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 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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 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by_o a_o little_a hole_n in_o the_o window_n upon_o the_o wall_n or_o ceiling_n of_o the_o chamber_n examination_n in_o this_o there_o be_v two_o experiment_n considerable_a the_o first_o be_v with_o a_o very_a little_a glass_n place_v so_o that_o it_o may_v be_v open_a to_o the_o beam_n of_o the_o sun_n the_o other_o have_v respect_n to_o a_o spacious_a or_o great_a glass_n place_v to_o a_o very_a little_a hole_n so_o that_o the_o sun_n may_v shine_v on_o it_o for_o then_o the_o shadow_n which_o be_v cast_v upon_o the_o dial_n be_v convert_v into_o beam_n of_o the_o sun_n and_o will_v reflect_v and_o beca_v upon_o a_o plain_a opposite_a and_o in_o the_o other_o it_o be_v a_o hole_n in_o the_o window_n or_o such_o like_a by_o which_o may_v pass_v the_o beam_n of_o the_o sun_n which_o represent_v the_o extremity_n of_o the_o style_n &_o the_o glass_n represent_v the_o plain_a of_o the_o dial_n upon_o which_o the_o beam_n be_v in_o manner_n of_o shadow_n reflect_v cast_v upon_o a_o 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the_o water_n itself_o which_o fall_v within_o it_o will_v show_v what_o of_o the_o clock_n it_o be_v far_o better_o than_o the_o run_n of_o sand_n for_o by_o this_o may_v you_o have_v the_o part_n of_o the_o hour_n most_o accurate_a which_o common_o by_o sand_n be_v not_o have_v and_o to_o which_o may_v be_v add_v the_o hour_n of_o other_o country_n with_o great_a ease_n and_o here_o note_v that_o as_o soon_o as_o the_o water_n be_v out_o of_o one_o of_o the_o glass_n you_o may_v turn_v it_o over_o into_o the_o same_o again_o out_o of_o the_o other_o and_o so_o let_v it_o run_v anew_o problem_n lxxxiii_o of_o cannon_n or_o great_a artillery_n soldier_n and_o other_o will_v willing_o see_v 〈◊〉_d problem_n which_o contain_v three_o or_o four_o subtle_a question_n the_o first_o be_v how_o to_o charge_v a_o cannon_n without_o powder_n this_o may_v be_v do_v with_o air_n and_o water_n only_o have_v throw_v cold_a water_n into_o the_o cannon_n which_o may_v be_v squirt_v forcible_o in_o by_o the_o closure_n of_o the_o mouth_n of_o the_o piece_n that_o so_o by_o this_o pressure_n the_o air_n may_v more_o condense_a then_o have_v a_o round_a piece_n of_o wood_n very_o just_a and_o oil_v well_o for_o the_o better_a to_o slide_v and_o thrust_v the_o bullet_n when_o it_o shall_v be_v time_n this_o piece_n of_o wood_n may_v be_v hold_v fast_o with_o some_o pole_n for_o fear_v it_o be_v not_o thrust_v out_o before_o his_o time_n then_o let_v fire_n be_v make_v about_o the_o trunion_n or_o hinder_v part_n of_o the_o piece_n to_o heat_v the_o air_n and_o water_n and_o then_o when_o one_o will_v shoot_v it_o let_v the_o pole_n be_v quick_o loosen_v for_o then_o the_o air_n search_v a_o great_a place_n and_o have_v way_n now_o offer_v will_v thrust_v out_o the_o wood_n and_o the_o bullet_n very_o quick_a the_o experiment_n which_o we_o have_v in_o long_a trunk_n shoot_v out_o pellat_n with_o air_n only_o show_v the_o verity_n of_o this_o problem_n 2_o in_o the_o second_o question_n it_o may_v be_v demand_v how_o much_o time_n do_v the_o bullâ—â—_n of_o a_o cannon_n spend_v in_o the_o air_n before_o iâ—_n fall_v to_o the_o ground_n the_o resolution_n of_o this_o question_n depend_v upon_o the_o goodness_n of_o the_o piece_n &_o charge_n thereof_o see_v in_o each_o there_o be_v great_a difference_n it_o be_v report_v that_o tichâ—_n braâ—e_n and_o the_o landsgrave_n do_v make_v a_o experiment_n upon_o a_o cannon_n in_o germany_n which_o be_v charge_v and_o shoot_v off_o the_o bullet_n spend_v two_o minute_n of_o time_n in_o the_o air_n before_o it_o fall_v and_o the_o distance_n be_v a_o german_a mile_n which_o distance_n proportionated_a to_o a_o hour_n time_n make_v 120_o italian_a mile_n 3._o in_o the_o three_o question_n it_o may_v be_v ask_v how_o it_o come_v to_o pass_v that_o a_o cannon_n shoot_v upward_o the_o bullet_n fly_v with_o more_o violence_n than_o be_v shoot_v pointblank_a or_o shoot_v downward_o if_o we_o regard_v the_o effect_n of_o a_o cannon_n when_o it_o be_v to_o batter_v a_o wall_n the_o question_n be_v false_a see_v it_o be_v most_o evident_a that_o the_o blow_n which_o fall_v perpendicular_a upon_o a_o wall_n be_v more_o violent_a than_o those_o which_o strike_v byas-wise_a or_o glaunse_o but_o consider_v the_o strength_n of_o the_o blow_n only_o the_o question_n be_v most_o true_a and_o often_o experiment_v to_o be_v find_v true_a a_o piece_n mount_v at_o the_o best_a of_o the_o random_n which_o be_v near_o half_a of_o the_o right_n convey_v her_o bullet_n with_o a_o far_o great_a violence_n than_o that_o which_o be_v shoot_v at_o point_n blank_a or_o mount_v parallel_n to_o the_o horizon_n the_o common_a reason_n be_v that_o shoot_v high_a the_o fire_n carry_v the_o bowl_n a_o long_a time_n in_o the_o air_n and_o the_o air_n move_v more_o facile_a upward_o than_o downwards_o because_o that_o the_o airy_a circle_n that_o the_o motion_n of_o the_o bullet_n make_v be_v soon_o break_v howsoever_o this_o be_v the_o general_a tenet_n it_o be_v curious_a to_o find_v out_o the_o inequality_n of_o move_v of_o the_o air_n whether_o the_o bullet_n fly_v upward_a downward_n or_o right_v forward_o to_o produce_v a_o sensible_a dfference_n of_o motion_n &_o some_o think_v that_o the_o cannon_n be_v mount_v the_o bullet_n press_v the_o powder_n make_v a_o great_a resistance_n and_o so_o cause_v all_o the_o powder_n to_o be_v inflame_v before_o the_o bullet_n be_v throw_v out_o which_o make_v it_o to_o be_v more_o violent_a than_o otherwise_o it_o will_v be_v when_o the_o cannon_n be_v otherwise_o dispose_v the_o contrary_a arrive_v the_o fire_n leave_v the_o bullet_n and_o the_o bullet_n roll_v from_o the_o powder_n resist_v less_o and_o it_o be_v usual_o see_v that_o shoot_v out_o of_o a_o musket_n charge_v only_o with_o powder_n to_o shoot_v to_o a_o mark_n of_o paper_n place_v point_n blank_a that_o there_o be_v see_v many_o small_a hole_n in_o the_o paper_n which_o can_v be_v other_o than_o the_o grain_n of_o powder_n which_o do_v not_o take_v fire_n but_o this_o latter_a accident_n may_v happen_v from_o the_o overcharging_a of_o the_o piece_n or_o the_o length_n of_o it_o or_o windy_a or_o dampenesse_n of_o the_o powder_n from_o which_o some_o may_v think_v that_o a_o cannon_n point_v right_a to_o the_o zenith_n shall_v shoot_v with_o great_a violence_n then_o in_o any_o other_o mount_n or_o form_n whatsoever_o and_o by_o some_o it_o have_v be_v imagine_v that_o a_o bullet_n shoot_v in_o this_o fashion_n have_v be_v consume_v melt_v and_o lose_v in_o the_o air_n by_o reason_n of_o the_o violence_n of_o the_o blow_n and_o the_o activity_n of_o the_o sire_n and_o that_o
water_n 198_o 11_o to_o find_v the_o weight_n of_o water_n 199_o 12_o to_o find_v the_o charge_n that_o a_o vessel_n may_v carry_v as_o ship_n boat_n or_o such_o like_a 200_o 13_o how_o come_v it_o that_o a_o ship_n have_v safe_o sail_v in_o the_o vast_a ocean_n and_o be_v come_v into_o the_o port_n or_o harbour_n will_v sink_v down_o right_a 200_o 14_o how_o a_o gross_a body_n of_o metal_n may_v swim_v upon_o the_o water_n 201_o 15_o how_o to_o weigh_v the_o lightness_n of_o the_o air_n 203_o 16_o be_v give_v a_o body_n to_o mark_v it_o about_o and_o show_v how_o much_o of_o it_o will_v sink_v in_o the_o water_n or_o swim_v above_o the_o water_n 204_o 17_o to_o find_v how_o much_o several_a metal_n or_o other_o body_n do_v weigh_v less_o in_o the_o water_n than_o in_o the_o air_n 204_o 18_o how_o be_v it_o that_o a_o balance_n have_v like_o weight_n in_o each_o scale_n and_o hang_v in_o aequilibrio_fw-la in_o the_o air_n be_v remove_v from_o that_o place_n without_o diminish_v the_o weight_n in_o each_o balance_n or_o add_v to_o it_o it_o shall_v cease_v to_o hang_v in_o aequilibrio_fw-la sensible_o yea_o by_o a_o great_a difference_n of_o weight_n 205_o 19_o to_o show_v what_o water_n be_v heavy_a one_o than_o another_o and_o how_o much_o 206_o 20_o how_o to_o make_v a_o pound_n of_o water_n weigh_v as_o much_o as_o 10_o 20_o 30_o or_o a_o hundred_o pound_n of_o lead_n nay_o as_o much_o as_o a_o thousand_o or_o ten_o thousand_o pound_n weight_n 207_o prob._n 86._o of_o sundry_a question_n of_o arithmetic_n and_o first_o of_o the_o number_n of_o sand_n calculate_v by_o archimedes_n and_o clavius_n 208_o 2_o divers_a metal_n be_v melt_v together_o in_o one_o body_n to_o find_v the_o mixture_n of_o they_o 210_o 3_o a_o subtle_a question_n of_o three_o partner_n about_o equality_n of_o wine_n and_o vessel_n 213_o 4_o of_o a_o ladder_n which_o stand_v upright_o against_o a_o wall_n of_o 10_o foot_n high_a the_o foot_n of_o it_o be_v pull_v out_o 6_o foot_n from_o the_o wall_n upon_o the_o pavement_n how_o much_o have_v the_o top_n of_o the_o ladder_n descend_v 214_o prob._n 87_o witty_a suit_n or_o debate_n between_o caius_n and_o sempronius_n upon_o the_o form_n of_o figure_n which_o geometrician_n call_v isoperimeter_n or_o equal_a in_o circuit_n or_o compass_n 214_o 1_o incident_a of_o change_v a_o field_n of_o 6_o measure_n square_a for_o a_o long_o rectrangle_v fiel_n of_o 9_o measure_n in_o length_n and_o 3_o in_o breadth_n both_o equal_a in_o circuit_n but_o not_o in_o quantity_n 215_o 2_o incident_a about_o two_o sack_n each_o of_o they_o hoâ—ding_v but_o a_o bushel_n and_o yet_o be_v able_a to_o hold_v 4_o bushel_n 217_o 3_o incident_a show_v the_o deceit_n of_o pipe_n which_o conveygh_v water_n that_o a_o pipe_n of_o two_o inch_n diameter_n do_v cast_v out_o four_o time_n as_o much_o water_n as_o a_o pipe_n of_o one_o such_o diameter_n 218_o 7_o heap_n of_o corn_n of_o 10_o foot_n every_o way_n be_v not_o as_o much_o as_o one_o heap_n of_o corn_n of_o 20_o foot_n every_o way_n 218_o prob._n 88_o of_o sundry_a question_n in_o matter_n of_o cosmographie_n and_o astronomy_n in_o what_o place_n the_o middle_n of_o the_o earth_n be_v suppose_v to_o be_v 219_o of_o the_o depth_n of_o the_o earth_n and_o height_n of_o the_o heaven_n and_o the_o compass_n of_o the_o world_n how_o much_o 219_o how_o much_o the_o starry_a firmament_n the_o sun_n and_o the_o moon_n be_v distant_a from_o the_o centre_n of_o the_o earth_n 220_o how_o long_o a_o millstone_n will_v be_v in_o fall_v to_o the_o centre_n of_o the_o earth_n from_o the_o superficies_n if_o it_o may_v have_v passage_n thither_o 220_o how_o long_a time_n a_o man_n or_o a_o bird_n may_v be_v in_o compass_v the_o whole_a earth_n 220_o if_o a_o man_n shall_v ascend_v by_o supposition_n 20_o mile_n every_o day_n how_o long_o it_o will_v be_v before_o he_o approach_v to_o the_o moon_n 221_o the_o sun_n move_v more_o in_o one_o day_n than_o the_o moon_n in_o 20_o day_n 221_o if_o a_o millstone_n from_o the_o orb_n of_o the_o sun_n shall_v descend_v a_o thousand_o mile_n in_o a_o hour_n how_o long_o it_o will_v be_v before_o it_o come_v to_o the_o earth_n 221_o of_o the_o sun_n quick_a motion_n of_o more_o than_o 7500_o mile_n in_o one_o minute_n 221_o of_o the_o rapt_a and_o violent_a motion_n of_o the_o starry_a firmament_n which_o if_o a_o horseman_n shall_v ride_v every_o day_n 40_o mile_n he_o can_v not_o in_o a_o thousand_o year_n make_v such_o a_o distance_n as_o it_o move_v every_o hour_n 221_o to_o find_v the_o circle_n of_o the_o sun_n by_o the_o finger_n 223_o prob._n 93_o of_o find_v the_o new_a and_o full_a moon_n in_o each_o month_n 224_o prob._n 94_o to_o find_v the_o latitude_n of_o country_n 225_o prob._n 95_o of_o the_o climate_n of_o country_n and_o how_o to_o find_v they_o 225_o prob._n 96_o of_o longitude_n and_o latitude_n of_o the_o place_n of_o the_o earth_n and_o of_o the_o star_n of_o the_o heaven_n 227_o to_o find_v the_o longitude_n of_o a_o country_n 228_o of_o the_o latitude_n of_o a_o country_n 229_o to_o find_v the_o latitude_n of_o a_o country_n 230_o to_o find_v the_o distance_n of_o place_n 230_o of_o the_o longitude_n latitude_n declination_n and_o distance_n of_o the_o star_n 231_o how_o be_v it_o that_o two_o horse_n or_o other_o creature_n come_v into_o the_o world_n at_o one_o time_n and_o die_v at_o one_o and_o the_o same_o instant_n yet_o the_o one_o of_o they_o to_o be_v a_o day_n old_a than_o the_o other_o 232_o certain_a fine_a observation_n in_o what_o place_n of_o the_o world_n be_v it_o that_o the_o needle_n hang_v in_o aequilibrio_fw-la and_o vertical_a 233_o in_o what_o place_n of_o the_o world_n be_v it_o the_o sun_n be_v east_n or_o west_n but_o twice_o in_o the_o year_n 233_o in_o what_o place_n of_o the_o world_n be_v it_o that_o the_o sun_n longitude_n from_o the_o equinoctial_a paint_v and_o altitude_n be_v equal_a the_o sun_n be_v due_a east_n or_o west_n that_o the_o sun_n come_v twice_o to_o one_o point_n of_o the_o compass_n in_o the_o forenoon_n or_o afternoon_n 233_o that_o in_o some_o place_n of_o the_o world_n there_o be_v but_o two_o kind_n of_o wind_n all_o the_o year_n 233_o two_o ship_n may_v be_v two_o league_n asunder_o under_o the_o equinoctial_a and_o sail_a north_n at_o a_o certain_a parallel_n they_o will_v be_v but_o just_a half_a so_o much_o 233_o to_o what_o inhabitant_n and_o at_o what_o time_n the_o sun_n will_v touch_v the_o north-part_n of_o the_o horizon_n at_o midnight_n 234_o how_o a_o man_n may_v know_v in_o his_o navigation_n when_o he_o be_v under_o the_o equinoctial_a 234_o at_o what_o day_n in_o the_o year_n the_o extremity_n of_o the_o style_n shadow_n in_o a_o dial_n make_v a_o right_a line_n 234_o what_o height_n the_o sun_n be_v of_o and_o how_o far_o from_o the_o zenith_n or_o horizon_n when_o a_o man_n shadow_n be_v as_o long_o as_o his_o height_n 234_o prob._n 97_o to_o make_v a_o triangle_n that_o shall_v have_v three_o right_a angle_n 234_o prob._n 98_o to_o divide_v a_o line_n in_o as_o many_o part_n as_o one_o will_n without_o compass_n or_o without_o see_v of_o it_o 235_o prob._n 99_o to_o draw_v a_o line_n which_o shall_v incline_v to_o another_o line_n yet_o never_o meet_v against_o the_o axiom_n of_o parallel_n 236_o prob._n 100_o to_o find_v the_o variation_n of_o the_o compass_n by_o the_o sun_n shine_v 237_o prob._n 101_o to_o know_v which_o way_n the_o wind_n be_v in_o one_o chamber_n without_o go_v abroad_o 238_o prob._n 102_o how_o to_o draw_v a_o parallel_n spherical_a line_n with_o great_a ease_n 239_o prob._n 103_o to_o measure_n a_o height_n only_o by_o help_n of_o one_o hat_n 240_o prob._n 104_o to_o take_v a_o height_n with_o two_o straw_n 240_o in_o architecture_n how_o statue_n or_o other_o thing_n in_o high_a building_n shall_v bear_v a_o proportion_n to_o the_o eye_n below_o either_o equal_a double_a etc._n etc._n 242_o prob._n 106_o of_o deform_a figure_n which_o have_v no_o exact_a proportion_n where_o to_o place_v the_o eye_n to_o see_v they_o direct_v 243_o prob._n 107_o how_o a_o cannon_n that_o have_v shoot_v may_v be_v cover_v from_o the_o battery_n of_o the_o enemy_n 244_o prob._n 108_o of_o a_o fine_a lever_n by_o which_o one_o man_n alone_o may_v place_v a_o cannon_n upon_o his_o carriage_n 245_o prob._n 109_o how_o to_o make_v a_o clock_n with_o one_o wheel_n 246_o of_o water-work_n prob._n 110_o how_o a_o child_n may_v draw_v up_o a_o hogshead_n of_o water_n with_o ease_n 247_o prob._n 111_o of_o a_o ladder_n of_o cord_n to_o carry_v in_o one_o
pocket_n by_o which_o he_o may_v mount_v a_o wall_n or_o tower_n alone_o 248_o prob._n 112_o of_o a_o marvellous_a pump_n which_o draw_v up_o great_a quantity_n of_o water_n 249_o prob._n 113_o how_o natural_o to_o cause_v water_n to_o ascend_v out_o of_o a_o pit_n 250_o prob._n 114_o how_o to_o cast_a water_n out_o of_o a_o fountain_n very_o high_a 252_o prob._n 115_o how_o to_o empty_a the_o water_n of_o a_o pit_n by_o help_n of_o a_o cistern_n 253_o prob._n 116_o how_o to_o spout_n out_o water_n very_o high_a 253_o prob._n 117_o how_o to_o re-animate_a simple_n though_o bring_v a_o thousand_o mile_n 255_o prob._n 118_o how_o to_o make_v a_o perpetual_a motion_n 255_o prob._n 119_o of_o the_o admirable_a invention_n of_o make_v the_o philosopher_n tree_n which_o one_o may_v see_v to_o grow_v by_o little_a and_o little_a 256_o prob._n 120_o how_o to_o make_v the_o representation_n of_o the_o great_a world_n 257_o prob._n 121_o of_o a_o cone_n or_o pyramidal_a figure_n that_o move_v upon_o a_o table_n 258_o prob._n 122_o how_o a_o anvil_n may_v be_v cleaved_a by_o the_o blow_n of_o a_o pistol_n 258_o prob._n 123_o how_o a_o capon_n may_v be_v roast_v in_o a_o man_n travel_n at_o his_o saâ—â—le-bowe_n 259_o prob._n 124_o how_o a_o candle_n may_v be_v make_v to_o burn_v three_o time_n long_o than_o usual_o it_o do_v 259_o prob._n 125_o how_o to_o draw_v wine_n out_o of_o water_n 260_o prob._n 126_o of_o two_o marmouzet_n the_o one_o of_o which_o light_v a_o candle_n and_o the_o other_o blow_v it_o out_o 261_o prob._n 127_o how_o to_o make_v wine_n fresh_a without_o ice_n or_o snow_n in_o the_o height_n of_o summer_n 262_o prob._n 128_o to_o make_v a_o cement_n which_o last_v as_o marble_n resist_v air_n and_o water_n 262_o prob._n 129_o how_o to_o melt_v metal_n upon_o a_o shell_n with_o little_a fire_n 263_o prob._n 130_o of_o the_o harden_v of_o iron_n and_o steel_n 263_o prob._n 131_o to_o preserve_v fire_n as_o long_o as_o you_o will_v imitate_v the_o inextinguible_n fire_n of_o the_o vestales_fw-la 264_o finis_fw-la ad_fw-la authorem_fw-la d.d._n henricum_fw-la van_fw-mi etenium_fw-la alumnum_fw-la academiae_fw-la ponta_fw-la mousson_n ardua_fw-la walkeri_fw-la sileant_fw-la secreta_fw-la profundi_fw-la desinat_fw-la occultam_fw-la carpere_fw-la porta_n viam_fw-la itala_n cardani_n mirata_fw-la est_fw-la lampada_fw-la docti_fw-la terra_fw-la syracusium_fw-la graecia_n tota_fw-la senem_fw-la orbi_fw-la terrarum_fw-la ptolemaei_fw-la clepsydra_n toti_fw-la rara_fw-la dioptra_fw-la procli_n mira_fw-la fuêre_fw-la duo_fw-la anglia_fw-it te_fw-la foveat_fw-la doctus_fw-la pont-mousson_a alumnum_fw-la quidquid_fw-la naturae_fw-la qui_fw-la legis_fw-la hortus_fw-la habet_fw-la docta_fw-la coronet_n opus_fw-la doctum_fw-la te_fw-la sit_fw-la tua_fw-la docto_fw-la digna_fw-la syracusii_n arca_fw-la corona_fw-la viri_fw-la arca_n syracusiis_fw-la utinam_fw-la sit_fw-la plumbea_fw-la seruis_fw-la aurea_fw-la sed_fw-la dominis_fw-la aurea_fw-la tota_fw-la suis._n mathematical_a recreation_n problem_n i._o to_o find_v a_o number_n think_v upon_o bid_v he_o that_o he_o quadruple_a the_o number_n think_v upon_o that_o be_v multiply_v it_o by_o 4_o and_o unto_o it_o bid_v he_o to_o add_v 6_o 8_o 10_o or_o any_o number_n at_o pleasure_n and_o let_v he_o take_v the_o half_a of_o the_o sum_n then_o ask_v how_o much_o it_o come_v to_o for_o than_o if_o you_o take_v away_o half_a the_o number_n from_o it_o which_o you_o will_v he_o at_o first_o to_o add_v to_o it_o there_o shall_v remain_v the_o double_a of_o the_o number_n think_v upon_o example_n the_o number_n think_v upon_o 5_o the_o quadruple_a of_o it_o 20_o put_v 8_o unto_o it_o make_v 28_o the_o half_a of_o it_o be_v 14_o take_v away_o half_a the_o number_n add_v from_o it_o viz_o 4_o the_o rest_n be_v 10_o the_o double_a of_o the_o number_n think_v upon_o viz._n 10_o another_o way_n to_o find_v what_o number_n be_v think_v upon_o bid_v he_o which_o think_v double_a his_o number_n and_o unto_o that_o double_a add_v 4_o and_o bid_v he_o multiply_v that_o same_o product_n by_o 5_o and_o unto_o that_o product_n bid_v he_o add_v 12_o and_o multiply_v that_o last_o number_n by_o 10_o which_o be_v do_v easy_o by_o set_v a_o cypher_n at_o the_o end_n of_o the_o number_n then_o ask_v he_o the_o last_o number_n or_o product_v and_o from_o it_o secret_o subtract_v 320_o the_o remainder_n in_o the_o hundred_o place_n be_v the_o number_n think_v upon_o example_n the_o number_n think_v upon_o 7_o for_o which_o 700_o account_n only_o but_o the_o number_n of_o the_o hundred_o viz._n 7._o so_o have_v you_o the_o number_n think_v upon_o his_o double_a 14_o for_o which_o 700_o account_n only_o but_o the_o number_n of_o the_o hundred_o viz._n 7._o so_o have_v you_o the_o number_n think_v upon_o to_o it_o add_v 4_o make_v 18_o for_o which_o 700_o account_n only_o but_o the_o number_n of_o the_o hundred_o viz._n 7._o so_o have_v you_o the_o number_n think_v 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the_o party_n which_o think_v the_o number_n that_o he_o triple_a his_o thought_n and_o cause_v he_o to_o take_v the_o half_a of_o it_o if_o it_o be_v odd_a take_v the_o least_o half_a and_o put_v one_o unto_o it_o then_o will_v he_o to_o treble_v the_o half_a and_o take_v half_a of_o it_o as_o before_o last_o ask_v he_o how_o many_o nine_o there_o be_v in_o the_o last_o half_n and_o for_o every_o nine_o account_v four_o in_o your_o memory_n for_o that_o shall_v show_v the_o number_n think_v upon_o if_o both_o the_o triple_n be_v even_o but_o if_o it_o be_v odd_a at_o the_o first_o triple_a and_o euâ—n_o at_o the_o second_o for_o the_o one_o add_v unto_o the_o least_o half_o keep_v one_o in_o memory_n if_o the_o first_o triple_a be_v even_o and_o the_o second_o odd_a for_o the_o one_o add_v unto_o the_o least_o half_o keep_v two_o in_o memory_n last_o if_o at_o both_o time_n in_o tripling_n the_o number_n be_v odd_a for_o the_o two_o add_v unto_o the_o least_o half_n keep_v three_o in_o memory_n these_o caution_n observe_v and_o add_v unto_o as_o many_o four_o as_o the_o party_n say_v there_o be_v nine_o contain_v in_o the_o last_o half_n shall_v never_o fail_v you_o to_o declare_v or_o discern_v true_o what_o number_n be_v think_v upon_o example_n the_o number_n think_v upon_o 4_o or_o 7_o the_o triple_a 12_o or_o 21_o the_o half_a thereof_o 6_o or_o 10_o one_o put_v to_o it_o make_v 11_o the_o triple_a of_o the_o half_a 18_o or_o 33_o the_o half_a 9_o or_o 1â—_n one_o put_v to_o it_o make_v 17_o the_o number_n of_o nine_o in_o the_o last_o half_a 1_o or_o 1_o the_o first_o 1._o represent_v the_o 4._o number_n think_v upon_o and_o the_o last_o 1._o with_o the_o caution_n make_v 7._o the_o other_o number_n think_v upon_o note_n order_n your_o method_n so_o that_o you_o be_v not_o discover_v which_o to_o help_v you_o may_v with_o dexterity_n and_o industry_n make_v addition_n subtraction_n multiplication_n division_n etc._n etc._n and_o instead_o of_o ask_v how_o many_o nine_o there_o be_v you_o may_v ask_v how_o many_o eight_o ten_o etc._n etc._n there_o be_v or_o subtract_v 8.10_o etc._n etc._n from_o the_o number_n which_o remain_v for_o to_o find_v out_o the_o number_n think_v upon_o now_o touch_v the_o demonstration_n of_o the_o former_a direction_n and_o other_o which_o follow_v they_o depend_v upon_o the_o 2_o 7_o 8_o and_o 9_o book_n of_o the_o element_n of_o euclid_n upon_o which_o 2._o book_n &_o 4._o proposition_n this_o may_v be_v extract_v for_o these_o which_o be_v more_o learned_a for_o the_o find_n of_o any_o number_n that_o any_o one_o think_v on_o bid_v the_o party_n that_o think_v that_o he_o break_v the_o number_n think_v upon_o into_o any_o two_o part_n and_o unto_o the_o square_n of_o the_o part_n let_v he_o add_v the_o double_a product_n of_o the_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
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 and_o set_v one_o of_o they_o apart_o as_o 5._o unto_o 10_o add_v the_o point_n which_o be_v under_o 3_o and_o 2_o which_o be_v 4_o and_o 5_o and_o it_o make_v 19_o then_o cast_v these_o two_o dice_n suppose_v there_o shall_v appear_v 4_o and_o 1_o this_o add_v unto_o 19_o make_v 24._o and_o set_v one_o of_o these_o two_o dice_n apart_o as_o the_o 4._o unto_o the_o former_a 24_o i_o add_v the_o number_n of_o point_n which_o be_v under_o the_o other_o dice_n viz._n under_o 1_o that_o be_v 6_o which_o make_v 30._o last_o of_o all_o i_o throw_v that_o one_o dice_n and_o suppose_v there_o do_v appear_v 2_o which_o i_o add_v to_o the_o former_a 30_o and_o it_o make_v 32_o then_o leave_v the_o 3_o dice_n thus_o the_o point_n which_o be_v upward_o will_v be_v these_o 5_o 4_o 2_o unto_o which_o add_v secret_o 21_o as_o before_o be_v say_v so_o have_v you_o 32_o the_o same_o number_n which_o he_o have_v and_o in_o the_o same_o manner_n you_o may_v practice_v with_o 4_o 5_o 6_o or_o many_o dice_n or_o other_o body_n observe_v only_o that_o you_o must_v add_v the_o point_n opposite_a of_o the_o dice_n for_o upon_o which_o depend_v the_o whole_a demonstration_n or_o secret_a of_o the_o play_n for_o always_o that_o which_o be_v above_o and_o underneath_o make_v 7._o but_o if_o it_o make_v another_o number_n then_o must_v you_o add_v as_o often_o that_o number_n problem_n xlii_o two_o metal_n as_o gold_n and_o silver_n or_o of_o other_o kinâ—â—_n weigh_v alike_o be_v private_o place_v into_o two_o like_a box_n to_o find_v which_o of_o they_o the_o gold_n or_o silver_n be_v in_o but_o because_o that_o this_o experiment_n in_o water_n have_v divers_a accident_n and_o therefore_o subject_a to_o a_o caution_n and_o namely_o because_o the_o matter_n of_o the_o chest_n mettle_n or_o other_o thing_n may_v hinder_v behold_v here_o a_o more_o subtle_a and_o certain_a invention_n to_o find_v and_o discover_v it_o out_o without_o weigh_v it_o in_o the_o water_n now_o experience_n and_o reason_n show_v we_o that_o two_o like_a body_n or_o magnitude_n of_o equal_a weight_n and_o of_o divers_a metal_n be_v not_o of_o equal_a quantity_n and_o see_v that_o gold_n be_v the_o heavy_a of_o all_o metal_n it_o will_v occupy_v less_o room_n or_o place_n from_o which_o will_v follow_v that_o the_o like_a weight_n of_o lead_n in_o the_o same_o form_n will_v occupy_v or_o take_v up_o more_o room_n or_o place_n now_o let_v there_o be_v therefore_o present_v two_o globe_n or_o chest_n of_o wood_n or_o other_o matter_n alike_o &_o equal_a one_o to_o the_o other_o in_o one_o of_o which_o in_o the_o middle_n there_o be_v another_o globe_n or_o body_n of_o lead_n weigh_v 12._o l._n as_o c_o and_o in_o the_o other_o a_o globe_n or_o like_a body_n of_o gold_n weigh_v 12_o pound_n as_o b._n now_o it_o be_v suppose_v that_o the_o wooden_a globe_n or_o chest_n be_v of_o equal_a weight_n form_n and_o magnitude_n and_o to_o discover_v in_o which_o the_o gold_n or_o lead_n be_v in_o take_v a_o broad_a pair_n of_o compass_n and_o clip_v one_o of_o the_o coffer_n or_o globe_n somewhat_o from_o the_o middle_n as_o at_o d._n then_o fix_v in_o the_o chest_n or_o globe_n a_o small_a piece_n of_o iron_n between_o the_o foot_n of_o the_o compass_n as_o eke_o at_o the_o end_n of_o which_o hang_v a_o weight_n g_o so_o that_o the_o other_o end_n may_v be_v counterpoyse_v and_o hang_v in_o aequilibrio_fw-la and_o do_v the_o like_a to_o the_o other_o chest_n or_o globe_n now_o if_o that_o the_o other_o chest_n or_o globe_n be_v clip_v in_o like_a distance_n from_o the_o end_n and_o hang_v at_o the_o other_o end_n the_o same_o weight_n g._n there_o be_v find_v no_o difference_n then_o clip_v they_o near_o towards_o the_o middle_n that_o so_o the_o point_n of_o the_o compass_n may_v be_v against_o some_o of_o the_o mettle_n which_o be_v enclose_v or_o just_o against_o the_o extremity_n of_o the_o gold_n as_o in_o d_o and_o suppose_v it_o hang_v thus_o in_o aequilibrio_fw-la it_o be_v certain_a that_o in_o the_o other_o coffer_n be_v the_o lead_n for_o the_o point_n of_o the_o compass_n be_v advance_v as_o much_o as_o before_o as_o at_o f_o which_o take_v up_o a_o part_n of_o the_o lead_n because_o it_o occupy_v a_o great_a place_n than_o the_o gold_n therefore_o that_o shall_v help_v the_o weight_n g._n to_o weigh_v and_o so_o will_v not_o hang_v in_o aequilibrio_fw-la except_z g_z be_v place_v near_o to_o f._n hence_o we_o may_v conclude_v that_o there_o be_v the_o lead_n and_o in_o the_o other_o chest_n or_o globe_n there_o be_v the_o gold_n examination_n if_o the_o two_o box_n be_v of_o equal_a magnitude_n weigh_v in_o the_o air_n be_v find_v to_o be_v of_o equal_a weight_n they_o shall_v necessary_o take_v up_o like_o place_n in_o the_o water_n and_o therefore_o weigh_v also_o one_o as_o much_o as_o another_o hence_o there_o be_v no_o possibility_n to_o find_v the_o inequality_n of_o the_o metal_n which_o be_v enclose_v in_o these_o box_n in_o the_o water_n 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
the_o open_a air_n the_o rupture_n or_o violence_n of_o water_n issue_v out_o of_o a_o fountain_n show_v we_o that_o water_n be_v contract_v into_o a_o pipe_n cause_v a_o violence_n in_o its_o passage_n the_o glass_n of_o galeileus_n make_v we_o see_v how_o useful_a pipe_n or_o trunk_n be_v to_o make_v the_o light_n and_o species_n more_o visible_a and_o proportionable_a to_o our_o eye_n it_o be_v say_v that_o a_o prince_n of_o italy_n have_v a_o fair_a hall_n in_o which_o he_o can_v with_o facility_n hear_v distinct_o the_o discourse_n of_o those_o which_o walk_v in_o the_o adjacent_a garden_n which_o be_v by_o certain_a vessel_n and_o pipe_n that_o answer_v from_o the_o garden_n to_o the_o hall_n vitruvius_n make_v mention_v also_o of_o such_o vessel_n and_o pipe_n to_o strengthen_v the_o voice_n and_o action_n of_o comedian_n and_o in_o these_o time_n among_o many_o noble_a personage_n the_o new_a kind_n of_o trunk_n be_v use_v to_o help_v the_o hear_n be_v make_v of_o silver_n copper_z or_o other_o resound_a material_a in_o funnell-wise_a put_v the_o wide_a end_n to_o he_o which_o speak_v to_o the_o end_n to_o contract_v the_o voice_n that_o so_o by_o the_o pipe_n apply_v to_o the_o ear_n it_o may_v be_v more_o uniform_a and_o less_o in_o danger_n to_o dissipate_v the_o voice_n and_o so_o consequent_o more_o fortify_v problem_n lx._n of_o a_o fine_a lamp_n which_o go_v not_o out_o though_o one_o carry_v it_o in_o one_o pocket_n or_o be_v roll_v upon_o the_o ground_n will_v still_o burn_v it_o must_v be_v observe_v that_o the_o vessel_n in_o which_o the_o oil_n be_v put_v into_o have_v two_o pin_n on_o the_o side_n of_o it_o one_o against_o another_o be_v include_v within_o a_o circle_n this_o circle_n ought_v to_o have_v two_o other_o pin_n to_o enter_v into_o another_o circle_n of_o brass_n or_o other_o solid_a matter_n last_o this_o second_o circle_n have_v two_o pin_n which_o may_v hang_v within_o some_o box_n to_o contain_v the_o whole_a lamp_n in_o such_o manner_n that_o there_o be_v 6_o pin_n in_o different_a position_n now_o by_o the_o aid_n of_o these_o peg_n or_o pin_n the_o lamp_n that_o be_v in_o the_o middle_n will_v be_v always_o well_o situate_v according_a to_o his_o centre_n of_o gravity_n though_o it_o be_v turn_v any_o way_n though_o if_o you_o endeavour_v to_o turn_v it_o upside_o down_o it_o will_v lie_v level_v which_o be_v pleasant_a and_o admirable_a to_o behold_v to_o those_o which_o know_v not_o the_o cause_n and_o it_o be_v facile_a from_o he_o to_o make_v a_o place_n to_o rest_v quiet_a in_o though_o there_o be_v great_a agitation_n in_o the_o outward_a part_n problem_n lxi_o any_o one_o have_v think_v a_o card_n among_o many_o card_n how_o artificial_o to_o discover_v it_o out_o take_v any_o number_n of_o card_n as_o 10_o 12_o etc._n etc._n and_o open_a some_o 4_o or_o 5_o to_o the_o party_n sight_n and_o bid_v he_o think_v one_o of_o they_o but_o let_v he_o note_v whether_o it_o be_v the_o first_o second_o three_o etc._n etc._n then_o with_o promptness_n learn_v what_o number_n of_o card_n you_o have_v in_o your_o hand_n and_o take_v the_o other_o part_n of_o the_o card_n and_o place_v they_o on_o the_o top_n of_o these_o you_o hold_v in_o your_o hand_n and_o have_v do_v so_o ask_v he_o whether_o his_o card_n be_v the_o first_o second_o etc._n etc._n then_o before_o know_v the_o number_n of_o card_n that_o be_v at_o the_o bottom_n account_v backward_o until_o you_o come_v to_o it_o so_o shall_v you_o easy_o take_v out_o the_o card_n that_o he_o think_v upon_o problem_n lxii_o three_o woman_n ab.c._n carry_v apple_n to_o a_o mark_n to_o sell_v a_o have_v 20_o b_o 30_o and_o c_o 40_o they_o sell_v as_o many_o for_o a_o penny_n the_o one_o as_o the_o other_o and_o bring_v home_o one_o as_o much_o money_n as_o another_o how_o can_v this_o be_v the_o answer_n to_o the_o problem_n be_v easy_a as_o suppose_v at_o the_o begin_n of_o the_o market_n he_o sell_v she_o apple_n at_o a_o penny_n a_o apple_n and_o sell_v but_o 2._o which_o be_v 2_o penny_n and_o so_o she_o have_v 18_o leave_v but_o b._n sell_v 17._o which_o be_v 17_o penny_n and_o so_o have_v 13_o leave_v c._n sell_v 32._o which_o be_v 32_o penny_n and_o so_o have_v 8_o apple_n leave_v than_o a_o say_v she_o will_v not_o sell_v her_o apple_n so_o cheap_a but_o will_v sell_v they_o for_o 3_o penny_n the_o piece_n which_o she_o do_v and_o so_o her_o apple_n come_v to_o 54_o penny_n and_o b_o have_v leave_v but_o 13_o apple_n sell_v they_o at_o the_o same_o rate_n which_o come_v to_o 39_o penny_n and_o last_o c._n have_v but_o 8_o apple_n which_o at_o the_o same_o rate_n come_v to_o 24_o penny_n these_o sum_n of_o money_n which_o each_o other_o before_o receive_v come_v to_o 56_o penny_n and_o so_o much_o each_o one_o receive_v and_o so_o consequent_o bring_v home_o one_o as_o much_o as_o another_o problem_n lxiii_o of_o the_o property_n of_o some_o number_n first_o any_o two_o number_n be_v just_a the_o sum_n of_o a_o number_n that_o have_v equal_a distance_n from_o the_o half_a of_o that_o number_n the_o one_o augment_v and_o the_o other_o diminish_v as_o 7_o and_o 7_o of_o 8_o and_o â—_o of_o 9_o and_o 5_o of_o 10_o and_o 4_o of_o 11_o and_o 3_o of_o 12_o and_o 2_o of_o 13_o and_o â—_o as_o the_o one_o be_v more_o than_o the_o half_a the_o other_o be_v less_o second_o it_o be_v difficult_a to_o find_v two_o number_n who_o sum_n and_o product_n be_v alike_o that_o be_v if_o the_o number_n be_v multiply_v one_o by_o another_o and_o add_v together_o will_v be_v equal_a which_o two_o number_n be_v 2_o and_o 2_o for_o to_o multiply_v 2_o by_o 2_o make_v 4_o and_o add_v 2_o unto_o 2_o make_v the_o same_o this_o property_n be_v in_o no_o other_o two_o whole_a number_n but_o in_o break_a number_n there_o be_v infinite_a who_o sum_n and_o product_n will_v be_v equal_a one_o to_o another_o as_o clavius_n show_v upon_o the_o 36_o pro._n of_o the_o 9t_n h_o book_n of_o euclid_n three_o the_o number_n 5_o and_o 6_o be_v call_v circular_a number_n because_o the_o circle_n turn_v to_o the_o point_n from_o whence_o it_o begin_v so_o these_o number_n multiply_v by_o themselves_o do_v end_n always_o in_o 5_o and_o 6_o as_o 5_o time_n 5_o make_v 25_o that_o again_o by_o 5_o make_v 125_o so_o 6_o time_n 6_o make_v 36_o and_o that_o by_o 6_o make_v 216_o etc._n etc._n four_o the_o number_n 6_o be_v the_o first_o which_o arithmetician_n call_v a_o perfect_a number_n that_o be_v who_o part_n be_v equal_a unto_o it_o so_o the_o 6_o part_n of_o it_o be_v 1_o the_o three_o part_n be_v 2_o the_o half_a be_v 3_o which_o be_v all_o his_o part_n now_o 1_o 2_o and_o 3_o be_v equal_a to_o 6._o it_o be_v wonderful_a to_o conceive_v that_o there_o be_v so_o few_o of_o they_o and_o how_o rare_a these_o number_n be_v 50_o of_o perfect_a man_n for_o betwixt_o 1_o &_o 1000000000000_o number_n there_o be_v but_o ten_o that_o be_v 6_o 28_o 486._o 8128._o 120816._o 2096128._o 33550336._o 536854528._o 8589869056_o &_o 137438691328_o with_o this_o admirable_a property_n that_o alternate_o they_o end_v all_o in_o 6_o and_o 8_o &_o the_o twenty_o perfect_a number_n be_v 151115727451553768931328._o five_o the_o number_n 9_o among_o other_o privilege_n carry_v with_o it_o a_o excellent_a property_n for_o take_v what_o number_n you_o will_v either_o in_o gross_a or_o in_o part_n the_o nine_o of_o the_o whole_a or_o in_o its_o part_n reject_v and_o take_v simple_o will_v be_v the_o same_o as_o â—7_n it_o make_v 3_o time_n 9_o so_o whether_o the_o nine_o be_v reject_v of_o 27_o or_o of_o the_o sum_n of_o 2_o and_o 7_o it_o be_v all_o one_o so_o if_o the_o nine_o be_v take_v away_o of_o 240._o it_o be_v all_o one_o if_o the_o nine_o be_v take_v away_o of_o 2_o 4_o and_o 0_o for_o there_o will_v remain_v 6_o in_o either_o and_o so_o of_o other_o six_o 11_o be_v multiply_v by_o 2_o 4_o 5_o 6_o 7_o 8_o or_o 9_o will_v end_v and_o begin_v with_o like_a number_n so_o 11_o multiply_v by_o 5_o make_v 55_o if_o multiply_v by_o 8_o it_o make_v 88_o etc._n etc._n seven_o the_o number_n 220_o and_o 284_o be_v unequal_a notwithstanding_o the_o part_n of_o the_o one_o number_n do_v always_o equalise_v the_o other_o number_n so_o the_o aliquot_fw-la part_n of_o 220_o be_v 110_o 54_o 44_o 22_o 20_o 11_o 10_o 5_o 4_o 2_o 1_o which_o together_o make_v 284._o the_o aliquot_fw-la part_n of_o 284_o be_v 142_o 71_o 4_o 2_o 1._o which_o together_o make_v 220_o a_o thing_n rare_a and_o admirable_a and_o difficult_a to_o find_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 if_o alone_a as_o for_o the_o proportion_n of_o those_o glass_n to_o the_o trunk_n though_o there_o be_v certain_a rule_n to_o make_v they_o yet_o it_o be_v often_o by_o hazard_n that_o there_o be_v make_v a_o excellent_a one_o there_o be_v so_o many_o difficulty_n in_o the_o action_n therefore_o many_o aught_o to_o be_v try_v see_v that_o exact_a proportion_n in_o geometrical_a calculation_n can_v serve_v for_o diversity_n of_o sight_n in_o the_o observation_n problem_n lxvii_o of_o the_o adamant_n or_o magnes_n and_o the_o needle_n touch_v therewith_o who_o will_v believe_v if_o he_o see_v not_o with_o his_o eye_n that_o a_o needle_n of_o steel_n be_v once_o touch_v with_o the_o magnes_fw-la turn_v not_o once_o not_o a_o year_n but_o as_o long_o as_o the_o world_n last_v his_o end_n towards_o the_o north_n and_o south_n yea_o though_o one_o remove_v it_o and_o turn_v it_o from_o his_o position_n it_o will_v come_v again_o to_o his_o point_n of_o north_n and_o south_n who_o will_v 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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sink_v 16._o be_v give_v a_o body_n to_o mark_v it_o about_o and_o show_v how_o much_o of_o it_o will_v sink_v in_o the_o water_n or_o swim_v above_o the_o water_n this_o be_v do_v by_o know_v the_o weight_n of_o the_o body_n which_o be_v give_v and_o the_o quantity_n of_o water_n which_o weigh_v as_o much_o as_o that_o body_n for_o then_o certain_o it_o will_v sink_v so_o deep_a until_o it_o occupy_v the_o place_n of_o that_o quantity_n of_o water_n 17._o to_o find_v how_o much_o several_a mettle_n or_o other_o body_n do_v weigh_v less_o in_o the_o water_n than_o in_o the_o air_n take_v a_o balance_n &_o weigh_v as_o for_o example_n 9_o pound_n of_o gold_n silver_n lead_v or_o stone_n in_o the_o air_n so_o it_o hang_v in_o aequilibrio_fw-la then_o come_v to_o the_o water_n take_v the_o same_o quantity_n of_o gold_n silver_n lead_v or_o stone_n and_o let_v it_o soft_o down_o into_o it_o and_o you_o shall_v see_v that_o you_o shall_v need_v a_o less_o counterpoise_n in_o the_o other_o balance_n to_o counterbalance_n it_o wherefore_o all_o solid_n or_o body_n weigh_v less_o in_o the_o water_n than_o in_o the_o air_n and_o so_o much_o the_o less_o it_o will_v be_v by_o how_o much_o the_o water_n be_v gross_a and_o thick_a because_o the_o weight_n find_v a_o great_a resistance_n and_o therefore_o the_o water_n support_v more_o than_o air_n and_o further_o because_o the_o water_n by_o the_o ponderosity_n be_v displease_v and_o so_o strive_v to_o be_v there_o again_o press_v to_o it_o by_o reason_n of_o the_o other_o water_n that_o be_v about_o it_o according_a to_o the_o proportion_n of_o his_o weight_n archimedes_n demonstrate_v that_o all_o body_n weigh_v less_o in_o the_o water_n or_o in_o like_a liquor_n by_o how_o much_o they_o occupy_v place_n and_o if_o the_o water_n weigh_v a_o pound_n weight_n the_o magnitude_n in_o the_o water_n shall_v weigh_v a_o pound_n less_o than_o in_o the_o air_n now_o by_o know_v the_o proportion_n of_o water_n and_o mettle_n it_o be_v 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give_v unto_o it_o the_o first_o way_n be_v thus_o take_v a_o magnitude_n which_o take_v up_o as_o much_o place_n as_o a_o hundred_o or_o a_o thousand_o pound_n of_o water_n and_o suppose_v that_o it_o be_v tie_v to_o some_o thing_n that_o it_o may_v hang_v in_o the_o air_n then_o make_v a_o balance_n that_o one_o of_o the_o scale_n may_v environ_v it_o yet_o so_o that_o it_o touch_v not_o the_o side_n of_o it_o but_o leave_v space_n enough_o for_o one_o pound_n of_o water_n then_o have_v place_v 100_o pound_n weight_n in_o the_o other_o scale_n throw_v in_o the_o water_n about_o the_o magnitude_n so_o that_o one_o pound_n of_o water_n shall_v weigh_v down_o the_o hundred_o pound_n in_o the_o other_o balance_n problem_n lxxxvi_o of_o sundry_a question_n of_o arithmetic_n and_o first_o of_o the_o number_n of_o sand_n it_o may_v be_v say_v incontinent_a that_o to_o undertake_v this_o be_v impossible_a either_o to_o number_v the_o sand_n of_o lybia_n or_o the_o sand_n of_o the_o sea_n and_o it_o be_v this_o that_o the_o poet_n sing_v and_o that_o which_o the_o vulgar_a believe_v nay_o that_o which_o long_o ago_o certain_a philosopher_n to_o gelon_n king_n of_o sicily_n report_v that_o the_o grain_n of_o sand_n be_v innumerable_a but_o i_o answer_v with_o archimedes_n that_o not_o only_o one_o may_v number_v those_o which_o be_v at_o the_o border_n and_o about_o the_o sea_n but_o those_o which_o be_v able_a to_o fill_v the_o whole_a world_n if_o there_o be_v nothing_o else_o but_o sand_n and_o the_o grain_n of_o sand_n admit_v to_o be_v so_o small_a that_o 10_o may_v make_v but_o one_o grain_n of_o poppy_n for_o at_o the_o end_n
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each_o equal_a to_o the_o weight_n of_o the_o crown_n and_o therefore_o unequal_a in_o magnitude_n or_o greatness_n and_o then_o know_v the_o several_a quantity_n of_o water_n which_o be_v answerable_a to_o the_o crown_n and_o the_o several_a mass_n he_o subtle_o collect_v that_o if_o the_o crown_n occupy_v more_o place_n within_o the_o water_n than_o the_o mass_n of_o gold_n do_v it_o appear_v that_o there_o be_v silver_n or_o other_o metal_n melt_v with_o it_o now_o by_o the_o rule_n of_o position_n suppose_v that_o each_o of_o the_o three_o mass_n weigh_v 18_o pound_n a_o piece_n and_o that_o the_o mass_n of_o gold_n do_v occupy_v the_o place_n of_o one_o pound_n of_o water_n that_o of_o silver_n a_o pound_n and_o a_o half_a and_o the_o crown_n one_o pound_n and_o a_o quarter_n only_o then_o thus_o he_o may_v operate_v the_o mass_n of_o silver_n which_o weigh_v 18_o pound_n cast_v into_o the_o water_n do_v cast_v out_o half_a a_o pound_n of_o water_n more_o than_o the_o mass_n of_o 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weigh_v 20_o pound_n and_o another_o of_o silver_n at_o a_o capacity_n or_o bigness_n at_o pleasure_n as_o suppose_v do_v weigh_v 12_o pound_n the_o crown_n or_o the_o mix_a body_n will_v weigh_v more_o than_o the_o silver_n and_o lesser_a than_o the_o gold_n suppose_v it_o weigh_v 16_o pound_n which_o be_v 4_o pound_n less_o than_o the_o gold_n by_o 8_o pound_n then_o may_v one_o say_v if_o 8_o pound_n of_o difference_n come_v from_o 12_o pound_n of_o silver_n from_o whence_o come_v 4_o pound_n which_o will_v be_v 6_o pound_n and_o so_o much_o silver_n be_v mix_v in_o it_o etc._n etc._n 3._o three_o man_n buy_v a_o quantity_n of_o wine_n each_o pay_v alike_o and_o each_o be_v to_o have_v alike_o it_o happen_v at_o the_o last_o partition_n that_o there_o be_v 21_o barrel_n of_o which_o 7_o be_v full_a 7_o half_a full_a and_o 7_o empty_a how_o must_v they_o share_v the_o wine_n and_o vessel_n that_o each_o have_v as_o many_o vessel_n one_o as_o another_o &_o as_o much_o wine_n one_o 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a_o pit_n continual_o to_o ascend_v without_o strength_n or_o the_o assistance_n of_o any_o other_o pump_n let_v il_fw-fr be_v the_o pit_n where_o one_o will_v cause_v water_n to_o ascend_v continual_o to_o â—â—ach_v office_n of_o a_o house_n or_o the_o place_n which_o be_v separate_v from_o it_o let_v there_o be_v make_v a_o receiveâ—_n as_o a_o well_o close_v up_o with_o lead_n or_o other_o matter_n that_o air_n enter_v not_o in_o to_o which_o fasten_v a_o pipe_n of_o lead_v as_o at_o e_o which_o may_v have_v vent_n at_o pleasure_n then_o let_v there_o be_v make_v a_o cistern_n as_o b_o which_o may_v be_v communicative_a to_o a_o by_o help_n of_o the_o pipe_n g_o from_o which_o cistern_n b_o may_v issue_v the_o water_n of_o pipe_n d_o which_o may_v descend_v to_o h_n which_o be_v a_o little_a below_o the_o level_n of_o the_o water_n of_o the_o pit_n as_o much_o as_o be_v gh_a to_o the_o end_n of_o which_o shall_v be_v solder_v close_o a_o cock_n which_o shall_v cast_v out_o the_o water_n by_o kh_n now_o to_o make_v use_n of_o it_o let_v b_o be_v fill_v full_a of_o water_n and_o when_o you_o will_v have_v it_o run_v turn_v the_o cock_n for_o then_o the_o water_n in_o b_o will_v descend_v by_o k._n and_o for_o fear_v that_o there_o shall_v be_v vacuity_n nature_n which_o abhor_v it_o will_v labour_v to_o furnish_v and_o supply_v that_o emptiness_n out_o of_o the_o spring_n f_o and_o that_o the_o pit_n dry_v not_o the_o pipe_n ought_v to_o be_v small_a of_o a_o indifferent_a capacity_n according_a to_o the_o greatness_n or_o smallness_n of_o the_o spring_n problem_n cxiiii_o how_o out_o of_o a_o fountain_n to_o cast_v the_o water_n very_o high_a different_a from_o a_o problem_n former_o deliver_v let_v the_o fountain_n be_v bd_o of_o a_o round_a form_n see_v it_o be_v the_o most_o capable_a and_o most_o perfect_a figure_n place_n into_o it_o two_o pipe_n conjoin_v as_o ea_fw-la and_o hc_n so_o that_o no_o air_n may_v enter_v in_o at_o the_o place_n of_o join_v 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by_o reason_n of_o distance_n of_o place_n take_v what_o simple_a you_o please_v burn_v it_o and_o take_v the_o ash_n of_o it_o and_o let_v it_o be_v calcinate_a two_o hour_n between_o two_o creuset_n well_o lute_v and_o extract_v the_o salt_n that_o be_v to_o put_v water_n into_o it_o in_o move_v of_o it_o then_o let_v it_o settle_v and_o do_v it_o two_o or_o three_o time_n afterward_o evaporate_v it_o that_o be_v let_v the_o water_n be_v boil_a in_o some_o vessel_n until_o it_o be_v all_o consume_v then_o there_o will_v remain_v a_o salt_n at_o the_o bottom_n which_o you_o shall_v afterward_o sow_v in_o good_a ground_n well_o prepare_v such_o as_o the_o theatre_n of_o husbandry_n show_v and_o you_o shall_v have_v your_o desire_n problem_n cviii_o how_o to_o make_v a_o infalliable_a perpetual_a motion_n myxe_n 5._o or_o 6._o ounce_n of_o ☿_o with_o be_v equal_a weight_n of_o ♃_o grind_v it_o together_o with_o 10._o or_o 12_o ounce_n of_o sublimate_n dissolve_v in_o a_o cellar_n upon_o a_o marble_n the_o space_n of_o four_o day_n and_o it_o will_v become_v like_o oil_n olive_n which_o distil_v with_o fire_n of_o chaff_n or_o drive_v fire_n and_o it_o will_v sublime_a dry_a substance_n than_o put_v water_n upon_o the_o earth_n in_o form_n of_o lie_n which_o will_v be_v at_o the_o bottom_n of_o the_o limbeck_n and_o dissolve_v that_o which_o you_o can_v filter_n it_o then_o distil_v it_o and_o there_o will_v be_v produce_v very_o subtle_a antome_n which_o put_v into_o a_o bottle_n close_o stop_v and_o keep_v it_o dry_a and_o you_o shall_v have_v your_o desire_n with_o astonishment_n to_o all_o the_o world_n and_o especial_o to_o those_o which_o have_v travel_v herein_o without_o fruit_n problem_n cxix_o of_o the_o admirable_a invention_n of_o make_v the_o philosopher_n tree_n which_o one_o may_v see_v with_o his_o eye_n to_o grow_v by_o little_a and_o little_a take_v two_o ounce_n of_o aqua_fw-la fortis_fw-la and_o dissolve_v in_o it_o half_a a_o ounce_n of_o fine_a silver_n refine_v in_o a_o cappell_n then_o take_v a_o ounce_n of_o aqua_fw-la fortis_fw-la and_o two_o dram_n of_o quicksilver_n which_o put_v in_o it_o and_o mix_v these_o two_o dissolve_a thing_n together_o then_o cast_v it_o into_o a_o vial_n of_o half_a a_o pound_n of_o water_n which_o may_v be_v well_o stop_v for_o then_o every_o day_n you_o may_v see_v it_o grow_v both_o in_o the_o tree_n and_o in_o the_o branch_n this_o liquid_a serve_v to_o black_a hair_n which_o be_v red_a or_o white_a without_o fade_v until_o they_o fall_v but_o here_o be_v to_o be_v note_v that_o great_a care_n ought_v to_o be_v
have_v in_o anoint_v the_o hair_n for_o fear_n of_o touch_v the_o flesh_n for_o this_o composition_n be_v very_o corrosive_a or_o search_a that_o as_o soon_o as_o it_o touch_v the_o flesh_n it_o raise_v blister_n and_o bladder_n very_o painful_a problem_n cxx_o how_o to_o make_v the_o representation_n of_o the_o great_a world_n draw_v salt_n niter_n out_o of_o salt_n earth_n which_o be_v find_v along_o the_o river_n side_n and_o at_o the_o foot_n of_o mountain_n where_o especial_o be_v mineral_n of_o gold_n and_o silver_n mix_v that_o niter_n well_o cleanse_v with_o ♃_o then_o calcinate_v it_o hermetical_o then_o put_v it_o in_o a_o limbeck_n and_o let_v the_o receiver_n be_v of_o glass_n well_o lute_v and_o always_o in_o which_o let_v there_o be_v place_v leaf_n of_o gold_n at_o the_o bottom_n then_o put_v fire_n under_o the_o limbeck_n until_o vapour_n arise_v which_o will_v cleave_v unto_o the_o gold_n augment_v your_o fire_n until_o there_o ascend_v no_o more_o then_o take_v away_o 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length_n of_o the_o capon_n and_o big_a enough_o to_o fill_v the_o belly_n of_o it_o and_o then_o stop_v it_o with_o butter_n then_o wrap_v it_o up_o well_o and_o enclose_v it_o in_o a_o box_n in_o the_o budget_n and_o you_o shall_v have_v your_o desire_n it_o be_v say_v that_o count_n mansfield_n serve_v himself_o with_o no_o other_o but_o such_o as_o be_v make_v ready_a in_o this_o kind_n for_o that_o it_o lose_v none_o of_o its_o substance_n and_o it_o be_v dress_v very_o equal_o problem_n cxxiv_o how_o to_o make_v a_o candle_n burn_v and_o continue_v three_o time_n as_o long_o as_o otherwise_o it_o will_v unto_o the_o end_n of_o a_o candle_n halfâ—burned_v stick_v a_o farthing_n less_o or_o more_o to_o make_v it_o hang_v perpendicular_a in_o a_o vessel_n of_o water_n so_o that_o it_o swim_v above_o the_o water_n then_o light_v it_o and_o it_o will_v sustain_v itself_o &_o float_v in_o this_o manner_n and_o be_v place_v into_o a_o fountain_n pond_n or_o lake_n that_o run_v slow_o where_o many_o people_n assemble_v it_o will_v cause_v a_o extreme_a fear_n to_o those_o which_o come_v therein_o in_o the_o night_n know_v not_o what_o it_o be_v problem_n cxxv_o how_o out_o of_o a_o quantity_n of_o wine_n to_o extract_v that_o which_o be_v most_o windy_a and_o evil_a that_o it_o hurt_v not_o a_o sick_a person_n take_v two_o vial_n in_o such_o sort_n that_o they_o be_v of_o like_a greatness_n both_o in_o thâ—_n belly_n and_o the_o neck_n fill_v one_o of_o they_o of_o wine_n and_o the_o other_o of_o water_n let_v the_o mouth_n of_o that_o which_o have_v the_o water_n be_v place_v into_o the_o mouth_n of_o that_o which_o have_v the_o wine_n so_o the_o water_n shall_v be_v uppermost_a now_o because_o the_o water_n be_v heavy_a than_o the_o wine_n it_o will_v descend_v into_o the_o other_o vial_n and_o the_o wine_n which_o be_v low_a because_o it_o be_v high_a will_v ascend_v above_o to_o supply_v the_o place_n of_o the_o water_n and_o so_o there_o will_v be_v a_o mutual_a interchange_n of_o liquid_n and_o by_o this_o penetration_n the_o wine_n will_v lose_v her_o vapour_n in_o pass_v through_o the_o water_n problem_n cxxvi_o how_o to_o make_v two_o marmouzet_n one_o of_o which_o shall_v light_v a_o candle_n and_o the_o other_o put_v it_o out_o upon_o the_o side_n of_o a_o wall_n make_v the_o figure_n of_o a_o marmouzet_n or_o other_o animal_n or_o form_n and_o right_a against_o it_o on_o the_o other_o wall_n make_v another_o in_o the_o mouth_n of_o each_o put_v a_o pipe_n or_o quill_n so_o artificial_o that_o it_o be_v not_o perceive_v in_o one_o of_o which_o place_n salt_n peter_n very_o fine_a and_o dry_a and_o pulverize_a and_o at_o the_o end_n set_v a_o little_a match_n of_o paper_n in_o the_o other_o place_n sulphur_n beat_v small_a then_o hold_v a_o candle_n light_v in_o your_o hand_n say_v to_o one_o of_o these_o image_n by_o way_n of_o command_n blow_v out_o the_o candle_n then_o light_v the_o paper_n with_o the_o candle_n the_o 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which_o be_v not_o near_o fresh_a water_n and_o who_o dwelling_n be_v much_o expose_v to_o the_o sun_n puoblem_n cxxviii_o to_o make_v a_o cement_n which_o endure_v or_o last_v as_o marble_n which_o resist_v air_n and_o water_n without_o ever_o disjoyn_v or_o uncement_n take_v a_o quantity_n of_o strong_a and_o glue_a mortar_n well_o beat_v mix_v with_o this_o as_o much_o new_a slake_a lime_n and_o upon_o it_o cast_v oil_n of_o olive_n or_o linseed-oile_n and_o it_o will_v become_v hard_a as_o marble_n be_v apply_v in_o time_n problem_n cxxix_o how_o to_o melt_v metal_n very_o quick_o yea_o in_o a_o shell_n upon_o a_o little_a fire_n make_v a_o bed_n upon_o a_o bed_n of_o metal_n with_o powder_n of_o sulphur_n of_o saltpetre_n and_o sawdust_n alike_o then_o put_v fire_n to_o the_o say_a powder_n with_o a_o burn_a charcoal_n and_o you_o shall_v see_v that_o the_o metal_n will_v dissolve_v incontinent_a and_o be_v in_o a_o mass_n this_o secret_a be_v most_o excellent_a and_o have_v be_v practise_v by_o the_o reverend_a father_n mercenâ—â—_n of_o the_o order_n of_o the_o minim_n problem_n cxxx_o how_o to_o make_v iron_n or_o steel_n exceed_v hard_a qvench_fw-mi your_o blade_n or_o other_o instrument_n seven_o time_n in_o the_o blood_n of_o a_o male_a hog_n mix_v with_o goose-grease_n and_o at_o each_o time_n dry_v it_o at_o the_o fire_n before_o you_o wet_v it_o and_o it_o will_v become_v exceed_o hard_a and_o not_o brittle_a which_o be_v not_o ordinary_a according_a to_o other_o tempering_n and_o quenching_n of_o iron_n a_o experiment_n of_o small_a cost_n often_o prove_v and_o of_o great_a consequence_n for_o armoury_n in_o warlike_a negotiation_n prbolem_fw-la cxxxi_o to_o preserve_v fire_n as_o long_o as_o
foot_n of_o ball_n of_o fâ—re_n these_o be_v very_o various_a according_a to_o a_o man_n fancy_n some_o of_o which_o be_v make_v with_o very_o small_a rocket_n the_o head_n of_o one_o tie_v to_o the_o neck_n of_o another_o the_o ball_n be_v make_v may_v be_v cover_v over_o with_o pitch_n except_o the_o hole_n to_o give_v fire_n to_o it_o this_o ball_n will_v make_v fine_a sport_n among_o the_o stander_n by_o which_o will_v take_v all_o a_o fire_n and_o roll_v sometime_o this_o way_n sometime_o that_o way_n between_o the_o leg_n of_o those_o that_o be_v stander_n by_o if_o they_o take_v not_o heed_n for_o the_o motion_n will_v be_v very_o irregular_a and_o in_o the_o motion_n will_v cast_v forth_o several_a fire_n with_o report_n in_o the_o second_o kind_n there_o may_v be_v a_o channel_n of_o iron_n place_v in_o divers_a place_n in_o spirall_n manner_n against_o which_o may_v be_v place_v as_o many_o small_a petard_n of_o paper_n as_o possible_a may_v be_v the_o channel_n must_v be_v 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