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
minute_n of_o time_n their_o motion_n be_v of_o such_o a_o velocity_n impress_v from_o the_o ambient_fw-la on_o the_o two_o extreme_a particle_n 1_o and_o 8._o first_o if_o by_o any_o external_a power_n on_o the_o two_o extreme_n 1_o and_o 8_o they_o be_v remove_v further_o asunder_o as_o to_o cd_o then_o shall_v all_o the_o vibrative_a particle_n be_v proportionable_o extend_v and_o the_o number_n of_o vibration_n and_o consequent_o of_o occursion_n be_v reciprocal_o diminish_v and_o consequent_o their_o endeavour_n of_o recede_v from_o each_o other_o be_v reciprocal_o diminish_v also_o for_o suppose_v this_o second_o dimension_n of_o length_n be_v to_o the_o first_o as_o 3_o to_o 2_o the_o length_n of_o the_o vibration_n and_o consequent_o of_o occursion_n be_v reciprocal_o diminish_v for_o whereas_o i_o suppose_v 1000000_o in_o a_o second_o of_o the_o former_a here_o can_v be_v but_o 666666_o in_o this_o and_o consequent_o the_o spring_n inward_a must_v be_v in_o proportion_n to_o the_o extension_n beyond_o its_o natural_a length_n second_o if_o by_o any_o external_a force_n the_o extreme_a particle_n be_v remove_v a_o three_o part_n near_o together_o than_o the_o external_a natural_a force_n be_v always_o the_o same_o both_o in_o this_o and_o the_o former_a instance_n which_o be_v the_o balance_n to_o it_o in_o its_o natural_a state_n the_o length_n of_o the_o vibration_n shall_v be_v proportionable_o diminish_v and_o the_o number_n of_o they_o and_o consequent_o of_o the_o occursion_n be_v reciprocal_o augment_v and_o instead_o of_o 1000000_o there_o shall_v be_v 1500000._o in_o the_o next_o place_n for_o fluid_fw-la body_n among_o which_o the_o great_a instance_n we_o have_v be_v air_n though_o the_o same_o be_v in_o some_o proportion_n in_o all_o other_o fluid_a body_n the_o air_n than_o be_v a_o body_n consist_v of_o particle_n so_o small_a as_o to_o be_v almost_o equal_a to_o the_o particle_n of_o the_o heterogeneous_a fluid_a medium_n encompass_v the_o earth_n it_o be_v bound_v but_o on_o one_o side_n namely_o towards_o the_o earth_n and_o be_v indefinite_o extend_v upward_o be_v only_o hinder_v from_o fly_v away_o that_o way_n by_o its_o own_o gravity_n the_o cause_n of_o which_o i_o shall_v some_o other_o time_n explain_v it_o consist_v of_o the_o same_o particle_n single_a and_o separate_v of_o which_o water_n and_o other_o fluid_n do_v conjoin_v and_o compound_v and_o be_v make_v of_o particle_n exceed_v small_a its_o motion_n to_o make_v its_o balance_n with_o the_o rest_n of_o the_o earthy_a body_n be_v exceed_v swift_a and_o its_o vibrative_a space_n exceed_v large_a comparative_a to_o the_o vibrative_a space_n of_o other_o terrestrial_a body_n i_o suppose_v that_o of_o the_o air_n next_o the_o earth_n in_o its_o natural_a state_n may_v be_v 8000_o time_n great_a than_o that_o of_o steel_n and_o above_o a_o thousand_o time_n great_a than_o that_o of_o common_a water_n and_o proportionable_o i_o suppose_v that_o its_o motion_n must_v be_v eight_o thousand_o time_n swift_a than_o the_o former_a and_o above_o a_o thousand_o time_n swift_a than_o the_o late_a if_o therefore_o a_o quantity_n of_o this_o body_n be_v enclose_v by_o a_o solid_a body_n and_o that_o be_v so_o contrive_v as_o to_o compress_v it_o into_o less_o room_n the_o motion_n thereof_o suppose_v the_o heat_n the_o same_o will_v continue_v the_o same_o and_o consequent_o the_o vibration_n and_o occursion_n will_v be_v increase_v in_o reciprocal_a proportion_n that_o be_v if_o it_o be_v condense_v into_o half_a the_o space_n the_o vibration_n and_o occursion_n will_v be_v double_a in_o number_n if_o into_o a_o quarter_n the_o vibration_n and_o occursion_n will_v be_v quadruple_a etc._n etc._n again_o if_o the_o contain_v vessel_n be_v so_o contrive_v as_o to_o leave_v it_o more_o space_n the_o length_n of_o the_o vibration_n will_v be_v proportionable_o enlarge_v and_o the_o number_n of_o vibration_n and_o occursion_n will_v be_v reciprocal_o diminish_v that_o be_v if_o it_o be_v suffer_v to_o extend_v to_o twice_o its_o former_a dimension_n its_o vibration_n will_v be_v twice_o as_o long_o and_o the_o number_n of_o its_o vibration_n and_o occursion_n will_v be_v few_o by_o half_a and_o consequent_o its_o endeavour_n outward_a will_v be_v also_o weak_a by_o half_a these_o explanation_n will_v serve_v mutatis_fw-la mutandis_fw-la for_o explain_v the_o spring_n of_o any_o other_o body_n whatsoever_o it_o now_o remain_v that_o i_o show_v how_o the_o constitution_n of_o springy_a body_n be_v such_o the_o vibration_n of_o a_o spring_n or_o a_o body_n move_v by_o a_o spring_n equal_o and_o uniform_o shall_v be_v of_o equal_a duration_n whether_o they_o be_v great_a or_o less_o i_o have_v here_o already_o show_v then_o that_o the_o power_n of_o all_o spring_n be_v proportionate_a to_o the_o degree_n of_o flexure_n viz._n one_o degree_n of_o flexure_n or_o one_o space_n bend_v have_v one_o power_n two_o have_v two_o and_o three_o have_v three_o and_o so_o forward_o and_o every_o point_n of_o the_o space_n of_o flexure_n have_v a_o peculiar_a power_n and_o consequent_o there_o be_v infinite_a point_n of_o the_o space_n there_o must_v be_v infinite_a degree_n of_o power_n and_o consequent_o all_o those_o power_n begin_v from_o nought_o and_o end_v at_o the_o last_o degree_n of_o tension_n or_o bend_n add_v together_o into_o one_o sum_n or_o aggregate_v will_v be_v in_o duplicate_v proportion_n to_o the_o space_n bend_a or_o degree_n of_o flexure_n that_o be_v the_o aggregate_v of_o the_o power_n of_o the_o spring_n tend_v from_o its_o quiescent_n posture_n by_o all_o the_o intermediate_v point_n to_o one_o space_n be_v it_o what_o length_n you_o please_v be_v equal_a or_o in_o the_o same_o proportion_n to_o the_o square_n of_o one_o suppose_v the_o say_a space_n infinite_o divisible_a into_o the_o fraction_n of_o one_o to_o two_o be_v equal_a or_o in_o the_o same_o proportion_n to_o the_o square_n of_o two_o that_o be_v four_o to_o three_o be_v equal_a or_o in_o the_o same_o proportion_n to_o the_o square_n of_o three_o that_o be_v nine_o and_o so_o forward_o and_o consequent_o the_o aggregate_v of_o the_o first_o space_n will_v be_v one_o of_o the_o second_o space_n will_v be_v three_o of_o the_o three_o space_n will_v be_v five_o of_o the_o four_o will_v be_v seven_o and_o so_o onward_o in_o a_o arithmetical_a proportion_n be_v the_o degree_n or_o excess_n by_o which_o these_o aggregate_n exceed_v one_o another_o the_o spring_n therefore_o in_o return_v from_o any_o degree_n of_o flexure_n to_o which_o it_o have_v be_v bend_v by_o any_o power_n receive_v at_o every_o point_n of_o the_o space_n return_v a_o impulse_n equal_a to_o the_o power_n of_o the_o spring_n in_o that_o point_n of_o tension_n and_o in_o return_v the_o whole_a it_o receive_v the_o whole_a aggregate_v of_o all_o the_o force_n belong_v to_o the_o great_a degree_n of_o that_o tension_n from_o which_o it_o return_v so_o a_o spring_n bend_v two_o space_n in_o its_o return_n receive_v four_o degree_n of_o impulse_n that_o be_v three_o in_o the_o first_o space_n return_v and_o one_o in_o the_o second_o so_o bend_v three_o space_n it_o receive_v in_o its_o whole_a return_n nine_o degree_n of_o impulse_n that_o be_v five_o in_o the_o first_o space_n return_v three_o in_o the_o second_o and_o one_o in_o the_o three_o so_o bend_v ten_o space_n it_o receive_v in_o its_o whole_a return_n one_o hundred_o degree_n of_o impulse_n to_o wit_n nineteen_o in_o the_o first_o seventeen_o in_o the_o second_o fifteen_o in_o the_o three_o thirteen_o in_o the_o four_o eleven_o in_o the_o five_o nine_o in_o the_o six_o seven_o in_o the_o seven_o five_o in_o the_o eight_o three_o in_o the_o nine_o and_o one_o in_o the_o ten_o now_o the_o comparative_a velocity_n of_o any_o body_n move_v be_v in_o subduplicate_v proportion_n to_o the_o aggregate_n or_o sum_n of_o the_o power_n by_o which_o it_o be_v move_v therefore_o the_o velocity_n of_o the_o whole_a space_n return_v be_v always_o in_o the_o same_o proportion_n with_o those_o space_n they_o be_v both_o subduplicate_v to_o the_o power_n and_o consequent_o all_o the_o time_n shall_v be_v equal_a next_o for_o the_o velocity_n of_o the_o part_n of_o the_o space_n return_v they_o will_v be_v always_o proportionate_a to_o the_o root_n of_o the_o aggregate_n of_o the_o power_n impress_v in_o every_o of_o these_o space_n for_o in_o the_o last_o instance_n where_o the_o spring_n be_v suppose_v bend_v ten_o space_n the_o velocity_n at_o the_o end_n of_o the_o first_o space_n return_v shall_v be_v as_o the_o root_n of_o 19_o at_o the_o end_n of_o the_o second_o as_o the_o root_n of_o 36._o that_o be_v of_o 19+17_n at_o the_o end_n of_o the_o three_o as_o the_o root_n of_o 51._o that_o be_v of_o 19+17_n +15._o at_o the_o end_n of_o the_o
the_o most_o part_n incomplete_a and_o essay_n or_o attempt_n only_o upon_o several_a subject_n which_o have_v no_o dependencie_n or_o coherencie_n one_o with_o another_o in_o the_o do_v hereof_o i_o design_v to_o avoid_v any_o kind_n of_o method_n or_o order_n that_o may_v require_v apology_n preface_n or_o needless_a repetition_n of_o what_o be_v already_o know_v or_o may_v have_v be_v say_v upon_o that_o occasion_n or_o may_v necessitate_v i_o to_o follow_v this_o or_o that_o subject_a that_o do_v not_o some_o way_n or_o other_o offer_v itself_o as_o it_o be_v and_o prompt_v i_o to_o the_o consideration_n thereof_o but_o because_o they_o may_v possible_o admit_v of_o some_o better_a order_n hereafter_o i_o design_v to_o print_v they_o all_o of_o the_o same_o volume_n that_o so_o they_o may_v be_v when_o range_v either_o stitch_v or_o bind_v together_o and_o may_v as_o occasion_n require_v be_v refer_v to_o under_o the_o title_n of_o their_o number_n and_o page_n this_o way_n i_o 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regulate_v navigation_n and_o geography_n detect_v the_o propriety_n and_o effect_n of_o motion_n for_o promote_a secret_a and_o swift_a conveyance_n and_o correspondence_n and_o many_o other_o considerable_a scrutiny_n of_o nature_n and_o shall_v only_o for_o the_o present_a hint_n that_o i_o have_v in_o some_o of_o my_o forego_v observation_n discover_v some_o new_a motion_n even_o in_o the_o earth_n itself_o which_o perhaps_o be_v not_o dream_v of_o before_o which_o i_o shall_v hereafter_o more_o at_o large_a describe_v when_o further_a trial_n have_v more_o full_o confirm_v and_o complete_v these_o begining_n at_o which_o time_n also_o i_o shall_v explain_v a_o system_fw-la of_o the_o world_n differ_v in_o many_o particular_n from_o any_o yet_o know_v answer_v in_o all_o thing_n to_o the_o common_a rule_n of_o mechanical_a motion_n this_o depend_v upon_o three_o supposition_n first_o that_o all_o celestial_a body_n whatsoever_o have_v a_o attraction_n or_o gravitate_v power_n towards_o their_o own_o centre_n whereby_o they_o attract_v not_o only_o their_o own_o part_n and_o keep_v they_o from_o fly_v from_o they_o as_o we_o may_v observe_v the_o earth_n to_o do_v but_o that_o they_o do_v also_o attract_v all_o the_o other_o celestial_a body_n that_o be_v within_o the_o sphere_n of_o their_o activity_n and_o consequent_o that_o not_o only_o the_o sun_n and_o moon_n have_v a_o influence_n upon_o the_o body_n and_o motion_n of_o the_o earth_n and_o the_o earth_n upon_o they_o but_o that_o ☿_o also_o ♀_o ♂_o ♄_o and_o ♃_o by_o their_o attractive_a power_n have_v a_o considerable_a influence_n upon_o its_o motion_n as_o in_o the_o same_o manner_n the_o correspond_v attractive_a power_n of_o the_o earth_n have_v a_o considerable_a influence_n upon_o every_o one_o of_o their_o motion_n also_o the_o second_o supposition_n be_v this_o that_o all_o body_n whatsoever_o that_o be_v put_v into_o a_o direct_a and_o simple_a motion_n will_v so_o continue_v to_o move_v forward_o in_o a_o straight_a line_n till_o they_o be_v by_o some_o other_o effectual_a power_n deflect_v and_o bend_v into_o a_o motion_n describe_v a_o circle_n ellipsis_n or_o some_o other_o more_o compound_v curve_v line_n the_o three_o supposition_n be_v that_o these_o attractive_a power_n be_v so_o much_o the_o more_o powerful_a in_o operate_n by_o how_o much_o the_o near_o the_o body_n wrought_v upon_o be_v to_o their_o own_o centre_n now_o what_o these_o several_a degree_n be_v i_o have_v not_o yet_o experimental_o verify_v but_o it_o be_v a_o notion_n which_o if_o full_o prosecute_v as_o it_o ought_v to_o be_v will_v mighty_o assist_v the_o astronomer_n to_o reduce_v all_o the_o celestial_a motion_n to_o a_o certain_a rule_n which_o i_o doubt_v will_v never_o be_v do_v true_a without_o it_o he_o that_o understand_v the_o nature_n of_o the_o circular_a pendulum_n and_o circular_a motion_n will_v easy_o understand_v the_o whole_a ground_n of_o this_o principle_n and_o will_v know_v where_o to_o find_v direction_n in_o nature_n for_o the_o true_a state_v thereof_o this_o i_o only_o hint_n at_o present_a to_o such_o as_o have_v ability_n and_o opportunity_n of_o prosecute_a this_o inquiry_n and_o be_v not_o want_v of_o industry_n for_o observe_v and_o calculate_v wish_v hearty_o such_o may_v be_v find_v have_v myself_o many_o other_o thing_n in_o hand_n which_o i_o will_v first_o complete_a and_o therefore_o can_v so_o well_o attend_v it_o but_o this_o i_o dare_v promise_v the_o undertaker_n that_o he_o will_v find_v all_o the_o great_a motion_n of_o the_o world_n to_o be_v influence_v by_o this_o principle_n and_o that_o the_o true_a understanding_n thereof_o will_v be_v the_o true_a perfection_n of_o astronomy_n london_n print_v for_o john_n martin_n printer_n to_o the_o royal_a society_n 1674._o animadversion_n on_o the_o first_o part_n of_o the_o machina_fw-la coelestibus_fw-la of_o the_o honourable_a learned_a and_o deserve_o famous_a astronomer_n johannes_n hevelius_n consul_n of_o dantzick_n together_o with_o a_o explication_n of_o some_o instrument_n make_v by_o robert_n hooke_n professor_n of_o geometry_n in_o gresham_n college_n and_o fellow_n of_o the_o royal_a society_n london_n print_v by_o t.r._n for_o john_n martin_n printer_n to_o the_o royal_a society_n at_o the_o bell_n in_o st._n paul_n churchyard_n 1674._o the_o content_n the_o reason_n of_o the_o present_a animadversion_n page_n 1._o how_o far_o hevelius_n have_v proceed_v that_o his_o instrument_n do_v not_o much_o exceed_v tycho_n the_o bigness_n sight_n and_o division_n not_o considerable_o differ_v tycho_n not_o ignorant_a of_o his_o new_a way_n of_o division_n p._n 2._o prove_v by_o several_a passage_n out_o of_o his_o work_n p._n 3_o 4._o that_o so_o great_a curiosity_n as_o hevelius_n strive_v for_o be_v needless_a without_o the_o use_n of_o telescopical_a sight_n the_o power_n of_o the_o naked_a eye_n be_v limit_v that_o no_o one_o part_n of_o a_o instrument_n shall_v be_v more_o perfect_a than_o another_o p._n 4_o 5._o hevelius_n his_o letter_n of_o 1665._o with_o his_o opinion_n of_o telescopical_a sight_n p._n 5_o 6._o that_o if_o hevelius_n can_v have_v be_v prevail_v on_o by_o the_o author_n to_o have_v use_v telescope_n sight_n his_o observation_n may_v have_v be_v 40_o time_n more_o exact_a than_o they_o be_v p_o 6_o 7._o that_o hevelius_n his_o objection_n against_o telescope_n sight_n be_v of_o no_o validity_n but_o that_o sight_n without_o telescope_n can_v distinguish_v a_o less_o angle_n then_o half_a a_o minute_n p._n 7._o that_o a_o instrument_n of_o 3_o foot_n radius_fw-la with_o telescope_n will_v do_v more_o than_o one_o of_o 3_o score_n foot_n radius_fw-la with_o common_a sight_n the_o eye_n be_v unable_a to_o distinguish_v this_o be_v prove_v by_o the_o undiscernableness_n of_o spot_n in_o the_o moon_n and_o by_o a_o experiment_n with_o line_n on_o a_o paper_n by_o which_o a_o standard_n be_v make_v of_o the_o power_n of_o the_o eye_n p._n 8._o that_o it_o have_v be_v much_o to_o be_v wish_v that_o tycho_n and_o hevelius_n have_v and_o that_o observator_n for_o the_o future_a will_v well_o consider_v this_o p._n 9_o that_o altitude_n of_o the_o sun_n and_o some_o of_o the_o moon_n may_v have_v be_v take_v to_o great_a exactness_n but_o still_o short_a of_o what_o may_v be_v do_v with_o telescope_n ibid._n the_o author_n engagement_n for_o describe_v a_o instrument_n more_o perfect_a in_o 7_o particular_n p._n 10._o a_o more_o particular_a examination_n of_o hevelius_n his_o instrument_n and_o first_o of_o his_o first_o instrument_n be_v a_o brass_n quadrant_n hevelius_n have_v a_o very_a great_a aversion_n to_o glass-sight_n use_v common_a p._n 11._o take_v great_a pain_n in_o the_o divide_v it_o himself_o p._n 12._o of_o which_o he_o may_v have_v spare_v almost_o 80_o 90_o if_o he_o have_v know_v either_o the_o first_o way_n of_o diagonal_a division_n describe_v in_o p._n 12_o 13._o or_o the_o second_o way_n describe_v and_o exemplify_v p._n 14_o 15._o some_o inconvenience_n in_o the_o contrivance_n about_o his_o first_o instrument_n p._n 16._o a_o description_n of_o his_o second_o three_o four_o five_o and_o six_o instrument_n and_o some_o of_o their_o convenience_n and_o inconvenience_n note_v p._n 16_o 17._o hevelius_n whole_o reject_v all_o wooden_a instrument_n make_v better_a of_o brass_n and_o iron_n p._n 18._o that_o notwithstanding_o there_o may_v be_v a_o good_a use_n make_v of_o wood_n for_o the_o material_a of_o instrument_n prove_v by_o the_o experiment_n of_o a_o instrument_n make_v long_o since_o by_o sr._n ch._n wren_n ibid._n hevelius_n his_o reason_n for_o reject_v the_o use_n of_o wood-instrument_n not_o without_o some_o exception_n p._n 19_o animadversion_n on_o the_o description_n of_o three_o small_a metalline_a instrument_n one_o of_o 24_o a_o second_o of_o 18_o and_o a_o three_o of_o 12_o inch_n and_o particular_o about_o the_o new_a way_n of_o division_n which_o he_o ascribe_v to_o benedictus_n hedreus_n p._n 20._o that_o hevelius_n be_v mistake_v in_o suppose_v hedreus_n his_o way_n more_o capable_a of_o demonstration_n than_o ticho_n by_o diagonal_n p._n 21._o tycho_n brahe_n calculation_n of_o the_o quantity_n of_o angles_n make_v by_o diagonal_n and_o equidistant_a parallel_n circle_n p_o 21_o 22._o it_o be_v strange_a that_o tycho_n and_o hevelius_n shall_v not_o think_v of_o put_v the_o parallel_a circle_n at_o unequal_a distance_n ibid._n how_o to_o calculate_v and_o what_o those_o unequal_a distance_n be_v p._n 23._o dr._n wallis_n his_o letter_n to_o hevelius_n about_o the_o same_o subject_a wherein_o that_o doctrine_n be_v large_o and_o full_o handle_v p._n 23._o 24_o 25_o 26_o the_o diagonal_a division_n more_o easy_a to_o be_v see_v then_o those_o of_o hedreus_n or_o nonnius_n ticho_n description_n of_o nonnius_n his_o way_n of_o division_n p_o 27._o hevelius_n his_o description_n of_o the_o way_n of_o hedreus_n p._n 28._o
figure_n now_o though_o the_o comet_n appearance_n be_v this_o way_n cause_v and_o so_o a_o man_n may_v conceive_v the_o globous_a body_n will_v in_o a_o little_a time_n by_o so_o copious_a a_o emanation_n be_v consume_v yet_o i_o do_v not_o believe_v that_o it_o do_v in_o a_o short_a time_n waste_v and_o disperse_v the_o whole_a ball_n nor_o can_v i_o conceive_v that_o the_o disappear_v of_o those_o blaze_a body_n towards_o the_o latter_a end_n do_v depend_v upon_o their_o dissolution_n though_o possible_o that_o may_v somewhat_o diminish_v they_o but_o that_o rather_o be_v to_o be_v ascribe_v to_o their_o distance_n and_o position_n in_o respect_n of_o we_o though_o this_o i_o remember_v i_o observe_v very_o manifest_o in_o that_o of_o 1664._o that_o the_o body_n towards_o the_o latter_a end_n of_o its_o appear_v be_v very_o much_o less_o in_o proportion_n to_o the_o radiation_n about_o it_o than_o it_o seem_v to_o be_v at_o the_o beginning_n but_o whether_o that_o may_v not_o be_v partly_o ascribe_v to_o the_o great_a distance_n it_o then_o be_v from_o we_o and_o the_o turn_n of_o the_o head_n pretty_a near_o towards_o we_o and_o thence_o the_o spread_a of_o the_o tail_n appear_v beyond_o it_o may_v add_v to_o the_o breadth_n of_o the_o radiation_n about_o the_o nucleus_n i_o will_v not_o positive_o determine_v now_o though_o for_o explication_n sake_n i_o have_v compare_v the_o part_n separate_v from_o the_o body_n of_o the_o comet_n to_o blaze_a granade_n or_o fire-ball_n yet_o i_o will_v not_o be_v understand_v to_o suppose_v these_o part_n so_o separate_v to_o be_v of_o any_o very_a large_a bulk_n for_o i_o see_v no_o necessity_n to_o suppose_v they_o big_a than_o the_o atom_n of_o smoke_n or_o the_o particle_n of_o any_o other_o steam_a body_n or_o than_o the_o part_n of_o the_o air_n which_o make_v the_o body_n of_o it_o appear_v thick_a and_o hazy_a nor_o do_v i_o believe_v that_o all_o the_o light_n of_o the_o star_n head_n and_o blaze_n do_v depend_v only_o upon_o the_o shine_a of_o the_o dissolve_v body_n and_o particle_n thereof_o but_o i_o do_v suppose_v that_o it_o do_v proceed_v both_o from_o the_o reflection_n of_o the_o sunbeam_n from_o those_o part_n and_o also_o from_o a_o innate_a and_o momentaneous_a light_n produce_v by_o the_o action_n of_o dissolution_n wrought_v on_o the_o part_n by_o the_o encompass_v aether_n it_o may_v possible_o seem_v very_o difficult_a to_o suppose_v that_o the_o dissolution_n of_o the_o part_n of_o the_o nucleus_n by_o the_o encompass_v aether_n shall_v cause_v or_o impress_v so_o violent_a a_o motion_n into_o the_o separate_a part_n as_o to_o make_v they_o depart_v from_o it_o to_o the_o space_n of_o four_o or_o five_o diameter_n before_o it_o be_v overpower_v by_o the_o power_n of_o levitation_n from_o the_o body_n of_o the_o sun_n and_o so_o deflect_v into_o a_o parabolical_a line_n upward_o it_o may_v likewise_o seem_v strange_a to_o suppose_v that_o the_o aether_n shall_v have_v such_o 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this_o aether_n do_v take_v up_o the_o particle_n of_o body_n to_o a_o very_a great_a distance_n from_o the_o surface_n from_o which_o they_o be_v separate_v and_o it_o do_v not_o only_o raise_v they_o but_o sustein_v they_o at_o those_o height_n nor_o be_v this_o peculiar_a only_o to_o the_o aether_n when_o a_o menstruum_fw-la but_o to_o all_o dissolve_v menstruum_n in_o general_n as_o to_o give_v one_o instance_n in_o stead_n of_o many_o we_o find_v that_o gold_n the_o heavy_a of_o all_o terrestrial_a body_n we_o yet_o know_v be_v dissolve_v by_o aqua_fw-la regis_fw-la be_v take_v up_o into_o it_o and_o keep_v suspend_v therein_o though_o the_o part_n of_o the_o gold_n be_v fifteen_o time_n heavy_a than_o the_o part_n of_o the_o aqua_fw-la regis_fw-la so_o pit-coal_n though_o very_o heavy_a be_v yet_o take_v up_o into_o the_o air_n and_o keep_v suspend_v therein_o though_o it_o will_v be_v find_v to_o be_v some_o thousand_o of_o time_n more_o ponderous_a than_o the_o menstruum_fw-la 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repossess_v its_o former_a seat_n and_o place_n and_o overwhelm_v again_o all_o those_o place_n which_o in_o the_o interim_n have_v be_v dry_a and_o uncovered_a with_o the_o return_n of_o the_o same_o water_n since_o nothing_o in_o nature_n be_v find_v exempt_a from_o the_o state_n of_o change_n and_o corruption_n further_o it_o be_v probable_a that_o earthquake_n may_v have_v be_v much_o more_o frequent_a in_o former_a age_n than_o they_o have_v be_v in_o these_o latter_a the_o consideration_n of_o which_o will_v possible_o make_v this_o assertion_n not_o so_o paradoxical_a as_o at_o first_o hear_v it_o may_v seem_v to_o be_v though_o even_o these_o latter_a age_n have_v not_o be_v whole_o barren_a of_o instance_n of_o the_o be_v and_o effect_n of_o they_o to_o convince_v you_o of_o which_o i_o have_v hereunto_o subjoin_v a_o relation_n and_o account_n of_o one_o very_o new_o which_o happen_v in_o the_o isle_n of_o palma_n among_o the_o canary_n next_o the_o clearness_n of_o the_o air_n be_v very_o remarkable_a which_o make_v a_o island_n which_o lie_v eight_o league_n off_o to_o look_v as_o if_o it_o be_v close_o by_o to_o this_o purpose_n i_o have_v often_o take_v notice_n of_o the_o great_a difference_n there_o be_v between_o the_o air_n very_o near_o the_o low_a surface_n of_o the_o earth_n and_o that_o which_o be_v at_o a_o good_a distance_n from_o it_o that_o which_o be_v very_o near_o the_o earth_n be_v general_o so_o thick_a and_o opacous_a that_o body_n can_v at_o any_o considerable_a distance_n be_v see_v distinct_o through_o it_o but_o the_o far_o the_o eye_n and_o object_n be_v elevate_v above_o this_o thick_a air_n the_o more_o clear_a do_v the_o object_n appear_v and_o i_o have_v divers_a time_n take_v notice_n that_o the_o same_o object_n see_v from_o the_o top_n and_o bottom_n of_o a_o high_a tower_n have_v appear_v twice_o as_o far_o off_o when_o see_v at_o the_o bottom_n as_o when_o see_v at_o the_o top_n for_o the_o eye_n do_v very_o much_o judge_n of_o the_o distance_n of_o object_n according_a as_o the_o density_n of_o the_o air_n between_o the_o eye_n and_o object_n do_v represent_v they_o hence_o i_o have_v see_v man_n look_v of_o gigantic_a bigness_n in_o a_o fog_n cause_v by_o reason_n that_o the_o fog_n make_v the_o eye_n judge_v the_o object_n much_o far_o off_o than_o real_o it_o be_v when_o at_o the_o same_o time_n the_o visible_a angle_n alter_v not_o this_o great_a thickness_n of_o the_o low_a air_n be_v sufficient_o manifest_a in_o the_o celestial_a body_n few_o of_o the_o fix_a star_n or_o small_a planet_n be_v visible_a till_o they_o be_v a_o considerable_a way_n raise_v above_o the_o horizon_n the_o three_o remark_n about_o the_o moistness_n of_o the_o fog_n and_o the_o production_n of_o water_n at_o that_o height_n i_o have_v before_o insist_v on_o only_o the_o almost_o continual_a fog_n that_o this_o gentleman_n observe_v in_o the_o wood_n they_o pass_v be_v very_o remarkable_a for_o the_o origine_fw-la of_o spring_n nor_o shall_v i_o say_v any_o thing_n concern_v the_o vast_a perpendicular_a height_n of_o the_o same_o but_o for_o a_o close_a of_o this_o present_a collection_n i_o shall_v add_v the_o short_a account_n of_o the_o eruption_n which_o late_o happen_v in_o the_o palma_n a_o true_a relation_n of_o the_o vulcanos_fw-la which_o break_v out_o in_o the_o island_n of_o the_o palma_n novemb_n 13._o 1677._o saturday_n the_o thirteen_o of_o november_n 1677._o a_o quarter_n of_o a_o hour_n after_o sun_n set_v happen_v a_o shake_n or_o earthquake_n in_o the_o island_n of_o st._n michael_n de_fw-fr la_fw-fr palma_n one_o of_o the_o canary_n island_n from_o the_o low_a pyrenna_n and_o within_o a_o league_n of_o the_o city_n unto_o the_o port_n of_o tassacorte_n which_o be_v account_v