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the_o flux_n of_o a_o point_n can_v be_v divide_v in_o that_o wise_a one_o may_v have_v therefore_o a_o instrument_n which_o be_v call_v maincordion_a because_o there_o be_v but_o one_o cord_n and_o if_o you_o desire_v to_o divide_v your_o line_n into_o 3_o part_n run_v your_o finger_n upon_o the_o fret_v until_o you_o sound_v a_o three_o in_o music_n if_o you_o will_v have_v the_o four_o part_n of_o the_o line_n then_o find_v the_o four_o sound_n a_o five_o etc._n etc._n so_o shall_v you_o have_v the_o answer_n problem_n xcix_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 this_o be_v do_v by_o help_n of_o a_o conoeide_a line_n produce_v by_o a_o right_a line_n upon_o one_o &_o the_o same_o plain_a hold_v in_o great_a account_n among_o the_o ancient_n and_o it_o be_v draw_v after_o this_o manner_n draw_v a_o right_a line_n infinite_o and_o upon_o some_o end_n of_o it_o as_o at_o i_o draw_v a_o 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part_n then_o ask_v what_o it_o amount_v unto_o so_o the_o root_n quadrat_fw-la shall_v be_v the_o number_n think_v upon_o the_o number_n think_v upon_o 5_o the_o part_n suppose_v 3_o and_o 2._o the_o square_a of_o 3_o make_v 9_o the_o sum_n of_o these_o three_o number_n 25_o the_o squaâ—e_a root_n of_o which_o be_v 5_o the_o number_n think_v upon_o the_o square_n of_o 2_o make_v 4_o the_o sum_n of_o these_o three_o number_n 25_o the_o squaâ—e_a root_n of_o which_o be_v 5_o the_o number_n think_v upon_o the_o product_n of_o the_o part_n viz._n 3_o by_o 2_o make_v 6_o which_o 6_o double_v make_v 12_o the_o sum_n of_o these_o three_o number_n 25_o the_o squaâ—e_a root_n of_o which_o be_v 5_o the_o number_n think_v upon_o or_o more_o compendious_o it_o may_v be_v deliver_v thus_o break_v the_o number_n into_o two_o part_n and_o to_o the_o product_n of_o the_o part_n add_v the_o square_n of_o half_a the_o difference_n of_o the_o part_n than_o the_o root_n quadrat_fw-la of_o the_o aggregate_v be_v half_a the_o number_n conceive_v examination_n the_o problem_n which_o concern_v arithmetic_n we_o examine_v not_o for_o these_o be_v easy_a to_o any_o one_o which_o have_v read_v the_o ground_n and_o principle_n of_o arithmetic_n but_o we_o especial_o touch_v upon_o that_o which_o tend_v to_o the_o speculation_n of_o physic_n geometry_n and_o opticke_n and_o such_o other_o which_o be_v of_o more_o difficulty_n and_o more_o principal_o to_o be_v examine_v and_o consider_v problem_n ii_o how_o to_o represent_v to_o those_o which_o be_v in_o a_o chamâ—er_a that_o which_o be_v without_o or_o all_o that_o which_o pass_v by_o it_o be_v pleasant_a to_o see_v the_o beautiful_a and_o goodly_a representation_n of_o the_o heaven_n intermix_v with_o cloud_n in_o the_o horizon_n upon_o a_o woody_a situation_n the_o motion_n of_o bird_n in_o the_o air_n of_o man_n and_o other_o creature_n upon_o the_o ground_n with_o the_o tremble_n of_o plant_n top_n of_o tree_n and_o such_o 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hollow_a of_o the_o eye_n be_v take_v as_o the_o close_a chamber_n the_o ball_n of_o the_o apple_n of_o the_o eye_n for_o the_o hole_n of_o the_o chamber_n the_o crystaline_a humour_n at_o the_o small_a of_o the_o glass_n and_o the_o bottom_n of_o the_o eye_n for_o the_o wall_n or_o leaf_n of_o paper_n examination_n the_o species_n be_v press_v together_o or_o contract_a do_v not_o perform_v it_o upon_o a_o wall_n for_o the_o species_n of_o any_o thing_n do_v represent_v itself_o not_o only_o in_o one_o hole_n of_o a_o window_n but_o in_o infinite_a hole_n even_o unto_o the_o whole_a sphere_n or_o at_o least_o unto_o a_o hemisphere_n intellectual_a in_o a_o free_a medium_n if_o the_o beam_n or_o reflection_n be_v not_o interpose_v and_o by_o how_o much_o the_o hole_n be_v make_v less_o to_o give_v passage_n to_o the_o species_n by_o so_o much_o the_o more_o lively_o be_v the_o image_n form_v in_o convexe_a or_o concave_a glass_n the_o image_n will_v be_v disproportionable_a to_o the_o 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down_o and_o it_o will_v be_v direct_a and_o to_o the_o life_n but_o the_o apparence_n may_v be_v direct_a if_o you_o place_v another_o hole_n opposite_a unto_o the_o former_a so_o that_o the_o spectator_n be_v under_o it_o or_o let_v the_o species_n reflect_v upon_o a_o concave_a glass_n and_o let_v that_o glass_n reflect_v upon_o a_o paper_n or_o some_o white_a thing_n problem_n iii_o to_o tell_v how_o much_o weigh_v the_o blow_n of_o one_o fist_n of_o a_o mallet_n hatchet_n or_o such_o like_a or_o rest_v without_o give_v the_o blow_n scaliger_n in_o his_o 331_o exercise_n against_o cardan_n relate_v that_o the_o mathematician_n of_o maximilian_n the_o emperor_n do_v propose_v upon_o a_o day_n this_o question_n and_o promise_v to_o give_v the_o resolution_n notwithstanding_o scaliger_n deliver_v it_o not_o and_o i_o conceive_v it_o to_o be_v thus_o take_v a_o balance_n and_o let_v the_o fist_n the_o mallet_n or_o hatchet_n rest_n upon_o the_o scale_n or_o upon_o the_o beam_n of_o the_o balance_n and_o put_v into_o the_o other_o scale_n as_o much_o weight_n as_o may_v counterpoise_v it_o then_o charge_v or_o lay_v more_o weight_n into_o the_o scale_n and_o strike_v upon_o the_o other_o end_n you_o may_v see_v how_o much_o one_o blow_n be_v heavy_a than_o another_o and_o so_o consequent_o how_o much_o it_o may_v weigh_v for_o as_o aristotle_n say_v the_o motion_n that_o be_v make_v in_o strike_v add_v great_a weight_n unto_o it_o and_o so_o much_o the_o more_o by_o how_o much_o it_o be_v quick_a therefore_o in_o effect_n if_o there_o be_v place_v a_o thousand_o mallet_n or_o a_o thousand_o pound_n weight_n upon_o a_o stone_n nay_o though_o it_o be_v exceed_o press_v down_o by_o way_n of_o a_o vice_n by_o lever_n or_o other_o mechanic_n engine_n it_o will_v be_v nothing_o to_o the_o rigour_n and_o violence_n of_o a_o blow_n be_v it_o not_o evident_a that_o the_o edge_n of_o a_o knife_n lay_v upon_o butter_n and_o a_o hatchet_n upon_o a_o leaf_n of_o paper_n without_o strike_v make_v no_o impression_n or_o at_o least_o enter_v not_o but_o strike_v upon_o the_o wood_n a_o little_a you_o may_v present_o see_v what_o effect_n it_o have_v which_o be_v from_o the_o quickness_n of_o the_o motion_n which_o break_v and_o enter_v without_o resistance_n if_o it_o be_v extreme_a quick_a as_o experience_n show_v we_o in_o the_o blow_n of_o arrow_n of_o cannon_n thunderbolt_n and_o such_o like_a examination_n this_o problem_n be_v extract_v from_o scaliger_n who_o have_v it_o from_o aristotle_n but_o somewhat_o refractory_a compile_v &_o the_o strength_n of_o the_o effect_n he_o say_v depend_v only_o in_o the_o violence_n of_o the_o motion_n then_o will_v it_o follow_v that_o a_o little_a light_a hammer_n upon_o a_o piece_n of_o wood_n be_v quick_o cause_v to_o smite_v will_v give_v a_o great_a blow_n and_o do_v more_o hurt_n than_o a_o great_a sledge_n strike_v soft_a this_o be_v absurd_a and_o contrary_a to_o experience_n therefore_o it_o consist_v 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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
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
here_o there_o must_v be_v find_v a_o number_n which_o multiply_v by_o 7_o and_o then_o divide_v by_o 2_o 3_o 4_o 5_o 6_o there_o may_v always_o remain_v a_o number_n less_o by_o 1_o than_o the_o divisor_n now_o the_o first_o number_n which_o arrive_v in_o this_o nature_n be_v 119_o unto_o which_o if_o 420_o be_v add_v make_v 539_o which_o also_o will_v do_v the_o same_o and_o so_o by_o add_v 420_o you_o may_v have_v other_o number_n to_o resolve_v this_o proposition_n problem_n xlviii_o how_o many_o sort_n of_o weight_n in_o the_o least_o manner_n must_v there_o be_v to_o weigh_v all_o sort_n of_o thing_n between_o 1_o pound_n and_o 40_o pound_n and_o so_o unto_o 121_o &_o 364_o pound_n to_o weigh_v thing_n between_v 1_o and_o 40_o take_v number_n in_o triple_a proportion_n so_o that_o their_o sum_n be_v equal_a or_o somewhat_o great_a than_o 40_o as_o be_v the_o number_n 1_o 3.9.27_o i_o say_v that_o with_o â—_o such_o weight_n the_o first_o be_v of_o 1_o pound_n the_o second_o be_v 3_o pound_n the_o three_o be_v 9_o pound_n and_o the_o four_o be_v 27_o any_o weight_n between_o 1_o and_o 40_o pound_n may_v be_v weigh_v as_o admit_v to_o weigh_v 21_o pound_n put_v unto_o the_o thing_n that_o be_v to_o be_v weigh_v the_o 9_o pound_n weight_n then_o in_o the_o other_o balance_n put_v 27_o pound_n and_o 3_o pound_n which_o do_v counterpoise_v 21_o pound_n and_o 9_o pound_n and_o if_o 20_o pound_n be_v to_o be_v weigh_v put_v to_o it_o in_o the_o balance_n 9_o and_o 1_o and_o in_o the_o other_o balance_n put_v 27_o and_o 3_o and_o so_o of_o other_o in_o the_o same_o manner_n take_v those_o 5_o weight_n 1_o 3_o 9_o 27_o 81_o you_o may_v weigh_v with_o they_o between_o 1_o pound_n and_o 121_o pound_n and_o take_v those_o 6_o weight_n as_o 1_o 3_o 9_o 2d_o 81_o 243_o you_o may_v weigh_v even_o from_o 1_o pound_n unto_o 364_o pound_n this_o depend_v upon_o the_o property_n of_o continue_a proportional_n the_o latter_a of_o which_o contain_v twice_o all_o the_o former_a problem_n xlix_o of_o a_o deceitful_a balance_n which_o be_v câ—â—â—ty_n seem_v iâ—_n be_v just_a because_o it_o hang_v in_o aequilibrio_fw-la notwithstanding_o put_v 12_o pound_n in_o one_o balance_n and_o 11_o in_o the_o other_o it_o will_v remain_v in_o aequilibrio_fw-la aristotle_n make_v mention_n of_o this_o balance_n in_o his_o mechanic_n question_n and_o say_v that_o the_o merchant_n of_o purpose_n in_o his_o time_n use_v they_o to_o deceive_v the_o world_n the_o subtlety_n or_o craft_n of_o which_o be_v thus_o that_o one_o arm_n of_o the_o balance_n be_v long_o than_o another_o by_o the_o same_o proportion_n that_o one_o weight_n be_v heavy_a than_o another_o as_o if_o the_o beam_n be_v 23_o inch_n long_o and_o the_o handle_v place_v so_o that_o 12_o inch_n shall_v be_v on_o one_o side_n of_o it_o and_o 11_o inch_n on_o the_o other_o side_n conditional_o that_o the_o short_a end_n shall_v be_v as_o heavy_a as_o the_o long_o a_o thing_n easy_a to_o be_v do_v then_o afterward_o put_v into_o the_o balance_n two_o unequal_a weight_n in_o such_o proportion_n as_o the_o part_n of_o the_o beam_n have_v one_o unto_o another_o which_o be_v 12_o to_o 11_o but_o so_o that_o the_o great_a be_v place_v in_o the_o balance_n which_o hang_v upon_o the_o short_a part_n of_o the_o beam_n and_o the_o lesser_a weight_n in_o the_o other_o balance_n it_o be_v most_o certain_a that_o the_o balance_n will_v hang_v in_o aequilibrio_fw-la which_o will_v seem_v most_o sincere_a and_o just_a though_o it_o be_v most_o deceitful_a abominable_a and_o false_a the_o reason_n of_o this_o be_v draw_v from_o the_o experiment_n of_o archimedes_n who_o show_v that_o two_o unequal_a weight_n will_v counterpoise_v one_o another_o when_o there_o be_v like_a proportion_n between_o the_o part_n of_o the_o beam_n that_o the_o handle_n separate_v and_o the_o weight_n themselves_o for_o in_o one_o and_o the_o same_o counterpoise_n by_o how_o much_o it_o be_v far_o from_o the_o centre_n of_o the_o handle_n by_o so_o much_o it_o seem_v heavy_a therefore_o if_o there_o be_v a_o diversity_n of_o distance_n that_o the_o balance_n hang_v from_o the_o handle_n there_o must_v necessary_o be_v a_o ineqality_n of_o weight_n in_o these_o balance_n to_o make_v they_o hang_v in_o aequilibrio_fw-la and_o to_o discover_v if_o there_o be_v deceit_n change_v the_o weight_n into_o the_o other_o balance_n for_o as_o soon_o as_o the_o great_a weight_n be_v place_v in_o the_o balance_n that_o hang_v on_o the_o long_a part_n of_o the_o beam_n it_o will_v weigh_v down_o the_o other_o instant_o problem_n l._n to_o heave_v or_o lift_v up_o a_o bottle_n with_o a_o straw_n take_v a_o straw_n that_o be_v not_o bruise_v bow_v it_o that_o it_o make_v a_o angle_n and_o put_v it_o into_o the_o bottle_n so_o that_o the_o great_a end_n be_v in_o the_o neck_n than_o the_o reed_n be_v put_v in_o the_o bow_v part_n will_v cast_v side-wise_a and_o make_v a_o angle_n as_o in_o the_o figure_n may_v be_v see_v then_o may_v you_o take_v the_o end_n which_o be_v out_o of_o the_o bottle_n in_o your_o hand_n and_o heave_v up_o the_o bottle_n and_o it_o be_v so_o much_o sure_a by_o how_o much_o the_o angle_n be_v acuter_n or_o sharp_a and_o the_o end_n which_o be_v bow_v approach_v to_o the_o other_o perpendicular_a part_n which_o come_v out_o of_o the_o bottle_n problem_n li._n how_o in_o the_o middle_n of_o a_o wood_n or_o desert_n without_o the_o sight_n of_o the_o sun_n star_n shadow_n or_o compass_n to_o find_v out_o the_o north_n or_o south_n or_o the_o four_o cardinal_n point_n of_o the_o world_n east_n west_n &_o c_o it_o be_v the_o opinion_n of_o some_o that_o the_o wind_n be_v to_o be_v observe_v in_o this_o if_o it_o be_v hot_a the_o south_n be_v find_v by_o the_o wind_n that_o blow_v that_o way_n but_o this_o observation_n be_v uncertain_a and_o subject_a to_o much_o error_n nature_n will_v help_v you_o in_o some_o measure_n to_o make_v it_o more_o manifest_a than_o any_o of_o the_o former_a from_o a_o tree_n thus_o cut_v a_o small_a tree_n off_o even_o to_o the_o ground_n and_o mark_v the_o many_o circle_n that_o be_v about_o the_o sap_n or_o pith_n of_o the_o tree_n which_o seem_v near_o together_o in_o some_o part_n than_o in_o other_o which_o be_v by_o reason_n of_o the_o sun_n motion_n about_o the_o tree_n for_o that_o the_o humidity_n of_o the_o part_n of_o the_o tree_n towards_o the_o south_n by_o the_o heat_n of_o the_o sun_n be_v rarify_v and_o cause_v to_o extend_v and_o the_o sâ—n_v not_o give_v such_o heat_n towards_o the_o north-part_n of_o the_o tree_n the_o sap_n be_v lesser_a rarefy_v but_o condense_v by_o which_o the_o circle_n be_v near_o together_o on_o the_o north-part_n than_o on_o the_o south-part_n therefore_o if_o a_o line_n be_v draw_v from_o the_o wide_a to_o the_o narrow_a part_n of_o the_o circle_n it_o shall_v show_v the_o north_n &_o south_n of_o the_o world_n another_o experiment_n may_v be_v thus_o take_v a_o small_a needle_n such_o as_o woman_n work_v with_o place_v it_o gentle_o down_o flatwise_o upon_o still_a water_n and_o it_o will_v not_o sink_v which_o be_v against_o the_o general_a tenet_n that_o iron_n will_v not_o swim_v which_o needle_n will_v by_o little_a and_o little_a turn_n to_o the_o north_n and_o south-point_n but_o if_o the_o needle_n be_v great_a and_o will_v not_o swim_v thrust_v it_o through_o a_o small_a piece_n of_o cork_n or_o some_o such_o like_a thing_n and_o then_o it_o will_v do_v the_o same_o for_o such_o be_v the_o property_n of_o iron_n when_o it_o be_v place_v in_o aequilibrio_fw-la it_o strive_v to_o find_v out_o the_o pole_n of_o the_o world_n or_o point_n of_o north_n and_o south_n in_o a_o manner_n as_o the_o magnes_fw-la do_v examination_n here_o be_v observable_a that_o the_o moisture_n which_o aid_v to_o the_o growth_n of_o the_o tree_n be_v dilate_v and_o rarefy_v by_o the_o meridional_a heat_n and_o contract_v by_o the_o septentrional_a cold_a this_o rarefaction_n work_v upon_o the_o part_n of_o the_o humour_n or_o moisture_n that_o be_v more_o thin_a which_o do_v easy_o dissipate_v and_o evaporate_v which_o evaporation_n carry_v a_o part_n of_o the_o salt_n with_o it_o and_o because_o that_o solidation_n or_o condensation_n so_o that_o there_o be_v leave_v but_o a_o part_n of_o the_o nourishment_n which_o the_o heat_n bake_v up_o and_o consume_v so_o contrary_o on_o the_o other_o side_n the_o condensation_n and_o restrictive_a quality_n of_o the_o moisture_n cause_v less_o evaporation_n and_o perdition_n and_o so_o consequent_o there_o remain_v more_o nourishment_n which_o make_v a_o great_a increase_n on_o that_o side_n than_o on_o the_o other_o
side_n for_o as_o tree_n have_v their_o growth_n in_o winter_n because_o of_o their_o pore_n and_o these_o of_o the_o earth_n be_v shut_v up_o so_o in_o the_o spring_n when_o their_o pore_n be_v open_a and_o when_o the_o sap_n and_o moisture_n be_v draw_v by_o it_o there_o be_v not_o such_o cold_a on_o the_o north-side_n that_o it_o may_v be_v condense_v at_o once_o but_o contrary_o to_o the_o side_n which_o be_v south_n the_o heat_n may_v be_v such_o that_o in_o little_a time_n by_o continuance_n this_o moisture_n be_v dissipate_v great_o and_o cold_a be_v nothing_o but_o that_o which_o harden_v and_o contract_v the_o moisture_n of_o the_o tree_n and_o so_o convert_v it_o into_o wood_n problem_n lii_o three_o person_n have_v take_v counter_n card_n or_o other_o thing_n to_o find_v how_o much_o each_o one_o have_v take_v cause_o the_o three_o party_n to_o take_v a_o number_n which_o maâ—_n be_v divide_v by_o 4_o and_o as_o often_o as_o he_o take_v 4_o let_v the_o second_o party_n take_v 7_o and_o the_o first_o take_v 13_o then_o cause_v they_o to_o put_v they_o all_o together_o and_o declare_v the_o sum_n of_o it_o which_o secret_o divide_v by_o 3_o and_o the_o quotient_n be_v the_o double_a of_o the_o number_n which_o the_o three_o person_n do_v take_v or_o cause_v the_o three_o to_o give_v unto_o the_o second_o and_o first_o as_o many_o as_o each_o of_o they_o have_v then_o let_v the_o second_o give_v unto_o the_o first_o and_o three_o as_o many_o as_o each_o of_o they_o have_v last_o let_v the_o three_o give_v unto_o the_o second_o and_o first_o as_o many_o as_o each_o of_o they_o have_v and_o then_o ask_v how_o much_o one_o of_o they_o have_v for_o they_o will_v have_v then_o all_o alike_o so_o half_a of_o that_o number_n be_v the_o number_n that_o the_o three_o person_n have_v at_o the_o first_o which_o know_v all_o be_v know_v problem_n liii_o how_o to_o make_v a_o consort_n of_o music_n of_o many_o part_n with_o one_o voice_n or_o one_o instrument_n only_o this_o problem_n be_v resolve_v so_o that_o a_o finger_n or_o player_n upon_o a_o instrument_n be_v near_o a_o echo_n which_o answer_v his_o voice_n or_o instrument_n and_o if_o the_o echo_n answer_v but_o once_o at_o a_o time_n he_o may_v make_v a_o double_a if_o twice_o than_o a_o triple_a if_o three_o time_n than_o a_o harmony_n of_o four_o part_n for_o it_o must_v be_v such_o a_o one_o that_o be_v able_a to_o exercise_v both_o tune_n and_o note_n as_o occasion_n require_v as_o when_o he_o begin_v ut_fw-la before_o the_o echo_n answer_n he_o may_v begin_v sol_fw-mi and_o pronounce_v it_o in_o the_o same_o tune_n that_o â—he_v echo_n answer_v by_o which_o mean_v you_o â—ave_n a_o five_o agreeable_a consort_n of_o music_n then_o in_o the_o same_o time_n that_o the_o echo_n follow_v to_o sound_v the_o second_o note_n sol_fw-mi he_o may_v sound_v forth_o another_o sol_fw-mi high_o or_o low_o to_o make_v a_o eight_o the_o most_o perfect_a consort_n of_o music_n and_o so_o of_o other_o if_o he_o will_v continue_v his_o voice_n with_o the_o echo_n and_o sing_v alone_o with_o two_o part_n now_o experience_n show_v this_o to_o be_v true_a which_o often_o come_v to_o pass_v in_o many_o church_n make_v one_o to_o believe_v that_o there_o be_v many_o more_o part_n in_o the_o music_n of_o a_o choir_n then_o in_o effect_n true_o there_o be_v because_o of_o the_o resound_a and_o multiply_v of_o the_o voice_n and_o redouble_v of_o the_o quire_n problem_n liiii_o tâ—_n make_v or_o describe_v a_o oval_a form_n or_o that_o which_o near_o resemble_v unto_o it_o at_o one_o turn_v with_o a_o pair_n of_o common_a compass_n there_o be_v many_o fine_a way_n in_o geometrical_a practice_n to_o make_v a_o oval_a figure_n or_o one_o near_a unto_o it_o by_o several_a centre_n any_o of_o which_o i_o will_v not_o touch_v upon_o but_o show_v how_o it_o may_v be_v do_v prompt_o upon_o one_o centre_n only_o in_o which_o i_o will_v say_v nothing_o of_o the_o oval_a form_n which_o appear_v when_o one_o describe_v circle_n with_o the_o point_n of_o a_o common_a compass_n somewhat_o deep_a upon_o a_o skin_n stretch_v forth_o hard_o which_o contract_v itself_o in_o some_o part_n of_o the_o skin_n make_v a_o oval_a form_n but_o it_o will_v more_o evident_o appear_v upon_o a_o column_n or_o cylinder_n if_o paper_n be_v place_v upon_o it_o then_o with_o a_o pair_n of_o compass_n describe_v as_o it_o be_v a_o circle_n upon_o it_o which_o paper_n afterward_o be_v extend_v will_v not_o be_v circular_a but_o ovall-wise_a and_o a_o pair_n of_o compass_n may_v be_v so_o accommodate_v that_o it_o may_v be_v do_v also_o upon_o a_o plain_a thus_o as_o let_v the_o length_n of_o the_o oval_n be_v h._n k_o fasten_v 2_o pin_n or_o nail_n near_o the_o end_n of_o that_o line_n as_o f._n g_o and_o take_v a_o thread_n which_o be_v double_a to_o the_o length_n of_o g._n h_n or_o f._n k_o then_o if_o you_o take_v a_o compass_n which_o may_v have_v one_o foot_n low_o than_o another_o with_o a_o spring_n between_o his_o leg_n and_o place_v one_o foot_n of_o this_o compass_n in_o the_o centre_n of_o the_o oval_n and_o guide_v the_o thread_n by_o the_o other_o foot_n of_o the_o compass_n and_o so_o carry_v it_o about_o the_o spring_n will_v help_v to_o describe_v and_o draw_v the_o oval_a form_n but_o in_o stead_n of_o the_o compass_n it_o may_v be_v do_v with_o one_o hand_n only_o as_o in_o the_o figure_n may_v appear_v problem_n lv._o of_o a_o puâ—se_n difficult_a to_o be_v open_v it_o be_v make_v to_o shut_v and_o open_v with_o ring_n first_o at_o each_o side_n there_o be_v a_o strap_n or_o string_n as_o ab_fw-la and_o cd_o at_o the_o end_n of_o which_o be_v 2_o ring_n b_o &_o d_o and_o the_o string_n cd_o pass_v through_o the_o ring_n b_o so_fw-mi that_o it_o may_v not_o come_v out_o again_o or_o be_v part_v one_o from_o another_o and_o so_o that_o the_o ring_n b_o may_v slide_v up_o and_o down_o upon_o the_o string_n cd_o then_o over_o the_o purse_n there_o be_v a_o piece_n of_o leather_n efgh_o which_o cover_v the_o open_n of_o the_o purse_n and_o there_o be_v another_o piece_n of_o leather_n ae_n which_o pass_v through_o many_o ring_n which_o have_v a_o slit_n towards_o the_o end_n i_o so_o great_a that_o the_o string_n bc_n may_v slide_v into_o it_o now_o all_o the_o cunning_a or_o craft_n be_v how_o to_o make_v fast_o or_o to_o open_v the_o purse_n which_o consist_v in_o make_v the_o string_n bc_n slide_v through_o the_o side_n at_o ay_o therefore_o bring_v down_o b_o to_o i_o then_o make_v the_o end_n i_o pass_v through_o the_o ring_n b_o and_o also_o d_o with_o his_o string_n to_o pass_v through_o the_o slit_n i_o so_o shall_v the_o purse_n be_v fast_o and_o then_o may_v the_o string_n be_v put_v as_o before_o and_o it_o will_v seem_v difficult_a to_o discover_v how_o it_o be_v do_v now_o to_o open_v the_o purse_n put_v through_o the_o end_n i_o through_o the_o ring_n b_o and_o then_o through_o the_o slit_n i_o by_o which_o you_o put_v through_o the_o string_n dc_o by_o this_o way_n the_o purse_n will_v be_v open_v problem_n lvi_o whether_o it_o be_v more_o hard_a and_o admirable_a without_o compass_n to_o make_v a_o perfect_a circle_n or_o be_v make_v to_o find_v out_o the_o centre_n of_o it_o it_o be_v say_v that_o upon_o a_o time_n past_a two_o mathematician_n meet_v and_o they_o will_v make_v trial_n of_o their_o industry_n the_o one_o make_v instant_o a_o perfect_a circle_n without_o compass_n and_o the_o other_o immediate_o point_v out_o the_o centre_n thereof_o with_o the_o point_n of_o a_o needle_n now_o which_o be_v the_o chief_a action_n it_o seem_v the_o first_o for_o to_o draw_v the_o most_o noble_a figure_n upon_o a_o plain_a table_n without_o other_o help_n than_o the_o hand_n and_o the_o mind_n be_v full_a of_o admiration_n to_o find_v the_o centre_n be_v but_o to_o find_v out_o only_o one_o point_n but_o to_o draw_v a_o round_a there_o must_v be_v almost_o infinite_a point_n equidistant_a from_o the_o centre_n or_o middle_n that_o in_o conclusion_n it_o be_v both_o the_o circle_n and_o the_o centre_n together_o but_o contrary_o it_o may_v seem_v that_o to_o find_v the_o centre_n be_v more_o difficult_a for_o what_o attention_n vivacity_n and_o subtlety_n must_v there_o be_v in_o the_o spirit_n in_o the_o eye_n in_o the_o hand_n which_o will_v choose_v the_o true_a point_n among_o a_o thousand_o other_o point_n he_o that_o make_v a_o circle_n keep_v always_o the_o same_o distance_n and_o be_v guide_v by_o a_o half_a distance_n to_o finish_v the_o rest_n but_o he_o that_o must_v find_v the_o centre_n must_v in_o the_o
piece_n to_o keep_v the_o same_o proportion_n as_o the_o body_n to_o his_o part_n so_o that_o by_o the_o greatness_n of_o the_o work_n and_o proportionable_a symmetry_n some_o dare_v assure_v themselves_o that_o by_o knowledge_n of_o one_o only_a part_n of_o that_o building_n one_o may_v know_v all_o the_o measure_n of_o that_o goodly_a structure_n some_o architect_n say_v that_o the_o foundation_n of_o house_n and_o basis_n of_o column_n be_v as_o the_o foot_n the_o top_n and_o roof_n as_o the_o head_n the_o rest_n as_o the_o body_n those_o which_o have_v be_v somewhat_o more_o curious_a have_v note_v that_o as_o in_o humane_a body_n the_o part_n be_v uniform_a as_o the_o nose_n the_o mouth_n etc._n etc._n these_o which_o be_v double_a be_v put_v on_o one_o side_n or_o other_o with_o a_o perfect_a equality_n in_o the_o same_o architecture_n in_o like_a manner_n some_o have_v be_v yet_o more_o curious_a than_o solid_a compare_v all_o the_o ornament_n of_o a_o corinth_n to_o the_o part_n of_o the_o face_n as_o the_o brow_n the_o eye_n the_o nose_n the_o mouth_n the_o round_v of_o pillar_n to_o the_o writhe_n of_o hair_n the_o channel_n of_o column_n to_o the_o fold_n of_o woman_n robe_n etc._n etc._n now_o building_n be_v a_o work_n of_o the_o best_a artist_n there_o be_v much_o reason_n why_o man_n ought_v to_o make_v his_o imitation_n from_o the_o chief_a work_n of_o nature_n which_o be_v man_n hence_o it_o be_v that_o vitruâ—ius_n in_o his_o three_o book_n and_o all_o the_o best_a architecte_n treat_v of_o the_o proportion_n of_o man_n among_o other_o albert_n durens_n have_v make_v a_o whole_a book_n of_o the_o measure_n of_o man_n body_n from_o the_o foot_n to_o the_o head_n let_v they_o read_v it_o who_o will_v they_o may_v have_v a_o perfect_a knowledge_n thereof_o but_o i_o will_v content_v myself_o and_o it_o may_v satisfy_v some_o with_o that_o which_o follow_v first_o the_o length_n of_o a_o man_n well_o make_v which_o common_o be_v call_v height_n be_v equal_a to_o the_o distance_n from_o one_o end_n of_o his_o finger_n to_o the_o other_o when_o the_o arm_n be_v extend_v as_o wide_a as_o they_o may_v be_v second_o if_o a_o man_n have_v his_o foot_n and_o hand_n extend_v or_o stretch_v in_o form_n of_o s._n andrews_n cross_n place_v one_o foot_n of_o a_o pair_n of_o compass_n upon_o his_o navel_n one_o may_v describe_v a_o circle_n which_o will_v pass_v by_o the_o end_n of_o his_o hand_n and_o foot_n and_o draw_v line_n by_o the_o term_n of_o the_o hand_n and_o foot_n you_o have_v a_o square_a within_o a_o circle_n three_o the_o breadth_n of_o man_n or_o the_o space_n which_o be_v from_o one_o side_n to_o another_o the_o breast_n the_o head_n and_o the_o neck_n make_v the_o 6_o part_n of_o all_o the_o body_n take_v in_o length_n or_o height_n four_o the_o length_n of_o the_o face_n be_v equal_a to_o the_o length_n of_o the_o hand_n take_v from_o the_o small_a of_o the_o arm_n unto_o the_o extremity_n of_o the_o long_a finger_n 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to_o be_v demonstrate_v that_o there_o need_v not_o but_o multiplication_n only_o to_o try_v each_o particular_a and_o first_o of_o grain_n of_o mustardseed_n first_o therefore_o it_o be_v certain_a that_o the_o increase_n of_o one_o grain_n of_o mustardseed_n for_o 20_o year_n space_n can_v be_v contain_v within_o the_o visible_a world_n nay_o if_o it_o be_v a_o hundred_o time_n great_a than_o it_o be_v and_o hold_v nothing_o beside_o from_o the_o centre_n of_o the_o earth_n even_o unto_o the_o firmament_n but_o only_o small_a grain_n of_o mustardseed_n now_o because_o this_o seem_v but_o word_n it_o must_v be_v prove_v by_o art_n as_o may_v be_v do_v in_o this_o wise_a as_o suppose_v one_o mustardseed_n sow_v to_o bring_v forth_o a_o tree_n or_o branch_n in_o each_o extendure_n of_o which_o may_v be_v a_o thousand_o grain_n but_o we_o will_v suppose_v only_o a_o thousand_o in_o the_o whole_a tree_n and_o let_v we_o proceed_v to_o â—0_n year_n every_o seed_n to_o bring_v forth_o 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shall_v it_o be_v then_o if_o it_o shall_v be_v multiply_v again_o by_o a_o thousand_o for_o the_o â—8_o year_n and_o that_o again_o by_o a_o thousand_o for_o every_o year_n increase_v until_o you_o come_v to_o the_o 20_o year_n it_o be_v a_o thing_n as_o clear_a as_o the_o day_n that_o such_o a_o heap_n of_o mustardseed_n will_v be_v a_o hundred_o thousand_o time_n great_a than_o the_o earth_n and_o bring_v only_o but_o the_o increase_n of_o one_o grain_n in_o 20_o year_n of_o pig_n second_o be_v it_o not_o a_o strange_a proposition_n to_o say_v that_o the_o great_a turk_n with_o all_o his_o revenue_n be_v not_o able_a to_o maintain_v for_o one_o year_n time_n all_o the_o pig_n that_o a_o sow_n may_v pig_n with_o all_o her_o race_n that_o be_v the_o increase_n with_o the_o increase_n unto_o 12_o year_n this_o seem_v impossible_a yet_o it_o be_v most_o true_a for_o let_v we_o suppose_v and_o put_v the_o case_n that_o a_o sow_n bring_v forth_o but_o 6_o two_o male_n and_o 4_o female_n and_o that_o each_o female_n shall_v bring_v forth_o as_o many_o every_o year_n during_o the_o space_n of_o 12_o year_n at_o the_o end_n of_o the_o time_n there_o will_v be_v find_v above_o 3â—_n million_o of_o pig_n now_o allow_v a_o crown_n for_o the_o maintenance_n of_o each_o pig_n for_o a_o year_n which_o be_v as_o little_a as_o may_v be_v be_v but_o near_o a_o half_a of_o a_o farthing_n allowance_n for_o each_o day_n there_o must_v be_v at_o the_o least_o so_o many_o crown_n to_o maintain_v they_o one_o a_o year_n viz._n 33_o million_o which_o exceed_v the_o turk_n revenue_n by_o much_o of_o grain_n of_o corne._n three_o it_o will_v make_v one_o astonish_v to_o think_v that_o a_o grain_n of_o corn_n with_o his_o increase_n successive_o for_o the_o space_n of_o 12_o year_n will_v produce_v in_o grain_n 24414062â—000000000000_n which_o be_v able_a to_o load_v almost_o all_o the_o creature_n in_o the_o world_n to_o open_v which_o let_v it_o be_v suppose_v that_o the_o first_o year_n one_o grain_n be_v sow_v bring_v forth_o 50_o but_o sometime_o there_o be_v see_v 70_o sometime_o 100_o fold_n which_o grain_n sow_v the_o next_o year_n every_o one_o to_o produce_v 50_o and_o so_o consequent_o the_o whole_a and_o increase_v to_o be_v sow_v every_o year_n until_o 12_o year_n be_v expire_v there_o will_v be_v of_o increase_v the_o aforesaid_a prodigious_a sum_n of_o grain_n viz._n 244140625000000000000_o which_o will_v make_v a_o cubical_a heap_n of_o 6258522_o grain_n every_o way_n which_o be_v more_o than_o a_o cubicall_a body_n of_o 31_o mile_n every_o way_n for_o allow_v 40_o grain_n in_o length_n to_o each_o foot_n the_o cube_n will_v be_v 156463_o foot_n every_o way_n from_o which_o it_o be_v evident_a that_o if_o there_o be_v two_o hundred_o thousand_o city_n as_o great_a as_o london_n allow_v to_o each_o 3_o mile_n square_v every_o way_n and_o 100_o foot_n in_o height_n there_o will_v not_o be_v sufficient_a room_n to_o contain_v the_o aforesaid_a quantity_n 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as_o ab_fw-la and_o a_o hour_n before_o noon_n mark_v the_o extremity_n of_o the_o shadow_n of_o ab_fw-la which_o suppose_v it_o be_v at_o c._n describe_v a_o circle_n at_o that_o semidiamiter_n cdf_n then_o after_o noon_n mark_v when_o the_o top_n of_o the_o shadow_n of_o ab_fw-la touch_v the_o circle_n which_o admit_v in_o d_o divide_v the_o distance_n cd_o into_o two_o equal_a part_n which_o suppose_v at_o e._n draw_v the_o line_n eaf_n which_o be_v the_o meridian_n line_n or_o line_n of_o north_n &_o south_n now_o if_o the_o ark_n of_o the_o circle_n cd_o be_v divide_v into_o degree_n place_n a_o needle_n gh_o upon_o a_o plain_a set_v up_o in_o the_o centre_n and_o mark_v how_o many_o degree_n the_o point_n of_o the_o needle_n g_o be_v from_o e._n so_o much_o do_v the_o needle_n vary_v from_o the_o north_n in_o that_o place_n problem_n ci._n how_o to_o find_v at_o any_o time_n which_o way_n the_o wind_n be_v in_o one_o chamber_n without_o go_v abroad_o upon_o the_o planck_a or_o 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line_n into_o 27_o part_n and_o according_o to_o ak_v describe_v a_o ark_n kine_n then_o from_o k_o in_o the_o perpendicular_a kx_n account_n parâ—s_n viz_o at_o l._n which_o shall_v represent_v the_o former_a three_o yard_n and_o draw_v the_o line_n la._n from_o l_o in_o the_o say_v perpendicular_a reckon_v the_o diameter_n of_o the_o lesser_a globe_n of_o what_o magnitude_n it_o be_v intend_v to_o be_v suppose_v slightall_n and_o draw_v the_o line_n sa_o cut_v the_o ark_n vk_n in_o n._n then_o from_o k._n in_o the_o perpendicular_a account_n 9_o yard_n which_o admit_v at_o t._n draw_v ta_n cut_v yk._n in_o o_o transfer_v the_o ark_n mn_v from_o a_o to_o p._n and_o draw_v ap._n which_o will_v cut_v the_o perpendicular_a in_o v._o so_o a_o line_n draw_v from_o the_o middle_n of_o vf_n unto_o the_o visual_a line_n a_z and_o hence_v shall_v be_v the_o diameter_n of_o the_o next_o globe_n last_o account_v from_o k._n in_o the_o perpendicular_a xk_n 22_o part_n and_o draw_v the_o line_n wa_n cut_v yk_n in_o q._n then_o take_v the_o ark_n mn_v and_o transfer_v it_o from_o q_o to_o r_o and_o draw_v be_v which_o will_v cut_v the_o perpendicular_a in_o x_o so_o the_o line_n which_o pass_v by_o the_o meddle_v of_o xw_n perpendicular_a to_o the_o visual_a line_n awe_o and_o ax._n be_v the_o diameter_n of_o the_o three_o globe_n to_o wit_n 5_o 6._o which_o measure_v transfer_v in_o the_o pillar_n bc._n which_o show_v the_o true_a magnitude_n of_o the_o globe_n 1_o 2_o 3._o from_o this_o a_o architect_n or_o do_v proportion_v his_o image_n &_o the_o fould_a of_o the_o robe_n which_o be_v most_o deform_v at_o the_o eye_n below_o in_o the_o make_n yet_o most_o perfect_a when_o it_o be_v set_v in_o his_o true_a height_n above_o the_o eye_n problem_n cvi_o how_o to_o disguise_n or_o disfigure_v a_o image_n as_o a_o head_n a_o arm_n a_o whole_a body_n etc._n etc._n so_o that_o it_o have_v no_o proportion_n the_o ear_n to_o become_v long_o the_o nose_n as_o that_o of_o a_o swan_n the_o mouth_n as_o a_o coach_n entrance_n &c_n &c_n yet_o the_o eye_n place_v at_o a_o certain_a point_n will_v be_v see_v in_o a_o direct_a &_o exact_a proportion_n i_o will_v not_o strive_v to_o set_v a_o geometrical_a figure_n here_o for_o fear_v it_o may_v seem_v too_o difficult_a to_o understand_v but_o i_o will_v endeavour_v by_o discourse_n how_o mechanical_o with_o a_o candle_n you_o may_v perceive_v it_o sensible_a first_o there_o must_v be_v make_v a_o figure_n upon_o paper_n such_o as_o you_o please_v according_a to_o his_o just_a proportion_n and_o paint_v it_o as_o
a_o picture_n which_o painter_n know_v well_o enough_o to_o do_v afterward_o put_v a_o candle_n upon_o the_o table_n and_o interpose_v this_o figure_n oblique_o between_o the_o say_a candle_n and_o the_o book_n of_o paper_n where_o you_o desire_v to_o have_v the_o figure_n disguise_v in_o such_o sort_n that_o the_o height_n pass_v athwart_o the_o hole_n of_o the_o picture_n then_o will_v it_o carry_v all_o the_o form_n of_o the_o picture_n upon_o the_o paper_n but_o with_o deformity_n follow_v these_o tract_n and_o mark_v out_o the_o light_n with_o a_o coal_n black_a head_n or_o ink_n and_o you_o have_v your_o desire_n to_o find_v now_o the_o point_n where_o the_o eye_n must_v see_v it_o in_o his_o natural_a form_n it_o be_v accustom_v according_a to_o the_o order_n of_o perspective_n to_o place_v this_o point_n in_o the_o line_n draw_v in_o height_n equal_a to_o the_o largeness_n of_o the_o narrow_a side_n of_o the_o deform_a square_n and_o it_o be_v by_o this_o way_n that_o it_o be_v 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wheel_n make_v the_o body_n of_o a_o ordinary_a dial_n and_o divide_v the_o hour_n in_o the_o circle_n into_o 12._o part_n make_v a_o great_a wheel_n in_o height_n above_o the_o axletree_n to_o the_o which_o you_o shall_v place_v the_o cord_n of_o your_o counterpoise_n so_o that_o it_o may_v descend_v that_o in_o 1â—_n hour_n of_o time_n your_o index_n or_o needle_n may_v make_v one_o revolution_n which_o may_v be_v know_v by_o a_o watch_n which_o you_o may_v have_v by_o you_o then_o put_v a_o balance_n which_o may_v stop_v the_o course_n of_o the_o wheel_n and_o give_v it_o a_o regular_a motion_n and_o you_o shall_v see_v a_o effect_n as_o just_a from_o this_o as_o from_o a_o clock_n with_o many_o wheel_n problem_n cx_o how_o by_o help_n of_o two_o wheel_n to_o make_v a_o child_n to_o draw_v up_o alone_o a_o hogshead_n of_o water_n at_o a_o time_n and_o be_v draw_v up_o shall_v cast_v out_o itself_o into_o another_o vessel_n as_o one_o will_v have_v it_o let_v r_o be_v the_o pit_n from_o whence_o water_n be_v to_o be_v draw_v p_o the_o hook_n to_o throw_v out_o the_o water_n when_o it_o be_v bring_v up_o this_o hook_n must_v be_v movable_a let_v ab_fw-la be_v the_o axis_n of_o the_o wheel_n sf_n which_o wheel_n have_v divers_a fork_n of_o iron_n make_v at_o g_o equal_o fasten_v at_o the_o wheel_n let_v i_o be_v a_o card_n which_o be_v draw_v by_o k_o to_o make_v the_o wheel_n s_o to_o turn_v which_o wheel_n saint_n bear_v proportion_n to_o the_o wheel_n t_o as_o 8_o to_z â—_o let_v n_o be_v a_o chain_n of_o iron_n to_o which_o be_v tie_v the_o vessel_n o_o and_o the_o other_o which_o be_v in_o the_o pit_n eâ—_n be_v a_o piece_n of_o wood_n which_o have_v a_o morte_n in_o 1_o and_o â—_o by_o which_o the_o cord_n i_o pass_v tie_v at_o the_o brickwall_n as_o kh_n and_o the_o other_o piece_n of_o timber_n of_o the_o little_a wheel_n as_o m_n mortify_v in_o likewise_o for_o the_o chain_n to_o pass_v through_o draw_v the_o cord_n i_o by_o k_o and_o the_o wheel_n will_v turn_v &_o so_o consequent_o the_o wheel_n t_o which_o will_v cause_v the_o vessel_n o_o to_o raise_v which_o be_v empty_a draw_v the_o cord_n again_o by_o y_o and_o the_o other_o vessel_n which_o be_v in_o the_o pit_n â—ill_v come_v out_o by_o the_o same_o reason_n this_o be_v a_o invention_n which_o will_v save_v labour_n if_o practise_v but_o here_o be_v to_o be_v note_v that_o the_o pit_n must_v be_v large_a enough_o to_o the_o end_n that_o it_o contain_v two_o great_a vessel_n to_o pass_v up_o and_o down_o one_o by_o another_o problem_n cxi_o to_o make_v a_o ladder_n of_o cord_n which_o may_v be_v carry_v in_o one_o pocket_n by_o which_o one_o may_v easy_o mount_v up_o a_o wall_n or_o tree_n alone_o take_v two_o pulley_n a_o &_o d_o unto_o that_o of_o a_o let_v there_o be_v fasten_v a_o cramp_n of_o iron_n as_o b_o and_o at_o d_o let_v there_o be_v fasten_v a_o staff_n of_o a_o foot_n and_o a_o half_a long_o as_o f_o than_o the_o poultry_n a_o place_n a_o hand_n of_o iron_n as_o e_o to_o which_o tie_n a_o cord_n of_o a_o half_a inch_n thick_a which_o may_v be_v of_o silk_n because_o it_o be_v for_o the_o pocket_n then_o strive_v to_o make_v fast_o the_o poultry_n a_o by_o the_o help_n of_o the_o cramp_n of_o iron_n b_o to_o the_o place_n that_o you_o intend_v to_o scale_v and_o the_o staff_n f_o be_v tie_v at_o the_o poultry_n d_o put_v it_o between_v your_o leg_n as_o though_o you_o will_v sit_v upon_o it_o then_o hold_v the_o cord_n c_o in_o your_o hand_n you_o may_v guide_v yourself_o to_o the_o place_n require_v which_o may_v be_v make_v more_o facile_a by_o the_o multiply_a of_o pulley_n this_o secret_a be_v most_o excellent_a in_o war_n and_o for_o lover_n its_o supportablenesse_n avoid_v suspicion_n problem_n cxii_o how_o to_o make_v a_o pump_n who_o strength_n be_v marvellous_a by_o reason_n of_o the_o great_a weight_n of_o water_n that_o it_o be_v able_a to_o bring_v up_o at_o once_o and_o so_o by_o continuance_n let_v 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d be_v the_o height_n of_o the_o case_n about_o two_o or_o three_o foot_n high_a and_o broad_a according_a to_o discretion_n the_o rest_n of_o the_o case_n or_o concavity_n let_v be_v o_o let_v the_o sucker_n of_o the_o pump_n which_o be_v make_v be_v just_a for_o the_o case_n or_o pump_n head_n 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d &_o may_v be_v make_v of_o wood_n or_o brass_n of_o 4_o inch_n thick_a have_v a_o hole_n at_o e_o which_o descend_v raise_v up_o the_o cover_n p_o by_o which_o issue_v forth_o the_o water_n &_o ascend_v or_o raise_v up_o it_o shut_v it_o or_o make_v it_o close_o r_n be_v the_o handle_n of_o the_o sucker_n tie_v to_o the_o handle_n tx_n which_o work_v in_o the_o post_n we_o let_v a_o b_o c_o d_o be_v a_o piece_n of_o brass_n g_o the_o piece_n which_o enter_v into_o the_o hole_n to_o f_o to_o keep_v out_o the_o air_n h_o i_o k_o l_o the_o piece_n tie_v at_o the_o funnel_n or_o pipe_n in_o which_o play_v the_o iron_n rod_n or_o axis_fw-la g_o so_fw-mi that_o it_o pass_v through_o the_o other_o piece_n mn_v which_o be_v tie_v with_o the_o end_n of_o the_o pipe_n of_o brass_n note_v that_o the_o low_a end_n of_o the_o cistern_n ought_v to_o be_v rest_v upon_o a_o gridiron_n or_o iron_n grate_n which_o may_v be_v tie_v in_o the_o pit_n by_o which_o mean_v lift_v up_o and_o put_v down_o the_o handle_n you_o may_v draw_v ten_o time_n more_o water_n than_o otherwise_o you_o can_v problem_n cxiii_o how_o by_o mean_n of_o a_o cistern_n to_o make_v water_n of_o
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 let_v each_o of_o the_o pipe_n have_v a_o cock_n g_o &_o l_o the_o cock_n at_o g_o be_v close_v open_z that_o at_o ay_o &_o so_o with_o a_o squirt_n force_v the_o water_n through_o the_o hole_n at_o h_n then_o close_a the_o cock_n at_o a_o &_o draw_v out_o the_o squirt_n and_o open_v the_o cock_n at_o g._n the_o air_n be_v before_o rarify_v will_v extend_v his_o dimension_n and_o force_v the_o water_n with_o such_o violence_n that_o it_o will_v amount_v above_o the_o height_n of_o one_o or_o two_o pipe_n and_o so_o much_o the_o more_o by_o how_o much_o the_o machine_n be_v great_a this_o violence_n will_v last_v but_o a_o little_a while_n if_o the_o pipe_n have_v too_o great_a a_o open_n for_o as_o the_o air_n approach_v to_o his_o natural_a place_n so_o the_o force_n will_v diminish_v problem_n cxv_o how_o to_o empty_v the_o water_n of_o a_o cistern_n by_o a_o pipe_n which_o shall_v have_v a_o motion_n of_o itself_o let_v ab_fw-la be_v the_o vessel_n cde_v the_o pipe_n hg_v a_o little_a vessel_n under_o the_o great_a in_o which_o one_o end_n of_o the_o pipe_n be_v viz._n c_o and_o let_v the_o other_o end_n of_o the_o pipe_n e._n pass_v through_o the_o bottom_n of_o the_o vessel_n at_o f_o then_o as_o the_o vessel_n fill_v so_o will_v the_o pipe_n and_o when_o the_o vessel_n shall_v be_v full_a as_o far_o as_o po_n the_o pipe_n will_v begin_v to_o run_v at_o e_o of_o his_o own_o accord_n and_o never_o cease_v until_o the_o vessel_n be_v whole_o empty_a problem_n cxvi_o how_o to_o squirt_n or_o spout_v out_o a_o great_a height_n so_o that_o one_o pot_n of_o water_n shall_v last_v a_o long_a time_n let_v there_o be_v prepare_v two_o vessel_n of_o brass_n lead_v or_o of_o other_o matter_n of_o equal_a substance_n as_o be_v the_o two_o vessel_n ab_fw-la and_o bd_o &_o let_v they_o be_v join_v together_o by_o the_o two_o pillar_n mn_v &_o of_o then_o let_v there_o be_v a_o pipe_n hg_v which_o may_v pass_v through_o the_o cover_n of_o the_o vessel_n cd_o and_o pass_v through_o ab_fw-la into_o g_o make_v a_o little_a bunch_n or_o rise_n in_o the_o cover_n of_o the_o vessel_n ab_fw-la so_o that_o the_o pipe_n touch_v it_o not_o at_o the_o bottom_n then_o let_v there_o be_v solder_v fast_o another_o pipe_n il_fw-fr which_o may_v be_v separate_v from_o the_o bottom_n of_o the_o vessel_n and_o may_v have_v his_o bunchie_a swell_n as_o the_o former_a without_o touch_v the_o bottom_n as_o be_v represent_v in_o l_o and_o pass_v through_o the_o bottom_n of_o ab_fw-la may_v be_v continue_v unto_o ay_o that_o be_v to_o say_v to_o make_v a_o open_n to_o the_o cover_n of_o the_o vessel_n ab_fw-la &_o let_v it_o have_v a_o little_a mouth_n as_o a_o trumpet_n to_o that_o end_n to_o receive_v the_o water_n then_o there_o must_v further_o be_v add_v a_o very_a small_a pipe_n which_o may_v pass_v through_o the_o bottom_n of_o the_o vessel_n ab_fw-la as_o let_v it_o be_v open_a and_o let_v there_o be_v a_o bunch_n or_o swell_v over_o it_o as_o at_o p_o so_o that_o it_o touch_v not_o also_o the_o bottom_n let_v there_o be_v further_o make_v to_o this_o lesser_a vessel_n a_o edge_n in_o form_n of_o a_o basin_n to_o receive_v the_o water_n which_o be_v do_v pour_v water_n into_o the_o pipe_n il_fw-fr until_o the_o vessel_n cd_o be_v full_a then_o turn_v the_o whole_a machine_n upside_o down_o that_o the_o vessel_n cd_o may_v be_v uppermost_a and_o ab_fw-la undermost_a so_o by_o help_n of_o the_o pipe_n gh_o the_o water_n of_o the_o vessel_n cd_o will_v run_v into_o the_o vessel_n ab_fw-la to_o have_v passage_n by_o the_o pipe_n po._n this_o motion_n be_v pleasant_a at_o a_o feast_n in_o fill_v the_o say_a vessel_n with_o wine_n which_o will_v spout_v it_o out_o as_o though_o it_o be_v from_o a_o boil_a fountain_n in_o the_o form_n of_o a_o thread_n very_o pleasant_a to_o behold_v problem_n cxviii_o how_o to_o practice_v excellent_o the_o reanimation_n of_o simple_n in_o case_n the_o plant_n may_v not_o be_v transport_v to_o be_v replant_v 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 your_o receiver_n and_o close_o it_o hermetical_o and_o make_v a_o lamp_n fire_n under_o it_o until_o you_o may_v see_v present_v in_o it_o that_o which_o nature_n afford_v we_o as_o flower_n tree_n fruit_n fountain_n sun_n moon_n star_n etc._n etc._n behold_v here_o the_o form_n of_o the_o limbeck_n and_o the_o receiver_n a_o represent_v the_o limbeck_n b_o stands_z for_o the_o receiver_n problem_n cxxi_o how_o to_o make_v a_o cone_n or_o a_o pyramidal_a body_n move_v upon_o a_o table_n without_o spring_n or_o other_o artificial_a mean_n so_o that_o it_o shall_v move_v by_o the_o edge_n of_o the_o table_n without_o fall_v this_o proposition_n be_v not_o so_o thorny_a and_o subtle_a as_o it_o seem_v to_o be_v for_o put_v under_o a_o cone_n of_o paper_n a_o beetle_n or_o such_o like_a creature_n you_o shall_v have_v pleasure_n with_o astonishment_n &_o admiration_n to_o those_o which_o be_v ignorant_a in_o the_o cause_n for_o this_o animal_n will_v strive_v always_o to_o free_v herself_o from_o the_o captivity_n in_o which_o she_o be_v in_o by_o the_o imprisonment_n of_o the_o cone_n for_o come_v near_o the_o edge_n of_o the_o table_n she_o will_v return_v to_o the_o other_o side_n for_o fear_n of_o fall_v problem_n cxxii_o to_o cleave_v a_o anvil_n with_o the_o blow_n of_o a_o pistol_n this_o be_v proper_a to_o a_o warrior_n and_o to_o perform_v it_o let_v the_o anvil_n be_v heat_v red_a hot_a as_o one_o can_v possible_a in_o such_o sort_n that_o all_o the_o solidity_n of_o the_o body_n be_v soften_v by_o the_o fire_n then_o charge_v the_o pistol_n with_o a_o bullet_n of_o silver_n and_o so_o have_v you_o infallible_o the_o experiment_n problem_n cxxiii_o how_o to_o râ—st_v a_o capon_n carry_v in_o a_o budget_n at_o a_o saddle-bowe_n in_o the_o space_n of_o ride_v 5_o or_o 6_o mile_n have_v make_v it_o ready_a and_o lard_v it_o stuff_n â—t_a with_o butter_n then_o heat_n a_o piece_n of_o steel_n which_o may_v be_v form_v round_o according_a to_o the_o 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 salt-peter_n will_v blow_v out_o the_o candle_n immediate_o and_o go_v to_o the_o other_o image_n before_o the_o match_n of_o the_o candle_n be_v out_o touch_v the_o sulphur_n with_o it_o and_o say_v light_v the_o candle_n &_o it_o will_v immediate_o be_v light_v which_o will_v cause_v a_o admiration_n to_o those_o which_o see_v the_o action_n if_o it_o be_v well_o do_v with_o a_o secret_a dexterity_n problem_n xxvii_o how_o to_o keep_v wine_n fresh_a as_o if_o it_o be_v in_o a_o cellar_n though_o it_o be_v in_o the_o heat_n of_o summer_n and_o without_o ice_n or_o snow_n yea_o though_o it_o be_v carry_v at_o a_o saddle_n bow_v and_o expose_v to_o the_o sun_n all_o the_o day_n set_v your_o wine_n in_o a_o vial_n of_o glass_n and_o place_v it_o in_o a_o box_n make_v of_o wood_n leather_n or_o such_o like_a about_o which_o vial_n place_n saltpetre_n and_o it_o will_v preserve_v it_o and_o keep_v it_o very_o fresh_a this_o experiment_n be_v not_o a_o little_a commodious_a for_o those_o 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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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end_n of_o small_a funnel_n these_o iron_n cannon_n may_v be_v pierce_v in_o sundry_a place_n to_o which_o hole_n may_v be_v set_v small_a ball_n full_a of_o composition_n for_o the_o water_n which_o small_a ball_n must_v be_v pierce_v deep_a and_o large_a and_o cover_v with_o pitch_n except_o the_o hole_n in_o which_o hole_n must_v be_v first_o place_v a_o little_a quantity_n of_o grain-powder_n and_o the_o rest_n of_o the_o hole_n fill_v up_o with_o composition_n and_o note_v further_o that_o these_o iron_n cannon_n must_v be_v fill_v with_o a_o slow_a composition_n but_o such_o which_o be_v proper_a to_o burn_v in_o the_o water_n then_o must_v these_o cannon_n with_o their_o small_a ball_n be_v put_v so_o together_o that_o it_o may_v make_v a_o globe_n and_o the_o hole_n in_o the_o cannon_n be_v answerable_a to_o the_o hollow_a ball_n and_o all_o cover_v over_o with_o pitch_n and_o tallow_n afterward_o pierce_v this_o ball_n against_o the_o great_a cannon_n to_o which_o all_o the_o lesser_a shall_v answer_v unto_o the_o composition_n than_o fire_n it_o and_o when_o it_o begin_v to_o blow_v throw_v it_o into_o the_o water_n so_o the_o fire_n come_v to_o the_o hole_n will_v fire_v the_o grain_n powder_n the_o which_o will_v cause_v the_o ball_n to_o separate_v and_o fly_v here_o and_o there_o sometime_o two_o at_o a_o time_n sometime_o three_o sometime_o more_o which_o will_v burn_v within_o the_o water_n with_o great_a astonishment_n and_o content_a to_o those_o which_o see_v it_o of_o lance_n of_o fire_n stand_v lance_n of_o fire_n be_v make_v common_o with_o hollow_a wood_n to_o contain_v sundry_a petard_n or_o rocket_n as_o the_o figure_n here_o show_v by_o which_o be_v easy_a to_o invent_v other_o occording_n to_o one_o fancy_n these_o lance_n have_v wooden_a handle_n that_o so_o they_o may_v be_v fasten_v at_o some_o post_n so_o that_o they_o be_v not_o overthrow_v in_o the_o fly_v out_o of_o the_o rocket_n or_o petard_n there_o be_v lesser_a sort_n of_o lance_n who_o case_n be_v of_o three_o or_o four_o fold_n of_o paper_n of_o a_o foot_n long_o and_o about_o the_o bigness_n of_o one_o finger_n which_o be_v fill_v with_o a_o composition_n for_o lance_n but_o if_o these_o lance_n be_v fill_v with_o a_o composition_n than_o unto_o every_o 4_o ounc_n of_o powder_n addâ—_n 2_o ounce_n of_o salt-peter_n and_o unto_o that_o add_v 1_o ounce_n of_o sulphur_n it_o will_v make_v a_o brick_n fire_n red_a before_o it_o be_v half_o spend_v if_o the_o lance_n be_v fire_v and_o hold_v to_o it_o and_o if_o 20_o such_o lance_n be_v place_v about_o a_o great_a rocket_n and_o shot_n to_o a_o house_n or_o ship_n it_o will_v produce_v a_o mischievous_a effect_n how_o to_o shoot_v a_o rocket_n horizontall_a or_o otherwise_o unto_o the_o end_n of_o the_o rocket_n place_n a_o arrow_n which_o may_v not_o be_v too_o heavy_a but_o in_o stead_n of_o the_o feather_n let_v that_o be_v of_o thin_a white_a tin_n plate_n and_o place_n it_o upon_o a_o rest_n as_o 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about_o the_o stick_n dm_o at_o 〈◊〉_d and_o at_o that_o point_n hang_v a_o bullet_n of_o some_o weight_n as_o k._n for_o then_o give_v fire_n at_o a._n it_o will_v burn_v to_o b._n by_o a_o small_a serpent_n fill_v there_o and_o tie_v at_o the_o end_n and_o cover_v so_o that_o the_o water_n injure_v it_o hot_a which_o will_v fire_v the_o rocket_n bd_o and_o so_o mount_v quick_a out_o of_o the_o water_n by_o the_o loose_a tie_n at_o c._n and_o the_o bullet_n at_o the_o pack-thread_n will_v leave_v the_o other_o rocket_n in_o the_o water_n and_o so_o ascend_v like_o a_o rocket_n in_o the_o air_n to_o the_o admiration_n of_o such_o as_o know_v not_o the_o secrecy_n of_o the_o frame_n of_o the_o part_n of_o a_o firework_a together_o that_o the_o several_a work_n may_v fire_v one_o after_o another_o cause_o a_o frame_n to_o be_v make_v as_o abcd._n of_o two_o foot_n square_v every_o way_n or_o thereabouts_o according_a to_o the_o quantity_n of_o your_o several_a work_n then_o may_v you_o 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