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angle_n of_o about_o two_o degree_n at_o once_o and_o furnish_v with_o a_o divide_v scale_n observe_v when_o the_o motion_n of_o the_o comet_n or_o planet_n be_v not_o too_o fast_o the_o position_n and_o distance_n of_o the_o small_a fix_a star_n which_o be_v next_o adjoin_v to_o the_o move_a body_n who_o parallax_n you_o will_v find_v of_o these_o small_a fix_a star_n you_o shall_v seldom_o miss_v a_o sufficient_a number_n which_o will_v be_v take_v into_o the_o glass_n at_o once_o if_o at_o least_o the_o object-glass_n be_v allow_v a_o very_a large_a aperture_n and_o have_v find_v such_o star_n as_o will_v be_v convenient_a for_o your_o purpose_n be_v very_o diligent_a in_o take_v by_o the_o help_n of_o the_o divide_v scale_n the_o exact_a distance_n of_o they_o one_o from_o a_o other_o and_o when_o the_o body_n be_v high_a above_o the_o horizon_n viz._n in_o or_o near_o the_o meridian_n by_o the_o same_o mean_n take_v the_o exact_a distance_n of_o it_o from_o two_o or_o three_o of_o 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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 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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 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part_n of_o a_o revolution_n and_o both_o these_o in_o character_n large_a and_o distinct_a enough_o and_o therefore_o the_o certainty_n and_o truth_n of_o this_o assertion_n can_v be_v further_o doubt_v the_o way_n then_o for_o these_o division_n be_v this_o make_v a_o frame_n of_o a_o quadrant_n of_o hammer_v iron_n after_o the_o manner_n express_v in_o the_o first_o figure_n and_o in_o the_o centre_n hereof_o fix_v or_o raise_v a_o hollow_a cylinder_n who_o hollow_a may_v be_v about_o a_o 40th_o part_n of_o its_o radius_fw-la and_o who_o convex_a part_n may_v be_v about_o a_o 30_o leave_v this_o stand_n above_o the_o plain_a of_o the_o quadrant_n about_o 1_o 90_o part_n of_o the_o radius_fw-la let_v the_o outside_n of_o this_o cylinder_n be_v make_v as_o exact_o round_a as_o it_o be_v possible_a to_o be_v turn_v or_o wrought_v then_o make_v a_o ruler_n or_o plate_n with_o a_o round_a hole_n in_o it_o at_o one_o end_n turn_v groun_v and_o fit_v exact_o about_o the_o abovementioned_a 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