Selected quad for the lemma: water_n

Word A	Word B	Word C	Word D	Occurrence	Frequency Band	MI	MI Band	Prominent
water_n	dram_n	ounce_n	pound_n	7,397	5	9.0519	4	true

Text snippets containing the quad

ID	Title	Author	Corrected Date of Publication (TCP Date of Publication)	STC	Words	Pages
A48262	Mathematicall recreations. Or, A collection of many problemes, extracted out of the ancient and modern philosophers as secrets and experiments in arithmetick, geometry, cosmographie, horologiographie, astronomie, navigation, musick, opticks, architecture, statick, mechanicks, chemistry, water-works, fire-works, &c. Not vulgarly manifest till now. Written first in Greeke and Latin, lately compi'ld in French, by Henry Van Etten, and now in English, with the examinations and augmentations of divers modern mathematicians whereunto is added the description and use of the generall horologicall ring: and the double horizontall diall. Invented and written by William Oughtred.; Récréation mathématique. English.	Oughtred, William, 1575-1660. aut	1653 (1653)	Wing L1790; ESTC R217635	140,825	339

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 ●●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 receive●_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

out_o of_o a_o vessel_n at_o the_o bunghole_n without_o pierce_v of_o a_o hole_n in_o the_o vessel_n in_o this_o there_o be_v no_o need_n but_o to_o have_v a_o cane_n or_o pipe_n of_o glass_n or_o such_o like_a one_o of_o the_o end_n of_o which_o may_v be_v close_v up_o almost_o leave_v some_o small_a hole_n at_o the_o end_n for_o than_o if_o that_o end_n be_v set_v into_o the_o vessel_n at_o the_o bunghole_n the_o whole_a cane_n or_o pipe_n will_v be_v fill_v by_o little_a and_o little_a and_o once_o be_v full_a stop_v the_o other_o end_n which_o be_v without_o and_o then_o pull_v out_o the_o cane_n or_o pipe_n so_o will_v it_o be_v full_a of_o wine_n then_o open_v a_o little_a the_o top_n above_o you_o may_v fill_v a_o glass_n or_o other_o pot_n with_o it_o for_o as_o the_o wine_n issue_v out_o the_o air_n come_v into_o the_o cane_n or_o pipe_n to_o supply_v vacuity_n 10._o ten_o how_o to_o measure_v irregular_a body_n by_o help_n of_o water_n some_o throw_n in_o the_o body_n or_o magnitude_n into_o a_o vessel_n and_o keep_v that_o which_o flow_v out_o over_o say_v it_o be_v always_o equal_a to_o the_o thing_n cast_v into_o the_o water_n let_v i●_n be_v more_o nea●er_n this_o way_n to_o pour_v into_o a_o vessel_n such_o a_o quantity_n of_o water_n which_o may_v be_v think_v sufficient_a to_o cover_v the_o body_n or_o magnitude_n and_o make_v a_o mark_n how_o high_a the_o water_n be_v in_o the_o vessel_n then_o pour_v out_o all_o this_o water_n into_o another_o vessel_n and_o let_v the_o body_n or_o magnitude_n be_v place_v into_o the_o first_o vessel_n then_o pour_v in_o water_n from_o the_o second_o vessel_n until_o it_o ascend_v unto_o the_o former_a mark_n make_v in_o the_o first_o vessel_n so_o the_o water_n which_o remain_v in_o the_o second_o vessel_n be_v equal_a to_o the_o body_n or_o magnitude_n put_v into_o the_o water_n but_o here_o note_n that_o this_o be_v not_o exact_a or_o free_a from_o error_n yet_o near_o the_o truth_n than_o any_o geometrician_n can_v otherwise_o possible_o measure_n and_o these_o body_n that_o be_v not_o so_o full_a of_o pore_n be_v more_o true_o measure_v this_o way_n than_o other_o be_v 11._o to_o find_v the_o weight_n of_o water_n see_v that_o 574_o 1000_o part_n of_o a_o ounce_n weight_n make_v a_o cubicall_a inch_n of_o water_n and_o every_o pound_n weight_n haverdepoize_n make_v 27_o cubicall_a inch_n and_o 1_o 9_o ●_o fere_n and_o that_o ●_o gallon_n and_o a_o half_a wine_n measure_n make_v a_o foot_n cubicall_a it_o be_v easy_a by_o inversion_n that_o know_v the_o quantity_n of_o a_o vessel_n in_o gallon_n to_o find_v his_o content_n in_o cubicall_a foot_n or_o weight_n and_o that_o late_a famous_a geometrician_n master_n brig_v find_v a_o cubical_a foot_n of_o water_n to_o weigh_v near_o 62_o pound_n weight_n haverdepoize_v but_o the_o late_a learned_a simon_n stevin_n find_v a_o cubicall_a foot_n of_o water_n to_o weigh_v 65_o pound_n which_o difference_n may_v arise_v from_o the_o inequality_n of_o water_n for_o some_o water_n be_v more_o ponderous_a than_o other_o and_o some_o difference_n may_v be_v from_o the_o weight_n of_o a_o pound_n and_o the_o measure_n of_o a_o foot_n thus_o the_o weight_n and_o quantity_n of_o a_o solid_a foot_n settle_v it_o be_v easy_a for_o arithmetician_n to_o give_v the_o content_n of_o vessel_n or_o body_n which_o contain_v liquid_n 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 this_o be_v general_o conceive_v that_o a_o vessel_n may_v carry_v as_o much_o weight_n as_o that_o water_n weigh_v which_o be_v equal_a unto_o the_o vessel_n in_o bigness_n in_o abate_v only_o the_o weight_n of_o the_o vessel_n we_o see_v that_o a_o barrel_n of_o wine_n or_o water_n cast_v into_o the_o water_n will_v not_o sink_v to_o the_o bottom_n but_o swim_v easy_o and_o if_o a_o ship_n have_v not_o iron_n and_o other_o ponderosity_n in_o it_o it_o may_v swim_v full_a of_o water_n without_o sink_v in_o the_o same_o manner_n if_o the_o vessel_n be_v load_v with_o lead_n so_o much_o shall_v the_o water_n weigh_v hence_o it_o be_v that_o mariner_n call_v ship_n of_o 50_o thousand_o ton_n because_o they_o may_v contain_v one_o or_o two_o thousand_o tun_n and_o so_o consequent_o carry_v as_o much_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 without_o any_o tempest_n will_v sink_v down_o right_a the_o cause_n of_o this_o be_v that_o a_o vessel_n may_v carry_v more_o upon_o some_o kind_n of_o water_n than_o upon_o other_o now_o the_o water_n of_o the_o sea_n be_v thick_a and_o heavy_a than_o that_o of_o river_n well_n or_o fountain_n therefore_o the_o load_n of_o a_o vessel_n which_o be_v account_v sufficient_a in_o the_o sea_n become_v too_o great_a in_o the_o hurbour_n or_o sweet_a water_n now_o some_o think_v that_o it_o be_v the_o depth_n of_o the_o water_n that_o make_v vessel_n more_o easy_a to_o swim_v but_o it_o be_v a_o abuse_n for_o if_o the_o load_n of_o a_o ship_n be_v no_o heavy_a than_o the_o water_n that_o will_v occupy_v that_o place_n the_o ship_n shall_v as_o easy_o swim_v upon_o that_o water_n as_o if_o it_o do_v swim_v upon_o a_o thousand_o fathom_n deep_a of_o water_n and_o if_o the_o water_n be_v no_o thick_a than_o a_o leaf_n of_o paper_n and_o weigh_v but_o a_o ounce_n under_o a_o heavy_a body_n it_o will_v support_v it_o as_o well_o as_o if_o the_o water_n under_o it_o weigh_v ten_o thousand_o pound_n weight_n hence_o it_o be_v if_o there_o be_v a_o vessel_n capable_a of_o a_o little_a more_o than_o a_o thousand_o pound_n weight_n of_o water_n you_o may_v put_v into_o this_o vessel_n a_o piece_n of_o wood_n which_o shall_v weigh_v a_o thousand_o pound_n weight_n but_o light_a in_o his_o kind_n than_o the_o like_a of_o magnitude_n of_o water_n for_o then_o pour_v in_o but_o a_o quart_n of_o water_n or_o a_o very_a little_a quantity_n of_o water_n the_o wood_n will_v swim_v on_o the_o top_n of_o it_o provide_v that_o the_o wood_n touch_v not_o the_o side_n of_o the_o vessel_n which_o be_v a_o fine_a experiment_n and_o seem_v admirable_a in_o the_o performance_n 14._o how_o a_o gross_a body_n of_o mettle_n may_v swim_v upon_o the_o water_n this_o be_v do_v by_o extend_v the_o mettle_n into_o a_o thin_a plate_n to_o make_v it_o hollow_v in_o form_n of_o a_o vessel_n so_o that_o the_o greatness_n of_o the_o vessel_n which_o the_o air_n with_o it_o contain_v be_v equal_a to_o the_o magnitude_n of_o the_o water_n which_o weigh_v as_o much_o as_o it_o for_o all_o body_n may_v swim_v without_o sink_v if_o they_o occupy_v the_o place_n of_o water_n equal_a in_o weight_n unto_o they_o as_o if_o it_o weigh_v 12_o pound_n it_o must_v have_v the_o place_n of_o 12_o pound_n of_o water_n hence_o it_o be_v that_o we_o see_v float_v upon_o the_o water_n great_a vessel_n of_o copper_n or_o brass_n when_o they_o be_v hollow_v in_o form_n of_o a_o cauldron_n and_o how_o can_v it_o be_v otherwise_o conceive_v of_o island_n in_o the_o sea_n that_o swim_v and_o float_v be_v it_o not_o that_o they_o be_v hollow_a and_o some_o part_n like_o unto_o a_o boat_n or_o that_o their_o earth_n be_v very_a light_n and_o spongeous_a or_o have_v many_o concavity_n in_o the_o body_n of_o it_o or_o much_o wood_n within_o it_o and_o it_o will_v be_v a_o pretty_a proposition_n to_o show_v how_o much_o every_o kind_n of_o metal_n shall_v be_v enlarge_v to_o make_v it_o swim_v upon_o the_o water_n which_o do_v depend_v upon_o the_o proportion_n that_o be_v between_o the_o weight_n of_o the_o water_n and_o each_o metal_n now_o the_o proportion_n that_o be_v between_o metal_n and_o water_n of_o equal_a magnitude_n according_a to_o some_o author_n be_v as_o follow_v a_o magnitude_n of_o 10_o pound_n weight_n of_o water_n will_v require_v for_o the_o like_a magnitude_n of_o gold_n 187_o ½_o lead_n 116_o ½_o silver_n 104_o copper_n 91_o iron_n 81_o tin_n 75_o from_o which_o be_v infer_v that_o to_o make_v a_o piece_n of_o copper_n of_o ●0_n pound_n weight_n to_o swim_v it_o must_v be_v so_o make_v hollow_a that_o it_o may_v hold_v 9_o time_n that_o weight_n of_o water_n and_o somewhat_o more_o that_o be_v to_o say_v 91_o pound_n see_v that_o copper_n and_o water_n of_o like_a magnitude_n in_o their_o ponderosity_n be_v as_o before_o as_o ●0_n to_o 91._o 15._o how_o to_o weigh_v the_o lightness_n of_o the_o air_n place_v a_o balance_n of_o wood_n turn_v upside_o down_o into_o the_o water_n that_o so_o it_o may_v swim_v then_o let_v water_n be_v enclose_v

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 ho●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 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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

within_o some_o body_n as_o within_z a_o bladder_n or_o such_o like_a and_o suppose_v that_o such_o a_o quantity_n of_o air_n shall_v weigh_v one_o pound_n place_v it_o under_o one_o of_o the_o balance_n and_o place_n under_o the_o other_o as_o much_o weight_n of_o lightness_n as_o may_v counterbalance_n and_o keep_v the_o other_o balance_n that_o it_o rise_v not_o out_o of_o the_o water_n by_o which_o you_o shall_v see_v how_o much_o the_o lightness_n be_v but_o without_o any_o balance_n do_v this_o take_v a_o cubicall_a hollow_a vessel_n or_o that_o which_o be_v cylindricall_a which_o may_v swim_v on_o the_o water_n and_o as_o it_o sink_v by_o place_v of_o weight_n upon_o it_o mark_v how_o much_o for_o than_o if_o you_o will_v examine_v the_o weight_n of_o any_o body_n you_o have_v nothing_o to_o do_v but_o to_o put_v it_o into_o this_o vessel_n and_o mark_v how_o deep_o it_o sink_v for_o so_o many_o pound_n it_o weigh_v as_o the_o weight_n put_v in_o do_v make_v it_o so_o to_o 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 find_v that_o gold_n lose_v in_o the_o water_n the_o 19_o part_n of_o his_o weight_n copper_n the_o 9_o part_n quicksilver_n the_o 15_o part_n lead_v the_o 12_o part_n silver_n the_o 10_o part_n iron_n the_o 8_o part_n tin_n the_o 7_o part_n and_o a_o little_a more_o wherefore_o in_o material_a and_o absolute_a weight_n gold_n in_o respect_n of_o the_o water_n that_o it_o occupy_v weigh_v 18_o and_o ¾_n time_n heavy_a than_o the_o like_a quantity_n of_o water_n that_o be_v as_o 18_o ¾_n to_o the_o quicksilver_n 15_o time_n lead_v 11_o and_o ⅗_n silver_n 10_o and_o ⅔_n copper_n 9_o and_o 1_o 10_o iron_n 8_o and_o ½_o and_o tin_n 8_o and_o 1_o ●_o contrary_o in_o respect_n of_o greatness_n if_o the_o water_n be_v as_o heavy_a as_o the_o gold_n then_o be_v the_o water_n almost_o 19_o time_n great_a than_o the_o magnitude_n of_o the_o gold_n and_o so_o may_v you_o judge_v of_o the_o rest_n 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 place_v in_o another_o place_n without_o remove_v any_o weight_n 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 this_o be_v easy_a to_o be_v resolve_v by_o consider_v different_a mettle_n which_o though_o they_o weigh_v equal_a in_o the_o air_n yet_o in_o the_o water_n there_o will_v be_v a_o apparent_a difference_n as_o suppose_v so_o that_o in_o the_o scale_n of_o each_o balance_n be_v place_v 18_o pound_n weight_n of_o several_a metal_n the_o one_o gold_n and_o the_o other_o copper_n which_o be_v in_o aequilibrio_fw-la in_o the_o air_n place_v in_o the_o water_n will_v not_o hang_v so_o because_o that_o the_o gold_n los●eth_v near_o the_o 18_o part_n of_o his_o weight_n which_o be_v about_o 1_o pound_n and_o the_o copper_n lose_v but_o his_o 9_o part_n which_o be_v 2_o pound_n wherefore_o the_o gold_n in_o the_o water_n weigh_v but_o 17_o pound_n and_o the_o copper_n 16_o pound_n which_o be_v a_o difference_n most_o sensible_a to_o confirm_v that_o point_n 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 physician_n have_v a_o especial_a respect_n unto_o this_o judge_v that_o water_n which_o be_v light_a be_v most_o healthful_a and_o medicinal_a for_o the_o body_n &_o seaman_n know_v that_o the_o heavy_a water_n do_v bear_v most_o and_o it_o be_v know_v which_o water_n be_v heavy_a thus_o take_v a_o piece_n of_o wax_n and_o fasten_v lead_n unto_o it_o or_o some_o such_o like_a thing_n that_o it_o may_v but_o precise_o swim_v for_o than_o it_o be_v equal_a to_o the_o like_a magnitude_n of_o water_n than_o put_v it_o into_o another_o vessel_n which_o have_v contrary_a water_n and_o if_o it_o sink_v then_o be_v that_o water_n light_a than_o the_o other_o but_o if_o it_o sink_v not_o so_o deep_a than_o it_o argue_v the_o water_n to_o be_v heavy_a or_o more_o grosser_n than_o the_o first_o water_n or_o one_o may_v take_v a_o piece_n of_o wood_n and_o mark_v the_o quantity_n of_o sink_v of_o it_o into_o several_a water_n by_o which_o you_o may_v judge_v which_o be_v light_a or_o heavy_a for_o in_o that_o which_o it_o sink_v most_o that_o be_v infallible_o the_o light_a and_o so_o contrary_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 2d_o ●0_n 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 and_o pound_n weight_n this_o proposition_n seem_v very_o impossible_a yet_o water_n enclose_v in_o a_o vessel_n be_v constrain_v to_o dilate_v itself_o do_v weigh_v so_o much_o as_o though_o there_o be_v in_o the_o concavitie_n of_o it_o a_o solid_a body_n of_o water_n there_o be_v many_o way_n to_o experiment_n this_o proposition_n but_o to_o verify_v it_o it_o may_v be_v sufficient_a to_o produce_v two_o excellent_a one_o only_o which_o have_v they_o not_o be_v real_o act_v little_a credit_n may_v have_v be_v give_v unto_o 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