Selected quad for the lemma: power_n

Word A	Word B	Word C	Word D	Occurrence	Frequency Band	MI	MI Band	Prominent
power_n	length_n	line_n	superficies_n	3,383	5	15.6048	5	false

Text snippets containing the quad

ID	Title	Author	Corrected Date of Publication (TCP Date of Publication)	STC	Words	Pages
A44320	Lectiones Cutlerianæ, or, A collection of lectures, physical, mechanical, geographical, & astronomical made before the Royal Society on several occasions at Gresham Colledge : to which are added divers miscellaneous discourses / by Robert Hooke ...	Hooke, Robert, 1635-1703.	1679 (1679)	Wing H2617; ESTC R4280	276,083	420

four_o as_o the_o root_n of_o 64._o that_o be_v of_o 19+17+15+13_n at_o the_o end_n of_o the_o ten_o or_o whole_a as_o the_o root_n of_o 100_o that_o be_v as_o equal_a to_o 100_o now_o since_o the_o velocity_n be_v in_o the_o same_o proportion_n to_o the_o root_n of_o the_o space_n as_o the_o root_n of_o the_o space_n be_v to_o the_o time_n it_o be_v easy_a to_o determine_v the_o particular_a time_n in_o which_o every_o one_o of_o these_o space_n be_v pass_v for_o divide_v the_o space_n by_o the_o velocity_n correspond_v the_o quotient_n give_v the_o particular_a time_n to_o explain_v this_o more_o intelligible_o let_v a_o in_o the_o four_o figure_n represent_v the_o end_n of_o a_o spring_n not_o bend_v or_o at_o least_o counterpoise_v in_o that_o posture_n by_o a_o power_n fix_v to_o it_o and_o movable_a with_o it_o draw_v the_o line_n a_o b_o c_o and_o let_v it_o represent_v the_o way_n in_o which_o the_o end_n of_o the_o spring_n by_o additional_a power_n be_v to_o be_v move_v draw_v to_o the_o end_n of_o it_o c_o at_o right_a angle_n the_o line_n c_o δ_n d_o d_o and_o let_v c_o d_o represent_v the_o power_n that_o be_v sufficient_a to_o bend_v or_o move_v the_o end_n of_o the_o spring_n a_o to_o c_o then_o draw_v the_o line_n d_o a_o and_o from_o any_o point_n of_o the_o line_n a_o c_o as_o b_o b._n draw_v line_n parallel_v to_o c_o d_o cut_v the_o line_n d_o a_o in_o e_o e_o the_o line_n b_o e_o b_o e_o will_v represent_v the_o respective_a power_n requisite_a to_o bend_v the_o end_n of_o the_o spring_n a_o to_o b_o which_o line_n b_o e_z b_o e_o c_o d_o will_n be_v in_o the_o same_o proportion_n with_o the_o length_n of_o the_o bent_n of_o the_o spring_n a_o b_o a_o b_o a_o c._n and_o because_o the_o spring_n have_v in_o every_o point_n of_o the_o line_n of_o bend_v a_o c_o a_o particular_a power_n therefore_o imagine_v infinite_a line_n draw_v from_o every_o point_n of_o a_o c_o parallel_n to_o c_o d_o till_o they_o touch_v the_o line_n a_o d_o they_o will_v all_o of_o they_o fill_v and_o compose_v the_o triangle_n a_o c_o d._n the_o triangle_n therefore_o a_o c_o d_o will_n represent_v the_o aggregate_v of_o the_o power_n of_o the_o spring_n bend_v from_o a_o to_o c_o and_o the_o lesser_a triangle_n a_o b_o e_o a_o b_o e_o will_n represent_v the_o aggregate_v of_o all_o the_o power_n of_o the_o spring_n bend_v from_o a_o to_o b_o b_o and_o the_o spring_n bend_v to_o any_o point_n of_o the_o line_n a_o c_o and_o let_v go_v from_o thence_o will_v exert_v in_o its_o return_n to_o a_o all_o those_o power_n which_o be_v equal_a to_o the_o respective_a ordinates_n b_o e_o b_o e_o in_o the_o triangle_n the_o sum_n of_o all_o which_o make_v up_o the_o triangle_n a_o b_o e_o a_o b_o e._n and_o the_o aggregate_v of_o the_o power_n with_o which_o it_o return_v from_o any_o point_n as_o from_o c_o to_o any_o point_n of_o the_o space_n c_o a_o as_o to_o b_o b_o be_v equal_a to_o the_o trapezium_fw-la c_o d_o e_o b_o c_o d_o e_o b_o or_o the_o excess_n of_o the_o great_a triangle_n above_o the_o less_o have_v therefore_o show_v a_o image_n to_o represent_v the_o flexure_n and_o the_o power_n so_o as_o plain_o to_o solve_v and_o answer_v all_o question_n and_o problem_n concern_v they_o in_o the_o next_o place_n i_o come_v to_o represent_v the_o velocity_n appropriate_v to_o the_o several_a power_n the_o velocity_n then_o be_v always_o in_o a_o subduplicate_v proportion_n of_o the_o power_n that_o be_v as_o the_o root_n of_o the_o power_n impress_v and_o the_o power_n impress_v be_v as_o the_o trapezium_fw-la or_o the_o excess_n of_o the_o triangle_n or_o square_n of_o the_o whole_a space_n to_o be_v pass_v above_o the_o square_n of_o the_o space_n yet_o unpassed_a if_o upon_o the_o centre_n a_o and_o space_n a_o c_o c_z being_z the_o point_n from_o which_o the_o spring_n be_v suppose_v let_v go_v a_o circle_n be_v describe_v as_o c_o g_o g_o f_o and_o ordinates_n draw_v from_o any_o point_n of_o c_o a_o the_o space_n to_o be_v past_a as_o from_o b_o b_o to_o the_o say_a circle_n as_o b_o g_z b_o g_o these_o line_n b_o g_z b_o g_o will_v represent_v the_o velocity_n of_o the_o spring_n return_v from_o c_o to_z b_o b_o etc._n etc._n the_o say_v ordinates_n being_n always_o in_o the_o same_o proportion_n with_o the_o root_n of_o the_o trapezium_n c_o d_o e_o b_o c_o d_o e_o b_o for_o putting_z a_o c_o =_o to_o a_o and_o a_o b_o =_o b_o b_o g_o will_n always_o be_v equal_a to_o the_o square_a of_o the_o ordinate_a be_v always_o equal_a to_o the_o rectangle_n of_o the_o intercept_a part_n of_o the_o diameter_n have_v thus_o find_v the_o velocity_n to_o wit_n b_o g_o b_o g_o a_o f_o to_o find_v the_o time_n correspond_v on_o the_o diameter_n a_o c_o draw_v a_o parabola_fw-la c_o h_o f_o who_o vertex_fw-la be_v c_o and_o which_o pass_v through_o the_o point_n f._n the_o ordinates_n of_o this_o parabola_fw-la b_o h_n b_o h_n a_o f_o be_v in_o the_o same_o proportion_n with_o the_o root_n of_o the_o space_n c_o b_o c_o b_o c_o a_o then_z making_z g_z b_o to_z h_z b_o as_o h_z b_o to_z ay_o b_o and_o through_o the_o point_n c_o i_o i_o f_o draw_v the_o curve_v c_z i_o i_o i_o f_o the_o respective_a ordinates_n of_o this_o curve_v shall_v represent_v the_o proportionate_a time_n that_o the_o spring_n spend_v in_o return_v the_o space_n c_o b_o c_o b_o c_o a._n if_o the_o power_n or_o stiffness_n of_o the_o spring_n be_v great_a than_o what_o i_o before_o suppose_v and_o therefore_o must_v be_v express_v by_o the_o triangle_n c_o de_fw-fr a._n then_o the_o velocity_n will_v be_v the_o ordinates_n in_o a_o ellipse_n as_o c_o γ_n γ_n n_n great_a than_o the_o circle_n as_o it_o will_v also_o if_o the_o power_n be_v the_o same_o and_o the_o bulk_n move_v by_o the_o spring_n be_v less_o then_o will_v the_o s-like_a line_n of_o time_n meet_v with_o the_o line_n a_o f_o at_o a_o point_n as_o x_o within_o the_o point_n f._n but_o if_o the_o power_n of_o the_o spring_n be_v weak_a than_o i_o suppose_v then_o will_v c_o δ_n e_o e_o a_o represent_v the_o power_n and_o c_o γ_n γ_n o_o the_o ellipsis_n of_o velocity_n who_o ordinates_n b_o γ_n b_o γ_n a_o o_o will_v give_v the_o particular_a velocity_n and_o the_o s-like_a line_n of_o time_n will_v extend_v beyond_o n._n the_o same_o will_v happen_v suppose_v the_o body_n move_v by_o the_o spring_n to_o be_v proportionate_o heavy_a and_o the_o power_n of_o the_o spring_n the_o same_o with_o the_o first_o and_o suppose_v the_o power_n of_o the_o spring_n the_o same_o as_o at_o first_o bend_v only_o to_o b_o 2_o and_o from_o thence_o let_v go_v b_o 2_o e_z a_o be_v the_o triangle_n of_o its_o power_n the_o ordinates_n of_o the_o circle_n b_o g_o l_o be_v the_o line_n of_o its_o velocity_n and_o the_o ordinates_n of_o the_o s-like_a line_n b_o i_o f_o be_v the_o live_v of_o time_n have_v thus_o show_v you_o how_o the_o velocity_n of_o a_o spring_n may_v be_v compute_v it_o will_v be_v easy_a to_o calculate_v to_o what_o distance_n it_o will_v be_v able_a to_o shoot_v or_o throw_v any_o body_n that_o be_v move_v by_o it_o and_o this_o must_v be_v do_v by_o compare_v the_o velocity_n of_o the_o ascent_n of_o a_o body_n throw_v with_o the_o velocity_n of_o the_o descent_n of_o gravity_n allowance_n be_v also_o make_v for_o the_o resistance_n and_o impediment_n of_o the_o medium_n through_o which_o it_o pass_v for_o instance_n suppose_v a_o bow_n or_o spring_n fix_v at_o 16_o foot_n above_o a_o horizontal_n floor_n which_o be_v near_o the_o space_n that_o a_o heavy_a body_n from_o rest_n will_v descend_v perpendicular_o in_o a_o second_o of_o time_n if_o a_o spring_n deliver_v the_o body_n in_o the_o horizontal_n line_n with_o a_o velocity_n that_o move_v it_o 16_o foot_n in_o a_o second_o of_o time_n then_o shall_v it_o fall_v at_o 16_o foot_n from_o the_o perpendicular_a point_n on_o the_o floor_n over_o which_o it_o be_v deliver_v with_o such_o velocity_n and_o by_o its_o motion_n shall_v describe_v in_o the_o air_n or_o space_n through_o which_o it_o pass_v a_o parabola_fw-la if_o the_o spring_n be_v bend_v to_o twice_o the_o former_a tension_n so_o as_o to_o deliver_v the_o body_n with_o double_a the_o velocity_n in_o a_o horizontal_n line_n that_o be_v with_o a_o velocity_n that_o move_v 32_o foot_n in_o a_o second_o then_o shall_v the_o body_n touch_v the_o floor_n in_o a_o point_n very_o near_o at_o 32_o foot_n from_o the_o aforesaid_a perpendicular_a point_n and_o the_o

with_o those_o feculency_n the_o reason_n of_o which_o be_v evident_a for_o the_o flame_n as_o i_o former_o prove_v be_v nothing_o but_o the_o part_n of_o the_o oil_n rarefy_v and_o raise_v by_o heat_n into_o the_o form_n of_o a_o vapour_n smoke_n or_o steam_n the_o free_a air_n that_o incompass_v this_o steam_n keep_v it_o into_o a_o cylindrical_a form_n and_o by_o its_o dissolve_v property_n prey_v upon_o or_o dissolve_v those_o part_n of_o it_o that_o be_v outward_o and_o next_o to_o the_o air_n so_o as_o by_o the_o say_a dissolution_n it_o continue_v the_o heat_n and_o produce_v the_o light_n which_o we_o observe_v but_o those_o part_n of_o the_o body_n of_o steam_n that_o rise_v from_o the_o wick_n which_o be_v in_o the_o middle_n and_o not_o contiguous_a to_o the_o outward_a air_n be_v not_o dissolve_v or_o turn_v into_o shine_a flame_n by_o the_o air_n till_o they_o rise_v towards_o the_o top_n of_o the_o cone_n of_o flame_n where_o the_o free_a air_n can_v come_v to_o reach_v and_o so_o to_o dissolve_v they_o and_o thence_o gather_v about_o the_o wick_n in_o the_o centre_n of_o the_o cone_n of_o flame_n they_o choke_v clog_n and_o quite_o stifle_v it_o that_o the_o flame_n will_v quick_o go_v out_o that_o this_o be_v so_o any_o one_o may_v easy_o find_v if_o he_o examine_v the_o flame_n of_o a_o lamp_n or_o candle_n by_o the_o help_n of_o a_o piece_n of_o glass_n for_o by_o the_o transparency_n thereof_o he_o will_v plain_o perceive_v that_o all_o the_o middle_n of_o the_o cone_n of_o flame_n neither_o shine_v nor_o burn_v but_o only_o the_o outward_a superficies_n thereof_o that_o be_v contiguous_a to_o the_o free_a and_o unsatiate_v air_n and_o that_o the_o middle_a part_n may_v be_v collect_v in_o the_o form_n of_o soot_n or_o very_o fine_a powder_a coal_n dust_n take_v then_o a_o piece_n of_o glass_n whether_o window-glass_n looking-glass_n plate_n or_o the_o side_n of_o a_o viol_n it_o matter_n not_o or_o which_o be_v best_a of_o all_o a_o thin_a plate_n of_o selenitis_n or_o muscovia_n talk_v and_o hold_v it_o horizontal_o in_o the_o middle_n of_o the_o flame_n so_o as_o to_o cut_v off_o the_o top_n or_o upper_a part_n of_o the_o cone_n thereof_o then_o present_o before_o it_o be_v choke_v with_o soot_n look_v down_o upon_o it_o and_o you_o shall_v plain_o see_v that_o all_o the_o middle_a part_n of_o the_o flame_n and_o the_o wick_n have_v no_o shine_a power_n or_o light_n at_o all_o nor_o be_v they_o dissolve_v by_o the_o air_n but_o remain_v in_o the_o form_n of_o soot_n but_o that_o only_o the_o superficies_n or_o outside_n of_o the_o say_a cone_n do_v burn_v shine_v and_o consume_v into_o and_o mix_v with_o the_o ambient_fw-la air._n in_o the_o same_o manner_n if_o you_o hold_v the_o glass_n or_o selenitis_n perpendicular_o and_o apply_v the_o side_n of_o it_o so_o as_o to_o cut_v the_o flame_n per_fw-mi axin_fw-mi coni_fw-la that_o the_o air_n can_v come_v to_o one_o side_n thereof_o you_o may_v plain_o perceive_v that_o the_o shine_a part_n of_o the_o flame_n be_v only_o that_o which_o be_v contiguous_a to_o and_o prey_v upon_o by_o the_o free_a and_o unsatiate_v air_n and_o that_o where_o that_o air_n can_v come_v free_a without_o be_v glut_v and_o satiate_v in_o its_o way_n there_o neither_o the_o consumption_n of_o the_o oil_n nor_o the_o heat_n and_o light_n of_o the_o flame_n be_v produce_v but_o only_o a_o sooty_a choke_a and_o stifle_a substance_n to_o make_v then_o the_o reason_n of_o the_o phaenomena_n observable_a about_o the_o last_a or_o stifle_v of_o the_o flame_n of_o a_o lamp_n the_o more_o clear_a and_o easy_a to_o be_v understand_v and_o comprehend_v give_v i_o leave_v to_o explain_v the_o manner_n of_o its_o production_n and_o continuation_n by_o a_o scheme_n delineation_n and_o description_n thereof_o let_v a_o a_o then_o in_o the_o second_o table_n represent_v a_o body_n of_o oil_n or_o any_o other_o combustible_a fluid_a substance_n the_o superficies_n whereof_o b_o b_o be_v horizontal_n and_o pretty_a near_o plain_a i_o say_v pretty_a near_a because_o it_o be_v always_o either_o concave_n or_o convex_v more_o or_o less_o according_a to_o several_a circumstance_n to_o wit_n the_o capacity_n and_o the_o nature_n of_o the_o vessel_n e_o e_o in_o which_o it_o be_v contain_v for_o if_o the_o vessel_n be_v small_a and_o that_o the_o oil_n have_v a_o great_a congruity_n with_o it_o than_o the_o air_n the_o superficies_n of_o the_o oil_n will_v be_v very_o much_o concavate_v especial_o towards_o the_o side_n of_o the_o vessel_n as_o at_o c_o c_o but_o if_o the_o vessel_n be_v incongruous_a to_o oil_n the_o superficies_n will_v be_v convex_a as_o at_o d_o d_o the_o reason_n of_o which_o i_o have_v long_o since_o explain_v in_o another_o place_n let_v f_o f_o than_o in_o the_o three_o figure_n represent_v the_o wick_n which_o consist_v of_o a_o great_a number_n of_o very_o fine_a cylinder_n or_o hair_n of_o cotton_n f_o f_o f_o twist_a and_o lay_v very_o close_o together_o into_z and_o between_o which_o the_o oil_n have_v a_o very_a great_a congruity_n therewith_o do_v ready_o insinuate_v itself_o and_o adhere_v and_o be_v by_o the_o pressure_n of_o the_o air_n much_o great_a without_o than_o between_o those_o cylinder_n or_o hair_n force_v up_o to_o a_o considerable_a height_n between_o they_o as_o to_o the_o height_n of_o a_o inch_n and_o half_a or_o two_o inch_n and_o if_o by_o any_o mean_v the_o oil_n be_v take_v out_o at_o the_o top_n thereof_o the_o remain_a part_n of_o the_o oil_n in_o the_o vessel_n will_v ascend_v to_o supply_v the_o vacancy_n of_o the_o part_n draw_v off_o which_o be_v evident_a in_o filtration_n about_o the_o side_n of_o this_o wick_n the_o oil_n will_v be_v sure_a to_o ascend_v and_o the_o superficies_n thereof_o will_v be_v concavate_v as_o at_o g_o g_o because_o unless_o there_o be_v a_o congruity_n between_o the_o oil_n and_o the_o wick_n there_o will_v be_v no_o ascent_n of_o the_o oil_n therein_o and_o therefore_o that_o substance_n that_o the_o oil_n do_v not_o ready_o adhere_v to_o can_v be_v a_o fit_a material_a for_o that_o purpose_n now_o to_o this_o wick_n thus_o fill_v with_o oil_n apply_v the_o flame_n of_o a_o lamp_n or_o candle_n or_o any_o other_o substance_n extreme_o hot_a as_o a_o glow_a piece_n of_o iron_n copper_n or_o the_o like_a and_o by_o this_o mean_v the_o part_n of_o the_o oil_n in_o the_o wick_n will_v be_v very_o much_o heat_v and_o expand_v themselves_o in_o vapour_n into_o the_o contiguous_a air_n by_o the_o steam_v h_z h_z h_z h_z h_z and_o fill_v all_o the_o ambient_fw-la space_n of_o the_o air_n h_o h_n therewith_o which_o vapour_n be_v very_o much_o rarify_v and_o consequent_o light_a than_o the_o encompass_v air_n be_v by_o the_o great_a gravity_n and_o pressure_n thereof_o carry_v upward_o by_o the_o curve_v line_n h_o i_o k._n these_o at_o first_o gush_v out_o of_o the_o wick_n at_o right_a angle_n but_o by_o the_o protrusion_n of_o the_o air_n be_v quick_o turn_v into_o a_o kind_n of_o parabolic_a curve_v h_z i_o k_o the_o motion_n of_o the_o particle_n in_o which_o be_v swift_a in_o k_n k_o that_o be_v to_o a_o certain_a degree_n of_o altitude_n the_o motion_n of_o ascent_n increase_v somewhat_o after_o the_o nature_n of_o the_o motion_n of_o descent_n in_o heavy_a body_n i_o say_v somewhat_o in_o that_o nature_n for_o if_o the_o ascend_a body_n be_v uniform_o light_a than_o the_o ambient_fw-la they_o will_v be_v the_o same_o but_o because_o the_o rarefaction_n and_o nature_n of_o they_o be_v vary_v by_o circumstance_n therefore_o it_o have_v but_o part_n of_o that_o analogy_n to_o proceed_v then_o with_o the_o explication_n i_o say_v these_o steam_n of_o the_o oil_n thus_o ascend_v if_o they_o be_v heat_v to_o a_o sufficient_a degree_n of_o heat_n be_v prey_v upon_o and_o dissolve_v or_o burn_v by_o the_o ambient_fw-la air_n which_o dissolution_n have_v this_o effect_n first_o that_o it_o produce_v light_a next_o that_o it_o produce_v heat_n enough_o to_o make_v the_o succeed_a part_n of_o the_o steam_n that_o rush_v out_o of_o the_o wick_n and_o follow_v after_o it_o to_o be_v sufficient_o heat_v for_o dissolution_n by_o the_o air_n the_o heat_n of_o which_o produce_v the_o same_o operation_n upon_o a_o three_o and_o that_o upon_o a_o four_o and_o that_o upon_o a_o five_o and_o so_o successive_o so_o long_o as_o there_o be_v steam_n of_o oil_n to_o be_v dissolve_v and_o plenty_n of_o fresh_a and_o unsatiate_v air_n to_o dissolve_v the_o action_n also_o of_o this_o dissolution_n cause_v heat_n sufficient_a to_o raise_v up_o the_o succeed_a part_n of_o the_o oil_n into_o the_o wick_n and_o expand_v they_o into_o vapour_n and_o so_o to_o make_v