the_o ark_n shall_v have_v recourse_n to_o a_o supernatural_a power_n in_o the_o propagation_n of_o these_o creature_n on_o the_o face_n of_o the_o earth_n wherefore_o to_o i_o the_o reason_n will_v seem_v better_o answer_v out_o of_o our_o ground_n which_o we_o shall_v prove_v hereafter_o that_o land_n be_v not_o from_o the_o first_o creation_n but_o afterward_o break_v from_o the_o main_a continent_n by_o the_o violence_n of_o the_o water_n hence_o it_o may_v come_v to_o pass_v that_o such_o beast_n as_o be_v in_o the_o part_n of_o the_o earth_n so_o break_v off_o have_v since_o there_o continue_v by_o continual_a propagation_n until_o this_o day_n i_o mean_v of_o ravenous_a and_o hurtful_a beast_n because_o of_o the_o other_o less_o doubt_n can_v be_v make_v but_o that_o they_o may_v be_v convey_v from_o one_o country_n into_o another_o by_o ship_v to_o serve_v the_o necessity_n of_o mankind_n here_o we_o see_v that_o no_o argument_n as_o yet_o have_v be_v urge_v so_o strong_a against_o the_o north-passage_n but_o may_v with_o reasonable_a probability_n be_v answer_v it_o remain_v in_o the_o second_o place_n that_o we_o descend_v somewhat_o to_o particular_n to_o inquire_v whether_o this_o be_v to_o be_v effect_v either_o towards_o the_o north-east_n or_o the_o northwest_n the_o north-east_n passage_n have_v heretofore_o be_v attempt_v by_o many_o of_o our_o english_a navigatour_n but_o with_o unhappy_a success_n yet_o be_v not_o these_o voyage_n altogether_o fruitless_a forasmuch_o as_o by_o this_o mean_n a_o way_n be_v find_v out_o to_o russia_n whence_o begin_v the_o first_o trade_n between_o we_o and_o the_o russian_a merchant_n but_o that_o little_a hope_n can_v hence_o arise_v sundry_a reason_n may_v be_v allege_v the_o chief_a whereof_o be_v these_o 1_o the_o dangerous_a rend_n of_o the_o scythick_n cape_n set_v by_o ortelius_n under_o 80_o degree_n northward_o together_o with_o the_o perilous_a sail_v in_o those_o northern_a sea_n always_o pester_v with_o ice_n and_o snow_n second_v by_o diverse_a bay_n or_o shelf_n mist_n fog_n long_a and_o darksome_a night_n most_o adverse_a to_o any_o happy_a navigation_n 2_o the_o observation_n of_o the_o water_n which_o be_v more_o shallow_a towards_o the_o east_n which_o give_v small_a hope_n of_o a_o through_o passage_n because_o all_o sea_n be_v feed_v with_o water_n and_o for_o the_o most_o part_n be_v observe_v to_o be_v more_o shallow_a towards_o the_o shore_n then_o in_o the_o middle_n but_o where_o in_o sail_v forward_o any_o sea_n be_v find_v to_o decrease_v in_o depth_n it_o be_v a_o likely_a argument_n that_o it_o be_v rather_o a_o creek_n bay_fw-mi or_o river_n than_o a_o straight_o notwithstanding_o these_o reason_n some_o have_v heretofore_o go_v about_o to_o prove_v a_o passage_n by_o the_o north-east_n to_o cathay_n of_o which_o opinion_n be_v antony_n jenkinson_n who_o reason_n be_v well_o answer_v by_o sr_n humphrey_n gilbert_n which_o i_o brief_o touch_v add_v some_o thing_n of_o my_o own_o as_o i_o find_v occasion_n the_o first_o reason_n be_v draw_v from_o a_o relation_n of_o tartarian_a who_o report_v that_o in_o hunt_v the_o morse_n he_o sail_v very_o far_o towards_o the_o southeast_n wherein_o he_o find_v no_o end_n which_o may_v give_v a_o likely_a conjecture_n that_o it_o be_v a_o passage_n throughout_o but_o to_o this_o we_o may_v easy_o answer_v that_o the_o tartarian_n be_v a_o barbarous_a nation_n altogether_o ignorant_a of_o navigation_n which_o neither_o know_v the_o use_n of_o the_o chart_fw-la compass_n or_o celestial_a observation_n &_o therefore_o in_o a_o wide_a sea_n know_v not_o how_o to_o distinguish_v the_o north-east_n from_o the_o southeast_n beside_o the_o curious_a search_n of_o this_o long_a passage_n must_v depend_v on_o better_a discovery_n than_o a_o poor_a fisherman_n who_o seldom_o dare_v adventure_v himself_o out_o of_o sight_n of_o land_n beside_o the_o fisherman_n judge_v by_o sight_n can_v not_o see_v about_o a_o ken_n at_o sea_n which_o will_v prove_v nothing_o in_o regard_n of_o so_o long_a a_o distance_n the_o second_o reason_n urge_v by_o mr_n jenkinson_n be_v this_o that_o there_o be_v a_o vnicorne_n horn_n find_v upon_o the_o coast_n of_o tartary_n which_o can_v not_o come_v say_v he_o by_o any_o other_o mean_v then_o with_o the_o tide_n in_o some_o straight_o in_o the_o north-east_n in_o the_o freeze_a sea_n there_o be_v no_o unicorn_n in_o all_o asia_n save_v in_o i●dia_n and_o cataia_n to_o this_o reason_n i_o may_v answer_v with_o sr_n humphrey_n gilbert_n many_o way_n 1_o we_o may_v well_o doubt_v whether_o tartarian_n know_v a_o true_a unicorn_n horn_n or_o no_o 2_o it_o be_v credible_a that_o it_o can_v be_v drive_v so_o far_o by_o the_o tide_n be_v of_o such_o a_o nature_n that_o it_o can_v swim_v 3_o the_o tide_n run_v to_o and_o fro_o will_v have_v drive_v it_o as_o far_o back_o with_o the_o ebb_n as_o it_o bring_v it_o forward_o with_o the_o flood_n 4_o the_o horn_n which_o be_v cast_v on_o this_o coast_n may_v be_v the_o horn_n of_o a_o asinus_fw-la indicu●_fw-la which_o have_v but_o one_o horn_n like_o a_o unicorn_n in_o his_o forehead_n whereof_o there_o be_v great_a plenty_n in_o all_o the_o north_n part_n as_o in_o lappia_n norvegia_n finmarke_n as_o zeigler_n testify_v in_o his_o history_n of_o scandia_n 5_o last_o there_o be_v a_o fish_n which_o have_v a_o horn_n in_o his_o sore-head_n c●lled_v the_o sea_n unicorn_n whereof_o martin_n frobisher_n find_v one_o on_o the_o coast_n of_o newfoundland_n and_o give_v it_o to_o queen_n elizabeth_n which_o be_v say_v to_o be_v put_v into_o her_o wardrobe_n but_o whether_o it_o be_v the_o same_o which_o be_v at_o this_o day_n to_o be_v see_v at_o windsor_n castle_n i_o can_v tell_v the_o three_o and_o strong_a reason_n which_o be_v urge_v for_o the_o north-east_n passage_n be_v this_o that_o there_o be_v a_o continual_a current_n through_o the_o freeze_a sea_n of_o such_o swiftness_n that_o if_o any_o thing_n be_v throw_v into_o the_o water_n it_o will_v present_o be_v carry_v out_o of_o sight_n to_o this_o we_o may_v easy_o answer_v that_o this_o strong_a current_n be_v not_o maintain_v by_o any_o tide_n come_v from_o another_o sea_n but_o by_o diverse_a great_a river_n fall_v into_o this_o straight_a in_o like_a sort_n we_o find_v a_o strong_a current_n from_o maeotis_n palus_n by_o pontus_n euxinus_n sinus_n bosphorus_n and_o along_o all_o the_o coast_n of_o greci_fw-la as_o contarenus_n and_o diverse_a other_o affirm_v out_o of_o their_o own_o experience_n and_o yet_o the_o sea_n lie_v not_o open_a to_o any_o other_o sea_n but_o be_v maintain_v by_o tanais_n and_o diverse_a other_o river_n so_o in_o this_o north-east_n part_n may_v this_o current_n of_o water_n be_v maintain_v by_o the_o river_n du●●a_n ob_fw-la and_o many_o other_o which_o continual_o fall_v into_o it_o hitherto_o have_v we_o treat_v of_o other_o passage_n either_o effect_v or_o attempt_v to_o cathay_n and_o the_o east_n indies_n the_o last_o and_o most_o desire_a and_o seek_v in_o our_o time_n be_v that_o by_o the_o north_n west_n this_o way_n have_v be_v often_o attempt_v as_o by_o cabot_n davis_n frobisher_n hudson_n sr_n thomas_n button_n and_o