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&_o a_o line_n strike_v perpendicular_a upon_o it_o apply_v the_o straight_a edge_n unto_o the_o wall_n at_o what_o time_n the_o sun_n shine_v upon_o it_o hold_v the_o board_n parallel_n to_o the_o horizon_n set_v the_o dyal_a thereon_o and_o move_v it_o gentle_o every_o way_n until_o the_o same_o hour_n and_o minute_n be_v show_v in_o both_o dial_n and_o so_o let_v it_o stand_v then_o if_o the_o dyal_a have_v one_o of_o the_o side_n parallel_v to_o the_o meridian_n strike_v a_o line_n along_o that_o side_n upon_o the_o board_n cross_v the_o perpendicular_a or_o else_o with_o a_o bodkin_n make_v a_o point_n upon_o the_o board_n at_o each_o end_n of_o the_o meridian_n and_o take_v away_o the_o instrument_n from_o the_o board_n and_o the_o board_n from_o the_o wall_n lay_v a_o ruler_n to_o those_o two_o point_n and_o draw_v a_o line_n cross_v the_o perpendicular_a for_o the_o angle_n which_o that_o line_n make_v with_o the_o perpendicular_a be_v the_o angle_n of_o the_o decliâ—nation_n 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a_o little_a ring_n to_o hang_v it_o by_o the_o two_o circle_n be_v so_o make_v that_o though_o they_o be_v to_o be_v set_v at_o right_a angle_n when_o you_o use_v the_o instrument_n yet_o for_o more_o convenient_a carry_v they_o may_v be_v one_o fold_v into_o the_o other_o the_o lesser_a of_o the_o two_o circle_n be_v for_o the_o aequinoctial_a have_v in_o the_o midst_n of_o the_o inner_a side_n or_o thickness_n a_o line_n round_o it_o which_o be_v the_o true_a aequinoctial_a circle_n divide_v into_o twice_o twelve_o hour_n from_o the_o two_o opposite_a point_n in_o which_o it_o be_v fasten_v within_o the_o great_a the_o great_a and_o outer_a of_o the_o two_o circle_n be_v the_o meridian_n one_o quarter_n whereof_o beginning_n at_o one_o of_o the_o point_n in_o which_o the_o equinoctial_a be_v hang_v be_v divide_v into_o ninety_o degree_n the_o diameter_n be_v fasten_v to_o the_o meridian_n in_o two_o opposite_a point_n or_o pole_n oâ—e_v of_o they_o be_v the_o very_a end_n of_o the_o quadrant_n and_o be_v the_o north_n pole_n wherefore_o it_o be_v perpendicular_a to_o the_o equinoctial_a have_v his_o due_a position_n the_o diameter_n be_v broad_a and_o slit_v in_o the_o middle_n and_o about_o the_o slit_n on_o both_o side_n be_v the_o month_n and_o day_n of_o the_o year_n and_o within_o this_o slit_n be_v a_o little_a slide_a plate_n pierce_v through_o with_o a_o small_a hole_n which_o hole_n in_o the_o motion_n of_o it_o while_o it_o be_v apply_v to_o the_o day_n of_o the_o year_n represent_v the_o axis_n of_o the_o world_n the_o little_a ring_n whereby_o the_o instrument_n hang_v be_v make_v to_o slip_v up_o and_o down_o along_o the_o quadrant_n that_o so_o by_o help_n of_o a_o little_a tooth_n annex_v the_o instrument_n may_v be_v rectify_v to_o any_o elevation_n of_o the_o pole_n ii_o the_o use_n of_o it_o in_o use_v this_o instrument_n first_o the_o tooth_n of_o the_o little_a ring_n must_v careful_o be_v set_v to_o the_o height_n of_o the_o pole_n in_o the_o quadrant_n for_o the_o place_n wherein_o you_o be_v second_o the_o hole_n of_o the_o slide_a plate_n within_o the_o slit_n must_v be_v bring_v exact_o unto_o the_o day_n of_o the_o month_n three_o the_o aeqinoctiall_a be_v to_o be_v draw_v out_o and_o by_o mean_n of_o the_o two_o stud_n in_o the_o meridian_n stay_v it_o it_o be_v to_o be_v set_v perpendicular_a thereto_o four_o guess_v as_o near_o as_o you_o can_v at_o the_o hour_n and_o turn_v the_o hole_n of_o the_o little_a plate_n towards_o it_o last_o hold_v the_o instrument_n up_o by_o the_o little_a ring_n that_o it_o may_v hang_v free_o with_o the_o north_n pole_n thereof_o towards_o the_o north_n and_o move_v it_o gentle_o this_o way_n and_o that_o way_n till_o the_o beam_n of_o the_o sunshining_a through_o that_o hole_n fall_v upon_o that_o middle_a line_n within_o the_o aequinoctial_a for_o there_o shall_v be_v the_o hour_n of_o the_o day_n and_o the_o meridan_n of_o the_o instrument_n shall_v hang_v direct_o north_n and_o south_n these_o instrument_n all_o dial_n be_v make_v in_o brass_n by_o elias_n allen_n dwell_v over_o against_o st._n clement_n church_n without_o temple_n bar_n at_o the_o sign_n of_o the_o horse-shoe_n near_o essex_n gate_n finis_fw-la
here_o there_o must_v be_v find_v a_o number_n which_o multiply_v by_o 7_o and_o then_o divide_v by_o 2_o 3_o 4_o 5_o 6_o there_o may_v always_o remain_v a_o number_n less_o by_o 1_o than_o the_o divisor_n now_o the_o first_o number_n which_o arrive_v in_o this_o nature_n be_v 119_o unto_o which_o if_o 420_o be_v add_v make_v 539_o which_o also_o will_v do_v the_o same_o and_o so_o by_o add_v 420_o you_o may_v have_v other_o number_n to_o resolve_v this_o proposition_n problem_n xlviii_o how_o many_o sort_n of_o weight_n in_o the_o least_o manner_n must_v there_o be_v to_o weigh_v all_o sort_n of_o thing_n between_o 1_o pound_n and_o 40_o pound_n and_o so_o unto_o 121_o &_o 364_o pound_n to_o weigh_v thing_n between_v 1_o and_o 40_o take_v number_n in_o triple_a proportion_n so_o that_o their_o sum_n be_v equal_a or_o somewhat_o great_a than_o 40_o as_o be_v the_o number_n 1_o 3.9.27_o i_o say_v that_o with_o â—_o such_o weight_n the_o first_o be_v of_o 1_o pound_n the_o second_o be_v 3_o pound_n the_o three_o be_v 9_o pound_n and_o the_o four_o be_v 27_o any_o weight_n between_o 1_o and_o 40_o pound_n may_v be_v weigh_v as_o admit_v to_o weigh_v 21_o pound_n put_v unto_o the_o thing_n that_o be_v to_o be_v weigh_v the_o 9_o pound_n weight_n then_o in_o the_o other_o balance_n put_v 27_o pound_n and_o 3_o pound_n which_o do_v counterpoise_v 21_o pound_n and_o 9_o pound_n and_o if_o 20_o pound_n be_v to_o be_v weigh_v put_v to_o it_o in_o the_o balance_n 9_o and_o 1_o and_o in_o the_o other_o balance_n put_v 27_o and_o 3_o and_o so_o of_o other_o in_o the_o same_o manner_n take_v those_o 5_o weight_n 1_o 3_o 9_o 27_o 81_o you_o may_v weigh_v with_o they_o between_o 1_o pound_n and_o 121_o pound_n and_o take_v those_o 6_o weight_n as_o 1_o 3_o 9_o 2d_o 81_o 243_o you_o may_v weigh_v even_o from_o 1_o pound_n unto_o 364_o pound_n this_o depend_v upon_o the_o property_n of_o continue_a proportional_n the_o latter_a of_o which_o contain_v twice_o all_o the_o former_a problem_n xlix_o of_o a_o deceitful_a balance_n which_o be_v câ—â—â—ty_n seem_v iâ—_n be_v just_a because_o it_o hang_v in_o aequilibrio_fw-la notwithstanding_o put_v 12_o pound_n in_o one_o balance_n and_o 11_o in_o the_o other_o it_o will_v remain_v in_o aequilibrio_fw-la aristotle_n make_v mention_n of_o this_o balance_n in_o his_o mechanic_n question_n and_o say_v that_o the_o merchant_n of_o purpose_n in_o his_o time_n use_v they_o to_o deceive_v the_o world_n the_o subtlety_n or_o craft_n of_o which_o be_v thus_o that_o one_o arm_n of_o the_o balance_n be_v long_o than_o another_o by_o the_o same_o proportion_n that_o one_o weight_n be_v heavy_a than_o another_o as_o if_o the_o beam_n be_v 23_o inch_n long_o and_o the_o handle_v place_v so_o that_o 12_o inch_n shall_v be_v on_o one_o side_n of_o it_o and_o 11_o inch_n on_o the_o other_o side_n conditional_o that_o the_o short_a end_n shall_v be_v as_o heavy_a as_o the_o long_o a_o thing_n easy_a to_o be_v do_v then_o afterward_o put_v into_o the_o balance_n two_o unequal_a weight_n in_o such_o proportion_n as_o the_o part_n of_o the_o beam_n have_v one_o unto_o another_o which_o be_v 12_o to_o 11_o but_o so_o that_o the_o great_a be_v place_v in_o the_o balance_n which_o hang_v upon_o the_o short_a part_n of_o the_o beam_n and_o the_o lesser_a weight_n in_o the_o other_o balance_n it_o be_v most_o certain_a that_o the_o balance_n will_v hang_v in_o aequilibrio_fw-la which_o will_v seem_v most_o sincere_a and_o just_a though_o it_o be_v most_o deceitful_a abominable_a and_o false_a the_o reason_n of_o this_o be_v draw_v from_o the_o experiment_n of_o archimedes_n who_o show_v that_o two_o unequal_a weight_n will_v counterpoise_v one_o another_o when_o there_o be_v like_a proportion_n between_o the_o part_n of_o the_o beam_n that_o the_o handle_n separate_v and_o the_o weight_n themselves_o for_o in_o one_o and_o the_o same_o counterpoise_n by_o how_o much_o it_o be_v far_o from_o the_o centre_n of_o the_o handle_n by_o so_o much_o it_o seem_v heavy_a therefore_o if_o there_o be_v a_o diversity_n of_o distance_n that_o the_o balance_n hang_v from_o the_o handle_n there_o must_v necessary_o be_v a_o ineqality_n of_o weight_n in_o these_o balance_n to_o make_v they_o hang_v in_o aequilibrio_fw-la and_o to_o discover_v if_o there_o be_v deceit_n change_v the_o weight_n into_o the_o other_o balance_n for_o as_o soon_o as_o the_o great_a weight_n be_v place_v in_o the_o balance_n that_o hang_v on_o the_o long_a part_n of_o the_o beam_n it_o will_v weigh_v down_o the_o other_o instant_o problem_n l._n to_o heave_v or_o lift_v up_o a_o bottle_n with_o a_o straw_n take_v a_o straw_n that_o be_v not_o bruise_v bow_v it_o that_o it_o make_v a_o angle_n and_o put_v it_o into_o the_o bottle_n so_o that_o the_o great_a end_n be_v in_o the_o neck_n than_o the_o reed_n be_v put_v in_o the_o bow_v part_n will_v cast_v side-wise_a and_o make_v a_o angle_n as_o in_o the_o figure_n may_v be_v see_v then_o may_v you_o take_v the_o end_n which_o be_v out_o of_o the_o bottle_n in_o your_o hand_n and_o heave_v up_o the_o bottle_n and_o it_o be_v so_o much_o sure_a by_o how_o much_o the_o angle_n be_v acuter_n or_o sharp_a and_o the_o end_n which_o be_v bow_v approach_v to_o the_o other_o perpendicular_a part_n which_o come_v out_o of_o the_o bottle_n problem_n li._n how_o in_o the_o middle_n of_o a_o wood_n or_o desert_n without_o the_o sight_n of_o the_o sun_n star_n shadow_n or_o compass_n to_o find_v out_o the_o north_n or_o south_n or_o the_o four_o cardinal_n point_n of_o the_o world_n east_n west_n &_o c_o it_o be_v the_o opinion_n of_o some_o that_o the_o wind_n be_v to_o be_v observe_v in_o this_o if_o it_o be_v hot_a the_o south_n be_v find_v by_o the_o wind_n that_o blow_v that_o way_n but_o this_o observation_n be_v uncertain_a and_o subject_a to_o much_o error_n nature_n will_v help_v you_o in_o some_o measure_n to_o make_v it_o more_o manifest_a than_o any_o of_o the_o former_a from_o a_o tree_n thus_o cut_v a_o small_a tree_n off_o even_o to_o the_o ground_n and_o mark_v the_o many_o circle_n that_o be_v about_o the_o sap_n or_o pith_n of_o the_o tree_n which_o seem_v near_o together_o in_o some_o part_n than_o in_o other_o which_o be_v by_o reason_n of_o the_o sun_n motion_n about_o the_o tree_n for_o that_o the_o humidity_n of_o the_o part_n of_o the_o tree_n towards_o the_o south_n by_o the_o heat_n of_o the_o sun_n be_v rarify_v and_o cause_v to_o extend_v and_o the_o sâ—n_v not_o give_v such_o heat_n towards_o the_o north-part_n of_o the_o tree_n the_o sap_n be_v lesser_a rarefy_v but_o condense_v by_o which_o the_o circle_n be_v near_o together_o on_o the_o north-part_n than_o on_o the_o south-part_n therefore_o if_o a_o line_n be_v draw_v from_o the_o wide_a to_o the_o narrow_a part_n of_o the_o circle_n it_o shall_v show_v the_o north_n &_o south_n of_o the_o world_n another_o experiment_n may_v be_v thus_o take_v a_o small_a needle_n such_o as_o woman_n work_v with_o place_v it_o gentle_o down_o flatwise_o upon_o still_a water_n and_o it_o will_v not_o sink_v which_o be_v against_o the_o general_a tenet_n that_o iron_n will_v not_o swim_v which_o needle_n will_v by_o little_a and_o little_a turn_n to_o the_o north_n and_o south-point_n but_o if_o the_o needle_n be_v great_a and_o will_v not_o swim_v thrust_v it_o through_o a_o small_a piece_n of_o cork_n or_o some_o such_o like_a thing_n and_o then_o it_o will_v do_v the_o same_o for_o such_o be_v the_o property_n of_o iron_n when_o it_o be_v place_v in_o aequilibrio_fw-la it_o strive_v to_o find_v out_o the_o pole_n of_o the_o world_n or_o point_n of_o north_n and_o south_n in_o a_o manner_n as_o the_o magnes_fw-la do_v examination_n here_o be_v observable_a that_o the_o moisture_n which_o aid_v to_o the_o growth_n of_o the_o tree_n be_v dilate_v and_o rarefy_v by_o the_o meridional_a heat_n and_o contract_v by_o the_o septentrional_a cold_a this_o rarefaction_n work_v upon_o the_o part_n of_o the_o humour_n or_o moisture_n that_o be_v more_o thin_a which_o do_v easy_o dissipate_v and_o evaporate_v which_o evaporation_n carry_v a_o part_n of_o the_o salt_n with_o it_o and_o because_o that_o solidation_n or_o condensation_n so_o that_o there_o be_v leave_v but_o a_o part_n of_o the_o nourishment_n which_o the_o heat_n bake_v up_o and_o consume_v so_o contrary_o on_o the_o other_o side_n the_o condensation_n and_o restrictive_a quality_n of_o the_o moisture_n cause_v less_o evaporation_n and_o perdition_n and_o so_o consequent_o there_o remain_v more_o nourishment_n which_o make_v a_o great_a increase_n on_o that_o side_n than_o on_o the_o other_o
mathematical_a recreation_n or_o a_o collection_n of_o many_o problem_n extract_v out_o of_o the_o ancient_n and_o modern_a philosopher_n as_o secret_n and_o experiment_n in_o arithmetic_n geometry_n cosmographie_n horologiographie_n astronomy_n navigation_n music_n optic_n architecture_n statiâ—k_n mechanic_n chemistry_n water-work_n firework_n etc._n etc._n not_o vulgar_o manifest_a till_o now_o write_a first_o in_o greek_a and_o latin_a late_o compi'ld_v in_o french_a by_z henry_n van_n etten_n and_o now_o in_o english_a with_o the_o examination_n and_o augmentation_n of_o divers_a modern_a mathematician_n whereunto_o be_v add_v the_o description_n and_o use_v of_o the_o general_n horologicall_a ring_n and_o the_o double_a horizontall_a dial_n invent_v and_o write_v by_o william_n oughtre_v london_n print_v for_o william_n leake_n at_o the_o sign_n of_o the_o crown_n in_o fleetstreet_n between_o the_o two_o temple_n gate_n mdcliii_o on_o the_o frontispiece_n and_o book_n all_o 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descry_v with_o strange_a experiment_n in_o astronomy_n and_o navigation_n with_o each_o several_a picture_n in_o music_n optic_n and_o in_o architecture_n in_o statick_a machanick_n and_o chemistry_n in_o water-work_n and_o to_o ascend_v more_o high_a in_o firework_n like_v to_o jove_n artillery_n all_o this_o i_o know_v thou_o in_o this_o book_n shall_v find_v and_o here_o be_v enough_o for_o to_o content_v thy_o mind_n for_o from_o good_a author_n this_o our_o author_n draw_v these_o recreation_n which_o be_v strange_a and_o true_a so_o that_o this_o book_n be_v a_o centre_n and_o it_o be_v fit_a that_o in_o this_o centre_n line_n of_o praise_n shall_v meet_v w._n mathematical_a recreation_n or_o a_o collection_n of_o sundry_a excellent_a problem_n out_o of_o ancient_a &_o modern_a philosopher_n both_o useful_a and_o recreative_a print_v for_o william_n leake_n and_o be_v to_o be_v sell_v at_o the_o crown_n in_o fleet_n street_n between_o the_o two_o temple_n gate_n to_o the_o thrice_o noble_a and_o most_o generous_a lo._n the_o lo._n lambert_n verreyken_n lo._n of_o hinden_n wolverthem_fw-mi etc._n etc._n my_o honourable_a lo._n among_o the_o rare_a and_o curious_a proposition_n which_o i_o have_v learn_v out_o of_o the_o study_n of_o the_o mathematics_n in_o the_o famous_a university_n of_o pont_n a_o mousson_n i_o have_v take_v singular_a pleasure_n in_o certain_a problem_n no_o less_o ingenious_a than_o recreative_a which_o draw_v i_o unto_o the_o search_n of_o demonstration_n more_o difficult_a and_o serious_a some_o of_o which_o i_o have_v amass_v and_o cause_v to_o pass_v the_o press_n and_o here_o dedicate_v they_o now_o unto_o your_o honour_n not_o that_o i_o account_v they_o worthy_a of_o your_o view_n but_o in_o part_n to_o testify_v my_o affectionate_a desire_n to_o serve_v you_o and_o to_o satisfy_v the_o curious_a who_o delight_n themselves_o in_o these_o pleasant_a study_n know_v well_o that_o the_o nobility_n and_o gentry_n rather_o study_v the_o mathematical_a art_n to_o content_v and_o satisfy_v their_o affection_n in_o the_o speculation_n of_o such_o admirable_a experiment_n as_o be_v extract_v from_o they_o than_o in_o hope_n of_o gain_n to_o fill_v their_o purse_n all_o which_o study_v and_o other_o with_o my_o whole_a endeavour_n i_o shall_v always_o dedicate_v unto_o your_o honour_n with_o a_o ardent_a desire_n to_o be_v account_v ever_o your_o most_o humble_a and_o obedient_a nephew_n and_o servant_n h._n van_n etten_n by_o way_n of_o advertisement_n five_o or_o six_o thing_n i_o have_v think_v worthy_a to_o declare_v before_o i_o pass_v further_o first_o that_o i_o place_v not_o the_o speculative_a demonstration_n with_o all_o these_o problem_n but_o content_v myself_o to_o show_v they_o as_o at_o the_o finger_n end_n which_o be_v my_o plot_n and_o intention_n because_o those_o which_o understand_v the_o mathematics_n can_v conceive_v they_o easy_o other_o for_o the_o most_o part_n will_v content_v themselves_o 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but_o in_o he_o that_o fail_v in_o the_o act_n of_o it_o four_o in_o certain_a arithmetical_a proposition_n they_o have_v only_o their_o answer_n as_o i_o find_v they_o in_o sundry_a author_n which_o any_o one_o be_v studious_a of_o mathematical_a learning_n may_v find_v their_o original_n and_o also_o the_o way_n of_o their_o operation_n five_o because_o the_o number_n of_o these_o problem_n and_o their_o dependence_n be_v many_o and_o intermix_v i_o think_v it_o convenient_a to_o gather_v they_o into_o a_o table_n that_o so_o each_o one_o according_a to_o his_o fancy_n may_v make_v best_a choice_n of_o that_o which_o may_v best_o please_v his_o palate_n the_o matter_n be_v not_o of_o one_o nature_n nor_o of_o like_a subtlety_n but_o whosoever_o will_v have_v patience_n to_o read_v on_o shall_v find_v the_o end_n better_o than_o the_o beginning_n to_o the_o reader_n it_o have_v be_v observe_v by_o many_o that_o sundry_a fine_a wit_n as_o well_o among_o the_o ancient_n as_o modern_a have_v sport_v and_o delight_v themselves_o upon_o several_a thing_n of_o small_a consequence_n as_o upon_o the_o foot_n of_o a_o fly_n upon_o a_o straw_n upon_o a_o point_n nay_o upon_o nothing_o strive_v as_o it_o be_v to_o show_v the_o greatness_n of_o their_o glory_n in_o the_o smallness_n of_o the_o subject_n and_o have_v among_o most_o solid_a and_o artificial_a conclusion_n compose_v and_o produce_v sundry_a invention_n both_o philosophical_a and_o mathematical_a to_o solace_v the_o mind_n and_o recreate_v the_o spirit_n which_o the_o succeed_a age_n have_v embrace_v and_o from_o they_o glean_v and_o extract_v many_o admirable_a and_o rare_a conclusion_n judge_v that_o borrow_a matter_n oftentime_o yield_v praise_n to_o the_o industry_n of_o its_o author_n hence_o for_o thy_o use_n courteous_a reader_n i_o have_v with_o great_a search_n and_o labour_v collect_v also_o and_o heap_v up_o together_o in_o a_o body_n of_o these_o pleasant_a and_o fine_a experiment_n to_o stir_v up_o and_o delight_v the_o affectionate_a out_o of_o the_o write_n of_o socrates_n plato_n aristotle_n demosthenes_n pythagoras_n democrates_n pliny_n hyparchus_n euclides_n vitruvius_n diaphantus_fw-la pergaeus_n archimedes_n papus_n alexandrinus_n vitellius_n ptolomaeus_n copernicus_n proclus_n mauralicus_n cardanus_n valalpandus_n kepleirus_n gilbertus_n tychonius_n dureirus_n josephus_n clavius_n gallileus_n maginus_fw-la euphanus_n tyberill_n and_o other_o know_v art_n imitate_v nature_n that_o glory_v always_o in_o the_o variety_n of_o thing_n which_o she_o produce_v to_o satisfy_v the_o mind_n of_o curious_a inquisitor_n and_o though_o perhaps_o these_o labour_n to_o some_o humourous_a person_n may_v seem_v vain_a and_o ridiculous_a for_o such_o it_o be_v not_o undertake_v but_o for_o those_o which_o intentive_o have_v desire_v and_o â—ought_v after_o the_o knowledge_n of_o those_o thing_n it_o be_v a_o invitation_n and_o motive_n to_o the_o search_n of_o great_a matter_n and_o to_o employ_v the_o mind_n in_o useful_a knowledge_n rather_o than_o to_o be_v busy_v in_o vain_a
pamphlet_n playbook_n fruitless_a legend_n and_o prodigious_a history_n that_o be_v invent_v out_o of_o fancy_n which_o abuse_v many_o noble_a spirit_n dull_a their_o wit_n &_o alienate_v their_o thought_n from_o laudable_a and_o honourable_a study_n in_o this_o tractate_n thou_o may_v therefore_o make_v choice_n of_o such_o mathematical_a problem_n and_o conclusion_n as_o may_v delight_v thou_o which_o kind_n of_o learning_n do_v excellent_o adorn_v a_o man_n see_v the_o usefulness_n thereof_o and_o the_o manly_a accomplishment_n it_o do_v produce_v be_v profitable_a and_o delightful_a for_o all_o sort_n of_o people_n who_o may_v furnish_v and_o adorn_v themselves_o with_o abundance_n of_o matter_n in_o that_o kind_n to_o help_v they_o by_o way_n of_o use_n and_o discourse_n and_o to_o this_o we_o have_v also_o add_v our_o pyrotechnie_n know_v that_o beast_n have_v for_o their_o object_n only_o the_o surface_n of_o the_o earth_n but_o hope_v that_o thy_o spirit_n which_o follow_v the_o motion_n of_o fire_n will_v abandon_v the_o low_a element_n and_o cause_v thou_o to_o lift_v up_o thy_o eye_n to_o soar_v in_o a_o high_a contemplation_n have_v so_o glitter_v a_o canopy_n to_o behold_v and_o these_o pleasant_a and_o recreative_a fire_n ascend_v may_v cause_v thy_o affection_n also_o to_o ascend_v the_o whole_a whereof_o we_o send_v forth_o to_o thou_o that_o desire_v the_o scrutability_n of_o thing_n nature_n have_v furnish_v we_o with_o matter_n thy_o spirit_n may_v easy_o digest_v they_o and_o put_v they_o fine_o in_o order_n though_o now_o in_o disorder_n a_o table_n of_o the_o particular_a head_n of_o this_o book_n contract_v according_a to_o the_o several_a art_n specify_v in_o the_o title-page_n experiment_n of_o arithmetic_n page_n 1_o 2_o 3_o 16_o 19_o 22_o 28_o 33_o 39_o 40_o 44_o 45_o 51_o 52_o 53_o 59_o 60_o 69_o 71_o 77_o 83_o 85_o 86_o 89_o 90_o 91_o 124_o 134_o 135_o 136_o 137_o 138_o 139_o 140_o 178_o 179_o 181_o 182_o 183_o 184_o 185_o 188_o 208_o 210_o 213._o experiment_n â—n_a geometry_n pag._n 12_o 15_o 24_o 26_o 27_o 30_o 35_o 37_o 41_o 42_o 47_o 48_o 49_o 62_o 65_o 72_o 79_o 82_o 113_o 117_o 118_o 119_o 214_o 215_o 217_o 218_o 234_o 235_o 236_o 239_o 240._o experiment_n in_o cosmographie_n pag._n 14_o 43_o 75_o 106_o 107_o 219_o 220_o 225_o 227_o 228_o 229_o 230_o 232._o experiment_n in_o horologiographie_n pag._n 137_o 166_o 167_o 168_o 169_o 171_o 234._o experiment_n in_o astronomy_n pag._n 220_o 221_o 222_o 223_o 224._o experiment_n in_o navigation_n pag._n 105_o 233_o 234_o 237_o 238._o experiment_n in_o music_n pag._n 78_o 87_o 126._o experiment_n in_o optic_n pag._n 6_o 66_o 98_o 99_o 100_o 102_o 129_o 131_o 141_o 142_o 143_o 144_o 146_o 149_o 151_o 152_o 153_o 155_o 156_o 157_o 158_o 160_o 161_o 162_o 163_o 164_o 165._o experiment_n in_o architecture_n pag._n 16_o 242_o 243._o experiment_n in_o staticke_a pag._n 27_o 30_o 32_o 71_o 199_o 200_o 201_o 283_o 204_o 205_o 207._o experiment_n in_o machanick_n pag._n 56_o 58_o 68_o 88_o 95_o 108_o 110_o 128_o 173_o 174_o 176_o 246_o 248_o 258_o 259._o experiment_n in_o chemistry_n pag._n 198_o 255_o 256_o 257_o 260_o 262_o 263_o 264._o experiment_n in_o water-work_n pag._n 190_o 191_o 192_o 193_o 194_o 196_o 247_o 249_o 250_o 252_o 253._o experiment_n in_o firework_n from_o page_n 265._o to_o the_o end_n finis_fw-la a_o table_n of_o the_o content_n and_o chief_a point_n contain_v in_o this_o book_n problem_n ii_o how_o visible_a object_n that_o be_v without_o and_o thing_n that_o pass_v by_o be_v most_o lively_o represent_v to_o those_o that_o be_v within_o page_z 6_o prob._n 1_o of_o find_v of_o number_n conceive_v in_o the_o mind_n 1_o 2_o 3_o prob._n 5_o of_o a_o geographical_a garden-plot_n fit_a for_o a_o prince_n or_o some_o great_a personage_n 14_o prob._n 37_o any_o liquid_a substance_n as_o water_n or_o wine_n place_v in_o a_o glass_n may_v be_v make_v to_o boil_v by_o the_o motion_n of_o the_o finger_n and_o yet_o not_o touch_v it_o 54_o prob._n 3_o how_o to_o weigh_v the_o blow_n of_o one_o fist_n of_o a_o mallet_n a_o hatchet_n or_o such_o like_a 9_o prob._n 30_o two_o several_a number_n be_v take_v by_o two_o sundry_a person_n how_o subtle_o to_o discover_v which_o of_o those_o number_n each_o of_o they_o take_v 46_o prob._n 4_o that_o a_o staff_n may_v be_v break_v place_v upon_o two_o glass_n without_o hurt_v of_o the_o glass_n 12_o prob._n 7_o how_o to_o dispose_v lot_n that_o the_o 5_o 6_o 9_o etc._n etc._n of_o any_o number_n of_o person_n may_v escape_v 16_o prob._n 13_o how_o the_o weight_n of_o smoke_n of_o a_o combustible_a body_n which_o be_v exhale_v may_v be_v weigh_v 27_o prob._n 12_o of_o three_o knife_n which_o may_v be_v so_o dispose_v to_o hang_v in_o the_o air_n and_o move_v upon_o the_o point_n of_o a_o needle_n 27_o prob._n 17_o of_o a_o deceitful_a bowl_n to_o bowl_n withal_o 32_o prob._n 16_o a_o ponderous_a or_o heavy_a body_n may_v be_v support_v in_o the_o air_n without_o any_o one_o touch_v it_o 30_o prob._n 18_o how_o a_o pear_n or_o apple_n may_v be_v part_v into_o any_o part_n without_o break_v the_o rind_n thereof_o 33_o prob._n 15_o of_o a_o fine_a kind_n of_o door_n which_o open_v and_o shut_v on_o both_o side_n 30_o prob._n 9_o how_o the_o half_a of_o a_o vessel_n which_o contain_v 8_o measure_n may_v be_v take_v be_v but_o only_o two_o other_o measure_n the_o one_o be_v 3_o and_o the_o other_o 8_o measure_n 22_o prob._n 8_o three_o person_n have_v take_v each_o of_o they_o several_a thing_n to_o find_v which_o each_o of_o they_o have_v take_v 19_o prob._n 6_o how_o to_o dispose_v three_o staff_n which_o may_v support_v each_o other_o in_o the_o air_n 15_o prob._n 14_o many_o thing_n be_v dispose_v circular_a or_o otherwise_o to_o find_v which_o of_o they_o any_o one_o think_v upon_o 28_o prob._n 19_o to_o find_v a_o number_n think_v upon_o without_o ask_v question_n 33_o prob._n 11_o how_o a_o millstone_n or_o other_o ponderosity_n may_v hang_v upon_o the_o point_n of_o a_o needle_n without_o bow_v or_o any_o wise_a break_n of_o it_o 26_o prob._n 20_o and_o 21_o how_o a_o body_n that_o be_v uniform_a and_o inflexible_a may_v pass_v through_o a_o hole_n which_o be_v round_o square_a and_o triangular_a or_o round_o square_a and_o ovall-wise_a and_o exact_o fill_v those_o several_a hole_n 35_o 37_o prob._n 10_o how_o a_o stick_n may_v stand_v upon_o one_o finger_n or_o a_o pike_n in_o the_o middle_n of_o a_o court_n without_o fall_v 24_o prob._n 22_o to_o find_v a_o number_n think_v upon_o after_o another_o manner_n than_o those_o which_o be_v former_o deliver_v 39_o prob._n 23_o to_o find_v out_o many_o number_n that_o sundry_a person_n or_o any_o one_o have_v think_v upon_o 40_o prob._n 24_o how_o be_v it_o that_o a_o man_n in_o one_o &_o the_o same_o time_n may_v have_v his_o head_n upward_o and_o his_o foot_n upward_o be_v in_o one_o and_o the_o same_o place_n 4â—_n prob._n 25_o of_o a_o ladder_n by_o which_o two_o man_n ascend_v at_o one_o time_n the_o more_o they_o ascend_v the_o more_o they_o shall_v be_v asunder_o notwith_o stand_v the_o one_o be_v as_o high_a as_o the_o other_o 42_o prob._n 26_o how_o be_v it_o that_o a_o man_n have_v but_o a_o rod_n or_o pole_n of_o land_n do_v brag_v that_o he_o may_v in_o a_o right_a line_n pass_v from_o place_n to_o place_v 3000_o mile_n 42_o prob._n 27_o how_o be_v it_o that_o a_o man_n stand_v upright_o and_o look_v which_o way_n he_o will_v he_o look_v true_a north_n or_o south_n 43_o prob._n 28_o to_o tell_v any_o one_o what_o number_n remain_v after_o certain_a operation_n be_v end_v without_o ask_v any_o question_n 44_o prob._n 29_o of_o the_o play_n with_o two_o several_a thing_n 45_o prob._n 31_o how_o to_o describe_v a_o circle_n that_o shall_v touch_v 3_o point_n place_v howsoever_o upon_o a_o plain_a if_o they_o be_v not_o in_o a_o right_a line_n 47_o prob._n 32_o how_o to_o change_v a_o circle_n into_o a_o square_a form_n 48_o prob._n 33_o with_o one_o and_o the_o same_o compass_n and_o at_o one_o and_o the_o same_o extent_n or_o open_n how_o to_o describe_v many_o circle_n concentricall_a that_o be_v great_a or_o lesser_a one_o than_o another_o 49_o prob._n 34_o any_o number_n under_o 10._o be_v think_v upon_o to_o find_v what_o number_n they_o be_v 51_o prob_n 35_o of_o the_o play_n with_o the_o ring_n 52_o prob._n 36_o the_o play_n of_o 3_o 4_o or_o more_o dice_n 53_o prob._n 38_o of_o a_o fine_a vessel_n which_o hold_v wine_n or_o water_n be_v cast_v into_o it_o at_o a_o certain_a height_n but_o be_v fill_v high_a it_o will_v run_v all_o out_o of_o its_o own_o
as_o they_o will_v be_v if_o there_o be_v a_o liquid_a substance_n in_o the_o glass_n hence_o they_o have_v a_o assure_a proof_n to_o conclude_v that_o the_o hollow_v of_o the_o glass_n be_v total_o empty_a problem_n xl._o if_o any_o one_o shall_v hold_v in_o each_o hand_n as_o many_o piece_n of_o money_n as_o in_o the_o other_o how_o to_o find_v how_o much_o there_o be_v bid_v he_o that_o hold_v the_o money_n that_o he_o put_v out_o of_o one_o hand_n into_o the_o other_o what_o number_n you_o think_v convenient_a provide_v that_o it_o may_v be_v do_v this_o do_v bid_v he_o that_o out_o of_o the_o hand_n that_o he_o put_v the_o other_o number_n into_o that_o he_o take_v out_o of_o it_o as_o many_o as_o remain_v in_o the_o other_o hand_n and_o put_v it_o into_o that_o hand_n for_o then_o be_v assure_v that_o in_o the_o hand_n which_o be_v put_v the_o first_o take_v away_o there_o will_v be_v find_v just_o the_o double_a of_o the_o number_n take_v away_o at_o the_o first_o example_n admit_v there_o be_v in_o each_o hand_n 12_o shilling_n or_o counter_n and_o that_o out_o of_o the_o right_a hand_n you_o bid_v he_o take_v 7._o and_o put_v it_o into_o the_o left_a and_o then_o put_v into_o the_o right_a hand_n from_o the_o left_a as_o many_o as_o do_v remain_v in_o the_o right_n which_o be_v 5._o so_o there_o will_v be_v in_o the_o left_a hand_n â—4_n which_o be_v the_o double_a of_o the_o number_n take_v out_o of_o the_o right_a hand_n to_o wit_v 7._o then_o by_o some_o of_o the_o rule_v before_o deliver_v it_o be_v easy_a to_o find_v how_o much_o be_v in_o the_o right_a hand_n viz._n 10._o problem_n xli_o many_o dice_n be_v cast_v how_o artificial_o to_o discover_v the_o number_n of_o the_o point_n that_o may_v arise_v svppose_v any_o one_o have_v cast_v three_o dice_n secret_o bid_v he_o that_o he_o add_v the_o point_n that_o be_v upmost_a together_o then_o put_v one_o of_o the_o dice_n apart_o unto_o the_o former_a sum_n add_v the_o point_n which_o be_v under_o the_o other_o two_o then_o bid_v he_o throw_v these_o two_o dice_n and_o mark_v how_o many_o point_v a_o pair_n be_v upward_o which_o add_v unto_o the_o former_a sum_n then_o put_v one_o of_o these_o dice_n away_o not_o change_v the_o side_n mark_v the_o point_n which_o be_v under_o the_o other_o dice_n and_o add_v it_o to_o the_o former_a sum_n last_o throw_v that_o one_o dice_n and_o whatsoever_o appear_v upward_o add_v it_o unto_o the_o former_a sum_n and_o let_v the_o dice_n remain_v thus_o this_o do_v come_v to_o the_o table_n note_v what_o point_n do_v appear_v upward_o upon_o the_o three_o dice_n which_o add_v private_o together_o and_o unto_o it_o add_v â—1_n or_o 3_o time_n 7_o so_o this_o addition_n or_o sum_n shall_v be_v equal_a to_o the_o sum_n which_o the_o party_n private_o make_v of_o all_o the_o operation_n which_o he_o former_o make_v as_o if_o he_o shall_v throw_v three_o dice_n and_o there_o shall_v appear_v upward_o 5_o 3_o 2._o the_o sum_n of_o they_o be_v 10._o 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the_o intention_n of_o archimedes_n be_v not_o upon_o contrary_a metal_n enclose_v in_o 〈…〉_z box_n but_o consist_v of_o compare_v mettaâ—â—â—_n simple_a in_o the_o water_n one_o with_o another_o therefore_o the_o inference_n be_v false_a and_o absurd_a problem_n xliii_o two_o globe_n of_o diverse_a metal_n as_o one_o gold_n and_o the_o other_o copper_n yet_o of_o equal_a weight_n be_v put_v into_o a_o box_n as_o bg_n to_o find_v in_o which_o end_n the_o gold_n or_o copper_n be_v this_o be_v discover_v by_o the_o change_n of_o the_o place_n of_o the_o two_o bowles_n or_o globe_n
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card_n then_o secret_o multiply_v 12_o by_o 4_o make_v 48_o to_o which_o add_v 4_o the_o number_n of_o card_n take_v make_v 52_o from_o which_o 52_o shall_v be_v take_v rest_v nothing_o therefore_o according_a to_o the_o direction_n of_o the_o remainder_n of_o the_o card_n which_o be_v 30_o be_v equal_a to_o the_o point_n of_o the_o four_o card_n take_v viz._n 7_o 10_o 5_o 8._o again_o let_v these_o five_o card_n be_v suppose_v to_o be_v take_v 8_o 6_o 10_o 3_o 7_o their_o difference_n to_o 15_o the_o term_n be_v 7_o 9_o 5_o 12_o 8_o which_o number_n of_o card_n take_v there_o will_v remain_v but_o 6_o card_n then_o private_o multiply_v 15_o by_o 5_o make_v 75_o to_o which_o add_v 5_o make_v 80_o from_o this_o take_v 52_o the_o number_n of_o card_n rest_v 28_o to_o which_o add_v the_o remainder_n of_o card_n make_v 34._o the_o sum_n with_o 8_o 6_o 10_o 3_o 7._o problem_n lvii_o many_o card_n place_v in_o diverse_a rank_n to_o find_v which_o of_o these_o card_n any_o one_o have_v think_v take_v 15_o card_n and_o place_v they_o in_o 3_o heap_n in_o rank-wise_a 5_o in_o a_o heap_n now_o suppose_v any_o one_o have_v think_v one_o of_o these_o card_n in_o any_o one_o of_o the_o heap_n it_o be_v easy_a to_o find_v which_o of_o the_o card_n it_o be_v and_o it_o be_v do_v thus_o ask_v he_o in_o which_o of_o the_o heap_n it_o be_v which_o place_n in_o the_o middle_n of_o the_o other_o two_o then_o throw_v down_o the_o card_n by_o 1_o and_o 1_o into_o three_o several_a heap_n in_o rank-wise_a until_o all_o be_v cast_v down_o then_o ask_v he_o in_o which_o of_o the_o rank_n his_o card_n be_v which_o heap_n place_n in_o the_o middle_n of_o the_o other_o two_o heap_n always_o and_o this_o do_v four_o time_n at_o least_o so_o in_o put_v the_o card_n altogether_o look_v upon_o the_o card_n or_o let_v their_o back_n be_v towards_o you_o and_o throw_v out_o the_o eight_o card_n for_o that_o be_v the_o card_n think_v upon_o without_o fail_v problem_n lviii_o many_o card_n be_v offer_v to_o sundry_a person_n to_o find_v which_o of_o these_o card_n any_o one_o think_v upon_o admit_v there_o be_v 4_o person_n then_o take_v 4_o card_n and_o show_v they_o to_o the_o first_o bid_v he_o think_v one_o of_o they_o and_o put_v these_o 4_o away_o then_o take_v 4_o other_o card_n and_o show_v they_o in_o like_a manner_n to_o the_o second_o person_n and_o bid_v he_o think_v any_o one_o of_o these_o card_n and_o so_o do_v to_o the_o three_o person_n and_o so_o the_o four_o etc._n etc._n then_o take_v the_o 4_o card_n of_o the_o first_o person_n and_o dispose_v they_o in_o 4_o rank_n and_o upon_o they_o the_o 4_o card_n of_o the_o second_o person_n upon_o they_o also_o these_o of_o the_o three_o person_n and_o last_o upon_o they_o these_o of_o the_o four_o person_n then_o show_v unto_o eaeh_n of_o these_o party_n each_o of_o these_o rank_n and_o ask_v he_o if_o his_o card_n be_v in_o it_o which_o he_o think_v for_o infallible_o that_o which_o the_o first_o party_n think_v 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hollow_a vault_n that_o a_o man_n speak_v but_o soft_o at_o one_o corner_n thereof_o may_v be_v audible_o understand_v at_o the_o other_o end_n notwithstanding_o those_o which_o be_v between_o the_o party_n can_v hear_v he_o speak_v at_o all_o and_o it_o be_v a_o general_a principle_n that_o pipe_n do_v great_o help_v to_o strengthen_v the_o activity_n of_o natural_a cause_n we_o see_v that_o 〈◊〉_d contract_v in_o a_o pipe_n burn_v 4_o or_o 5_o foot_n high_a which_o will_v scarce_o heat_v be_v in_o
his_o most_o glorious_a beauty_n this_o glass_n have_v also_o a_o most_o excellent_a use_n in_o observe_v the_o body_n of_o the_o moon_n in_o time_n of_o eclipse_n for_o it_o augment_v it_o manifold_a and_o most_o manifest_o show_v the_o true_a form_n of_o the_o cloudy_a substance_n in_o the_o sun_n and_o by_o it_o be_v see_v when_o the_o shadow_n of_o the_o earth_n begin_v to_o eclipse_v the_o moon_n &_o when_o total_o she_o be_v over_o shadow_a beside_o the_o celestial_a use_n which_o be_v make_v of_o this_o glass_n it_o have_v another_o noble_a property_n it_o far_o exceed_v the_o ordinary_a perspective_n glass_n which_o be_v use_v to_o see_v thing_n remote_a upon_o the_o earth_n for_o as_o this_o glass_n reach_v up_o to_o the_o heaven_n and_o excel_v they_o there_o in_o his_o performance_n so_o on_o the_o earth_n it_o claim_v preeminency_n for_o the_o object_n which_o be_v far_a remote_a and_o most_o obscure_a be_v see_v plain_a than_o those_o which_o be_v near_o at_o hand_n 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the_o iron_n away_o &_o attract_v it_o with_o the_o other_o from_o whence_o come_v it_o that_o all_o the_o magnes_fw-la be_v not_o proper_a to_o give_v a_o true_a touch_n to_o the_o needle_n but_o only_o in_o the_o two_o pole_n of_o the_o stone_n which_o be_v know_v by_o hang_v the_o stone_n by_o a_o thread_n in_o the_o air_n until_o it_o be_v quiet_a or_o place_v upon_o a_o piece_n of_o cork_n in_o a_o dish_n of_o water_n or_o upon_o some_o thin_a board_n for_o the_o pole_n of_o the_o stone_n will_v then_o turn_v towards_o the_o pole_n of_o the_o world_n and_o point_n out_o the_o north_n and_o south_n and_o so_o show_v by_o which_o of_o these_o end_v the_o needle_n be_v to_o be_v touch_v from_o whence_o come_v it_o that_o there_o be_v a_o variation_n in_o the_o needle_n and_o point_v not_o out_o true_o the_o north_n and_o south_n of_o the_o world_n but_o only_o in_o some_o place_n of_o the_o earth_n how_o be_v it_o that_o the_o needle_n make_v with_o peg_n and_o enclose_a within_o two_o glass_n show_v the_o height_n of_o the_o pole_n be_v elevate_v as_o many_o degree_n as_o the_o pole_n be_v above_o the_o horizon_n what_o be_v the_o cause_n that_o fire_n and_o garlic_n take_v away_o the_o property_n of_o the_o magnes_fw-la there_o be_v many_o great_a hide_a mystery_n in_o this_o stone_n which_o have_v trouble_v the_o head_n of_o the_o most_o learned_a in_o all_o age_n and_o to_o this_o time_n the_o world_n remain_v ignorant_a of_o declare_v the_o rrue_a cause_n thereof_o some_o say_v that_o by_o help_n of_o the_o magnes_n person_n which_o be_v absent_a may_v know_v each_o other_o mind_n as_o if_o one_o be_v here_o at_o london_n and_o another_o at_o prague_n in_o germany_n if_o each_o of_o they_o have_v a_o needle_n touch_v with_o one_o magnes_fw-la than_o the_o virtue_n be_v such_o that_o in_o the_o same_o time_n that_o the_o needle_n which_o be_v at_o prague_n shall_v move_v this_o that_o be_v at_o london_n shall_v also_o provide_v that_o the_o party_n have_v like_o secret_a note_n or_o alphabet_n and_o the_o observation_n be_v at_o a_o set_a hour_n of_o the_o day_n or_o night_n and_o when_o the_o one_o party_n will_v declare_v unto_o the_o other_o then_o let_v that_o party_n move_v the_o needle_n to_o these_o letter_n which_o will_v declare_v the_o matter_n to_o the_o other_o and_o the_o move_n of_o the_o other_o party_n needle_n shall_v open_v his_o intention_n the_o invention_n be_v subtle_a but_o i_o doubt_v whether_o in_o the_o world_n there_o can_v be_v find_v so_o great_a a_o stone_n or_o such_o a_o magnes_n which_o carry_v with_o it_o such_o virtue_n neither_o be_v it_o expedient_a for_o treason_n will_v be_v then_o too_o frequent_a and_o open_a examination_n the_o experimental_a difference_n of_o rejection_n and_o attraction_n proceed_v not_o from_o the_o different_a nature_n of_o stone_n but_o from_o the_o quality_n of_o the_o iron_n and_o the_o virtue_n of_o the_o stone_n consist_v only_o and_o especial_o in_o his_o pole_n which_o be_v hang_v in_o the_o air_n turn_v one_o of_o his_o end_n always_o natural_o towards_o the_o south_n and_o the_o other_o towards_o the_o north_n but_o if_o a_o rod_n of_o iron_n be_v touch_v with_o one_o of_o the_o end_n thereof_o it_o have_v the_o like_a property_n in_o turn_v north_n and_o south_n as_o the_o magnes_fw-la have_v notwithstanding_o the_o end_n of_o the_o iron_n rod_n touch_v have_v a_o contrary_a position_n to_o that_o end_n of_o the_o stone_n that_o touch_v it_o yet_o the_o same_o end_n will_v attract_v it_o and_o the_o other_o end_n reject_v it_o and_o so_o contrary_o this_o may_v easy_o be_v experiment_a upon_o two_o needle_n touch_v with_o one_o or_o different_a stone_n though_o they_o have_v
one_o and_o the_o same_o position_n for_o as_o you_o come_v unto_o they_o apply_v one_o end_n of_o the_o magnes_fw-la near_o unto_o they_o the_o north_n of_o the_o one_o will_v abhor_v the_o north_n of_o the_o other_o but_o the_o north_n of_o the_o one_o will_v always_o approach_v to_o the_o south_n of_o the_o other_o and_o the_o same_o affection_n be_v in_o the_o stone_n themselves_o for_o the_o find_n of_o the_o pole_n of_o the_o magnes_fw-la it_o may_v be_v do_v by_o hold_v a_o small_a needle_n between_o your_o finger_n soft_o and_o so_o move_v it_o from_o part_n to_o part_v over_o the_o stone_n until_o it_o be_v hold_v perpendicular_a for_o that_o shall_v be_v one_o of_o the_o pole_n of_o the_o stone_n which_o you_o may_v mark_v out_o in_o like_a manner_n find_v out_o the_o other_o pole_n now_o to_o find_v out_o which_o of_o those_o pole_n be_v north_n or_o south_n place_v a_o needle_n be_v touch_v with_o one_o of_o the_o pole_n upon_o a_o smooth_a convex_a body_n as_o the_o nail_n of_o one_o finger_n or_o such_o like_a and_o mark_v which_o way_n the_o end_n of_o the_o needle_n that_o be_v touch_v turn_v if_o to_o the_o south_n than_o the_o point_n that_o touch_v it_o be_v the_o south-pole_n etc._n etc._n and_o it_o be_v most_o certain_a and_o according_a to_o reason_n and_o experience_n that_o if_o it_o be_v suspend_v in_o aequilibrio_fw-la in_o the_o air_n or_o support_v upon_o the_o water_n it_o will_v turn_v contrary_a to_o the_o needle_n that_o touch_v it_o for_o then_o the_o pole_n that_o be_v mark_v for_o the_o south_n shall_v turn_v to_o the_o north_n etc._n etc._n problem_n lxviii_o of_o the_o property_n of_o aeolipile_n or_o bowel_n to_o blow_v the_o fire_n these_o be_v concave_a vessel_n of_o brass_n or_o copper_n or_o other_o material_a which_o may_v endure_v the_o fire_n have_v a_o small_a hole_n very_o narrow_a by_o which_o it_o be_v fill_v with_o water_n then_o place_v it_o to_o the_o fire_n before_o it_o be_v hot_a there_o be_v no_o effect_n see_v but_o assoon_o as_o the_o heat_n do_v penetrate_v it_o the_o water_n begin_v to_o rarefie_v &_o issue_v forth_o with_o a_o hideous_a and_o marvellous_a force_n it_o be_v pleasure_n to_o see_v how_o it_o blow_v the_o fire_n with_o great_a noise_n now_o touch_v the_o form_n of_o these_o vessel_n they_o be_v not_o make_v of_o one_o like_o fashion_n some_o make_v they_o like_o a_o bowl_n some_o like_o a_o head_n paint_v represent_v the_o wind_n some_o make_v they_o like_o a_o pear_n as_o though_o one_o will_v put_v it_o to_o roast_v at_o the_o fire_n when_o one_o will_v have_v it_o to_o blow_v for_o the_o tail_n of_o it_o be_v hollow_v in_o form_n of_o a_o funnel_n have_v at_o the_o top_n a_o very_a little_a hole_n no_o great_a than_o the_o head_n of_o a_o pin_n some_o do_v accustom_v to_o put_v within_o the_o aeolipile_n a_o crooked_a funnel_n of_o many_o folding_n to_o the_o end_n that_o the_o wind_n that_o impetuous_o roll_n to_o and_o fro_o within_o may_v imitate_v the_o noise_n of_o thunder_n other_o content_v themselves_o with_o a_o simple_a funnel_n place_v right_o upward_a somewhat_o wide_a at_o the_o top_n than_o elsewhere_o like_o a_o cone_n who_o basis_n be_v the_o mouth_n of_o the_o funnel_n and_o there_o may_v be_v place_v a_o bowl_n of_o iron_n or_o brass_n which_o by_o the_o vapour_n that_o be_v cast_v out_o will_v cause_v it_o to_o leap_v up_o and_o dance_v over_o the_o mouth_n of_o the_o aeolipile_n last_o some_o apply_v near_o to_o the_o hole_n small_a windmill_n or_o such_o like_a which_o easy_o turn_v by_o reason_n of_o the_o vapour_n or_o by_o help_n of_o two_o or_o more_o bow_v funnel_n a_o bowl_n may_v be_v make_v to_o turneâ—_n these_o aeolipile_n be_v of_o excellent_a use_n for_o the_o melt_a of_o metal_n and_o such_o like_a now_o it_o be_v cunning_a and_o subtlety_n to_o fill_v one_o of_o these_o aeolipile_n with_o water_n at_o so_o little_a a_o hole_n and_o therefore_o require_v the_o knowledge_n of_o a_o philosopher_n to_o find_v it_o out_o and_o the_o way_n be_v thus_o heat_v the_o aeolipile_n be_v empty_a and_o the_o air_n which_o be_v within_o it_o will_v become_v extreme_o rarefy_v then_o be_v thus_o hot_a throw_v it_o into_o water_n and_o the_o air_n will_v begin_v to_o be_v condense_v by_o which_o mean_v it_o will_v occupy_v less_o room_n therefore_o the_o water_n will_v immediate_o enter_v in_o at_o the_o hole_n to_o avoid_v vacuity_n thus_o you_o have_v some_o practical_a speculation_n upon_o the_o aeolipile_n problem_n lxix_o of_o the_o thermometer_n or_o a_o instrument_n to_o measure_v the_o degree_n of_o heat_n and_o cold_a in_o the_o air_n this_o instrument_n be_v like_o a_o cylindricall_a pipe_n of_o glass_n which_o have_v a_o little_a ball_n or_o bowl_n at_o the_o top_n the_o small_a end_n of_o which_o be_v place_v into_o a_o vessel_n of_o water_n below_o as_o by_o the_o figure_n may_v be_v see_v then_o put_v some_o colour_a liquor_n into_o the_o cylindricall_a glass_n as_o blue_a red_a yellow_a green_a or_o such_o like_a such_o as_o be_v not_o thick_a this_o be_v do_v the_o use_n may_v be_v thus_o those_o that_o will_v determine_v this_o change_n by_o number_n and_o degree_n may_v draw_v a_o line_n upon_o the_o cylinder_n of_o the_o thermometer_n and_o divide_v it_o into_o 4_o degree_n according_a to_o the_o ancient_a philosopher_n or_o into_o 4_o degree_n according_a to_o the_o physician_n divide_v each_o of_o these_o 8_o into_o 8_o other_o to_o have_v in_o all_o 64_o division_n &_o by_o this_o way_n they_o may_v not_o only_o distinguish_v upon_o what_o degree_n the_o water_n ascend_v in_o the_o morning_n at_o midday_n &_o at_o any_o other_o hour_n but_o also_o one_o may_v know_v how_o much_o one_o day_n be_v hot_a or_o cold_a than_o another_o by_o mark_v how_o many_o degree_n the_o water_n ascend_v or_o descend_v one_o may_v compare_v the_o hot_a and_o cold_a day_n in_o a_o whole_a year_n together_o with_o these_o of_o another_o year_n again_o one_o may_v know_v how_o much_o hot_a one_o room_n be_v than_o another_o by_o which_o also_o one_o may_v keep_v a_o chamber_n a_o furnace_n a_o stove_n etc._n etc._n always_o in_o a_o equality_n of_o heat_n by_o make_v the_o water_n of_o the_o thermometer_n rest_v always_o upon_o one_o &_o the_o same_o degree_n in_o brief_a one_o may_v judge_v in_o some_o measure_n the_o burn_a of_o fever_n and_o near_o unto_o what_o extension_n the_o air_n can_v be_v rarefy_v by_o the_o great_a heat_n many_o make_v use_v of_o these_o glass_n to_o judge_v of_o the_o weather_n for_o it_o be_v observe_v that_o if_o the_o water_n fall_v in_o 3_o or_o 4_o hour_n a_o degree_n or_o thereabouts_o that_o rain_n ensue_v and_o the_o water_n will_v stand_v at_o that_o stay_n until_o the_o weather_n change_n mark_v the_o water_n at_o your_o go_v to_o bed_n for_o if_o in_o the_o morning_n it_o have_v descend_v rain_n follow_v but_o if_o it_o be_v mount_v high_a it_o argue_v fair_a weather_n so_o in_o very_o cold_a weather_n if_o it_o fall_v sudden_o it_o be_v snow_n or_o some_o sleekey_n weather_n that_o wiil_n ensue_v problem_n lxx_o of_o the_o proportion_n of_o humane_a body_n of_o statue_n of_o colossus_n or_o huge_a image_n and_o of_o monstrous_a giant_n pythagoras_n have_v reason_n to_o say_v that_o man_n be_v the_o measure_n of_o all_o thing_n first_o because_o he_o be_v the_o most_o perfect_a among_o all_o bodily_a creature_n &_o according_a to_o the_o maxim_n of_o philosopher_n that_o which_o be_v most_o perfect_a and_o the_o first_o in_o rank_n measure_v all_o the_o rest_n second_o because_o in_o effect_v the_o ordinary_a measure_n of_o a_o foot_n the_o inch_n the_o cubit_n the_o pace_n have_v take_v their_o name_n and_o greatness_n from_o humane_a body_n three_o because_o the_o symmetry_n and_o concordancie_n of_o the_o part_n be_v so_o admirable_a that_o all_o work_n which_o be_v well_o proportionable_a as_o namely_o the_o build_n of_o temple_n of_o ship_n of_o pillar_n and_o such_o like_a piece_n of_o architecture_n be_v in_o some_o measure_n fashion_v and_o compose_v after_o his_o proportion_n and_o we_o know_v that_o the_o ark_n of_o noah_n build_v by_o the_o commandment_n of_o god_n be_v in_o length_n 300_o cubit_n in_o breadth_n 50_o cubit_n in_o height_n or_o depth_n 30_o cubit_n so_o that_o the_o length_n contain_v the_o breadth_n 6_o time_n and_o 10_o time_n the_o depth_n now_o a_o man_n be_v measure_v you_o will_v find_v he_o to_o have_v the_o same_o proportion_n in_o length_n breadth_n and_o depth_n vilalpandus_n treat_v of_o the_o temple_n of_o solomon_n that_o chieftain_n of_o work_n be_v modulate_v all_o of_o good_a architecture_n and_o curious_o to_o be_v observe_v in_o many_o
because_o the_o mark_n c_o be_v see_v at_o d_o move_z the_o musket_n to_o and_o fro_o until_o it_o do_v agree_v with_o the_o line_n of_o reflection_n mb_n which_o suppose_v at_o li_n so_o shall_v it_o be_v true_o place_v and_o give_v fire_n to_o the_o musket_n it_o shall_v not_o fail_v to_o strike_v the_o say_a mark_n at_o c._n problem_n lxxx_o how_o to_o make_v a_o image_n to_o be_v see_v hang_v in_o the_o air_n have_v his_o head_n downward_o take_v two_o glass_n and_o place_v they_o at_o right_a angle_n one_o unto_o the_o other_o as_o admit_v ab_fw-la and_o cb_n of_o which_o admit_v cb_n hoâ—izontall_a and_o let_v the_o eye_n be_v at_o h_n and_o the_o object_n or_o image_n to_o be_v de_fw-fr so_o d_o will_v be_v reflect_v at_o f_o so_o to_o n_o so_o to_o he_o then_o at_o g_z so_o to_o â—_o and_o then_o to_o h_n and_o by_o a_o double_a reflection_n ed_z will_v seem_v in_o qr_n the_o high_a point_n d_o in_o r_o and_o the_o point_n l_o in_o q_n inverse_v as_o be_v say_v take_v d_o for_o 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