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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
have_v the_o same_o counterpoise_v h_n to_o be_v hang_v at_o the_o other_o side_n as_o in_o n._n and_o if_o the_o gold_n which_o be_v the_o lesser_a globe_n be_v before_o the_o near_a to_o the_o handle_n dâ—_n have_v now_o change_v his_o place_n will_v be_v far_a from_o the_o handle_n de_fw-fr as_o in_o k._n therefore_o the_o centre_n of_o gravity_n of_o the_o two_o globe_n take_v together_o shall_v be_v far_o separate_v from_o the_o middle_n of_o the_o handle_n under_o which_o be_v the_o centre_n of_o gravity_n of_o the_o box_n than_o it_o be_v before_o and_o see_v that_o the_o handle_n be_v always_o in_o the_o middle_n of_o the_o box_n the_o weight_n n._n must_v be_v augment_v to_o keep_v it_o in_o equilâ—â—â—â—_n and_o by_o this_o way_n one_o may_v know_v that_o if_o at_o the_o second_o time_n the_o counterpoise_n be_v too_o light_a it_o be_v a_o sign_n that_o the_o gold_n be_v far_a off_o the_o handle_n as_o at_o the_o first_o trial_n it_o be_v near_a problem_n xliiii_o how_o to_o represent_v diverse_a sort_n of_o rainbow_n here_o below_o the_o rainbow_n be_v a_o thing_n admirable_a in_o the_o world_n which_o ravish_v often_o the_o eye_n and_o spirit_n of_o man_n in_o consideration_n of_o his_o rich_a intermingle_v colour_n which_o be_v see_v under_o the_o cloud_n seem_v as_o the_o glister_n of_o the_o star_n precious_a stone_n and_o ornament_n of_o the_o most_o beauteous_a flower_n some_o part_n of_o it_o as_o the_o resplendent_a star_n or_o as_o a_o rose_n or_o burn_a coal_n of_o fire_n in_o it_o one_o may_v see_v die_v of_o sundry_a sort_n the_o violet_n the_o blue_n the_o orange_n the_o saphir_n the_o jacinct_n and_o the_o emerald_n colour_n as_o a_o lively_a plant_n place_v in_o a_o green_a soil_n and_o as_o a_o most_o rich_a treasure_n of_o nature_n it_o be_v a_o high_a work_n of_o the_o sun_n who_o cast_v his_o ray_n or_o beam_n as_o a_o curious_a painter_n draw_v stroke_n with_o his_o pencil_n and_o place_v his_o colour_n in_o a_o exquisite_a situation_n and_o solomon_n say_v eccles._n 43._o it_o be_v a_o chief_a and_o principal_a work_n of_o god_n notwithstanding_o there_o be_v leave_v to_o industry_n how_o to_o represent_v it_o from_o above_o here_o below_o though_o not_o in_o perfection_n yet_o in_o part_n with_o the_o same_o intermixture_n of_o colour_n that_o be_v above_o have_v you_o not_o see_v how_o by_o oar_n of_o a_o boat_n it_o do_v exceed_v quick_o glide_v upon_o the_o water_n with_o a_o pleasant_a grace_n aristotle_n say_v that_o it_o colour_v the_o water_n and_o make_v a_o thousand_o atom_n upon_o which_o the_o beam_n of_o the_o sun_n reflect_v make_v a_o kind_n of_o colour_a rainbow_n or_o may_v we_o not_o see_v in_o house_n or_o garden_n of_o pleasure_n artificial_a fountain_n which_o pour_v forth_o their_o droppie_n stream_n of_o water_n that_o be_v between_o the_o sun_n and_o the_o fountain_n there_o will_v be_v present_v as_o a_o continual_a rainbow_n but_o not_o to_o go_v far_o i_o will_v show_v you_o how_o you_o may_v do_v it_o at_o your_o door_n by_o a_o fine_a and_o facile_a experiment_n take_v water_n in_o your_o mouth_n and_o turn_v your_o back_n to_o the_o sun_n and_o your_o face_n against_o some_o obscure_a place_n then_o blow_v out_o the_o water_n which_o be_v in_o your_o mouth_n that_o it_o may_v be_v sprinkle_v in_o small_a drop_n and_o vapour_n you_o shall_v see_v those_o atom_n vapour_n in_o the_o beam_n of_o the_o sun_n to_o turn_v into_o a_o fair_a rainbow_n but_o all_o the_o grief_n be_v that_o it_o last_v not_o but_o soon_o be_v vanish_v but_o to_o have_v one_o more_o stable_a and_o permanent_a in_o his_o colour_n take_v a_o glass_n full_a of_o water_n and_o expose_v it_o to_o the_o sun_n so_o that_o the_o ray_n that_o pass_v through_o strike_v upon_o a_o shadow_a place_n you_o will_v have_v pleasure_n to_o see_v the_o fine_a form_n of_o a_o rainbow_n by_o this_o reflection_n or_o take_v a_o trigonall_a glass_n or_o crystal_n glass_n of_o diverse_a angle_n and_o look_v through_o it_o or_o let_v the_o beam_n of_o the_o sun_n pass_v through_o it_o or_o with_o a_o candle_n let_v the_o appearance_n be_v receive_v upon_o a_o shadow_v place_n you_o will_v have_v the_o same_o contentment_n problem_n xlv_o how_o that_o if_o all_o the_o powder_n in_o the_o world_n be_v in_o close_v within_o a_o bowl_n of_o paper_n or_o glass_n and_o be_v fire_v on_o all_o part_n it_o can_v not_o break_v that_o bowl_n if_o the_o bowl_n and_o the_o powder_n be_v uniform_a in_o all_o his_o part_n then_o by_o that_o mean_v the_o powder_n will_v press_v and_o move_v equal_o on_o each_o side_n in_o which_o there_o be_v no_o possibility_n whereby_o it_o ought_v to_o begin_v by_o one_o side_n more_o than_o another_o now_o it_o be_v impossible_a that_o the_o bowl_n shall_v be_v break_v in_o all_o his_o part_n for_o they_o be_v infinite_a of_o like_a fineness_n or_o subtlety_n may_v it_o be_v that_o a_o bowl_n of_o iron_n fall_v from_o a_o high_a place_n upon_o a_o plain_a pavement_n of_o thin_a glass_n it_o be_v impossible_a any_o wise_a to_o break_v it_o if_o the_o bowl_n be_v perfect_o round_a and_o the_o glass_n flat_a and_o uniform_a in_o all_o his_o part_n for_o the_o bowl_n will_v touch_v the_o glass_n but_o in_o one_o point_n which_o be_v in_o the_o middle_n of_o infinite_a part_n which_o be_v about_o it_o neither_o be_v there_o any_o cause_n why_o it_o ought_v more_v on_o one_o side_n than_o on_o another_o see_v that_o it_o may_v not_o be_v do_v with_o all_o his_o side_n together_o it_o may_v be_v conclude_v as_o speak_v natural_o that_o such_o a_o bowl_n fall_v upon_o such_o a_o glass_n will_v not_o break_v it_o but_o this_o matter_n be_v mere_a metaphysical_a and_o all_o the_o workman_n in_o the_o world_n can_v ever_o with_o all_o their_o industry_n make_v a_o bowl_n perfect_o round_a or_o a_o glass_n uniform_a problem_n xlvi_o to_o find_v a_o number_n which_o be_v divide_v by_o 2_o there_o will_v remain_v 1_o be_v divide_v by_o 3_o there_o will_v remain_v 1_o and_o so_o likewise_o be_v divide_v by_o 4_o 5_o or_o 6_o there_o will_v still_o remain_v 1_o but_o be_v didivide_v by_o 7_o there_o will_v remain_v nothing_o in_o many_o author_n of_o arithmetic_n this_o problem_n be_v thus_o propose_v a_o woman_n carry_v egg_n to_o market_n in_o a_o basket_n meet_v a_o unruly_a fellow_n who_o break_v they_o who_o be_v by_o order_n make_v to_o pay_v for_o they_o and_o she_o be_v demand_v what_o number_n she_o have_v she_o can_v not_o tell_v but_o she_o remember_v that_o count_v they_o by_o 2_o &_o 2_o there_o remain_v 1_o likewise_o by_o 3_o and_o 3_o by_o 4_o and_o 4_o by_z 5_o and_o 5_o by_z 6_o and_o 6_o there_o still_o remain_v 1._o but_o when_o she_o count_v they_o by_o 7_o and_o 7_o there_o remain_v nothing_o now_o how_o may_v the_o number_n of_o egg_n be_v discover_v find_v a_o number_n which_o may_v exact_o be_v measure_v by_o 7_o and_o be_v measure_v by_o 2_o 3_o 4_o 5_o and_o 6_o there_o will_v still_o remain_v a_o unite_v multiply_v these_o number_n together_o make_v 720_o to_o which_o add_v 1_o so_o have_v you_o the_o number_n viz._n 721._o in_o like_a manner_n 301_o will_v be_v measure_v by_o 2_o 3_o 4_o 5_o 6_o so_o that_o 1_o remain_v but_o be_v measure_v by_o 7_o nothing_o will_v remain_v to_o which_o continual_o add_v 220_o and_o you_o have_v other_o number_n which_o will_v do_v the_o same_o hence_o it_o be_v doubtful_a what_o number_n she_o have_v therefore_o not_o to_o fail_v it_o must_v be_v know_v whether_o they_o do_v exceed_v 400_o 800_o etc._n etc._n in_o which_o it_o may_v be_v conjecture_v that_o it_o can_v not_o exceed_v 4_o or_o 5_o hundred_o see_v a_o man_n or_o woman_n can_v not_o carry_v 7_o or_o 8_o hundred_o egg_n therefore_o the_o number_n be_v the_o former_a â—01_n which_o she_o have_v in_o her_o basket_n which_o be_v count_v by_o 2_o and_o 2_o there_o will_v remain_v 1_o by_z 3_o and_o 3_o etc._n etc._n but_o count_v by_o 7_o and_o 7_o there_o will_v remain_v nothing_o problem_n xlvii_o one_o have_v a_o certain_a number_n of_o crown_n and_o count_v they_o by_o 2_o and_o 2_o there_o rest_v 1._o count_v they_o by_o 3_o and_o 3_o there_o rest_v 2._o count_v they_o by_o 4_o and_o 4_o there_o rest_v 3._o count_v they_o by_o 5_o and_o 5_o there_o rest_v 4._o count_v they_o by_o 6_o &_o 6_o there_o rest_v 5._o but_o count_v they_o by_o 7_o and_o 7_o there_o remain_v nothing_o how_o many_o crown_n may_v he_o have_v this_o question_n have_v some_o affinity_n to_o the_o precedent_n and_o the_o resolution_n be_v almost_o in_o the_o same_o manner_n for_o
other_o number_n iâ—_n one_o be_v take_v from_o any_o square_a number_n which_o be_v odd_a the_o square_a oâ—_n half_a of_o it_o be_v add_v to_o the_o first_o square_n will_v make_v a_o square_a number_n the_o square_a of_o half_a any_o even_a number_n +_o 1_o be_v add_v to_o that_o even_a number_n make_v a_o square_a number_n and_o the_o even_a number_n take_v from_o it_o leave_v a_o square_a number_n if_o odd_a number_n be_v continual_o add_v from_o the_o unity_n successive_o there_o will_v be_v make_v all_o square_a number_n and_o if_o cubick_a number_n be_v add_v successive_o from_o the_o unity_n there_o will_v be_v likewise_o make_v square_a number_n problem_n lxiv_o of_o a_o excellent_a lamp_n which_o serve_v or_o furnish_v itself_o with_o oil_n and_o burn_v a_o long_a time_n i_o speak_v not_o here_o of_o a_o common_a lamp_n which_o caâ—danus_n write_v upon_o in_o his_o book_n the_o subtilitaâ—â—_n for_o that_o be_v a_o little_a vessel_n in_o columne-wise_a which_o be_v full_a of_o oil_n and_o because_o there_o be_v but_o one_o little_a hole_n at_o the_o bottom_n near_o the_o week_n or_o match_n the_o oil_n run_v not_o for_o fear_v that_o there_o be_v emptiness_n above_o when_o the_o match_n be_v kindle_v it_o begin_v to_o heat_v the_o lamp_n and_o rarefy_v the_o oil_n it_o issue_v by_o this_o occasion_n and_o so_o send_v his_o more_o airy_a part_n above_o to_o avoid_v vacuity_n it_o be_v certain_a that_o such_o a_o lamp_n the_o atheniaus_n use_v which_o last_v a_o whole_a year_n without_o be_v touch_v which_o be_v place_v before_o the_o statue_n of_o minerva_n for_o they_o may_v put_v a_o certain_a quantity_n of_o oil_n in_o the_o lamp_n cd_o and_o a_o match_n to_o burn_v without_o be_v consume_v such_o as_o the_o naturalist_n write_v of_o by_o which_o the_o lamp_n will_v furnish_v itself_o and_o so_o continue_v in_o burn_v and_o here_o may_v be_v note_v that_o the_o oil_n may_v be_v pour_v in_o at_o the_o top_n of_o thâ—_n vessel_n at_o a_o little_a hole_n and_o then_o make_v fast_o again_o that_o the_o air_n get_v not_o in_o problem_n lxv_o of_o the_o play_n at_o keyle_n or_o nine_o pin_n you_o will_v scarce_o believe_v that_o with_o one_o bowl_n and_o at_o one_o blow_n play_v free_o one_o may_v strike_v down_o all_o the_o keyle_n at_o once_o yet_o from_o mathematical_a principle_n it_o be_v easy_a to_o be_v demonstrate_v that_o if_o the_o hand_n of_o he_o that_o play_v be_v so_o well_o assure_v by_o experience_n as_o reason_n induce_v one_o thereto_o one_o may_v at_o one_o blow_v strike_v down_o all_o the_o keyle_n of_o at_o least_o 7_o or_o 8_o or_o such_o a_o number_n as_o one_o please_v for_o they_o be_v but_o 9_o in_o all_o dispose_v or_o place_v in_o a_o perfect_a square_n have_v three_o every_o way_n let_v we_o suppose_v then_o that_o a_o good_a player_n beginning_n to_o play_v at_o 1_o somewhat_o low_a shall_v so_o strike_v it_o that_o it_o shall_v strike_v down_o the_o keyles_a 2_o and_o 5_o and_o these_o might_n in_o their_o violence_n strike_v down_o the_o keyles_a 3_o 6_o and_o 9_o and_o the_o bowl_n be_v in_o motion_n may_v strike_v down_o the_o keyle_n 4_o and_o 7_o which_o 4_o keyle_n may_v strike_v the_o keyle_n 8_o &_o so_o all_o the_o 9_o keyle_n may_v be_v strike_v down_o at_o once_o problem_n lxiv_o of_o spectacle_n of_o pleasure_n simple_n spectacle_n of_o blue_a yellow_a red_a or_o green_a colour_n be_v proper_a to_o recreate_v the_o sight_n and_o will_v present_v the_o object_n die_v in_o like_a colour_n that_o the_o glass_n be_v only_o those_o of_o the_o green_a do_v somewhat_o degenerate_a instead_o of_o show_v a_o lively_a colour_n it_o will_v represent_v a_o pale_a dead_a colour_n and_o it_o be_v because_o they_o be_v not_o die_v green_a enough_o or_o receive_v not_o light_a enough_o for_o green_a and_o colour_v these_o image_n that_o pass_v through_o these_o glass_n unto_o the_o bottom_n of_o the_o eye_n examination_n it_o be_v certain_a that_o not_o only_a glass_n die_v green_a but_o all_o other_o glass_n colour_v yield_v the_o appearance_n of_o object_n strong_a or_o weak_a in_o colour_n according_a to_o the_o quantity_n of_o the_o dye_n more_o or_o less_o as_o one_o be_v very_o yellow_a another_o a_o pale_a yellow_a now_o all_o colour_n be_v not_o proper_a to_o glass_n to_o give_v colour_n hence_o the_o defect_n be_v not_o that_o they_o want_v faculty_n to_o receive_v light_n or_o resist_v the_o penetration_n of_o the_o beam_n for_o in_o the_o same_o glass_n those_o which_o be_v most_o die_v give_v always_o the_o object_n more_o high_a colour_a and_o obscure_a and_o those_o which_o be_v less_o die_v give_v they_o more_o pale_a and_o clear_a and_o this_o be_v daily_o make_v manifest_a by_o the_o paint_n of_o glass_n which_o hinder_v more_o the_o penetration_n of_o the_o light_n than_o die_a do_v where_o all_o the_o matter_n by_o fire_n be_v force_v into_o the_o glass_n leave_v it_o in_o all_o part_n transparent_a spectacle_n of_o crystal_n cut_v with_o divers_a angle_n diamond-wise_a do_v make_v a_o marvellous_a multiplication_n of_o the_o appearance_n for_o look_v towards_o a_o house_n it_o become_v as_o a_o town_n a_o town_n become_v like_o a_o city_n a_o arm_a man_n seem_v as_o a_o whole_a company_n cause_v sole_o by_o the_o diversity_n of_o refraction_n for_o as_o many_o plain_n as_o there_o be_v on_o the_o outside_n of_o the_o spectacle_n so_o many_o time_n will_v the_o object_n be_v multiply_v in_o the_o appearance_n because_o of_o diverse_a image_n cast_v into_o the_o eye_n these_o be_v pleasurable_a spectacle_n for_o avaricious_a person_n that_o love_v gold_n and_o silver_n for_o one_o piece_n will_v seem_v many_o or_o one_o heap_n of_o money_n will_v seem_v as_o a_o treasury_n but_o all_o the_o mischief_n be_v he_o will_v not_o have_v his_o end_n in_o the_o enjoy_n of_o it_o for_o endeavour_v to_o take_v it_o it_o will_v appear_v but_o a_o deceitful_a image_n or_o delusion_n of_o nothing_o here_o may_v you_o note_v that_o if_o the_o finger_n be_v direct_v by_o one_o and_o the_o same_o ray_n or_o beam_n which_o point_v to_o one_o and_o the_o same_o object_n then_o at_o the_o first_o you_o may_v touch_v that_o visible_a object_n without_o be_v deceive_v otherwise_o you_o may_v fail_v often_o in_o touch_v that_o which_o you_o see_v again_o there_o be_v spectacle_n make_v which_o do_v diminish_v the_o thing_n see_v very_o much_o and_o bring_v it_o to_o a_o fair_a perspective_n form_n especial_o if_o one_o look_v upon_o a_o fair_a garden_n plat_n a_o great_a walk_n a_o stately_a building_n or_o great_a court_n the_o industry_n of_o a_o exquisite_a painter_n can_v come_v near_o to_o express_v the_o lively_a form_n of_o it_o as_o this_o glass_n will_v represent_v it_o you_o will_v have_v pleasure_n to_o see_v it_o real_o experiment_a and_o the_o cause_n of_o this_o be_v that_o the_o glass_n of_o thâ—se_a spectacle_n be_v hollow_a and_o thin_a in_o the_o middle_n than_o at_o the_o edge_n by_o which_o the_o visual_a angle_n be_v make_v lesser_a you_o may_v observe_v a_o further_a secret_n in_o these_o spectacle_n for_o in_o place_v they_o upon_o a_o window_n one_o may_v see_v those_o that_o pass_v to_o and_o fro_o in_o the_o street_n without_o be_v see_v of_o any_o for_o their_o property_n be_v to_o raise_v up_o the_o object_n that_o it_o look_v upon_o now_o i_o will_v not_o pass_v this_o problem_n without_o say_v something_o of_o galileus_n admirable_a glass_n for_o the_o common_a simple_a perspective_n glass_n give_v to_o age_a man_n but_o the_o eye_n or_o sight_n of_o young_a man_n but_o this_o of_o galileus_n give_v a_o man_n a_o eagle's_n eye_n or_o a_o eye_n that_o pierce_v the_o heaven_n first_o it_o discover_v the_o spottie_a and_o shadow_a opacous_a body_n that_o be_v find_v about_o the_o sun_n which_o darknet_n and_o diminish_v the_o splendour_n of_o that_o beautiful_a and_o shine_a luminary_n second_o it_o show_v the_o new_a planet_n that_o accompany_v saturn_n and_o jupiter_n three_o in_o venus_n be_v see_v the_o new_a full_a and_o quartill_a increase_n as_o in_o the_o moon_n by_o her_o separation_n from_o the_o sun_n four_a the_o artificial_a structure_n of_o this_o instrument_n help_v we_o to_o see_v a_o innumerable_a number_n of_o star_n which_o otherwise_o be_v obscure_v by_o reason_n of_o the_o natural_a weakness_n of_o our_o sight_n yea_o the_o star_n in_o via_fw-la lactea_fw-la be_v see_v most_o apparent_o where_o there_o seem_v no_o star_n to_o be_v this_o instrument_n make_v apparent_o to_o be_v see_v and_o further_o deliver_v they_o to_o the_o eye_n in_o their_o true_a and_o lively_a colour_n as_o they_o be_v in_o the_o heaven_n in_o which_o the_o splendour_n of_o some_o be_v as_o the_o sun_n in_o
full_a so_o in_o c_o there_o be_v now_o but_o 1_o pint_n 5_o in_o b_o and_o 2_o in_o a_o pour_v all_o that_o be_v in_o b_o into_o a_o then_o pour_v the_o wine_n which_o be_v in_o c_o into_o b_o so_o there_o be_v in_o c_o nothing_o in_o b_o only_a 1_o pint_n and_o in_o 7_o a_o 7_o pint_n last_o out_o of_o a_o fill_v the_o pot_n c_o so_fw-mi there_o will_v remain_v in_o a_o 4_o pint_n or_o be_v but_o half_a full_a then_o if_o the_o liquor_n in_o c_o be_v pour_v into_o b_o it_o will_v be_v the_o other_o half_o in_o like_a manner_n may_v be_v take_v the_o half_a of_o a_o vessel_n which_o contain_v 12_o pint_n by_o have_v but_o the_o measure_n 5_o and_o 7_o or_o 5_o and_o 8._o now_o such_o other_o may_v be_v propose_v but_o we_o omit_v many_o in_o one_o and_o the_o same_o nature_n problem_n x._o to_o make_v a_o stick_n stand_v upon_o the_o tip_n of_o one_o finger_n without_o fall_v fasten_v the_o edge_n of_o two_o knife_n or_o such_o like_a of_o equal_a poise_n at_o the_o end_n of_o the_o stick_n lean_v out_o somewhat_o from_o the_o stick_n so_o that_o they_o may_v counterpoise_v one_o another_o the_o stick_n be_v sharp_a at_o the_o end_n and_o hold_v upon_o the_o top_n of_o the_o finger_n will_v there_o rest_v without_o support_v if_o it_o fall_v it_o must_v fall_v together_o and_o that_o perpendicular_a or_o plumb-wise_a or_o it_o must_v fall_v side-wise_a or_o before_o one_o another_o in_o the_o first_o manner_n it_o can_v for_o the_o centre_n of_o gravity_n be_v support_v by_o the_o top_n of_o the_o finger_n and_o see_v that_o each_o part_n by_o the_o knife_n be_v counterpoise_v it_o can_v fall_v sidewise_o therefore_o it_o can_v fall_v no_o wise_a in_o like_a manner_n may_v great_a piece_n of_o timber_n as_o joist_n &c_n &c_n be_v support_v if_o unto_o one_o of_o the_o end_n be_v apply_v convenient_a proportional_a counterpoise_n yea_o a_o lance_n or_o pike_n may_v stand_v perpendicular_a in_o the_o air_n upon_o the_o top_n of_o one_o finger_n or_o place_v in_o the_o midst_n of_o a_o court_n by_o help_n of_o his_o centre_n of_o gravity_n examination_n this_o proposition_n seem_v doubtful_a for_o to_o imagine_v absolute_o that_o a_o pike_n or_o such_o like_a arm_v with_o two_o knife_n or_o other_o thing_n shall_v stand_v upright_o in_o the_o air_n and_o so_o remain_v without_o any_o other_o support_n see_v that_o all_o the_o part_n have_v a_o infinite_a difference_n of_o propensity_n to_o fall_v and_o it_o be_v without_o question_n that_o a_o staff_n so_o accommodate_v upon_o his_o centre_n of_o gravity_n but_o that_o it_o may_v incline_v to_o some_o one_o part_n without_o some_o remedy_n be_v apply_v and_o such_o as_o be_v here_o specify_v in_o the_o problem_n will_v not_o warrant_v the_o thing_n nor_o keep_v it_o from_o fall_v and_o if_o more_o knife_n shall_v be_v place_v about_o it_o it_o shall_v cause_v it_o to_o fall_v more_o swift_o forasmuch_o as_o the_o superior_a part_n by_o reason_n of_o the_o centrical_a motion_n be_v make_v more_o ponderous_a and_o therefore_o less_o in_o rest_n to_o place_v therefore_o this_o prop_n real_o let_v the_o two_o knife_n or_o that_o which_o be_v for_o counterpoise_v be_v long_o always_o then_o the_o staff_n and_o so_o it_o will_v hang_v together_o as_o one_o body_n and_o it_o will_v appear_v admirable_a if_o you_o place_v the_o centre_n of_o gravity_n near_o the_o side_n of_o the_o top_n of_o the_o finger_n or_o point_n for_o it_o will_v then_o hang_v horizontall_a and_o seem_v to_o hang_v only_o by_o a_o touch_n yet_o more_o strange_a if_o you_o turn_v the_o point_n or_o top_n of_o the_o finger_n upside_o down_o problem_n xi_o how_o a_o millstone_n or_o other_o ponderosity_n may_v be_v support_v by_o a_o small_a needle_n without_o break_v oâ—_n any_o wise_a bow_v the_o same_o let_v a_o needle_n be_v set_v perpendicular_a to_o the_o horizon_n and_o the_o centre_n of_o gravity_n of_o the_o stone_n be_v place_v on_o the_o top_n of_o the_o needle_n it_o be_v evident_a that_o the_o stone_n can_v fall_v forasmuch_o as_o it_o hang_v in_o aequilibra_n or_o be_v counterpoyse_v in_o all_o part_n alike_o and_o moreover_o it_o can_v bow_v the_o needle_n more_o on_o the_o one_o side_n then_o on_o the_o other_o the_o needle_n will_v not_o therefore_o be_v either_o break_a or_o bow_v if_o otherwise_o then_o the_o part_n of_o the_o needle_n must_v penetrate_v and_o sink_v one_o with_o another_o that_o which_o be_v absurd_a and_o impossible_a to_o nature_n therefore_o it_o shall_v be_v support_v the_o experiment_n which_o be_v make_v upon_o trencher_n plate_n or_o such_o like_o lesser_a thing_n do_v make_v it_o most_o credible_a in_o great_a body_n but_o here_o especial_o be_v to_o be_v note_v that_o the_o needle_n ought_v to_o be_v uniform_a in_o matter_n and_o figure_n and_o that_o it_o be_v erect_v perpendicular_a to_o the_o horizon_n and_o last_o that_o the_o centre_n of_o gravity_n be_v exact_o find_v problem_n xii_o to_o make_v three_o knife_n hang_v and_o move_v upon_o the_o point_n of_o a_o needle_n fit_a the_o three_o knife_n in_o form_n of_o a_o balance_n and_o hold_v a_o needle_n in_o your_o hand_n and_o place_v the_o back_n of_o that_o knife_n which_o lie_v crosswise_o to_o the_o other_o two_o upon_o the_o point_n of_o the_o needle_n as_o the_o figure_n here_o show_v you_o for_o then_o in_o blow_v soft_o upon_o they_o they_o will_v easy_o turn_v and_o move_v upon_o the_o point_n of_o the_o needle_n with_o â—ou_n fall_v problem_n xiii_o to_o find_v the_o weight_n of_o smoke_n which_o be_v exhale_v of_o any_o combustible_a body_n whatsoever_o let_v it_o be_v suppose_v that_o a_o great_a heap_n of_o faggot_n or_o a_o load_n of_o straw_n weigh_v 500_o pound_n shall_v be_v fire_v it_o be_v evident_a that_o this_o gross_a substance_n will_v be_v all_o invert_v into_o smoke_n and_o ash_n now_o it_o seem_v that_o the_o smoke_n weigh_v nothing_o see_v it_o be_v of_o a_o thin_a substance_n now_o dilate_v in_o the_o air_n notwithstanding_o if_o it_o be_v gather_v and_o reduce_v into_o the_o thick_a that_o it_o be_v at_o first_o it_o will_v be_v sensible_o weighty_a weigh_v therefore_o the_o ash_n which_o admit_v 50_o pound_n now_o see_v that_o the_o rest_n of_o the_o matter_n be_v not_o lose_v but_o be_v exhale_v into_o smoke_n it_o must_v necessary_o be_v that_o the_o rest_n of_o the_o weight_n to_o wit_n 450_o pound_n must_v be_v the_o weight_n of_o the_o smoke_n require_v examination_n now_o although_o it_o be_v thus_o deliver_v yet_o here_o may_v be_v note_v that_o a_o ponderosity_n in_o his_o own_o medium_n be_v not_o weighty_a for_o thing_n be_v say_v to_o be_v weighty_a when_o they_o be_v out_o of_o their_o place_n or_o medium_n and_o the_o difference_n of_o such_o gravity_n be_v according_a to_o the_o motion_n the_o smoke_n therefore_o certain_o be_v light_n be_v in_o its_o true_a medium_n the_o air_n if_o it_o shall_v change_v his_o medium_n then_o will_v we_o change_v our_o discourse_n problem_n xvi_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 suppose_v that_o have_v rank_v 10_o thing_n as_o abcdefghik_n circular_a as_o the_o figure_n show_v and_o that_o one_o have_v touch_v or_o think_v upon_o g_o which_o be_v the_o 7_o ask_v the_o party_n at_o what_o letter_n he_o will_v begin_v to_o account_v for_o account_n he_o must_v otherwise_o it_o can_v be_v do_v which_o suppose_v at_o e_z which_o be_v the_o 5_o place_n then_o add_v secret_o to_o this_o 5_o 10_o which_o be_v the_o number_n of_o the_o circle_n and_o it_o make_v 15_o bid_v he_o account_v 15_o backward_a from_o e_z beginning_z his_o account_n with_o that_o number_n he_o think_v upon_o so_o at_o e_z he_o shall_v account_v to_o himself_o 7_o at_z d_o account_n 8_o at_z c_o account_n 9_o etc._n etc._n so_o the_o account_n of_o 15_o will_v exact_o fall_v upon_o g_o the_o thing_n or_o number_n think_v upon_o and_o so_o of_o other_o but_o to_o conceal_v it_o the_o more_o you_o may_v will_v the_o party_n from_o e_z to_o account_v 25_o 35_o etc._n etc._n and_o it_o will_v be_v the_o same_o there_o be_v some_o that_o use_v this_o play_n at_o card_n turn_v upside_o down_o as_o the_o ten_o simple_a card_n with_o the_o king_n and_o queen_n the_o king_n stand_v for_o 12_o and_o the_o queen_n for_o 11_o and_o so_o know_v the_o situation_n of_o the_o card_n and_o think_v a_o certain_a hour_n of_o the_o day_n cause_n the_o party_n to_o account_v from_o what_o card_n he_o please_v with_o this_o proviso_n that_o when_o you_o see_v where_o he_o intend_v to_o account_v set_v 12_o to_o that_o number_n so_o in_o count_v as_o
a_o line_n and_o place_v a_o ruler_n upon_o e._n and_o f._n cut_v the_o other_o line_n in_o k_o so_o k_o be_v the_o centre_n of_o the_o circumference_n of_o a_o circle_n which_o will_v pass_v by_o the_o say_v three_o point_n a.b.c._n or_o it_o may_v be_v invert_v have_v a_o circle_n draw_v to_o find_v the_o centre_n of_o that_o circle_n make_v 3._o point_n in_o the_o circumference_n and_o then_o use_v the_o same_o way_n so_o shall_v you_o have_v the_o centre_n a_o thing_n most_o facile_a to_o every_o practitioner_n in_o the_o principle_n of_o geometry_n problem_n xxxii_o how_o to_o change_v a_o circle_n into_o a_o square_a form_n mâ—ke_v a_o circle_n upon_o pasteboard_n or_o other_o material_a as_o the_o circle_n a.c.d.e._n of_o which_o a._n be_v the_o centre_n then_o cut_v it_o into_o 4_o quarter_n and_o dispose_v they_o so_o that_o a._n at_o the_o centre_n of_o the_o circle_n may_v always_o be_v at_o the_o angle_n of_o the_o square_n and_o so_o the_o four_o quarter_n of_o the_o circle_n be_v place_v so_o it_o will_v make_v a_o perfect_a square_n who_o side_n a.a._n be_v equal_a to_o the_o diameter_n b.d._n now_o here_o be_v to_o be_v note_v that_o the_o square_n be_v great_a than_o the_o circle_n by_o the_o vacuity_n in_o the_o middle_n viz._n m._n problem_n xxxiii_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_v 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 it_o be_v not_o without_o cause_n that_o many_o admire_v how_o this_o proposition_n be_v to_o be_v resolve_v yea_o in_o the_o judgement_n of_o some_o it_o be_v think_v impossible_a who_o consider_v not_o the_o industry_n of_o a_o ingenious_a geometrician_n who_o make_v it_o possible_a and_o that_o most_o facile_a sundry_a way_n for_o in_o the_o first_o place_n if_o you_o make_v a_o circle_n upon_o a_o fine_a plain_n and_o upon_o the_o centre_n of_o that_o circle_n a_o small_a peg_n of_o wood_n be_v place_v to_o be_v raise_v up_o and_o put_v down_o at_o pleasure_n by_o help_n of_o a_o small_a hoâ—e_n make_v in_o the_o centre_n then_o with_o the_o same_o open_n of_o the_o compass_n you_o may_v describe_v circle_n concentricall_a that_o be_v one_o great_a or_o lesser_a than_o another_o for_o the_o high_a the_o centre_n be_v lift_v up_o the_o lesser_a the_o circle_n will_v be_v second_o the_o compass_n be_v at_o that_o extent_n upon_o a_o gibus_fw-la body_n a_o circle_n may_v be_v describe_v which_o will_v be_v less_o than_o the_o former_a upon_o a_o plain_a and_o more_o artificial_o upon_o a_o globe_n or_o round_a bowl_n and_o this_o again_o be_v most_o obvious_a upon_o a_o round_a pyramid_n place_v the_o compass_n upon_o the_o top_n of_o it_o which_o will_v be_v far_o less_o than_o any_o of_o the_o former_a and_o this_o be_v demonstrate_v by_o the_o 20._o prop._n of_o the_o first_o of_o euclid_n for_o the_o diameter_n â—_o d._n be_v less_o than_o the_o line_n ad.a.e._n take_v together_o and_o the_o line_n ad.ae._n be_v equal_a to_o the_o diameter_n bc._n because_o of_o the_o same_o distance_n or_o extent_n of_o open_v the_o compass_n it_o follow_v that_o the_o diameter_n e.d._n and_o all_o his_o circle_n together_o be_v much_o less_o than_o the_o diameter_n and_o the_o circle_n bc._n which_o be_v to_o be_v perform_v problem_n xxxiv_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 let_v the_o first_o number_n be_v double_v and_o unto_o it_o add_v 5._o and_o multiply_v that_o sum_n by_o 5._o and_o unto_o it_o add_v 10._o and_o unto_o this_o product_n add_v the_o next_o number_n think_v upon_o multiply_v this_o same_o again_o by_o 10._o and_o add_v unto_o it_o the_o next_o number_n and_o so_o proceed_v now_o if_o he_o declare_v the_o last_o sum_n mark_v if_o he_o think_v but_o upon_o one_o figure_n for_o then_o subtract_v only_o 35._o from_o it_o and_o the_o first_o figure_n in_o the_o place_n of_o ten_o be_v the_o number_n think_v upon_o if_o he_o think_v upon_o two_o figure_n then_o subtract_v also_o the_o say_a â—5_n from_o his_o last_o sum_n and_o the_o two_o figure_n which_o remain_v be_v the_o number_n think_v upon_o if_o he_o think_v upoâ—_n three_o figure_n then_o subtract_v 350._o and_o then_o the_o first_o three_o figure_n be_v the_o number_n think_v upon_o etc._n etc._n so_o if_o one_o think_v upon_o these_o number_n 5.7.9.6_o double_a the_o first_o make_v 1â—_n to_o which_o add_v 5._o make_v 15._o this_o multiply_v by_o 5._o make_v 75._o to_o which_o add_v 1â—_n make_v 85._o to_o this_o add_v the_o next_o number_n viz._n 7._o make_v 92._o this_o multiply_v by_o 10._o make_v 920._o to_o which_o add_v the_o next_o number_n viz._n 9_o make_v 929._o which_o multiply_v by_o 10._o make_v 9290._o to_o which_o add_v 6._o make_v 9296._o from_o which_o subtract_v 3500._o rest_v 5796._o the_o four_o number_n think_v upon_o now_o because_o the_o two_o last_o figure_n be_v like_o the_o two_o number_n think_v upon_o to_o conceal_v this_o bid_v he_o take_v the_o half_a of_o it_o or_o put_v first_o 12._o or_o any_o other_o number_n to_o it_o and_o then_o it_o will_v not_o be_v so_o open_a problem_n xxxv_o of_o the_o play_n with_o the_o ring_n among_o a_o company_n of_o 9_o or_o 10._o person_n one_o of_o they_o have_v a_o ring_n or_o such_o like_a to_o find_v out_o in_o which_o hand_n upon_o which_o finger_n &_o joint_n it_o be_v this_o will_v cause_v great_a astonishment_n to_o ignorant_a spirit_n which_o will_v make_v they_o believe_v that_o he_o that_o do_v it_o work_v by_o magic_n or_o witchcraft_n but_o in_o effect_v it_o be_v nothing_o else_o but_o a_o nimble_a act_n of_o arithmetic_n found_v upon_o the_o precedent_a problem_n for_o first_o it_o be_v suppose_v that_o the_o person_n stand_v or_o sit_v in_o order_n that_o one_o be_v first_o the_o next_o second_o etc._n etc._n likewise_o there_o must_v be_v imagine_v that_o of_o these_o two_o hand_n the_o one_o be_v first_o and_o the_o other_o second_o and_o also_o of_o the_o five_o finger_n the_o one_o be_v first_o the_o next_o be_v second_v and_o last_o of_o the_o joint_n the_o one_o be_v as_o 1._o the_o other_o be_v as_o 2._o the_o other_o as_o 3._o etc._n etc._n from_o whence_o it_o appear_v that_o in_o perform_v this_o play_n there_o be_v nothing_o else_o to_o be_v do_v than_o to_o think_v 4._o number_n for_o example_n if_o the_o four_o person_n have_v the_o ring_n in_o his_o left_a hand_n and_o upon_o the_o five_o finger_n and_o three_o joint_n and_o i_o will_v divine_v and_o find_v it_o out_o thus_o i_o will_v proceed_v as_o in_o the_o 34_o problem_n in_o cause_v he_o to_o double_v the_o first_o number_n that_o be_v the_o number_n of_o person_n which_o be_v 4._o and_o it_o make_v 8._o to_o which_o add_v 5._o make_v 13._o this_o multiply_v by_o 5._o make_v 65._o put_v 10._o to_o it_o make_v 75._o unto_o this_o put_v â—_o for_o the_o number_n belong_v to_o the_o left_a hand_n and_o so_o it_o make_v 77._o which_o multiply_v by_o 10._o make_v 770._o to_o this_o add_v the_o number_n of_o the_o finger_n upon_o which_o the_o ring_n be_v viz._n 5._o make_v 775._o this_o multiply_v by_o 10._o make_v 7750._o to_o which_o add_v the_o number_n for_o the_o joint_n upon_o which_o the_o ring_n be_v viz_o the_o three_o joint_n make_v 7â—53_n to_o which_o cause_n he_o to_o add_v 14._o or_o some_o other_o number_n to_o conceal_v it_o the_o better_a and_o it_o make_v 7767._o which_o be_v declare_v unto_o you_o subtract_v 3514_o and_o there_o will_v remain_v 4.2.5.3_o which_o figure_v in_o order_n declare_v the_o whole_a mystery_n of_o that_o which_o be_v to_o be_v know_v 4._o signify_v the_o four_o person_n 2._o the_o left_a hand_n 5._o the_o five_o finger_n and_o 3._o the_o three_o joint_n of_o that_o finger_n problem_n xxxvi_o the_o play_n of_o 34._o or_o more_o dice_n that_o which_o be_v say_v of_o the_o two_o precedent_a problem_n may_v be_v apply_v to_o this_o of_o dice_n and_o many_o other_o particular_a thing_n to_o find_v what_o number_n appear_v upon_o each_o dice_n be_v cast_v by_o some_o one_o for_o the_o point_n that_o be_v upon_o any_o side_n of_o a_o dice_n be_v always_o less_o than_o 10_o and_o the_o point_n of_o each_o side_n of_o a_o dice_n may_v be_v take_v for_o a_o number_n think_v upon_o therefore_o the_o rule_n will_v be_v as_o the_o former_a as_o for_o example_n one_o have_v throw_v three_o dice_n and_o you_o will_v declare_v the_o number_n of_o each_o one_o or_o how_o much_o they_o make_v together_o bid_v he_o double_v the_o point_n of_o one_o of_o the_o dice_n to_o which_o bid_v he_o add_v 5_o
then_o multiply_v that_o by_o 5._o and_o to_o it_o add_v 10_o and_o to_o the_o sum_n bid_v he_o add_v the_o number_n of_o the_o second_o dice_n and_o multiply_v that_o by_o 10_o last_o to_o this_o bid_v he_o add_v the_o number_n of_o the_o last_o dice_n and_o then_o let_v he_o declare_v the_o whole_a number_n then_o if_o from_o it_o you_o subtract_v â—50_n there_o will_v remain_v the_o number_n of_o the_o three_o dice_n throw_v problem_n xxxvii_o how_o to_o make_v water_n in_o a_o glass_n seem_v to_o boil_v and_o sparkle_v take_v a_o glass_n near_o full_a of_o water_n or_o other_o liquor_n and_o set_v one_o hand_n upon_o the_o foot_n of_o it_o to_o hold_v it_o fast_o turn_v slight_o one_o of_o the_o finger_n of_o your_o other_o hand_n upon_o the_o brim_n or_o edge_n of_o the_o glass_n have_v before_o private_o wet_v your_o finger_n and_o so_o pass_v soft_o on_o with_o your_o finger_n in_o press_v a_o little_a for_o than_o first_o the_o glass_n will_v begin_v to_o make_v a_o noise_n second_o the_o part_n of_o the_o glass_n will_v sensible_o appear_v to_o tremble_v with_o notable_a rarefaction_n and_o condensation_n three_o the_o water_n will_v shake_v seem_v to_o boil_v four_a it_o will_v cast_v itself_o out_o of_o the_o glass_n and_o leap_v out_o by_o small_a drop_n with_o great_a astonishment_n to_o the_o stander_n by_o if_o they_o be_v ignorant_a of_o the_o cause_n of_o it_o which_o be_v only_o in_o the_o rarefaction_n of_o the_o part_n of_o the_o glass_n occasion_v by_o the_o motion_n and_o pressure_n of_o the_o finger_n examination_n the_o cause_n of_o this_o be_v not_o in_o the_o rarefaction_n of_o the_o part_n of_o the_o glass_n but_o it_o be_v rather_o in_o the_o quick_a local_a motion_n of_o the_o finger_n for_o reason_n show_v we_o that_o by_o how_o much_o a_o body_n draw_v near_a to_o a_o quality_n the_o less_o be_v it_o subject_a or_o capable_a of_o another_o which_o be_v contrary_a unto_o it_o now_o condensation_n and_o rarefaction_n be_v contrary_a quality_n and_o in_o this_o problem_n there_o be_v three_o body_n consider_v the_o glass_n the_o water_n and_o the_o air_n now_o it_o be_v evident_a that_o the_o glass_n be_v the_o most_o solid_a and_o impenetrable_a body_n be_v less_o subject_a and_o capable_a of_o rarefaction_n than_o the_o water_n the_o water_n be_v less_o subject_a than_o the_o air_n and_o if_o there_o be_v any_o rarefaction_n it_o be_v rather_o considerable_a in_o the_o air_n then_o in_o the_o water_n which_o be_v inscribe_v by_o the_o glass_n and_o above_o the_o water_n and_o rather_o in_o the_o water_n then_o in_o the_o glass_n the_o agitation_n or_o the_o tremble_n of_o the_o part_n of_o the_o glass_n to_o the_o sense_n appear_v not_o for_o it_o be_v a_o continue_a body_n if_o in_o part_n why_o then_o not_o in_o the_o whole_a and_o that_o the_o water_n turn_v in_o the_o glass_n this_o appear_v not_o but_o only_o the_o upper_a contiguous_a part_n of_o the_o water_n that_o at_o the_o bottom_n be_v less_o subject_a to_o this_o agitation_n and_o it_o be_v most_o certain_a that_o by_o how_o much_o quick_a the_o circular_a motion_n of_o the_o finger_n upon_o the_o edge_n of_o the_o glass_n be_v by_o so_o much_o the_o more_o shall_v the_o air_n be_v agitate_a and_o so_o the_o water_n shall_v receive_v some_o apparent_a affection_n more_o or_o less_o from_o it_o according_a to_o that_o motion_n as_o we_o see_v from_o the_o quickness_n of_o wind_n upon_o the_o sea_n or_o câ—lme_v thereof_o that_o there_o be_v a_o great_a or_o lesser_a agitation_n in_o the_o water_n and_o for_o further_a examination_n we_o leave_v it_o to_o the_o search_n of_o those_o which_o be_v curious_a problem_n xxxviii_o of_o a_o fine_a vessel_n which_o hold_v wine_n or_o water_n be_v cast_v inâ—o_o it_o at_o a_o certain_a height_n but_o be_v fill_v high_o it_o will_v run_v out_o of_o its_o own_o accord_n let_v there_o be_v a_o vessel_n a.b.c.d._n in_o the_o middle_n of_o which_o place_n a_o pipe_n who_o end_n both_o above_o at_o e_o and_o below_z at_o the_o bottom_n of_o the_o vessel_n as_o at_o â—_o be_v open_a let_v the_o end_n â—_o be_v somewhat_o low_a than_o the_o brim_n of_o the_o glass_n about_o this_o pipe_n place_v another_o pipe_n as_o h._n l_o which_o mount_v a_o little_a above_o e_z and_o let_v it_o most_o diligent_o be_v close_v at_o h_n that_o no_o air_n enter_v in_o thereby_o and_o this_o pipe_n at_o the_o bottom_n may_v have_v a_o small_a hole_n to_o give_v passage_n unto_o the_o water_n then_o pour_v in_o water_n or_o wine_n and_o as_o long_o as_o it_o mount_v not_o above_o e_z it_o be_v safe_a but_o if_o you_o pour_v in_o the_o water_n so_o that_o it_o mount_v above_o it_o farewell_n all_o for_o it_o will_v not_o cease_v until_o it_o be_v all_o go_v out_o the_o same_o may_v be_v do_v in_o dispose_v any_o crooked_a pipe_n in_o a_o vessel_n in_o the_o manner_n of_o a_o faucet_n or_o funnel_n as_o in_o the_o figure_n h_n for_o fill_v it_o under_o h_n at_o pleasure_n and_o all_o will_v go_v well_o but_o if_o you_o fill_v it_o unto_o h._n you_o will_v see_v fine_a sport_n for_o then_o all_o the_o vessel_n will_v be_v empty_a incontinent_a and_o the_o subtlety_n of_o this_o will_v seem_v more_o admirable_a if_o you_o conceal_v the_o pipe_n by_o a_o bird_n serpent_n or_o such_o like_a in_o the_o middle_n of_o the_o glass_n now_o the_o reason_n of_o this_o be_v not_o difficult_a to_o those_o which_o know_v the_o nature_n of_o a_o cock_n or_o faucet_n for_o it_o be_v a_o bow_a pipe_n one_o end_n of_o which_o be_v put_v into_o the_o water_n or_o liquor_n and_o suck_v at_o the_o other_o end_n until_o the_o pipe_n be_v full_a then_o will_v it_o run_v of_o itself_o and_o it_o be_v a_o fine_a secret_a in_o nature_n to_o see_v that_o if_o the_o end_n of_o the_o pipe_n which_o be_v out_o of_o the_o water_n be_v low_a than_o the_o water_n it_o will_v run_v out_o without_o cease_v but_o if_o the_o mouth_n of_o the_o pipe_n be_v high_o than_o the_o water_n or_o level_v with_o it_o it_o will_v not_o run_v although_o the_o pipe_n which_o be_v without_o be_v many_o time_n big_a than_o that_o which_o be_v in_o the_o water_n for_o it_o be_v the_o property_n of_o water_n to_o keep_v always_o exact_o level_v examination_n here_o be_v to_o be_v note_v that_o if_o the_o face_n of_o the_o water_n without_o be_v in_o one_o and_o the_o same_o plain_a with_o that_o which_o be_v within_o though_o the_o outtermost_a pipe_n be_v ten_o time_n great_a than_o that_o which_o be_v within_o the_o water_n natural_o will_v not_o run_v but_o if_o the_o plain_a of_o the_o water_n without_o be_v any_o part_n low_o than_o that_o which_o be_v within_o it_o will_v free_o run_v and_o here_o may_v be_v note_v further_o that_o if_o the_o mouth_n of_o the_o pipe_n which_o be_v full_a of_o water_n do_v but_o only_o touch_v the_o superficies_n of_o the_o water_n within_o although_o the_o other_o end_n of_o the_o pipe_n without_o be_v much_o low_a than_o that_o within_o the_o water_n it_o will_v not_o run_v at_o all_o which_o contradict_v the_o first_o ground_n hence_o we_o gather_v that_o the_o pressure_n or_o ponderosity_n of_o the_o water_n within_o be_v the_o cause_n of_o run_v in_o some_o respect_n problem_n thirty-nine_o of_o a_o glass_n very_o pleasant_a sometime_o there_o be_v glass_n which_o be_v make_v of_o a_o double_a fashion_n as_o if_o one_o glass_n be_v within_o another_o so_o that_o they_o seem_v but_o one_o but_o there_o be_v a_o little_a space_n between_o they_o noâ—_n pour_v wine_n or_o other_o liquor_n between_o the_o two_o edge_n by_o help_n of_o a_o tunnell_n into_o a_o little_a hole_n leave_v to_o this_o end_n so_o will_v there_o appear_v two_o fine_a delusion_n or_o fallacy_n for_o though_o there_o be_v not_o a_o drop_n of_o wine_n within_o the_o hollow_v of_o the_o glass_n it_o will_v seem_v to_o those_o which_o behold_v it_o that_o it_o be_v a_o ordinary_a glass_n full_a of_o wine_n and_o that_o especial_o to_o those_o which_o be_v side-wise_a of_o it_o and_o if_o any_o one_o move_v it_o it_o will_v much_o confirm_v it_o because_o of_o the_o motion_n of_o the_o wine_n but_o that_o which_o will_v give_v most_o delight_n be_v that_o if_o any_o one_o shall_v take_v the_o glass_n and_o put_v it_o to_o his_o mouth_n shall_v think_v to_o drink_v the_o wine_n instead_o of_o which_o he_o shall_v sup_v the_o air_n and_o so_o will_v cause_v laughter_n to_o those_o that_o stand_v by_o who_o be_v deceive_v will_v hold_v the_o glass_n to_o the_o light_n &_o thereby_o consider_v that_o the_o ray_n or_o beam_n of_o the_o light_n be_v not_o reflect_v to_o the_o eye_n
same_o time_n take_v heed_n to_o the_o part_n about_o it_o and_o choose_v one_o only_a point_n which_o be_v equal_a distant_a from_o a_o infinite_a of_o other_o point_n which_o be_v in_o the_o circumference_n which_o be_v very_o difficult_a aristotle_n confirm_v this_o among_o his_o moral_n and_o seem_v to_o explain_v the_o difficulty_n which_o be_v to_o be_v find_v in_o the_o middle_n of_o virtue_n for_o it_o may_v want_v a_o thousand_o way_n and_o be_v far_o separate_v from_o the_o true_a centre_n of_o the_o end_n of_o a_o right_a mediocrity_n of_o a_o virtuous_a action_n for_o to_o do_v well_o it_o must_v touch_v the_o middle_a point_n which_o be_v but_o one_o and_o there_o must_v be_v a_o true_a point_n which_o respect_v the_o end_n and_o that_o be_v but_o one_o only_a now_o to_o judge_v which_o be_v the_o most_o difficult_a as_o before_o be_v say_v either_o to_o draw_v the_o round_a or_o to_o find_v the_o centre_n the_o round_o seem_v to_o be_v hard_a than_o to_o find_v the_o centre_n because_o that_o in_o find_v of_o it_o it_o be_v do_v at_o once_o and_o have_v a_o equal_a distance_n from_o the_o whole_a but_o as_o before_o to_o draw_v a_o round_a there_o be_v a_o visible_a point_n imagine_v about_o which_o the_o circle_n be_v to_o be_v draw_v i_o esteem_v that_o it_o be_v as_o difficult_a therefore_o if_o not_o more_o to_o make_v the_o circle_n without_o a_o centre_n as_o to_o find_v the_o middle_n or_o centre_n of_o that_o circle_n problem_n lvii_o any_o one_o have_v take_v 3_o card_n to_o find_v how_o many_o point_n they_o contain_v this_o be_v to_o be_v exercise_v upon_o a_o full_a pack_n of_o card_n of_o 52_o then_o let_v one_o choose_v any_o three_o at_o pleasure_n secret_o from_o your_o sight_n and_o bid_v he_o secret_o account_v the_o point_n in_o each_o card_n and_o will_v he_o to_o take_v as_o many_o card_n as_o will_v make_v up_o 15_o to_o each_o of_o the_o point_n of_o his_o card_n then_o will_v he_o to_o give_v you_o the_o rest_n of_o the_o card_n for_o 4_o of_o they_o be_v reject_v the_o rest_n show_v the_o number_n of_o point_n that_o his_o three_o card_n which_o he_o take_v at_o the_o first_o do_v contain_v as_o if_o the_o 3_o card_n be_v 7_o 10_o and_o 4_o now_o 7_o want_n of_o 15_o 8._o take_v 8_o card_n therefore_o for_o your_o first_o card_n the_o 10_o want_n of_o 15_o 5_o take_z 5_o card_n for_o your_o second_o card_n last_o 4_o want_n of_o 15_o 11_o take_v 11_o card_n for_o your_o three_o card_n &_o give_v he_o the_o rest_n of_o the_o card_n there_o will_v be_v 25_o from_o which_o take_v 4_o there_o remain_v 21_o the_o number_n of_o the_o three_o card_n take_v viz._n 7_o 10_o and_o 4._o whosoever_o will_v practice_v this_o play_n with_o 4_o 5_o 6_o or_o more_o card_n and_o that_o the_o whole_a number_n of_o card_n be_v more_o or_o less_o than_o 52_o and_o that_o the_o term_n be_v 15_o 14_o 12_o &c_n &c_n this_o general_a rule_n ensue_a may_v serve_v multiply_v the_o term_n by_o the_o number_n of_o card_n take_v at_o first_o to_o the_o product_n add_v the_o number_n of_o card_n take_v then_o subtract_v this_o sum_n from_o the_o whole_a number_n of_o card_n the_o remainder_n be_v the_o number_n which_o must_v be_v subtract_v from_o the_o card_n which_o remain_v to_o make_v up_o the_o game_n if_o there_o remain_v nothing_o after_o the_o subtraction_n than_o the_o number_n of_o card_n remain_v do_v just_o show_v the_o number_n of_o point_n which_o be_v in_o the_o card_n choose_v if_o the_o subtraction_n can_v be_v make_v then_o subtract_v the_o number_n of_o card_n from_o that_o number_n and_o the_o remainder_n add_v unto_o the_o card_n that_o do_v remain_v the_o sum_n will_v be_v the_o number_n of_o point_n in_o the_o card_n take_v as_o if_o the_o card_n be_v 7_o 10_o 5_o 8_o and_o the_o term_v give_v be_v 12_o so_o the_o first_o want_v 5_o the_o second_o want_v 2_o the_o three_o want_v 7_o and_o the_o four_o want_v 4_o card_n which_o take_v the_o party_n give_v you_o the_o rest_n of_o the_o 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 scorn_v as_o it_o be_v all_o small_a and_o trivial_a service_n as_o leave_v they_o to_o a_o inferior_a help_n great_a use_n may_v be_v make_v of_o this_o glass_n in_o discover_v of_o ship_n army_n etc._n etc._n now_o the_o apparel_n or_o part_n of_o this_o instrument_n or_o glass_n be_v very_o mean_a or_o simple_a which_o make_v it_o the_o more_o admirable_a see_v it_o perform_v such_o great_a service_n have_v but_o a_o convex_a glass_n thick_a in_o the_o middle_n to_o unite_v and_o amass_n the_o ray_n and_o make_v the_o object_n the_o great_a to_o the_o augment_v the_o visual_a angle_n as_o also_o a_o pipe_n or_o trunk_n to_o amass_o the_o species_n and_o hinder_v the_o greatness_n of_o the_o light_n which_o be_v about_o it_o to_o see_v well_o the_o object_n must_v be_v well_o enlighten_v and_o the_o eye_n in_o obscurity_n then_o there_o be_v adjoin_v unto_o it_o a_o glass_n of_o a_o short_a sight_n to_o distinguish_v the_o ray_n which_o the_o other_o will_v make_v more_o confuse_v 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have_v ever_o think_v that_o a_o brute_n stone_n black_a and_o ill_o form_v touch_v a_o ring_n of_o iron_n shall_v hang_v it_o in_o the_o air_n and_o that_o ring_v support_v a_o second_o that_o to_o support_v a_o three_o and_o so_o unto_o 10_o 12_o or_o more_o according_a to_o the_o strength_n of_o the_o magnes_fw-la make_v as_o it_o be_v a_o chain_n without_o a_o line_n without_o soulder_v together_o or_o without_o any_o other_o thing_n to_o support_v they_o only_o but_o a_o most_o occult_a and_o hide_a virtue_n yet_o most_o evident_a in_o this_o effect_n which_o penetrate_v insensible_o from_o the_o first_o to_o the_o second_o from_o the_o second_o to_o the_o three_o etc._n etc._n what_o be_v there_o in_o the_o world_n that_o be_v more_o capable_a to_o cast_v a_o deep_a astonishment_n in_o our_o mind_n than_o a_o great_a massy_a substance_n of_o iron_n to_o hang_v in_o the_o air_n in_o the_o midst_n of_o a_o build_n without_o any_o thing_n in_o the_o world_n touch_v it_o only_o but_o 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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 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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
of_o square_a form_n nvmber_n have_v a_o admirable_a secrecy_n diverse_o apply_v as_o before_o in_o part_n be_v show_v and_o here_o i_o will_v say_v something_o by_o way_n of_o transmutation_n of_o number_n it_o be_v answer_v thus_o in_o the_o first_o form_n the_o man_n be_v as_o the_o figure_n a_o than_o each_o of_o these_o 4_o soldier_n place_v themselves_o at_o each_o gate_n and_o remove_v one_o man_n from_o each_o angle_n to_o each_o gate_n then_o will_v they_o be_v also_o 9_o in_o each_o side_n according_a to_o the_o figure_n b._n last_o these_o 4_o soldier_n at_o the_o gate_n take_v away_o each_o one_o his_o comrade_n and_o place_v two_o of_o these_o man_n which_o be_v at_o each_o gate_n to_o each_o angle_n there_o will_v be_v still_o 9_o for_o each_o side_n of_o the_o square_n according_a to_o the_o figure_n c._n in_o like_a manner_n if_o there_o be_v 12_o man_n how_o may_v they_o be_v place_v about_o a_o square_n that_o the_o first_o side_n shall_v have_v 3_o every_o way_n then_o disorder_v so_o that_o they_o may_v be_v 4_o every_o way_n and_o last_o be_v transport_v may_v make_v 5_o every_o way_n &_o this_o be_v according_a to_o the_o figure_n f._n g.h_o problem_n lxxiii_o how_o to_o make_v the_o string_n of_o a_o viol_n sensible_o shake_v without_o any_o one_o touch_v it_o this_o be_v a_o miracle_n in_o music_n yet_o easy_a to_o be_v experiment_a take_v a_o viol_n or_o other_o instrument_n and_o choose_v two_o string_n so_o that_o there_o be_v one_o between_o they_o make_v these_o two_o string_n agree_v in_o one_o and_o the_o same_o tune_n then_o move_v the_o viole-bowe_n upon_o the_o great_a string_n and_o you_o shall_v see_v a_o wonder_n for_o in_o the_o same_o time_n that_o that_o shake_v which_o you_o play_v upon_o the_o other_o will_v likewise_o sensible_o shake_v without_o any_o one_o touch_v it_o and_o it_o be_v more_o admirable_a that_o the_o string_n which_o be_v between_o they_o will_v not_o shake_v at_o all_o and_o if_o you_o put_v the_o first_o string_n to_o another_o tune_n or_o note_n and_o lose_v the_o pin_n of_o the_o string_n or_o stop_v it_o with_o your_o finger_n in_o any_o fret_n the_o other_o string_n will_v not_o shake_v and_o the_o same_o will_v happen_v if_o you_o take_v two_o viol_n and_o strike_v upon_o a_o string_n of_o the_o one_o the_o string_n of_o the_o other_o will_v sensible_o shake_v now_o it_o may_v be_v demand_v how_o come_v this_o shake_n be_v it_o in_o the_o occult_a sympathy_n or_o be_v it_o in_o the_o string_n be_v wind_v up_o to_o like_a note_n or_o tune_n that_o so_o easy_o the_o other_o may_v receive_v the_o impression_n of_o the_o air_n which_o be_v agitate_a or_o move_v by_o the_o shake_n or_o the_o tremble_n of_o the_o other_o &_o whence_o be_v it_o that_o the_o viole-bowe_n move_v upon_o the_o first_o string_n do_v instant_o in_o the_o same_o time_n move_v the_o three_o string_n and_o not_o the_o second_o if_o the_o cause_n be_v not_o either_o in_o the_o first_o or_o second_o i_o leave_v to_o other_o to_o descant_v on_o examination_n in_o this_o examination_n we_o have_v something_o else_o to_o imagine_v than_o the_o bare_a sympathy_n of_o the_o cord_n one_o to_o another_o for_o first_o there_o aught_o to_o be_v consider_v the_o different_a effect_n that_o it_o produce_v by_o extension_n upon_o one_o and_o the_o same_o cord_n in_o capacity_n then_o what_o may_v be_v produce_v upon_o different_a cord_n of_o length_n and_o bigness_n to_o make_v they_o accord_v in_o a_o unisone_n or_o octavo_fw-la or_o some_o consort_n intermediate_v this_o be_v natural_o examine_v it_o will_v be_v facile_a to_o lay_v open_a a_o way_n to_o the_o knowledge_n of_o the_o true_a and_o immediate_a cause_n of_o this_o noble_a and_o admirable_a phaenomeny_n now_o this_o will_v sensible_o appear_v when_o the_o cord_n be_v of_o equal_a length_n and_o greatness_n and_o set_v to_o a_o unisone_n but_o when_o the_o cord_n differ_v from_o their_o equality_n it_o will_v be_v less_o sensible_a hence_o in_o one_o and_o the_o same_o instrument_n cord_n at_o a_o unisone_n shall_v excite_v or_o shake_v more_o than_o that_o which_o be_v at_o a_o octavo_fw-la and_o more_o than_o those_o which_o be_v of_o a_o intermediate_v proportional_a consort_n as_o for_o the_o other_o consort_n they_o be_v not_o exempt_v though_o the_o effect_n be_v not_o so_o sensible_a yet_o more_o in_o one_o than_o in_o another_o and_o the_o experiment_n will_v seem_v more_o admirable_a in_o take_v 2_o lute_n viol_n etc._n etc._n &_o in_o set_v they_o to_o one_o tune_n for_o then_o in_o touch_v the_o cord_n of_o the_o one_o it_o will_v give_v a_o sensible_a motion_n to_o the_o cord_n of_o the_o other_o and_o not_o only_o so_o but_o also_o a_o harmony_n problem_n lxxiiii_o of_o a_o vessel_n which_o contain_v three_o several_a kind_n of_o liquor_n all_o put_v in_o at_o one_o bunghole_n and_o draw_v out_o at_o one_o tap_n several_o without_o mixture_n the_o vessel_n be_v thus_o make_v it_o must_v be_v divide_v 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up_o like_o a_o ordinary_a lookingglass_n have_v a_o image_n in_o the_o middle_n in_o this_o respect_n it_o will_v be_v sufficient_o pleasant_a and_o that_o which_o will_v admire_v the_o ignorant_a and_o able_a to_o exercise_v the_o most_o subtle_a and_o that_o principal_o if_o the_o glass_n be_v in_o a_o obscure_a place_n and_o the_o light_n which_o be_v give_v to_o it_o be_v somewhat_o far_o off_o place_v a_o glass_n near_o the_o floor_n of_o a_o chamber_n &_o make_v a_o hole_n through_o the_o place_n under_o the_o glass_n so_o that_o those_o which_o be_v below_o may_v not_o perceive_v it_o and_o dispose_v a_o bright_a image_n under_o the_o hole_n so_o that_o it_o may_v cast_v his_o species_n upon_o the_o glass_n and_o it_o will_v cause_v admiration_n to_o those_o which_o be_v below_o that_o know_v not_o the_o cause_n the_o same_o may_v be_v do_v by_o place_v the_o image_n in_o a_o chamber_n adjoin_v and_o so_o make_v it_o to_o be_v see_v upon_o the_o side_n of_o the_o wall_n 14_o in_o these_o channel-image_n which_o show_v one_o side_n a_o death_n head_n &_o another_o side_n a_o fair_a face_n and_o right_o before_o some_o other_o thing_n it_o be_v a_o thing_n evident_a that_o set_v a_o plain_a glass_n sidewise_o to_o this_o image_n you_o shall_v see_v it_o in_o a_o contrary_a thing_n then_o that_o which_o be_v present_v before_o sidewise_o 15_o last_o it_o be_v a_o fine_a secret_a to_o present_v unto_o a_o plain_a glass_n write_v with_o such_o industry_n that_o one_o may_v read_v it_o in_o the_o glass_n and_o yet_o out_o of_o the_o glass_n there_o be_v nothing_o to_o be_v know_v which_o will_v thus_o happen_v if_o the_o writing_n be_v write_v backward_o but_o that_o which_o be_v more_o strange_a to_o show_v a_o kind_n of_o write_v to_o a_o plain_a glass_n it_o shall_v appear_v another_o kind_n of_o writing_n both_o against_o sense_n and_o form_n as_o if_o there_o be_v present_v to_o the_o glass_n well_o it_o will_v show_v it_o meet_v if_o it_o be_v write_v thus_o miv_o and_o present_v to_o the_o glass_n it_o will_v appear_v thus_o vim_fw-la for_o in_o the_o first_o if_o the_o glass_n lie_v flat_a than_o the_o thing_n be_v inverse_v that_o be_v perpendicular_a to_o the_o glass_n if_o the_o glass_n and_o the_o object_n be_v upright_o then_o that_o on_o the_o right_a hand_n be_v turn_v to_o the_o left_a as_o in_o the_o latter_a and_o here_o i_o cease_v to_o speak_v further_o of_o these_o plain_a glass_n either_o of_o the_o admirable_a multiplication_n or_o appearance_n which_o be_v make_v in_o a_o great_a number_n of_o they_o for_o to_o content_v the_o sight_n in_o this_o particular_a one_o must_v have_v recourse_n to_o the_o cabinet_n of_o great_a personage_n who_o enrich_v themselves_o with_o most_o beautiful_a one_o experiment_n upon_o gibbous_a or_o convex_v spherical_a glass_n if_o they_o be_v in_o the_o form_n of_o a_o bowl_n or_o part_n of_o a_o great_a globe_n of_o glass_n there_o be_v singular_a contentment_n to_o contemplate_v on_o they_o first_o because_o they_o present_v the_o object_n less_o and_o more_o gracious_a and_o by_o how_o much_o more_o the_o image_n be_v separate_v from_o the_o glass_n by_o so_o much_o the_o more_o they_o diminish_v in_o magnitude_n second_o they_o that_o show_v the_o image_n plait_v or_o fold_v which_o be_v very_o pleasant_a especial_o when_o the_o glass_n be_v place_v down_o and_o behold_v in_o it_o some_o blanch_a feel_a etc._n etc._n the_o upper_a part_n of_o a_o gallery_n the_o porch_n of_o a_o hall_n etc._n etc._n for_o they_o will_v be_v represent_v as_o a_o great_a vessel_n have_v more_o belly_n in_o the_o middle_n then_o at_o the_o two_o end_n and_o post_n and_o joist_n of_o timber_n will_v
seem_v as_o circle_n three_o that_o which_o ravish_v the_o spirit_n by_o the_o eye_n and_o which_o shame_v the_o best_a perspective_n paint_v that_o a_o painter_n can_v make_v be_v the_o beautiful_a contraction_n of_o the_o image_n that_o appear_v within_o the_o sphericity_n of_o these_o small_a glass_n for_o present_v the_o glass_n to_o the_o low_a end_n of_o a_o gallery_n or_o at_o the_o corner_n of_o a_o great_a court_n full_a of_o people_n or_o towards_o a_o great_a street_n church_n fortification_n a_o army_n of_o man_n to_o a_o whole_a city_n all_o the_o fair_a architecture_n and_o appearance_n will_v be_v see_v contract_v within_o the_o circuit_n of_o the_o glass_n with_o such_o variety_n of_o colour_n and_o distinction_n in_o the_o lesser_a part_n that_o i_o know_v not_o in_o the_o world_n what_o be_v more_o agreeable_a to_o the_o sight_n and_o pleasant_a to_o behold_v in_o which_o you_o will_v not_o have_v a_o exact_a proportion_n but_o it_o will_v be_v variable_a according_a to_o the_o distance_n of_o the_o object_n from_o the_o glass_n exptriment_n upon_o hollow_a or_o concave_a spherical_a glass_n i_o have_v heretofore_o speak_v how_o they_o may_v burn_v be_v make_v of_o glass_n or_o metal_n it_o remain_v now_o that_o i_o deliver_v some_o pleasant_a use_n of_o they_o which_o they_o represent_v unto_o our_o sight_n and_o so_o much_o the_o more_o notable_a it_o will_v be_v by_o how_o much_o the_o great_a the_o glass_n be_v and_o the_o globe_n from_o whence_o it_o be_v extract_v for_o it_o must_v in_o proportion_n as_o a_o segment_n of_o some_o be_v make_v circle_n or_o orb_n examination_n in_o this_o we_o may_v observe_v that_o a_o section_n of_o 2.3_o or_o 4._o inch_n in_o diameter_n may_v be_v segment_n of_o sphere_n of_o 2.3_o or_o 4._o foot_n â—_o nay_o of_o so_o many_o fathom_n for_o it_o be_v certain_a that_o among_o those_o which_o comprehend_v a_o great_a portion_n of_o a_o lesser_a sphere_n and_o those_o which_o comprehend_v a_o little_a segment_n 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the_o ancient_n who_o be_v not_o sufficient_o circumspect_a in_o experience_n upon_o which_o the_o principle_n of_o this_o subâ—ect_a aught_o to_o be_v build_v anâ—_n search_v not_o full_o into_o the_o true_a cause_n of_o these_o appearance_n see_v they_o leave_v unto_o posterity_n many_o 〈◊〉_d in_o their_o write_n â—nd_v those_o that_o follow_v they_o for_o the_o most_o part_n fall_v into_o the_o like_a error_n as_o for_o the_o jmage_n to_o bidâ—_n in_o the_o eye_n it_o can_v be_v but_o be_v impertinent_a and_o absurd_a but_o it_o follow_v that_o by_o how_o much_o near_o the_o obâ—ect_n approach_v to_o the_o glass_n by_o so_o much_o the_o more_o the_o appearance_n seem_v to_o come_v to_o the_o eye_n and_o if_o the_o eye_n be_v without_o the_o point_n of_o concourse_n and_o the_o object_n also_o as_o long_o as_o the_o object_n approach_v thereto_o the_o representation_n of_o the_o image_n come_v near_o the_o eye_n but_o pass_v the_o point_n of_o concourse_n it_o go_v back_o again_o 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there_o intermix_v themselves_o sometime_o in_o the_o air_n sometime_o in_o the_o planch_a one_o among_o another_o like_o the_o crawl_a of_o serpent_n continue_v for_o a_o pretty_a while_n in_o this_o posture_n and_o in_o extinguish_v every_o one_o will_v give_v his_o report_n like_o a_o pistol_n this_o will_v not_o a_o little_a astonish_v some_o think_v the_o house_n will_v be_v fire_v though_o the_o whole_a powder_n together_o make_v not_o a_o ounce_n and_o have_v no_o strength_n to_o do_v such_o a_o effect_n how_o to_o make_v fire_n run_v up_o and_o down_o forward_o and_o backward_o take_v small_a rocket_n and_o place_v the_o tail_n of_o one_o to_o the_o head_n of_o the_o other_o upon_o a_o cord_n according_a to_o your_o fancy_n as_o admit_v the_o cord_n to_o be_v abcdefg_v give_v fire_n to_o the_o rocket_n at_o a_o which_o will_v fly_v to_o b_o which_o will_v come_v back_o again_o to_o a_o and_o fire_z another_o at_z c_z that_o will_v fly_v at_o d_o which_o will_v fire_v another_o 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circle_n place_n your_o rocket_n to_o which_o you_o may_v place_v lance_n of_o fire_n between_o each_o rocket_n let_v this_o wheel_n be_v place_v upon_o a_o standard_n as_o here_o be_v represent_v and_o place_v a_o piece_n of_o primer_n from_o one_o lance_n to_o another_o then_o give_v fire_n at_o g_o which_o will_v fire_v f_o that_o b_o that_o will_v fire_v d_o that_z c_o and_o that_o will_v fire_v the_o rocket_n at_o a_o than_o immediate_o the_o wheel_n will_v begin_v to_o move_v and_o represent_v unto_o the_o spectator_n a_o circle_n of_o changeable_a fire_n and_o if_o pot_n of_o fire_n be_v tie_v to_o it_o you_o will_v have_v fine_a sport_n in_o the_o turn_n of_o the_o wheel_n and_o cast_v out_o of_o the_o serpent_n of_o night-combatant_n club_n target_n faulchon_n and_o mace_n charge_v with_o several_a fire_n do_v make_v your_o night-combatant_n or_o be_v use_v to_o make_v place_n among_o a_o throng_n of_o people_n the_o club_n at_o the_o end_n be_v make_v like_o a_o round_a 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the_o common_a people_n w_o ch_o be_v stander_n by_o for_o those_o pot_n be_v fill_v with_o ball_n of_o fire_n and_o fly_a serpent_n for_o the_o air_n they_o will_v so_o intermix_v one_o within_o another_o in_o fly_v here_o and_o there_o a_o little_a above_o the_o ground_n and_o give_v such_o a_o volley_n of_o report_n that_o the_o air_n will_v rebound_v with_o their_o noise_n and_o the_o whole_a place_n be_v fill_v with_o sundry_a stream_n of_o pleasant_a fire_n which_o serpent_n will_v much_o occupy_v these_o about_o the_o place_n to_o defend_v themselves_o in_o their_o upper_a part_n when_o they_o will_v no_o less_o be_v busy_v by_o the_o ball_n of_o fire_n which_o seem_v to_o annoy_v their_o