Selected quad for the lemma: earth_n

Word A	Word B	Word C	Word D	Occurrence	Frequency Band	MI	MI Band	Prominent
earth_n	air_n	body_n	water_n	10,358	5	6.5960	4	true

Text snippets containing the quad

ID	Title	Author	Corrected Date of Publication (TCP Date of Publication)	STC	Words	Pages
A42066	The great and new art of weighing vanity, or, A discovery of the ignorance and arrogance of the great and new artist, in his pseudo-philosophical writings by M. Patrick Mathers, Arch-Bedal to the University of S. Andrews ; to which are annexed some Tentamina de motu penduli & projectorum.	Gregory, James, 1638-1675.; Sanders, William, 17th cent.	1672 (1672)	Wing G1910; ESTC R13096	40,784	128

surface_v they_o press_v as_o it_o be_v know_v by_o all_o mathematician_n except_o only_o such_o pitiful_a one_o as_o our_o author_n the_o twelve_o be_v evident_o false_a for_o if_o you_o take_v a_o bladder_n or_o any_o tender_a vessel_n half_o full_a of_o water_n and_o put_v the_o side_n of_o it_o together_o the_o fluid_n shall_v be_v move_v from_o the_o unequal_a pressure_n of_o the_o vertical_a surface_n the_o one_o half_a of_o the_o thirteen_o be_v a_o part_n but_o a_o very_a small_a one_o of_o archimedes_n seven_o and_o eigth_n the_o other_o half_o be_v also_o a_o small_a parcel_n of_o archimedes_n six_o his_o fourteen_o be_v so_o much_o as_o he_o understand_v of_o archimedes_n five_o and_o stevinus_n five_o the_o fifteen_o seventeen_o and_o nineteen_o be_v false_a unless_o the_o fluid_n have_v a_o spring_n or_o be_v heterogeneous_a none_o of_o which_o he_o have_v make_v out_o but_o if_o it_o be_v make_v out_o the_o thing_n be_v obious_a and_o notice_v by_o m._n boyl_n in_o the_o thirty-sixth_a experiment_n yet_o only_o in_o the_o air_n which_o be_v know_v to_o have_v a_o spring_n his_o sixteen_o be_v ridiculous_a see_v we_o see_v daily_a fish_n little_a particle_n of_o earth_n horse_n hair_n and_o many_o other_o such_o body_n betwixt_o the_o surface_n and_o bottom_n of_o the_o water_n yea_o by_o add_v a_o sufficient_a quantity_n of_o lead_n to_o a_o body_n light_a in_o specie_fw-la then_o water_n it_o may_v be_v make_v practicable_a and_o be_v demonstrat_fw-la both_o by_o archimedes_n and_o stevinus_n suppose_v the_o water_n homogeneous_a the_o contrair_a of_o which_o our_o author_n have_v not_o yet_o make_v out_o and_o more_o even_o a_o body_n considerable_o heavy_a in_o specie_fw-la then_o water_n beat_v out_o thin_a and_o broad_a especial_o if_o it_o be_v concave_a below_o may_v be_v suspend_v for_o a_o considerable_a time_n betwixt_o the_o surface_n and_o bottom_n of_o the_o water_n provide_v it_o be_v lay_v parallel_n to_o the_o horizon_n but_o pass_v by_o all_o this_o his_o method_n be_v unpracticable_a and_o suppose_v without_o prove_v any_o thing_n that_o water_n can_v suffer_v any_o degree_n of_o compression_n and_o stone_n lead_z with_o other_o body_n none_o at_o all_o his_o eighteen_o be_v the_o same_o with_o archimede_n seven_o and_o stevinus_n eight_o his_o twenty_o be_v the_o same_o with_o his_o seven_o otherways_o he_o grant_v it_o not_o exact_o true_a his_o twentyone_n as_o he_o word_v it_o be_v most_o manifest_a from_o that_o statical_a demonstration_n i_o mention_v for_o see_v pressure_n of_o the_o same_o weight_n be_v in_o reciprocal_a proportion_n with_o their_o resistance_n and_o the_o resistance_n or_o resist_a surface_n can_v be_v diminish_v in_o infinitum_fw-la it_o be_v evident_a that_o the_o least_o weight_n can_v produce_v any_o pressure_n whether_o the_o heavy_a body_n be_v fluid_a or_o solid_a but_o he_o explicate_v himself_o otherways_o relate_v to_o the_o spring_n of_o fluid_n which_o be_v not_o yet_o prove_v in_o any_o fluid_fw-la save_v air_n and_o beside_o this_o the_o theorem_fw-la be_v ridiculous_a see_v the_o spring_n of_o any_o part_n where_o all_o be_v equal_o press_v be_v equal_a to_o the_o spring_n of_o the_o whole_a for_o one_o pound_n weight_n press_v one_o foot_n as_o much_o as_o two_o pound_n press_v two_o and_o even_o so_o in_o any_o spring_n his_o 22._o and_o 23._o be_v make_v manifest_a by_o pecquet_n in_o his_o four_o experiment_n and_o m._n boyl_n in_o his_o 19_o physico-mechanical_a experiment_n yea_o throughout_o all_o that_o book_n and_o many_o other_o constant_o call_v the_o weight_n and_o spring_n of_o the_o air_n diverse_a and_o yet_o bring_v they_o both_o in_o for_o that_o same_o effect_n the_o 24._o be_v ridiculous_a see_v it_o be_v true_a and_o obvious_a in_o all_o thing_n if_o there_o be_v no_o penetration_n of_o body_n the_o 25._o be_v evident_o false_a see_v water_n upon_o the_o top_n of_o hill_n support_v less_o and_o in_o valley_n more_o yea_o doctor_n wallace_n show_v in_o his_o mechanic_n pag._n 728._o that_o the_o mercury_n both_o in_o m._n boil_v baroscop_n and_o he_o fall_v sometime_o at_o oxford_n below_o 28._o inch_n and_o other_o time_n above_o thirty_o and_o in_o the_o page_n 740._o he_o mention_v unquestionable_a experiment_n of_o 34._o 52._o and_o 55._o inch_n the_o contrair_a of_o this_o theorem_fw-la be_v also_o evident_a from_o many_o of_o our_o author_n own_o experiment_n if_o any_o man_n think_v they_o worthy_a the_o look_v over_o and_o suppose_v he_o have_v hit_v right_a this_o be_v nothing_o but_o the_o old_a toricellian_a experiment_n his_o 26._o be_v imperfect_a first_o see_v he_o speak_v only_o of_o fluid_n to_o be_v press_v up_o it_o be_v also_o true_a in_o all_o other_o body_n second_o he_o do_v not_o determine_v how_o far_o the_o sphere_n of_o activity_n reach_v and_o yet_o all_o this_o be_v easy_o do_v and_o demonstrat_fw-la from_o stevinus_n his_o 10._o for_o the_o body_n be_v press_v up_o till_o it_o together_o with_o the_o fluid_a betwixt_o it_o and_o the_o bottom_n not_o regard_v what_o else_o intervene_v but_o reckon_v all_o for_o fluid_a be_v equal_a in_o weight_n with_o a_o column_n of_o fluid_a who_o height_n be_v the_o same_o with_o the_o height_n of_o the_o fluid_a and_o its_o base_a the_o same_o with_o the_o base_a of_o the_o former_a fluid_n portion_n or_o equal_a to_o it_o and_o beside_o all_o these_o this_o be_v not_o different_a from_o m._n boil_v eleven_o paradox_n his_o 27._o be_v to_o say_v that_o a_o pound_n of_o wool_n weigh_v as_o much_o as_o a_o pound_n of_o lead_n his_o 28._o be_v the_o same_o with_o that_o which_o he_o will_v say_v in_o the_o 4._o and_o be_v true_a also_o in_o solid_n if_o you_o speak_v only_o of_o column_n for_o two_o unequal_a column_n of_o the_o same_o height_n and_o matter_n press_v equal_o see_v their_o resistance_n be_v proportional_a with_o their_o weight_n in_o fluid_n as_o i_o say_v already_o it_o be_v the_o same_o with_o archimedes_n second_o his_o 29._o may_v have_v be_v more_o general_a to_o wit_n that_o there_o can_v be_v no_o motion_n in_o fluid_n without_o a_o unequal_a pressure_n and_o then_o it_o have_v be_v the_o same_o with_o archimedes_n first_o position_n his_o 30._o be_v also_o a_o part_n of_o archimedes_n first_o position_n for_o see_v pressure_n be_v judge_v only_o by_o expulsion_n the_o effect_n of_o it_o and_o the_o expulsion_n be_v always_o cause_v where_o the_o least_o resistance_n be_v which_o may_v be_v in_o a_o crooked_a line_n wherefore_o then_o be_v not_o pressure_n also_o in_o crooked_a line_n his_o 31._o be_v the_o 10_o of_o stevinus_n here_o again_o he_o justle_v with_o that_o great_a difficulty_n which_o i_o discuss_v in_o the_o 4._o and_o tell_v there_o be_v no_o way_n to_o answer_v but_o he_o in_o his_o 32._o the_o pondus_fw-la &_o potentia_fw-la be_v to_o say_v in_o plain_a scot_n a_o pressure_n and_o a_o resistance_n he_o have_v tell_v in_o his_o 5._o that_o in_o all_o fluid_v there_o be_v a_o pressure_n but_o now_o it_o come_v in_o his_o head_n that_o a_o man_n may_v fancy_v a_o pressure_n without_o a_o resistance_n &_o therefore_o he_o must_v guard_v against_o that_o i_o suppose_v here_o that_o his_o definition_n of_o the_o staticks_n be_v new_a otherwise_o the_o tron-lord_n be_v the_o great_a professor_n of_o it_o his_o 33._o be_v to_o say_v that_o there_o must_v be_v a_o motion_n when_o the_o pressure_n be_v great_a than_o the_o resistance_n which_o be_v yet_o a_o part_n of_o archimedes_n first_o position_n and_o never_o doubt_v of_o by_o the_o great_a ignorant_o §._o ii_o the_o author_n last_o theorem_n for_o its_o good_a service_n examine_v by_o itself_o now_o let_v we_o examine_v his_o last_o theorem_fw-la which_o certain_o shall_v be_v the_o utmost_a reach_n of_o his_o wit_n and_o therefore_o i_o will_v examine_v it_o more_o narrow_o first_o let_v his_o two_o fluid_n in_o aquilibrio_n be_v water_v the_o one_o and_o quicksilver_n the_o other_o the_o natural_a weight_n of_o water_n be_v 1._o the_o natural_a weight_n of_o quicksilver_n be_v 14._o therefore_o according_a to_o his_o theorem_fw-la as_o 1._o the_o weight_n of_o the_o one_o be_v to_o 14._o the_o weight_n of_o the_o other_o so_o be_v the_o height_n of_o the_o one_o to_o wit_n water_n to_o the_o height_n of_o the_o other_o to_o wit_n quicksilver_n and_o therefore_o the_o quicksilver_n shall_v be_v 14._o time_n high_o than_o water_n which_o i_o leave_v to_o be_v determine_v by_o experience_n he_o shall_v have_v say_v as_o the_o natural_a weight_n of_o the_o second_o be_v to_o the_o natural_a weight_n of_o the_o first_o or_o rather_o that_o their_o altitude_n be_v in_o reciprocal_a proportion_n with_o their_o weight_n or_o in_o direct_a proportion_n with_o their_o levities_n second_o then_o in_o his_o progress_n he_o say_v

that_o by_o what_o proportion_n the_o one_o liquor_n be_v natural_o heavy_a or_o light_a than_o the_o other_o by_o that_o same_o proportion_n the_o one_o cylinder_n be_v high_a or_o low_a than_o the_o other_o here_o insinuate_v that_o the_o weight_n and_o levities_n of_o two_o body_n be_v in_o the_o same_o proportion_n and_o yet_o their_o proportion_n be_v reciprocal_a and_o that_o be_v to_o say_v just_a contrair_n or_o otherwise_o he_o must_v take_v the_o height_n proportional_a with_o the_o weight_n and_o the_o lowness_n with_o the_o levities_n which_o be_v both_o false_a at_o last_o when_o he_o come_v to_o his_o example_n he_o make_v the_o height_n proportional_a with_o the_o levities_n which_o i_o grant_v to_o be_v his_o meaning_n but_o this_o show_v a_o intolerable_o confuse_a wit_n three_o even_o this_o be_v grant_v i_o shall_v demonstrat_fw-la that_o it_o do_v contradict_v almost_o all_o his_o theorem_n and_o to_o that_o purpose_n i_o assume_v these_o two_o postulata_fw-la post_n 1._o fluid_n which_o have_v their_o weight_n or_o pressure_n proportional_a to_o their_o profundity_n can_v have_v no_o bensil_n for_o if_o they_o have_v a_o bensil_n their_o pressure_n be_v not_o proportional_a to_o their_o profundity_n as_o i_o do_v demonstrat_fw-la at_o his_o 8._o theor._n which_o be_v against_o the_o hypothesis_n post_n 2._o quicksilver_n or_o water_n have_v their_o weight_n and_o pressure_n in_o proportion_n with_o their_o altitude_n at_o least_o so_o far_o as_o any_o man_n yet_o have_v make_v trial_n as_o m._n boyl_n witness_v in_o the_o first_o appendix_n to_o his_o paradox_n yea_o our_o author_n affirm_v it_o of_o all_o fluid_n in_o his_o 8._o theor._n and_o many_o place_n of_o his_o experiment_n the_o demonstration_n follow_v here_o upon_o the_o surface_n of_o the_o earth_n let_v the_o height_n of_o a_o cylinder_n of_o mercury_n be_v a_o its_o weight_n or_o the_o weight_n of_o the_o cylinder_n of_o air_n counterpoyse_v it_o b_o the_o height_n of_o this_o cylinder_n of_o air_n c._n also_o let_v the_o same_o cylinder_n of_o mercury_n be_v lift_v up_o some_o distance_n from_o the_o earth_n and_o the_o mercury_n will_v fall_v so_o that_o the_o cylinder_n of_o mercury_n be_v now_o low_o who_o height_n we_o call_v d_o and_o weight_n or_o the_o weight_n of_o its_o counterpoyse_v aërial_n cylinder_n e_z the_o weight_n of_o this_o aërial_n cylinder_n f_o let_v the_o proportion_n betwixt_o the_o weight_n of_o mercury_n and_o air_n be_v as_o g_o unto_o h._n by_o our_o second_o postulatum_fw-la a_o be_v unto_o d_o as_o b_o be_v unto_z e_z and_o by_o this_o 34._o theorem_fw-la h_n be_v unto_o g_o as_o a_o be_v unto_o c_o and_o also_o h_n be_v unto_o g_o as_o d_o be_v unto_o f_o and_o therefore_o a_o be_v unto_o c_o as_o d_o be_v unto_o f_o &_o permutando_fw-la a_o be_v unto_o d_o as_o c_z be_v unto_o f_o but_o a_o be_v unto_o d_o as_o b_o be_v unto_z e_z and_o therefore_o b_o be_v unto_o e_o as_o c_z be_v unto_o f_o and_o consequent_o by_o the_o first_o postulatum_fw-la the_o air_n have_v no_o bensil_n which_o be_v contrair_a to_o many_o of_o his_o theorem_n and_o all_o his_o experiment_n this_o destroy_v all_o his_o method_n of_o measure_v the_o height_n of_o the_o air_n cloud_n and_o atmosphere_n both_o here_o and_o in_o his_o ars_fw-la magna_fw-la &_o nova_fw-la he_o may_v have_v know_v this_o mistake_n many_o year_n ago_o for_o m._n boyl_n reject_v this_o proportion_n betwixt_o the_o altitude_n of_o the_o air_n and_o of_o the_o quicksilver_n in_o his_o 36._o physico-mechanical_a experiment_n upon_o the_o same_o account_n this_o let_v our_o author_n see_v that_o if_o fluid_n have_v no_o bensil_n his_o theorem_fw-la be_v obvious_a and_o know_v to_o all_o §._o iii_o the_o author_n great_a skill_n in_o dioptric_n examine_v in_o his_o three_o observation_n he_o make_v himself_o exceed_o ridiculous_a for_o first_o he_o show_v hot_a how_o much_o the_o telescop_n require_v shall_v magnify_v second_o he_o show_v not_o how_o far_o the_o telescop_n shall_v be_v draw_v out_o for_o this_o effect_n for_o that_o draught_n which_o serve_v for_o a_o distinct_a and_o clear_a sight_n will_v not_o serve_v exact_o to_o project_v a_o image_n see_v sight_n require_v always_o parallel_a or_o diverge_v ray_n and_o the_o projection_n of_o a_o image_n converge_v three_o he_o seem_v to_o attribute_v the_o magnify_v of_o telescops_n to_o their_o length_n and_o goodness_n of_o the_o glass_n and_o yet_o there_o may_v be_v the_o best_a glass_n imaginable_a place_v in_o their_o due_a distance_n in_o a_o tube_n of_o 50._o foot_n long_o and_o not_o do_v so_o much_o as_o a_o ordinar_n tube_n of_o 5._o inch_n and_o yet_o both_o the_o glass_n may_v do_v wonder_n with_o other_o which_o give_v they_o their_o due_a charge_n four_o he_o require_v both_o the_o glass_n to_o be_v very_o good_a and_o there_o be_v no_o excellency_n require_v but_o in_o the_o object_n glass_n five_o he_o speak_v of_o the_o image_n as_o if_o it_o be_v both_o near_a to_o the_o tube_n and_o far_o from_o it_o and_o yet_o it_o have_v one_o determinat_fw-la place_n the_o draught_n of_o the_o tube_n never_o be_v alter_v which_o he_o never_o once_o mention_v six_o he_o speak_v of_o the_o image_n of_o the_o sun_n that_o it_o be_v the_o more_o distinct_a the_o near_a the_o glass_n and_o yet_o this_o brightness_n near_o the_o glass_n be_v nothing_o but_o a_o confuse_a concourse_n of_o ray_n seven_o when_o he_o have_v observe_v his_o inch_n he_o reduce_v they_o not_o to_o degree_n minute_n or_o second_o etc._n etc._n for_o the_o sun_n motion_n be_v not_o reckon_v in_o inch_n last_o suppose_v he_o have_v do_v all_o these_o thing_n aright_o this_o method_n have_v be_v ordinary_o practise_v above_o these_o thirty_o year_n let_v he_o look_v hevelij_fw-la selenographia_fw-la scheineri_fw-la rosa_fw-la vrsina_fw-la and_o doctor_n wallace_n in_o the_o end_n of_o his_o arithmetica_fw-la infinitorum_fw-la it_o be_v here_o to_o be_v observe_v that_o these_o author_n by_o such_o observation_n design_v not_o to_o render_v the_o sun_n motion_n sensible_a to_o the_o eye_n which_o our_o author_n value_v so_o much_o and_o by_o some_o here_o be_v former_o call_v ridiculous_a but_o only_a to_o observe_v its_o spot_n together_o with_o their_o motion_n or_o else_o its_o eclipse_n noticing_z only_o by_o the_o way_n that_o swift_a motion_n of_o the_o sun_n image_n which_o be_v troublesome_a and_o constrain_v they_o oft_o to_o alter_v the_o position_n of_o their_o telescop_n §._o iv._o our_o author_n new_a dive_v ark_n put_v to_o trial_n there_o be_v nothing_o in_o which_o our_o author_n be_v more_o mistake_v then_o in_o his_o dive_v ark_n for_o in_o all_o his_o discourse_n he_o not_o only_o contradict_v himself_o which_o be_v ordinar_n and_o no_o great_a matter_n but_o also_o the_o general_a doctrine_n of_o the_o hydrostaticks_n i_o shall_v therefore_o to_o undeceive_v his_o reader_n demonstrat_fw-la that_o his_o dive_v ark_n sustain_v precise_o as_o much_o pressure_n under_o water_n as_o if_o it_o be_v hang_v in_o the_o air_n with_o as_o much_o water_n in_o it_o as_o now_o it_o have_v of_o air_n rebate_n only_o a_o small_a matter_n which_o the_o compress_a air_n in_o the_o ark_n weigh_v i_o do_v it_o thus_o in_o his_o own_o figure_n pag._n 179._o let_v pq_n be_v the_o sufface_n of_o the_o water_n within_o the_o ark_n by_a the_o distance_n of_o that_o surface_n from_o the_o upper_a horizontal_a surface_n nigh_o the_o distance_n of_o the_o top_n of_o the_o ark_n from_o the_o upper_a surface_n according_a to_o his_o 7._o theorem_fw-la the_o pressure_n be_v equal_a at_o p_o and_o at_o 4_o and_o therefore_o according_a to_o his_o 8._o theor._n see_v the_o water_n have_v no_o sensible_a spring_n the_o pressure_n at_o n_o without_o the_o ark_n be_v to_o the_o pressure_n at_o p_o as_o yn_v to_o yp_n therefore_o the_o pressure_n at_o pq_n overcome_v the_o pressure_n without_o the_o ark_n at_o eh_n by_o the_o pressure_n of_o a_o column_n of_o water_n who_o base_a be_v pq_n and_o the_o altitude_n hq_n but_o the_o pressure_n at_o eh_n within_o the_o ark_n want_v only_o the_o weight_n of_o the_o column_n of_o air_n pqhe_n to_o make_v up_o the_o pressure_n at_o pq_n therefore_o the_o pressure_n within_o at_o eh_n exceed_v the_o pressure_n without_o at_o eh_n by_o the_o weight_n or_o pressure_n of_o a_o column_n of_o water_n who_o base_a be_v pq_n and_o altitude_n qh_o abate_v the_o weight_n of_o the_o column_n of_o air_n pqhe_n which_o wa●_n the_o conclusion_n to_o be_v demonstrate_v i_o demonstrat_fw-la this_o conclusion_n suppose_v no_o man_n within_o the_o ark_n but_o if_o a_o man_n be_v there_o it_o hold_v only_o of_o the_o air_n about_o he_o take_v the_o man_n to_o be_v equal_a in_o weight_n with_o so_o much_o water_n i_o