not_o the_o same_o though_o at_o the_o same_o time_n neither_o will_v such_o a_o star_n to_o both_o place_n seem_v in_o the_o same_o point_n of_o the_o heaven_n which_o can_v not_o possible_o be_v except_o we_o admit_v a_o sensible_a difference_n betwixt_o the_o rational_a and_o sensible_a horizon_n and_o so_o grant_v the_o earth_n in_o respect_n of_o such_o orb_n some_o quantity_n and_o greatness_n this_o diversity_n of_o aspect_n which_o they_o call_v the_o parallax_n may_v be_v see_v in_o this_o figure_n let_v a_o be_v the_o centre_n of_o the_o earth_n l_o the_o moon_n or_o other_o star_n to_o be_v observe_v egg_v the_o firmament_n or_o orb_n of_o the_o fix_a star_n suppose_v then_o the_o eye_n to_o be_v in_o the_o fix_a point_n m_o of_o the_o sensible_a horizon_n xmy_n the_o say_a planet_n will_v appear_v in_o the_o point_n of_o the_o firmament_n s_o according_a to_o opticall_a principle_n whereby_o all_o thing_n be_v say_v to_o be_v see_v in_o the_o place_n direct_o opposite_a 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as_o in_o logic_a man_n have_v invent_v certain_a intentional_a notion_n serve_v as_o so_o many_o instrument_n to_o direct_v and_o regulate_v our_o understanding_n in_o the_o apprehension_n of_o thing_n so_o in_o cosmographie_n can_v there_o not_o be_v want_v such_o imaginary_a sign_n and_o circle_n to_o confirm_v and_o aid_v our_o fantasy_n and_o as_o in_o logic_n such_o notion_n in_o themselves_o be_v mere_o imaginary_a and_o intentional_a yet_o may_v be_v term_v real_a so_o far_o forth_o as_o they_o be_v ground_v in_o the_o thing_n themselves_o so_o may_v we_o speak_v of_o these_o circle_n conceive_v in_o the_o face_n of_o the_o terrene_a globe_n which_o we_o be_v not_o to_o conceive_v to_o be_v fictious_a and_o imaginary_a as_o if_o they_o have_v no_o ground_n at_o all_o in_o nature_n for_o although_o there_o be_v no_o such_o circle_n paint_v on_o the_o face_n of_o the_o earth_n as_o we_o find_v in_o a_o artificial_a sphere_n yet_o must_v we_o of_o necessity_n conceive_v such_o 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have_v find_v these_o circle_n all_o except_o the_o horizon_n to_o wit_n the_o meridian_n and_o parallel_n to_o be_v immediate_o ground_v in_o the_o earth_n itself_o who_o opinion_n we_o can_v reject_v as_o be_v support_v by_o experimental_a demonstration_n as_o we_o shall_v show_v in_o particular_a 2_o the_o distinction_n of_o a_o circle_n into_o any_o certain_a number_n of_o part_n have_v no_o certain_a ground_n in_o the_o nature_n of_o the_o earthly_a sphere_n but_o only_a inconueniency_n leave_v our_o judgement_n free_a to_o take_v such_o a_o number_n as_o may_v best_o serve_v our_o purpose_n some_o astronomer_n more_o curious_a than_o wise_a have_v go_v about_o to_o seek_v a_o ground_n of_o this_o distinction_n of_o a_o circle_n into_o 360_o part_n out_o of_o the_o sun_n course_n in_o the_o zodiac_n a_o circle_n say_v they_o by_o the_o open_n of_o the_o compass_n be_v describe_v in_o a_o plain_a be_v divide_v into_o six_o equal_a part_n now_o because_o the_o sun_n be_v the_o 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calculate_v the_o motion_n of_o the_o sun_n in_o his_o ecliptic_a not_o that_o this_o division_n have_v any_o ground_n in_o nature_n more_o than_o other_o because_o be_v a_o continuate_a quantity_n according_a to_o philosophy_n it_o may_v suffer_v infinite_a division_n for_o it_o be_v in_o the_o beginning_n leave_v free_a to_o cosmographer_n to_o choose_v what_o number_n they_o please_v to_o express_v the_o part_n or_o section_n of_o a_o circle_n which_o they_o take_v as_o it_o seem_v not_o mere_o from_o the_o motion_n of_o the_o sun_n but_o from_o their_o conveniency_n and_o commodity_n find_v this_o number_n most_o commodious_a for_o the_o distinction_n of_o every_o circle_n the_o reason_n be_v because_o no_o number_n can_v be_v find_v which_o suffer_v more_o part_n and_o division_n than_o this_o for_o as_o much_o as_o in_o 60_o whereof_o
the_o scripture_n especial_o in_o the_o 8_o of_o the_o proverb_n and_o the_o 103_o psalm_n where_o god_n be_v say_v to_o have_v set_v a_o bind_v upon_o the_o sea_n which_o they_o shall_v not_o pass_v but_o this_o reason_n seem_v not_o warrantable_a that_o the_o great_a creator_n of_o all_o thing_n shall_v in_o the_o first_o institution_n of_o nature_n impose_v a_o perpetual_a violence_n upon_o nature_n moreover_o all_o miracle_n be_v temporary_a and_o not_o perpetual_a for_o than_o be_v it_o ordinary_a and_o so_o scarce_o a_o miracle_n other_o upon_o less_o ground_n have_v imagine_v that_o there_o be_v certain_a northern_a star_n in_o vrsa_fw-la maior_fw-la and_o draco_n of_o so_o great_a virtue_n that_o they_o can_v draw_v the_o ocean_n from_o this_o habitable_a part_n of_o the_o earth_n towards_o the_o north_n and_o so_o constrain_v the_o water_n that_o they_o can_v overwhelm_v the_o earth_n but_o this_o opinion_n be_v ridiculous_a and_o deserve_v no_o solid_a refutation_n be_v a_o mere_a conjecture_n without_o ground_n or_o probability_n other_o upon_o the_o like_a reason_n have_v dream_v that_o there_o be_v more_o water_n than_o earth_n in_o the_o globe_n and_o that_o the_o water_n by_o his_o extraordinary_a mass_n occupy_v the_o centre_n of_o the_o world_n turn_v the_o earth_n on_o one_o side_n make_v it_o to_o swim_v as_o a_o ship_n upon_o the_o sea_n but_o this_o assertion_n we_o have_v refute_v in_o our_o first_o chapter_n of_o the_o first_o book_n all_o these_o author_n suppose_v that_o the_o earth_n be_v uncover_v towards_o the_o north-pole_n but_o overflow_v with_o water_n towards_o the_o south_n which_o the_o experience_n of_o navigatour_n at_o this_o day_n have_v sufficient_o disannul_v other_o again_o affirm_v out_o of_o a_o peripatetical_a dream_n that_o the_o water_n be_v ten_o time_n great_a than_o the_o earth_n suppose_v the_o earth_n to_o be_v like_o a_o sponge_n to_o drink_v up_o the_o water_n to_o prove_v which_o assertion_n they_o produce_v a_o experiment_n that_o the_o earth_n be_v dig_v any_o thing_n deep_a in_o most_o place_n there_o will_v appear_v water_n whence_o they_o collect_v that_o the_o water_n be_v mix_v with_o the_o whole_a earth_n and_o receive_v into_o it's_o concavity_n but_o howsoever_o we_o may_v grant_v that_o there_o be_v many_o and_o vast_a concavity_n in_o the_o earth_n capable_a of_o water_n yet_o it_o be_v impossible_a that_o the_o water_n shall_v be_v ten_o time_n as_o great_a as_o the_o earth_n for_o by_o this_o reason_n although_o all_o the_o terrestrial_a globe_n be_v water_n it_o can_v not_o be_v but_o that_o a_o great_a portion_n of_o water_n then_o that_o in_o the_o earth_n shall_v arise_v above_o the_o earth_n because_o according_a to_o their_o own_o supposition_n 9_o part_n shall_v be_v above_o the_o earth_n neither_o can_v aristotle_n word_n be_v well_o wrest_v to_o this_o interpretation_n for_o as_o much_o as_o he_o understand_v this_o tenfold_o proportion_n of_o the_o water_n to_o the_o earth_n not_o of_o the_o space_n which_o they_o replenish_v measure_v by_o their_o circle_n and_o diameter_n but_o of_o the_o proportion_n they_o bear_v one_o to_o the_o other_o in_o their_o transmutation_n as_o that_o one_o measure_n of_o earth_n turn_v into_o water_n shall_v be_v as_o much_o as_o 10._o all_o these_o opinion_n seem_v so_o absurd_a it_o seem_v more_o probable_a to_o imagine_v that_o either_o the_o water_n be_v condensated_a and_o thicken_v which_o be_v in_o the_o beginning_n create_v thin_a whence_o will_v follow_v that_o they_o shall_v occupy_v a_o less_o place_n and_o by_o consequence_n leave_v the_o dry-land_n in_o many_o place_n habitable_a or_o which_o be_v more_o probable_a that_o god_n in_o the_o first_o creation_n make_v certain_a hollow_a concavity_n and_o channel_n in_o the_o earth_n which_o be_v before_o plain_a and_o uniform_a into_o which_o the_o water_n be_v receive_v and_o bound_v in_o so_o much_o that_o they_o can_v not_o flow_v abroad_o this_o seem_v enough_o to_o satisfy_v the_o search_n of_o such_o as_o be_v not_o too_o curious_a to_o search_v into_o his_o secret_n who_o power_n and_o omnipotence_n transcend_v the_o capacity_n of_o the_o wise_a in_o this_o division_n of_o a_o place_n into_o water_n and_o land_n we_o will_v first_o treat_v of_o the_o sea_n and_o the_o accident_n belong_v thereunto_o not_o that_o the_o water_n be_v worthy_a or_o great_a than_o the_o earth_n the_o contrary_a whereof_o we_o have_v prove_v heretofore_o but_o because_o the_o consideration_n of_o it_o be_v more_o simple_a as_o that_o wherein_o few_o matter_n be_v to_o be_v handle_v then_o in_o the_o land_n for_o rivers_n and_o lake_n although_o consist_v of_o this_o watery_a element_n we_o think_v fit_a to_o handle_v apart_o as_o adjunct_n belong_v to_o the_o land_n 4_o in_o the_o sea_n be_v consider_v two_o thing_n 1_o the_o adjunct_n 2_o the_o division_n the_o accident_n of_o the_o sea_n whereof_o we_o be_v to_o treat_v be_v either_o internal_a or_o eâ—ternall_n 5_o the_o internal_a be_v such_o as_o be_v inbred_a in_o the_o sea_n these_o again_o be_v either_o absolute_a or_o relative_n 6_o the_o absolute_a be_v such_o as_o agree_v to_o the_o sea_n without_o any_o comparison_n with_o the_o land_n such_o be_v either_o figure_n quality_n or_o motion_n 7_o the_o figure_n be_v the_o conformity_n of_o the_o external_a superficies_n of_o the_o sea_n whereof_o observe_v this_o theorem_n 1_o although_o the_o whole_a body_n of_o the_o water_n be_v spherical_a yet_o it_o be_v probable_a that_o the_o part_n of_o it_o incline_v to_o a_o conicall_a figure_n that_o the_o whole_a water_n according_a to_o its_o outward_a superficies_n iâ—_n spherical_a and_o round_a be_v sufficient_o demonstrate_v before_o in_o the_o first_o book_n but_o notwithstanding_o this_o roundness_n of_o the_o whole_a the_o part_n of_o it_o may_v for_o aught_o i_o see_v admit_v of_o a_o conicall_a figure_n for_o as_o much_o as_o this_o have_v little_a or_o no_o proportion_n to_o the_o vast_a spheracity_n of_o the_o water_n no_o more_o then_o little_a hill_n to_o the_o greatness_n of_o the_o earth_n for_o the_o prosecution_n of_o which_o point_n i_o will_v first_o show_v the_o reason_n of_o this_o my_o conjecture_n ground_v on_o experience_n and_o afterward_o out_o of_o the_o ground_n and_o demonstration_n of_o the_o principle_n of_o mathematical_a philosophy_n endeavour_v to_o make_v it_o more_o manifest_a first_o therefore_o by_o a_o conicall_a line_n we_o understand_v a_o crooked_a line_n which_o differ_v from_o a_o periphery_a or_o circle_n in_o as_o much_o as_o it_o keep_v not_o always_o a_o equal_a distance_n from_o the_o centre_n but_o be_v high_a in_o the_o midst_n then_o on_o either_o side_n now_o if_o the_o part_n of_o the_o water_n stand_v still_o be_v in_o their_o high_a superficies_n exact_o spherical_a they_o shall_v by_o the_o same_o ground_n be_v concentricall_a or_o have_v the_o same_o centre_n with_o the_o whole_a earth_n but_o that_o it_o have_v not_o the_o same_o centre_n will_v appear_v by_o little_a drop_n of_o water_n fall_v on_o the_o ground_n which_o incline_v as_o we_o see_v to_o a_o round_a figure_n yet_o be_v it_o more_o than_o ridiculous_a to_o say_v that_o this_o round_a convexity_n of_o a_o drop_n can_v be_v concentricall_a with_o the_o whole_a earth_n since_o in_o so_o great_a a_o mass_n it_o be_v hardly_o sensible_a but_o here_o our_o ordinary_a philosopher_n be_v ready_a to_o answer_v that_o this_o conformity_n of_o the_o water_n drop_n in_o a_o round_a figure_n be_v rather_o violent_a then_o natural_a because_o the_o water_n be_v by_o nature_n moist_a be_v ready_a to_o fly_v and_o avoid_v the_o touch_n or_o drought_n or_o any_o dry_a thing_n and_o because_o the_o water_n thus_o avoid_v the_o drought_n can_v of_o necessity_n but_o some_o way_n touch_v it_o it_o be_v imagine_v to_o conform_v itself_o to_o that_o figure_n whereit_v it_o may_v least_o of_o all_o touch_n this_o be_v the_o round_a or_o spherical_a figure_n wherein_o any_o body_n contain_v can_v touch_v a_o plain_a otherwise_o then_o in_o one_o only_a point_n but_o against_o this_o conjecture_n of_o moisture_n fly_v drought_n strong_a enough_o be_v the_o experiment_n of_o scaliger_n in_o his_o 105_o exercitation_n that_o quicksilver_n a_o moist_a substance_n be_v cast_v either_o into_o water_n or_o iron-oare_n will_v gather_v itself_o to_o a_o round_a body_n notwithstanding_o it_o be_v manifest_a that_o quicksilver_n natural_o neither_o avoid_v the_o touch_n of_o water_n or_o iron_n for_o as_o much_o as_o the_o one_o be_v very_a mâ—â—st_n the_o other_o of_o great_a affinity_n as_o our_o chimick_n teach_v with_o quicksilver_n the_o parent_n of_o all_o metal_n moreover_o it_o be_v manifest_a that_o this_o conformity_n to_o roundness_n be_v in_o drop_n of_o rain_n fall_v to_o the_o earth_n through_o the_o air_n yet_o will_v not_o our_o
we_o call_v it_o natural_a forasmuch_o as_o it_o issue_v and_o arise_v from_o the_o natural_a disposition_n and_o inclination_n of_o all_o the_o part_n to_o understand_v which_o clause_n the_o better_a we_o be_v to_o consider_v that_o a_o thing_n may_v be_v call_v natural_a two_o manner_n of_o way_n first_o in_o regard_n of_o the_o primary_n intent_n of_o nature_n as_o the_o near_a and_o immediate_a end_n or_o scope_n to_o which_o she_o be_v direct_v second_o in_o respect_n of_o her_o secundary_a intent_n or_o purpose_n as_o that_o which_o must_v of_o necessity_n follow_v the_o former_a true_a it_o be_v that_o every_o terrene_a body_n according_a to_o nature_n first_o intention_n seek_v and_o work_v it_o be_v own_o perfection_n and_o conservation_n nevertheless_o according_a to_o her_o secundary_a intent_n it_o concurre_v to_o the_o perfection_n and_o good_a of_o the_o whole_a universe_n which_o we_o shall_v plain_o see_v in_o a_o stone_n or_o clodd_n of_o earth_n which_o separate_v and_o remove_v from_o its_o mother_n the_o sphere_n of_o the_o earth_n by_o his_o descent_n and_o fall_v downward_o seek_v first_o his_o own_o conservation_n by_o reunite_a itself_o to_o the_o earth_n whence_o it_o be_v take_v second_o of_o the_o whole_a globe_n of_o the_o earth_n which_o by_o this_o union_n and_o addition_n no_o doubt_n be_v make_v more_o complete_a and_o perfect_a this_o conformity_n of_o the_o terrestrial_a part_n out_o of_o which_o arise_v the_o earth_n sphaericity_n i_o call_v the_o natural_a inclination_n they_o have_v to_o move_v and_o settle_v themselves_o in_o such_o a_o site_n or_o position_n as_o may_v bring_v forth_o a_o spherical_a consistency_n so_o that_o if_o it_o be_v possible_a as_o what_o can_v be_v to_o god_n almighty_a power_n that_o the_o whole_a globe_n of_o the_o earth_n be_v dissolve_v and_o rend_v into_o little_a piece_n yet_o be_v that_o vigour_n and_o motive_n inclination_n remain_v in_o the_o part_n whereby_o they_o may_v settle_v and_o conform_v themselves_o to_o the_o same_o spherical_a nature_n and_o composition_n which_o it_o former_o enjoy_v for_o all_o the_o part_n thus_o suppose_v to_o be_v distract_v will_v no_o question_n meet_v together_o &_o conform_v themselves_o to_o the_o same_o point_n or_o centre_n and_o so_o equal_o poise_v themselves_o will_v restore_v the_o same_o sphere_n so_o dissolve_v so_o that_o we_o here_o note_v a_o double_a inclination_n and_o motion_n of_o earthly_a body_n first_o by_o a_o right_a line_n of_o the_o part_n tend_v towards_o the_o centre_n the_o other_o spherical_a of_o the_o whole_a sphere_n whereof_o the_o first_o in_o nature_n preceede_v the_o composition_n of_o the_o sphere_n the_o other_o follow_v but_o this_o latter_a motion_n i_o leave_v doubtful_a till_o place_v convenient_a 6_o the_o conformity_n of_o the_o terrene_a part_n be_v twofold_a primarie_n or_o secondary_a the_o former_a be_v that_o whereby_o all_o earthly_a body_n be_v by_o a_o right_a line_n carry_v and_o direct_v to_o the_o centre_n of_o the_o terrestrial_a globe_n as_o in_o a_o artificial_a sphere_n or_o circle_n draw_v by_o a_o geometrician_n their_o principal_a part_n be_v express_v to_o wit_n the_o centre_n ray_n and_o circumference_n so_o in_o the_o natural_a globe_n of_o the_o earth_n these_o three_o as_o it_o be_v naturally_n &_o real_o discover_v themselves_o unto_o us._n for_o first_o there_o be_v set_v a_o fix_a point_n to_o which_o all_o heavy_a body_n move_v and_o conform_v themselves_o second_o there_o be_v set_v the_o line_n or_o radius_fw-la in_o which_o such_o body_n be_v carry_v and_o convey_v three_o the_o confluence_n of_o all_o these_o part_n beget_v the_o roundness_n and_o spherical_a form_n to_o begin_v first_o with_o that_o which_o be_v first_o in_o nature_n we_o will_v take_v these_o ground_n 1_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 this_o proposition_n so_o far_o forth_o as_o it_o concern_v the_o two_o element_n of_o earth_n and_o water_n be_v confirm_v by_o common_a experience_n and_o therefore_o need_v no_o long_a demonstration_n for_o we_o see_v plain_o that_o not_o only_o these_o two_o do_v incline_v as_o much_o as_o may_v be_v all_o obstacle_n be_v remove_v to_o the_o centre_n of_o the_o earth_n but_o also_o all_o mix_a body_n compound_v of_o they_o be_v oversway_v with_o the_o most_o predominant_a element_n do_v challenge_n to_o themselves_o the_o same_o motion_n i_o say_v not_o that_o all_o these_o terrestrial_a body_n drive_v &_o meeâ—_n in_o the_o centre_n for_o that_o be_v impossible_a that_o all_o this_o massy_a sphere_n shall_v be_v contract_v to_o one_o point_n but_o that_o all_o the_o part_n have_v a_o mutual_a inclination_n to_o approach_v as_o near_o the_o centre_n as_o the_o necessity_n of_o the_o place_n and_o the_o concurrence_n of_o they_o among_o themselves_o will_v suffer_v by_o these_o terrestrial_a body_n which_o enjoy_v this_o motion_n and_o inclination_n we_o understand_v first_o the_o two_o element_n of_o earth_n and_o water_n with_o all_o other_o body_n arise_v out_o of_o their_o mixture_n to_o these_o i_o may_v add_v the_o air_n which_o by_o reason_n of_o his_o affinity_n with_o the_o earth_n and_o water_n and_o natural_a comformity_n to_o the_o same_o centre_n we_o may_v well_o term_v a_o earthly_a body_n it_o be_v common_o report_v that_o the_o air_n be_v lâ—ght_v and_o therefore_o carry_v upward_o not_o incline_v at_o all_o to_o the_o centre_n of_o the_o terrestrial_a globe_n as_o the_o part_n of_o these_o two_o element_n be_v but_o this_o assertion_n although_o bolster_v up_o both_o with_o antiquity_n and_o authority_n i_o take_v either_o to_o be_v false_a or_o misunderstand_v and_o that_o i_o speak_v no_o more_o herein_o than_o i_o can_v prove_v i_o will_v produce_v some_o reason_n strong_a enough_o as_o i_o think_v to_o persuade_v that_o the_o air_n be_v a_o heavy_a body_n have_v a_o due_a inclination_n and_o conformity_n to_o the_o centre_n of_o the_o earth_n first_o therefore_o will_v i_o produce_v this_o experiment_n when_o a_o well_o or_o deep_a trench_n be_v dig_v up_o in_o the_o earth_n i_o will_v willing_o demand_v whether_o the_o air_n descend_v to_o fill_v up_o this_o trench_n or_o concavity_n or_o else_o a_o void_a space_n be_v leave_v unfurnished_a of_o any_o natural_a body_n to_o fill_v it_o if_o they_o admit_v the_o latter_a they_o will_v consequent_o bring_v in_o again_o that_o vacuum_n or_o void_a space_n which_o arist._n and_o all_o sound_a philosopher_n have_v long_a since_o proscribe_v the_o confine_n of_o nature_n if_o they_o affirm_v the_o former_a that_o the_o air_n descend_v to_o fill_v up_o this_o empty_a space_n i_o will_v ask_v again_o whether_o this_o descent_n of_o the_o air_n be_v violent_a or_o natural_a if_o they_o say_v natural_a they_o admit_v our_o assertion_n that_o the_o air_n natural_o descend_v towards_o the_o centre_n and_o so_o by_o consequence_n that_o it_o be_v heavy_a and_o not_o light_a by_o nature_n neither_o according_a to_o our_o peripateticall-philosophy_n can_v we_o ascribe_v more_o than_o one_o motion_n to_o the_o air_n because_o it_o be_v a_o ground_n general_o receive_v among_o aristotelean_n that_o one_o simple_a body_n can_v claim_v but_o one_o simple_a motion_n much_o less_o one_o simple_a form_n as_o that_o of_o the_o air_n can_v produce_v two_o opposite_a and_o contrary_a motion_n such_o as_o be_v ascent_n and_o descent_n of_o the_o same_o body_n if_o they_o chance_v to_o light_v on_o the_o other_o member_n of_o our_o distinction_n and_o say_v that_o the_o motion_n of_o the_o air_n in_o this_o sort_n be_v violent_a it_o must_v needs_o follow_v that_o it_o must_v have_v some_o external_a cause_n or_o principle_n whence_o it_o shall_v proceed_v because_o all_o such_o motion_n proceed_v from_o external_a cause_n but_o here_o no_o such_o cause_n can_v be_v assign_v for_o the_o cause_n will_v be_v either_o the_o earth_n which_o be_v so_o make_v hollow_a or_o the_o emptiness_n or_o vacuum_n or_o at_o least_o the_o other_o part_n of_o the_o air_n that_o it_o be_v not_o the_o earth_n may_v be_v prove_v first_o because_o no_o philosopher_n have_v ever_o show_v any_o such_o attractive_a power_n to_o reside_v in_o the_o earth_n but_o rather_o the_o contrary_a because_o the_o earth_n and_o air_n by_o most_o have_v be_v think_v opposite_a in_o nature_n and_o repugnant_a one_o to_o the_o other_o second_o because_o philosophy_n teach_v that_o no_o agent_n can_v work_v upon_o a_o separate_a and_o distinct_a patient_n except_o there_o be_v a_o meeting_n of_o the_o agent_n and_o patient_n in_o some_o means_n but_o hear_v in_o this_o supposition_n the_o earth_n be_v imagine_v to_o draw_v and_o attract_v the_o air_n which_o as_o yet_o it_o touch_v not_o that_o this_o external_a cause_n be_v not_o the_o vacuum_n or_o emptiness_n be_v plain_a because_o it_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
see_v in_o this_o figure_n wherein_o the_o line_n cd_o represent_v unto_o we_o the_o sensible_a horizon_n the_o line_n ab_fw-la the_o rational_a the_o former_a be_v call_v natural_a or_o physical_a because_o it_o come_v under_o the_o measure_n and_o apprehension_n of_o the_o sense_n the_o other_o astronomical_a because_o it_o be_v of_o great_a use_n in_o astronomy_n in_o the_o resolution_n of_o the_o horizon_n into_o his_o part_n we_o ought_v to_o consider_v two_o thing_n first_o the_o pole_n of_o the_o horizon_n second_o his_o periphery_n or_o circumference_n the_o pole_n be_v common_o call_v zenith_n or_o nadir_n the_o zenith_n be_v the_o vertical_a point_n direct_o place_v over_o our_o head_n whereunto_o be_v opposite_a on_o the_o other_o side_n the_o nadir_n direct_o under_o our_o foot_n and_o therefore_o may_v be_v call_v the_o pedal_n point_n the_o part_n or_o intersection_n in_o the_o circumference_n be_v design_v out_o unto_o we_o by_o certain_a line_n discover_v the_o coast_n in_o the_o terrestrial_a globe_n these_o line_n be_v call_v either_o wind_n or_o rhumbe_n the_o wind_n with_o the_o grecian_n be_v only_a 8._o but_o the_o latter_a navigator_n have_v increase_v they_o to_o the_o number_n of_o 32_o whereof_o four_o be_v call_v cardinal_n to_o wit_n such_o as_o be_v direct_v to_o the_o four_o coast_n of_o east_n west_n north_n and_o south_n the_o other_o be_v collateral_a be_v place_v on_o each_o side_n of_o the_o cardinal_n wind_n the_o rhumbe_n be_v line_n pass_v by_o the_o vertical_a point_n of_o any_o place_n as_o you_o may_v see_v in_o the_o compass_n go_v before_o now_o because_o one_o rhumbe_n answer_v to_o two_o coast_n or_o wind_n the_o number_n of_o the_o rhumbe_n be_v but_o half_a the_o number_n of_o the_o wind_n to_o wit_n 16._o here_o it_o be_v to_o be_v note_v that_o a_o rhumbe_n differ_v from_o a_o wind_n whereas_o a_o rhumber_n be_v one_o line_n point_v out_o unto_o we_o two_o wind_n or_o coast_n these_o rhumbe_n as_o they_o be_v conceive_v in_o the_o globe_n be_v think_v by_o nonnus_n to_o be_v the_o portion_n of_o great_a circle_n but_o learned_a mr_n hues_n in_o his_o book_n out_o of_o undoubted_a principle_n strong_o confute_v he_o the_o ground_n which_o he_o take_v be_v these_o first_o that_o all_o meridian_n of_o all_o place_n pass_v the_o pole_n and_o cut_v the_o equatour_n and_o all_o his_o parallel_n at_o right_a angle_n second_o if_o our_o course_n shall_v be_v direct_o any_o way_n else_o then_o towards_o one_o of_o the_o pole_n a_o new_a meridian_n must_v succeed_v and_o a_o new_a horizon_n three_o that_o the_o iron_n needle_n be_v touch_v with_o the_o loadstone_n show_v the_o common_a section_n of_o the_o meridian_n and_o the_o horizon_n and_o on_o one_o side_n perpetual_o respect_v the_o north_n on_o the_o other_o the_o south_n four_o the_o same_o rhumbe_n cut_v all_o the_o meridian_n atall_a place_n at_o equal_a angle_n and_o every_o where_o respect_v the_o like_a coast_n in_o the_o world_n five_o that_o a_o great_a circle_n draw_v by_o the_o vertical_a point_n if_o remove_v from_o the_o equatour_n can_v cut_v diverse_a meridian_n at_o equal_a angle_n six_o a_o great_a circle_n draw_v by_o the_o vertical_a point_n of_o any_o place_n make_v great_a angle_n with_o all_o other_o meridian_n then_o with_o that_o from_o which_o it_o be_v first_o draw_v whence_o it_o be_v necessary_a that_o the_o line_n which_o shall_v be_v suppose_v to_o make_v angle_n with_o diverse_a meridian_n as_o the_o rhumbe_n shall_v be_v bow_v towards_o the_o meridian_n i_o know_v not_o what_o will_v be_v more_o say_v against_o the_o opinion_n of_o p._n nonnus_n who_o will_v have_v all_o the_o rhumbe_n to_o be_v portion_n of_o great_a circle_n to_o illustrate_v further_o the_o nature_n and_o use_n of_o the_o horizon_n we_o will_v insert_v these_o theorem_n 2_o the_o sensible_a and_o rational_a horizon_n in_o the_o earth_n be_v much_o different_a in_o respect_n of_o the_o firmament_n all_o one_o 6._o it_o may_v be_v gather_v out_o of_o the_o supposition_n of_o ptolemy_n and_o alphraganus_n and_o almost_o all_o other_o astronomer_n that_o no_o man_n be_v place_v on_o the_o surface_n of_o the_o earth_n can_v precise_o see_v the_o half_a of_o it_o for_o that_o horizon_n which_o terminate_v our_o sight_n as_o we_o have_v show_v be_v a_o plain_a superficies_n every_o way_n circular_o extend_v in_o the_o earth_n in_o such_o sort_n as_o man_n place_v either_o in_o the_o sea_n in_o a_o ship_n or_o in_o a_o great_a field_n or_o country_n will_v think_v the_o visible_a part_n of_o the_o earth_n to_o be_v plain_a who_o end_n will_v seem_v to_o touch_v the_o heaven_n whence_o must_v needs_o come_v to_o pass_v that_o such_o a_o horizon_n can_v divide_v the_o sphere_n of_o the_o â—arth_n into_o two_o equal_a part_n for_o so_o much_o will_v be_v find_v want_v as_o be_v measure_v betwixt_o that_o superficies_n which_o touch_v the_o earth_n and_o that_o which_o pass_v by_o the_o centre_n of_o it_o equidistant_a from_o the_o other_o for_o this_o late_a only_o can_v divide_v the_o earth_n into_o 2_o equal_a part_n 1._o according_a to_o theodosius_n and_o may_v well_o be_v see_v in_o the_o 149._o former_a figure_n wherein_o be_v express_v both_o orison_n as_o well_o the_o visible_a as_o invisible_a touch_v the_o sphere_n in_o a_o point_n on_o the_o superficies_n as_o the_o rational_a pass_v by_o the_o centre_n nevertheless_o we_o must_v consider_v that_o the_o quantity_n intercept_v betwixt_o these_o two_o orison_n in_o the_o terrestrial_a sphere_n be_v of_o little_a or_o no_o moment_n compare_v with_o the_o whole_a frame_n of_o the_o heaven_n for_o since_o the_o heaven_n be_v so_o far_o distant_a from_o we_o it_o will_v come_v to_o pass_v that_o if_o two_o equidistant_a line_n shall_v be_v draw_v the_o one_o from_o the_o eye_n the_o other_o from_o the_o centre_n of_o the_o earth_n to_o the_o firmament_n they_o will_v according_a to_o sense_n appear_v one_o and_o the_o selfsame_o by_o reason_n of_o the_o wonderful_a distance_n as_o we_o see_v in_o a_o long_a gallery_n who_o wall_n have_v a_o equal_a distance_n the_o one_o from_o the_o other_o the_o wall_n will_v notwithstanding_o according_a to_o opticall_a principle_n seem_v wide_a where_o they_o be_v near_o and_o to_o close_v and_o shut_v up_o at_o the_o end_n or_o at_o least_o to_o concur_v near_o much_o more_o must_v we_o imagine_v this_o to_o happen_v in_o the_o sight_n if_o we_o compare_v the_o greatness_n of_o the_o firmament_n with_o the_o sphere_n of_o the_o earth_n in_o who_o magnitude_n we_o shall_v find_v a_o incomparable_a disparity_n this_o will_v appear_v by_o the_o apparence_n for_o we_o shall_v see_v the_o six_o sign_n of_o the_o zodiac_n conspicuous_a above_o our_o horizon_n and_o the_o other_o six_o under_o it_o hide_v from_o our_o sight_n also_o the_o sun_n and_o moon_n when_o they_o be_v diametral_o oppose_v almost_o at_o the_o same_o moment_n will_v appear_v the_o one_o in_o the_o east_n the_o other_o in_o the_o west_n at_o least_o the_o one_o will_v rise_v soon_o upon_o the_o set_n of_o the_o other_o and_o if_o we_o believe_v pliny_n the_o moon_n be_v observe_v to_o be_v eclipse_v in_o the_o east_n point_n the_o sun_n at_o the_o same_o time_n be_v in_o a_o sort_n above_o the_o horizon_n in_o the_o west_n such_o a_o eclipse_n can_v not_o happen_v without_o a_o diametrall_a opposition_n of_o the_o two_o light_n and_o therefore_o can_v the_o sensible_n and_o the_o rational_a horizon_n have_v no_o sensible_a difference_n in_o respect_n of_o the_o firmament_n 2_o the_o sensible_a horizon_n may_v be_v great_a or_o lesser_a according_a to_o the_o nature_n and_o disposition_n of_o the_o place_n in_o this_o consideration_n we_o take_v no_o notice_n of_o the_o difference_n of_o sight_n whether_o they_o be_v weak_a or_o sharp_a but_o suppose_v a_o eye_n sufficient_a to_o ken_v so_o far_o in_o the_o earth_n as_o the_o place_n will_v permit_v the_o difference_n then_o betwixt_o diverse_a orison_n must_v be_v seek_v out_o in_o the_o condition_n of_o the_o place_n a_o sight_n place_v on_o the_o top_n of_o a_o high_a mountain_n may_v see_v much_o far_a than_o one_o in_o a_o low_a valley_n compass_v about_o with_o hill_n for_o as_o much_o as_o the_o semidiameter_n of_o the_o sensible_a horizon_n which_o be_v equal_a to_o the_o ray_n or_o line_n draw_v from_o the_o extreme_a part_n of_o the_o visible_a earth_n be_v much_o great_a the_o most_o indifferent_a judgement_n of_o this_o horizon_n may_v be_v take_v from_o the_o superficies_n of_o the_o sea_n beyond_o sight_n of_o land_n for_o a_o man_n thereon_o sail_v in_o a_o ship_n may_v perceive_v the_o surface_n of_o the_o sea_n as_o a_o plain_a on_o every_o side_n to_o bound_v the_o sight_n in_o a_o round_a circle_n
on_o this_o superficies_n successive_o grow_v great_a from_o the_o equinoctial_a towards_o either_o pole_n until_o it_o challenge_v equal_a diameter_n with_o the_o cylinder_n and_o likewise_o all_o the_o meridian_n grow_a wide_a and_o far_o off_o till_o they_o be_v as_o far_o distant_a everywhere_a as_o be_v the_o equinoctial_a one_o from_o the_o other_o hence_o may_v easy_o be_v understand_v the_o true_a mathematical_a production_n or_o generation_n of_o this_o part_n for_o first_o of_o a_o spherical_a superficies_n it_o be_v make_v a_o cylinder_n and_o second_o of_o a_o cylinder_n it_o be_v make_v a_o parallellogramme_n or_o plain_a superficies_n for_o the_o concave_a superficies_n of_o a_o cylinder_n be_v nothing_o else_o but_o a_o plain_a parallellogramme_n imagine_v to_o be_v wound_n about_o two_o equal_a equidistant_a circle_n have_v one_o common_a axletree_n perpendicular_a upon_o the_o centre_n of_o they_o both_o and_o the_o periphery_n of_o they_o both_o equal_a to_o the_o length_n of_o the_o parallellogramme_n as_o the_o distance_n betwixt_o those_o centre_n be_v equal_a to_o the_o breadth_n thereof_o in_o this_o chart_n so_o conceive_v to_o be_v make_v all_o place_n must_v needs_o be_v situate_a in_o the_o same_o longitude_n and_o latitude_n meridian_n parallel_n and_o rhumbe_n which_o they_o have_v in_o the_o globe_n itself_o because_o we_o have_v imagine_v every_o point_n betwixt_o the_o equatour_n and_o the_o pole_n to_o swell_v equal_o in_o longitude_n and_o latitude_n till_o it_o apply_v itself_o to_o the_o concavity_n of_o the_o cylinder_n so_o that_o no_o point_n can_v be_v displace_v from_o his_o proper_a seat_n but_o only_o dilate_v in_o certain_a proportion_n and_o this_o i_o take_v to_o be_v the_o best_a conceit_n for_o the_o groundwork_n or_o platform_n of_o this_o geographical_a chart._n 2_o except_o the_o distance_n betwixt_o the_o parallel_n in_o a_o plaine-chart_n be_v vary_v it_o can_v be_v excuse_v from_o sensible_a error_n it_o 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which_o escape_n be_v excellent_o open_v and_o reform_v by_o our_o countryman_n edward_n wright_n in_o his_o correction_n of_o nautical_a error_n the_o reason_n or_o ground_n which_o draw_v these_o man_n to_o think_v that_o the_o earth_n can_v not_o be_v proportionable_o describe_v in_o a_o plain_a superficies_n proceed_v from_o the_o common_a proportion_n of_o the_o line_n and_o circle_n on_o the_o chart._n for_o suppose_v the_o parallel_n cut_v the_o meridian_n at_o equal_a angle_n to_o observe_v a_o equal_a distance_n everywhere_a one_o from_o the_o other_o these_o error_n and_o absurdity_n must_v of_o necessity_n ensue_v first_o what_o place_n soever_o be_v delineate_v in_o the_o ordinary_a chart_n the_o length_n of_o they_o from_o east_n to_o west_n have_v a_o great_a proportion_n to_o the_o breadth_n from_o north_n to_o south_n then_o it_o ought_v to_o have_v except_o only_o under_o the_o equinoctial_a and_o this_o error_n be_v so_o much_o the_o more_o augment_v by_o how_o much_o 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parallel_n the_o one_o to_o the_o other_o but_o by_o how_o much_o they_o approach_v the_o pole_n by_o so_o much_o they_o be_v near_o that_o in_o the_o end_n they_o all_o concur_v and_o meet_v in_o the_o pole_n itself_o second_o this_o common_a chart_n admit_v there_o will_v arise_v great_a error_n not_o only_o in_o the_o situation_n of_o diverse_a place_n which_o appear_v to_o be_v under_o the_o same_o meridian_n but_o also_o in_o the_o bear_n of_o place_n one_o to_o the_o other_o the_o reason_n be_v manifest_a for_o that_o the_o meridian_n be_v a_o certain_a rule_n of_o the_o site_n and_o position_n of_o place_n therefore_o whensoever_o any_o error_n shall_v be_v commit_v in_o the_o site_n and_o position_n of_o the_o meridian_n there_o must_v needs_o follow_v error_n in_o the_o designation_n of_o the_o rhumbe_n and_o other_o point_n of_o the_o compass_n and_o therefore_o every_o respective_a position_n of_o place_n to_o place_n set_v down_o in_o the_o common_a chart_n can_v be_v warrant_v a_o pregnant_a example_n we_o have_v in_o the_o way_n from_o india_n for_o the_o promontory_n of_o africa_n call_v the_o promontory_n of_o three_o point_n have_v of_o northern_a latitude_n 4_o degree_n and_o a_o half_a and_o the_o island_n of_o tristan_n acugna_fw-la have_v 36_o degree_n of_o southern_a latitude_n be_v in_o the_o common_a chart_n set_v under_o the_o same_o meridian_n but_o the_o chart_n show_v the_o distance_n between_o these_o land_n and_o the_o cape_n of_o good_a hope_n to_o come_v near_o to_o 400_o league_n both_o which_o can_v stand_v together_o for_o if_o all_o the_o coast_n from_o the_o promontory_n of_o three_o point_n unto_o the_o cape_n of_o good-hope_a be_v right_o measure_v and_o the_o promontory_n of_o three_o point_n lie_v also_o under_o the_o same_o meridian_n with_o those_o land_n yet_o must_v the_o distance_n be_v much_o less_o but_o if_o it_o be_v not_o less_o it_o can_v stand_v with_o reason_n that_o it_o shall_v have_v the_o same_o 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line_n
as_o meridian_n parallel_n &_o rhumbe_n on_o the_o chart_n in_o such_o sort_n as_o these_o error_n may_v be_v prevent_v and_o the_o due_a proportion_n and_o symmetry_n of_o place_n well_o observe_v but_o our_o industrious_a countryman_n have_v wade_v through_o all_o these_o difficulty_n and_o find_v out_o the_o true_a demonstration_n of_o a_o projection_n of_o these_o line_n to_o be_v inscribe_v in_o the_o chart_n in_o such_o sort_n as_o no_o sensible_a error_n can_v show_v itself_o from_o who_o copious_a industry_n we_o will_v extract_v so_o much_o as_o may_v serve_v our_o purpose_n only_o contract_v his_o invention_n into_o a_o short_a method_n have_v many_o matter_n to_o pass_v through_o in_o this_o treatise_n 2_o the_o distance_n of_o the_o parallel_n in_o the_o chart_n must_v increase_v proportionable_o as_o the_o secantes_fw-la of_o the_o latitude_n it_o have_v be_v a_o conceive_a error_n as_o we_o have_v show_v that_o all_o the_o parallel_n in_o the_o chart_n here_o mention_v shall_v everywhere_a keep_v the_o same_o distance_n one_o from_o the_o other_o from_o the_o equator_fw-la to_o the_o pole_n yet_o because_o no_o man_n for_o aught_o i_o know_v have_v out_o of_o geometrical_a ground_n discover_v the_o true_a proportion_n beside_o my_o forenamed_a author_n i_o must_v herein_o also_o follow_v his_o direrection_n as_o near_o as_o i_o can_v in_o his_o own_o footstep_n because_o i_o will_v not_o any_o way_n prejudice_n his_o invention_n first_o therefore_o we_o must_v consider_v in_o that_o chart_n because_o the_o parallel_n be_v equal_a one_o to_o the_o other_o for_o every_o one_o be_v set_v equal_a to_o the_o equinoctial_a the_o meridian_n also_o must_v be_v parallel_n and_o straight_a line_n and_o by_o consequence_n the_o rhumbe_n make_v equal_a angle_n with_o every_o meridian_n must_v be_v also_o straight_a line_n second_o because_o the_o spherical_a superficies_n whereof_o the_o chart_n be_v imagine_v to_o be_v produce_v be_v conceive_v to_o swell_v and_o enlarge_v itself_o everywhere_a equal_o that_o be_v as_o well_o in_o longitude_n as_o latitude_n till_o it_o accommodate_v itself_o to_o the_o hollowness_n of_o the_o cylinder_n round_o about_o therefore_o at_o every_o point_n of_o latitude_n in_o this_o cylinder_n so_o dilate_a a_o part_n of_o the_o meridian_n obtain_v the_o same_o proportion_n to_o the_o like_a part_n of_o the_o parallel_n that_o the_o like_a part_n of_o the_o meridian_n and_o parallel_n have_v to_o each_o other_o in_o the_o globe_n without_o sensible_a error_n now_o for_o as_o much_o as_o like_a part_n of_o the_o whole_n have_v the_o same_o proportion_n that_o these_o whole_n have_v therefore_o the_o like_a part_n of_o any_o parallel_n or_o meridian_n of_o the_o sphere_n have_v the_o same_o proportion_n that_o the_o same_o parallel_n and_o meridian_n have_v for_o example_n sake_n as_o the_o meridian_n be_v double_a to_o the_o parallel_n of_o 60_o degree_n so_o a_o degree_n minute_n or_o other_o part_n be_v also_o double_a to_o a_o degree_n minute_n or_o other_o part_n of_o the_o parallel_n and_o what_o proportion_n the_o parallel_n have_v to_o the_o meridian_n the_o same_o must_v their_o diameter_n and_o semidiameter_n have_v one_o to_o the_o other_o as_o be_v teach_v by_o geometrician_n now_o the_o sign_n of_o the_o compliment_n of_o the_o parallel_n latiude_n or_o distance_n from_o the_o equinoctial_a be_v the_o semi-diameter_n of_o the_o say_a parallel_n as_o in_o this_o diagramme_n here_o insert_v may_v easy_o appear_v for_o ae_n the_o sign_n of_o ah_o the_o compliment_n of_o of_o the_o latitude_n of_o the_o parallel_n abcd_v from_o the_o equinoctial_a be_v the_o semi-diameter_n of_o the_o parallel_n abcd_v and_o as_o the_o semi-diameter_n of_o the_o meridian_n or_o whole_a sign_n be_v to_o the_o semi-diameter_n of_o the_o parallel_n so_o be_v the_o secant_fw-la or_o hypotenuse_n of_o the_o parallel_n latitude_n to_o the_o semi-diameter_n of_o the_o meridian_n or_o to_o the_o whole_a sign_n as_o fk_v that_o be_v ak_v to_o ae_n as_o be_v gk_n so_o be_v ik_fw-mi to_o fk_n therefore_o in_o this_o geographical_a chart_n the_o semi-diameter_n of_o each_o parallel_n be_v equal_a to_o the_o semidiameter_n of_o the_o equinoctial_a or_o whole_a sign_n the_o part_n of_o the_o meridian_n at_o every_o point_n of_o latitude_n must_v of_o necessity_n increase_v with_o the_o same_o proportion_n wherewith_o the_o secant_v of_o the_o arch_n contain_v between_o these_o point_n of_o latitude_n and_o the_o equinoctial_a increase_n out_o of_o which_o geometrical_a ground_n thus_o explain_v will_v arise_v a_o certain_a and_o easy_a method_n for_o the_o make_n of_o a_o table_n by_o the_o help_n of_o trigonometry_n whereby_o the_o meridian_n in_o any_o geographical_a or_o hydrographical_a table_n may_v true_o and_o in_o due_a proportion_n divide_v itself_o into_o part_n from_o the_o equinoctial_a towards_o either_o pole_n for_o take_v for_o grant_v each_o distance_n of_o each_o point_n of_o latitude_n or_o of_o each_o parallel_n one_o from_o the_o other_o to_o comprehend_v so_o many_o point_n as_o the_o secant_v of_o the_o latitude_n of_o each_o point_n or_o parallel_n contain_v we_o may_v draw_v out_o a_o table_n by_o continual_a addition_n of_o the_o secant_v answerable_a unto_o the_o latitude_n of_o each_o parallel_n unto_o the_o sum_n compound_v of_o all_o the_o former_a secant_v beginning_n with_o the_o secant_v of_o the_o first_o parallel_n latitude_n and_o thereunto_o add_v the_o second_o parallel_n latitude_n and_o to_o the_o sum_n of_o both_o these_o add_v the_o three_o parallel_n latitude_n and_o so_o forth_o in_o all_o the_o rest_n and_o this_o table_n will_v show_v the_o section_n and_o point_n of_o latitude_n in_o the_o meridian_n of_o the_o geographical_a map_n through_o which_o section_n the_o parallel_n ought_v to_o be_v draw_v which_o table_n we_o have_v late_o set_v out_o by_o edward_n wright_n in_o his_o correction_n of_o nautical_a error_n to_o who_o for_o further_a satisfaction_n in_o this_o kind_n i_o refer_v the_o diligent_a reader_n out_o of_o the_o same_o ground_n we_o may_v also_o deduce_v the_o rumbe_n for_o since_o that_o the_o chart_n as_o we_o have_v show_v be_v nothing_o else_o but_o a_o plain_a parallellogramme_n conceive_v to_o be_v make_v of_o the_o extension_n of_o a_o spherical_a superficies_n inscribe_v in_o a_o concave_n cylinder_n it_o must_v needs_o be_v that_o the_o rumbe_n make_v equal_a angle_n with_o all_o the_o meridian_n therefore_o if_o in_o the_o chart_n a_o circle_n be_v draw_v divide_v into_o 32_o equal_a part_n begin_v with_o the_o meridian_n pass_v by_o the_o centre_n of_o that_o circle_n the_o line_n draw_v from_o the_o centre_n of_o these_o section_n will_v be_v the_o rumbe_n for_o that_o place_n 9_o of_o the_o geographical_a plaine-chart_n we_o have_v speak_v it_o behoove_v we_o next_o to_o treat_v of_o the_o geographical_a planispheare_n the_o planispheare_n be_v a_o table_n or_o map_n of_o two_o face_n whereon_o the_o line_n be_v project_v circular_o betwixt_o the_o planispheare_n and_o the_o plaine-chart_n a_o double_a difference_n may_v be_v observe_v 1_o that_o the_o former_a consist_v altogether_o of_o right_a line_n aswell_o in_o regard_n of_o the_o parallel_n as_o meridian_n whereas_o the_o late_a be_v compose_v of_o circular_a or_o crooked_a line_n as_o well_o as_o right_v 2_o the_o former_a may_v well_o be_v express_v in_o one_o form_n or_o front_n as_o we_o may_v see_v not_o only_o in_o the_o nautical_a and_o common_a chart_n which_o we_o have_v show_v to_o be_v all_o one_o with_o the_o other_o in_o respect_n of_o these_o line_n but_o in_o many_o other_o common_a map_n as_o namely_o those_o of_o hondius_n whereas_o the_o planispheare_n can_v be_v express_v without_o two_o face_n or_o hemisphere_n whereof_o the_o one_o represent_v the_o eastern_a the_o other_o the_o western_a part_n of_o the_o terrene_a globe_n for_o herein_o we_o must_v imagine_v a_o globe_n to_o be_v cut_v into_o two_o equal_a hemisphere_n which_o be_v at_o once_o represent_v to_o our_o sight_n of_o this_o description_n of_o the_o earth_n by_o crooked_a line_n ptolemy_n in_o his_o 24_o chapt._n of_o his_o geography_n have_v teach_v we_o two_o way_n whereof_o the_o first_o depend_v from_o the_o aspect_n of_o a_o sphere_n turn_v and_o move_v round_o in_o which_o all_o the_o meridian_n be_v describe_v as_o right_a line_n but_o the_o parallel_n as_o circumference_n or_o crooked_a line_n the_o other_o delineation_n take_v his_o ground_n from_o a_o sphere_n represent_v to_o the_o sight_n not_o move_v but_o rest_v still_o in_o his_o place_n in_o which_o both_o meridian_n and_o parallel_n be_v draw_v circular_a these_o two_o way_n of_o ptolemy_n howsoever_o judicious_o invent_v in_o those_o time_n wherein_o a_o small_a part_n of_o the_o earth_n be_v discover_v and_o geography_n very_o unperfect_a have_v be_v by_o late_a geographer_n much_o reform_v and_o correct_v
yet_o among_o the_o late_a have_v not_o all_o express_v themselves_o alike_o some_o have_v portray_v out_o of_o the_o earth_n in_o fashion_n of_o a_o heart_n some_o according_a to_o other_o figure_n but_o in_o this_o perhaps_o as_o painter_n they_o have_v be_v more_o iudulgent_a to_o fancy_v then_o common_a use_n other_o have_v go_v about_o to_o express_v the_o globe_n of_o the_o earth_n in_o elipticke_a line_n which_o the_o machanicians_n call_v oval_a but_o we_o as_o well_o in_o this_o as_o other_o matter_n prefer_v choice_n before_o abundance_n will_v content_v ourselves_o with_o one_o or_o two_o which_o use_n have_v stamp_v more_o current_n and_o experience_n have_v find_v most_o useful_a to_o which_o as_o a_o ground_n we_o will_v premise_v this_o theorem_a 1_o the_o planispheare_n be_v ground_v on_o a_o certain_a aspect_n of_o the_o terrestrial_a sphere_n wherein_o the_o eye_n of_o the_o beholder_n be_v so_o conceive_v to_o be_v fix_v in_o some_o point_n of_o the_o globe_n that_o it_o may_v see_v the_o one_o half_a or_o hemisphere_n concern_v the_o position_n of_o the_o eye_n two_o thing_n be_v here_o remarkable_a 1_o where_o the_o eye_n be_v suppose_v to_o be_v place_v either_o above_o the_o convexe_n superficies_n or_o in_o the_o concave_n some_o seem_v to_o place_v it_o above_o the_o convexe_n superficies_n of_o which_o opinion_n gemma_fw-la frisius_n seem_v to_o be_v who_o will_v have_v the_o eye_n to_o be_v set_v at_o a_o infinite_a distance_n other_o although_o not_o admit_v of_o such_o a_o infinite_a distance_n deny_v not_o the_o eye_n to_o be_v above_o the_o convexe_n superficies_n but_o neither_o way_n can_v be_v warrant_v not_o the_o former_a because_o of_o the_o impossibility_n of_o the_o supposition_n for_o to_o imagine_v the_o eye_n to_o be_v set_v at_o a_o infinite_a distance_n be_v to_o deny_v a_o sight_n or_o aspect_n which_o they_o will_v have_v to_o be_v the_o ground_n of_o this_o projection_n for_o no_o object_n can_v be_v perceive_v but_o such_o as_o be_v bound_v and_o determine_v in_o a_o certain_a and_o proportionate_a space_n neither_o can_v the_o late_a way_n pass_v clear_a without_o exception_n because_o to_o such_o a_o projection_n such_o a_o sight_n be_v require_v which_o can_v see_v the_o whole_a hemisphere_n for_o otherwise_o will_v it_o be_v unperfect_a and_o want_v of_o the_o perfection_n of_o the_o globe_n which_o contain_v two_o absolute_a and_o entire_a hemisphere_n but_o now_o no_o place_n can_v be_v imagine_v without_o the_o globe_n wherein_o the_o eye_n can_v be_v so_o place_v as_o to_o see_v the_o one_o half_a or_o hemisphere_n for_o as_o much_o as_o it_o be_v impossible_a from_o the_o opposite_a point_n of_o any_o diameter_n to_o draw_v two_o tangent_fw-la line_n which_o may_v meet_v together_o or_o cut_v one_o the_o other_o in_o the_o same_o point_n but_o will_v be_v parallel_n the_o one_o to_o the_o other_o wherefore_o we_o may_v conclude_v that_o the_o eye_n in_o this_o projection_n can_v be_v 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superficies_n the_o eye_n be_v place_v to_o which_o we_o answer_v that_o the_o place_n of_o the_o eye_n be_v of_o itself_o indifferent_a because_o it_o may_v be_v imagine_v any_o where_o in_o what_o point_n soever_o nevertheless_o we_o will_v only_o fasten_v on_o two_o especial_a way_n which_o be_v of_o most_o use_n wherein_o the_o proposition_n follow_v shall_v inform_v us._n 9_o this_o planispheare_n be_v twofold_a the_o first_o we_o term_v equinoctial_a which_o suppose_v the_o eye_n to_o be_v fix_v on_o some_o point_n of_o the_o equinoctial_a circle_n the_o other_o polar_a wherein_o the_o sight_n be_v conceive_v to_o be_v fix_v on_o the_o pole_n of_o the_o terrestrial_a globe_n the_o ground_n and_o fabric_n of_o the_o former_a be_v teach_v in_o these_o proposition_n 1_o the_o eye_n conceive_v to_o be_v fix_v on_o any_o point_n of_o the_o equatour_n will_v design_n out_o unto_o we_o a_o planispheare_n wherein_o all_o the_o circle_n be_v project_v circular_o except_o the_o 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unto_o the_o table_n of_o sign_n and_o tangent_n exact_o seâ—_n out_o by_o our_o forename_a author_n and_o other_o for_o a_o example_n of_o this_o we_o may_v take_v two_o famous_a city_n of_o germany_n noremberg_n and_o hamberg_n which_o without_o any_o sensible_a difference_n have_v the_o same_o latitude_n but_o differ_v in_o longitude_n for_o the_o longitude_n of_o noremberg_n be_v 31_o degree_n 45_o minute_n of_o hamberg_n 32_o degree_n 30_o minute_n the_o difference_n of_o longitude_n than_o be_v 0_o degree_n 45_o minute_n these_o thing_n suppose_v to_o be_v know_v we_o will_v imagine_v noremberg_n to_o be_v in_o f_o hamberg_n in_o g_z and_o therefore_o of_o or_o eglantine_n will_v have_v 49_o degree_n 23_o minute_n fb_n or_o gb_n will_v have_v 40_o degree_n 37_o minute_n fbg_n or_o ae_n will_v have_v 0_o degree_n 45_o minute_n ke_n 0_o degree_n 22_o ½_o minute_n eh_n 89_o degree_n 37_o ½_o minute_n if_o we_o work_v by_o the_o table_n of_o sign_n tangentâ—_n and_o secant_v the_o 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