produce_v and_o power_n in_o respect_n of_o the_o same_o effect_n to_o be_v produce_v hereafter_o so_o that_o cause_o respect_v the_o past_a power_n the_o future_a time_n also_o the_o power_n of_o the_o agent_n be_v that_o which_o be_v common_o call_v active_a power_n in_o like_a manner_n whensoever_o any_o patient_n have_v all_o those_o accident_n which_o it_o be_v requisite_a it_o shall_v have_v for_o the_o production_n of_o some_o effect_n in_o it_o we_o say_v it_o be_v in_o the_o power_n of_o that_o patient_n to_o produce_v that_o effect_n if_o it_o be_v apply_v to_o a_o fit_a agent_n but_o those_o accident_n as_o be_v define_v in_o the_o precedent_a chapter_n constitute_v the_o material_a cause_n and_o therefore_o the_o power_n of_o the_o patient_n common_o call_v passive_a power_n and_o material_a cause_n be_v the_o same_o thing_n but_o with_o this_o different_a consideration_n that_o in_o cause_n the_o past_a time_n and_o in_o power_n the_o future_a be_v respect_v wherefore_o the_o power_n of_o the_o agent_n and_o patient_n together_o which_o may_v be_v call_v entire_a or_o plenary_a power_n be_v the_o same_o thing_n with_o entire_a cause_n for_o they_o both_o consist_v in_o the_o sum_n or_o aggregate_v of_o all_o the_o accident_n as_o well_o in_o the_o agent_n as_o in_o the_o patient_n which_o be_v requisite_a for_o the_o production_n of_o the_o effect_n last_o as_o the_o accident_n produce_v be_v in_o respect_n of_o the_o cause_n call_v a_o effect_n so_o in_o respect_n of_o the_o power_n it_o be_v call_v a_o act._n 2_o as_o therefore_o the_o effect_n be_v produce_v in_o the_o same_o instant_n in_o which_o the_o cause_n be_v entire_a so_o also_o every_o act_n that_o may_v be_v produce_v be_v produce_v in_o the_o same_o instant_n in_o which_o the_o power_n be_v plenary_a and_o as_o there_o can_v be_v no_o effect_n but_o from_o a_o sufficient_a and_o necessary_a cause_n so_o also_o no_o act_n can_v be_v produce_v but_o by_o sufficient_a power_n or_o that_o power_n by_o which_o it_o can_v not_o but_o be_v produce_v 3_o and_o as_o it_o be_v manifest_a as_o i_o have_v show_v that_o the_o efficient_a and_o material_a cause_n be_v several_o and_o by_o themselves_o part_v only_o of_o a_o entire_a cause_n and_o can_v produce_v any_o effect_n but_o by_o be_v join_v together_o so_o also_o power_n active_a and_o passive_a be_v part_n only_o of_o plenary_a and_o entire_a power_n nor_o except_o they_o be_v join_v can_v any_o act_n proceed_v from_o they_o and_o therefore_o these_o power_n as_o i_o say_v in_o the_o first_o article_n be_v but_o conditional_a namely_o the_o agent_n have_v power_n if_o it_o be_v apply_v to_o a_o patient_n and_o the_o patient_n have_v power_n if_o it_o be_v apply_v to_o a_o agent_n otherwise_o neither_o of_o they_o have_v power_n nor_o can_v the_o accident_n which_o be_v in_o they_o several_o be_v proper_o call_v power_n nor_o any_o action_n be_v say_v to_o be_v possible_a for_o the_o power_n of_o the_o agent_n alone_o or_o of_o the_o patient_n alone_o 4_o for_o that_o be_v a_o impossible_a act_n for_o the_o production_n of_o which_o there_o be_v no_o power_n plenary_a for_o see_v plenary_a power_n be_v that_o in_o which_o all_o thing_n concur_v which_o be_v requisite_a for_o the_o production_n of_o a_o act_n if_o the_o power_n shall_v never_o be_v plenary_a there_o will_v always_o be_v want_v some_o of_o those_o thing_n without_o which_o the_o act_n can_v be_v produce_v wherefore_o that_o act_n shall_v never_o be_v produce_v that_o be_v that_o act_n be_v impossible_a and_o every_o act_n which_o be_v not_o impossible_a be_v possible_a every_o act_n therefore_o which_o be_v possible_a shall_v at_o some_o time_n be_v produce_v for_o if_o it_o shall_v never_o be_v produce_v than_o those_o thing_n shall_v never_o concur_v which_o be_v requisite_a for_o the_o production_n of_o it_o wherefore_o that_o act_n be_v impossible_a by_o the_o definition_n which_o be_v contrary_a to_o what_o be_v suppose_v 5_o a_o necessary_a act_n be_v that_o the_o production_n whereof_o it_o be_v impossible_a to_o hinder_v and_o therefore_o every_o act_n that_o shall_v be_v produce_v shall_v necessary_o be_v produce_v for_o that_o it_o shall_v not_o be_v produce_v be_v impossible_a because_o as_o be_v already_o demonstrate_v every_o possible_a act_n shall_v at_o some_o time_n be_v produce_v nay_o this_o proposition_n what_o shall_v be_v shall_v be_v be_v as_o necessary_a a_o proposition_n as_o this_o a_o man_n be_v a_o man._n but_o here_o perhaps_o some_o man_n may_v ask_v whether_o those_o future_a thing_n which_o be_v common_o call_v contingent_n be_v necessary_a i_o say_v therefore_o that_o general_o all_o contingent_n have_v their_o necessary_a cause_n as_o be_v show_v in_o the_o precede_a chapter_n but_o be_v call_v contingent_n in_o respect_n of_o other_o event_n upon_o which_o they_o do_v not_o depend_v as_o the_o rain_n which_o shall_v be_v to_o morrow_n shall_v be_v necessary_o that_o be_v from_o necessary_a cause_n but_o we_o think_v and_o say_v it_o happen_v by_o chance_n because_o we_o do_v not_o yet_o perceive_v the_o cause_n thereof_o though_o they_o exist_v now_o for_o man_n common_o call_v that_o casual_a or_o contingent_a whereof_o they_o do_v not_o perceive_v the_o necessary_a cause_n and_o in_o the_o same_o manner_n they_o use_v to_o speak_v of_o thing_n past_a when_o not_o know_v whether_o a_o thing_n be_v do_v or_o no_o they_o say_v it_o be_v possible_a it_o never_o be_v do_v wherefore_o all_o proposition_n concern_v future_a thing_n contingent_a or_o not_o contingent_a as_o this_o it_o will_v rain_v to_o morrow_n or_o this_o to_o morrow_n the_o sun_n will_v rise_v be_v either_o necessary_o true_a or_o necessary_o false_a but_o we_o call_v they_o contingent_a because_o we_o do_v not_o yet_o know_v whether_o they_o be_v true_a or_o false_a whereas_o their_o verity_n depend_v not_o upon_o our_o knowledge_n but_o upon_o the_o forego_n of_o their_o cause_n but_o there_o be_v some_o who_o though_o they_o confess_v this_o whole_a proposition_n to_o morrow_n it_o will_v either_o rain_n or_o not_o rain_n to_o be_v true_a yet_o they_o will_v not_o acknowledge_v the_o part_n of_o it_o as_o to_z morrow_n it_o will_v rain_v or_o to_o morrow_n it_o will_v not_o rain_v to_o be_v either_o of_o they_o true_a by_o itself_o because_o they_o say_v neither_o this_o nor_o that_o be_v true_a determinate_o but_o what_o be_v this_o determinate_o true_a but_o true_a upon_o our_o knowledge_n or_o evident_o true_a and_o therefore_o they_o say_v no_o more_o but_o that_o it_o be_v not_o yet_o know_v whether_o it_o be_v true_a or_o no_o but_o they_o say_v it_o more_o obscure_o and_o darken_v the_o evidence_n of_o the_o truth_n with_o the_o same_o word_n with_o which_o they_o endeavour_v to_o hide_v their_o own_o ignorance_n 6_o in_o the_o 9th_o article_n of_o the_o precedent_a chapter_n i_o have_v show_v that_o the_o efficient_a cause_n of_o all_o motion_n and_o mutation_n consist_v in_o the_o motion_n of_o the_o agent_n or_o agent_n and_o in_o the_o first_o article_n of_o this_o chapter_n that_o the_o power_n of_o the_o agent_n be_v the_o same_o thing_n with_o the_o efficient_a cause_n from_o whence_o it_o may_v be_v understand_v that_o all_o active_a power_n consist_v in_o motion_n also_o and_o that_o power_n be_v not_o a_o certain_a accident_n which_o differ_v from_o all_o act_n but_o be_v indeed_o a_o act_n namely_o motion_n which_o be_v therefore_o call_v power_n because_o another_o act_n shall_v be_v produce_v by_o it_o afterward_o for_o example_n if_o of_o three_o body_n the_o first_o put_v forward_o the_o second_o and_o this_o the_o three_o the_o motion_n of_o the_o second_o in_o respect_n of_o the_o first_o which_o produce_v it_o be_v the_o act_n of_o the_o second_o body_n but_o in_o respect_n of_o the_o three_o it_o be_v the_o active_a power_n of_o the_o same_o second_o body_n 7_o the_o writer_n of_o metaphysic_n reckon_v up_o two_o other_o cause_n beside_o the_o efficient_a and_o material_a namely_o the_o essence_n which_o some_o call_v the_o formal_a cause_n and_o the_o end_n or_o final_a cause_n both_o which_o be_v nevertheless_o efficient_a cause_n for_o when_o it_o be_v say_v the_o essence_n of_o a_o thing_n be_v the_o cause_n thereof_o as_o to_o be_v rational_a be_v the_o cause_n of_o man_n it_o be_v not_o intelligible_a for_o it_o be_v all_o one_o as_o if_o it_o be_v say_v to_o be_v a_o man_n be_v the_o cause_n of_o man_n which_o be_v not_o well_o say_v and_o yet_o the_o knowledge_n of_o the_o essence_n of_o any_o thing_n be_v the_o cause_n of_o the_o knowledge_n of_o the_o thing_n itself_o for_o if_o i_o first_o know_v that_o a_o thing_n be_v rational_a i_o know_v from_o thence_o that_o the_o same_o be_v man_n but_o this_o be_v no_o
other_o than_o a_o efficient_a cause_n a_o final_a cause_n have_v no_o place_n but_o in_o such_o thing_n as_o have_v sense_n and_o will_n and_o this_o also_o i_o shall_v prove_v hereafter_o to_o be_v a_o efficient_a cause_n chap._n xi_o of_o identity_n and_o difference_n 1_o what_o it_o be_v for_o one_o thing_n to_o differ_v from_o another_o 2_o to_o differ_v in_o number_n magnitude_n species_n and_o genus_fw-la what_o 3_o what_o be_v relation_n proportion_n and_o relative_n 4_o proportional_n what_o 5_o the_o proportion_n of_o magnitude_n to_o one_o another_o wherein_o it_o consist_v 6_o relation_n be_v no_o new_a accident_n but_o one_o of_o those_o that_o be_v in_o the_o relative_n before_o the_o relation_n or_o comparison_n be_v make_v also_o the_o cause_n of_o accident_n in_o the_o correlative_n be_v the_o cause_n of_o relation_n 7_o of_o the_o beginning_n of_o individuation_n 1hitherto_o i_o have_v speak_v of_o body_n simple_o and_o of_o accident_n common_a to_o all_o body_n as_o magnitude_n motion_n rest_v action_n passion_n power_n possible_a etc._n etc._n and_o i_o shall_v now_o descend_v to_o those_o accident_n by_o which_o one_o body_n be_v distinguish_v from_o another_o but_o that_o it_o be_v first_o to_o be_v declare_v what_o it_o be_v to_o be_v distinct_a and_o not_o distinct_a namely_o what_o be_v the_o same_o and_o different_n for_o this_o also_o be_v common_a to_o all_o body_n that_o they_o may_v be_v distinguish_v and_o difference_v from_o one_o another_o now_o two_o body_n be_v say_v to_o differ_v from_o one_o another_o when_o something_o may_v be_v say_v of_o one_o of_o they_o which_o can_v be_v say_v of_o the_o other_o at_o the_o same_o time_n 2_o and_o first_o of_o all_o it_o be_v manifest_a that_o no_o two_o body_n be_v the_o same_o for_o see_v they_o be_v two_o they_o be_v in_o two_o place_n at_o the_o same_o time_n as_o that_o which_o be_v the_o same_o be_v at_o the_o same_o time_n in_o one_o and_o the_o same_o place_n all_o body_n therefore_o differ_v from_o one_o another_o in_o number_n namely_o as_o one_o and_o another_o so_o that_o the_o same_o and_o different_a in_o number_n be_v name_n oppose_v to_o one_o another_o by_o contradiction_n in_o magnitude_n body_n differ_v when_o one_o be_v great_a than_o another_o as_o a_o cubit_n long_o and_o two_o cubit_n long_o of_o two_o pound_n weight_n and_o of_o three_o pound_n weight_n and_o to_o these_o equal_n be_v oppose_v body_n which_o differ_v more_o then_o in_o magnitude_n be_v call_v unlike_a and_o those_o which_o differ_v only_o in_o magnitude_n like_a also_o of_o unlike_a body_n some_o be_v say_v to_o differ_v in_o the_o species_n other_o in_o the_o genus_fw-la in_o the_o species_n when_o their_o difference_n be_v perceive_v by_o one_o and_o the_o same_o sense_n as_o white_a and_o black_a and_o in_o the_o genus_fw-la when_o their_o difference_n be_v not_o perceive_v but_o by_o divers_a sense_n as_o white_a and_o hot._n 3_o and_o the_o likeness_n or_o unlikeness_n equality_n or_o inequality_n of_o one_o body_n to_o another_o be_v call_v their_o relation_n and_o the_o body_n themselves_o relative_n or_o correlative_n aristotle_n call_v they_o 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d the_o first_o whereof_o be_v usual_o name_v the_o antecedent_n and_o the_o second_o the_o consequent_a and_o the_o relation_n of_o the_o antecedent_n to_o the_o consequent_a according_a to_o magnitude_n namely_o the_o equality_n the_o excess_n or_o defect_n thereof_o be_v call_v the_o proportion_n of_o the_o antecedent_n to_o the_o consequent_a so_o that_o proportion_n be_v nothing_o but_o the_o equality_n or_o inequality_n of_o the_o magnitude_n of_o the_o antecedent_n compare_v to_o the_o magnitude_n of_o the_o consequent_a by_o their_o difference_n only_o or_o compare_v also_o with_o their_o difference_n for_o example_n the_o proportion_n of_o three_o to_o two_o consist_v only_o in_o this_o that_o three_o exceed_v two_o by_o unity_n and_o the_o proportion_n of_o two_o to_o five_o in_o this_o that_o two_o compare_v with_o five_o be_v deficient_a of_o it_o by_o three_o either_o simple_o or_o compare_v with_o the_o number_n different_a and_o therefore_o in_o the_o proportion_n of_o unequal_o the_o proportion_n of_o the_o less_o to_o the_o great_a be_v call_v defect_n and_o that_o of_o the_o great_a to_o the_o less_o excess_n 4_o beside_o of_o unequal_o some_o be_v more_o some_o less_o and_o some_o equal_o unequal_a so_o that_o there_o be_v proportion_n of_o proportion_n as_o well_o as_o of_o magnitude_n namely_o where_o two_o unequal_o have_v relation_n to_o two_o other_o unequal_o as_o when_o the_o inequality_n which_o be_v between_o 2_o and_o 3_o be_v compare_v with_o the_o inequality_n which_o be_v between_o 4_o and_o 5._o in_o which_o comparison_n there_o be_v always_o four_o magnitude_n or_o which_o be_v all_o one_o if_o there_o be_v but_o three_o the_o middlemost_a be_v twice_o number_v and_o if_o the_o proportion_n of_o the_o first_o to_o the_o second_o be_v equal_a to_o the_o proportion_n of_o the_o three_o to_o the_o four_o than_o the_o four_o be_v say_v to_o be_v proportional_n otherwise_o they_o be_v not_o proportional_n 5_o the_o proportion_n of_o the_o antecedent_n to_o the_o consequent_a consist_v in_o their_o difference_n not_o only_o simple_o take_v but_o also_o as_o compare_v with_o one_o of_o the_o relative_n that_o be_v either_o in_o that_o part_n of_o the_o great_a by_o which_o it_o exceed_v the_o less_o or_o in_o the_o remainder_n after_o the_o less_o be_v take_v out_o of_o the_o great_a as_o the_o proportion_n of_o two_o to_o five_o consist_v in_o the_o three_o by_o which_o five_o exceed_v two_o not_o in_o three_o simple_o only_a but_o also_o as_o compare_v with_o five_o or_o two_n for_o though_o there_o be_v the_o same_o difference_n between_o two_o &_o five_o which_o be_v between_o nine_o and_o twelve_o namely_o three_o yet_o there_o be_v not_o the_o same_o inequality_n and_o therefore_o the_o proportion_n of_o two_o to_o five_o be_v not_o in_o all_o relation_n the_o same_o with_o that_o of_o nine_o to_o twelve_o but_o only_o in_o that_o which_o be_v call_v arithmetical_a 6_o but_o we_o must_v not_o so_o think_v of_o relation_n as_o if_o it_o be_v a_o accident_n differ_v from_o all_o the_o other_o accident_n of_o the_o relative_n but_o one_o of_o they_o namely_o that_o by_o which_o the_o comparison_n be_v make_v for_o example_n the_o likeness_n of_o one_o white_a to_o another_o white_a or_o its_o unlikeness_n to_o black_a be_v the_o same_o accident_n with_o its_o whiteness_n and_o equality_n and_o inequality_n the_o same_o accident_n with_o the_o magnitude_n of_o the_o thing_n compare_v though_o under_o another_o name_n for_o that_o which_o be_v call_v white_a or_o great_a when_o it_o be_v not_o compare_v with_o something_o else_o the_o same_o when_o it_o be_v compare_v be_v call_v like_a or_o unlike_a equal_a or_o unequal_a and_o from_o this_o it_o follow_v that_o the_o cause_n of_o the_o accident_n which_o be_v in_o relative_n be_v the_o cause_n also_o of_o likeness_n unlikeness_n equality_n and_o inequality_n namely_o that_o he_o that_o make_v two_o unequal_a body_n make_v also_o their_o inequality_n and_o he_o that_o make_v a_o rule_n and_o a_o action_n make_v also_o if_o the_o action_n be_v congruous_a to_o the_o rule_n their_o congruity_n if_o incongruous_a their_o incongruity_n and_o thus_o much_o concern_v comparison_n of_o one_o body_n with_o another_o 7_o but_o the_o same_o body_n may_v at_o different_a time_n be_v compare_v with_o itself_o and_o from_o hence_o spring_v a_o great_a controversy_n among_o philosopher_n about_o the_o beginning_n of_o individuation_n namely_o in_o what_o sense_n it_o may_v be_v conceive_v that_o a_o body_n be_v at_o one_o time_n the_o same_o at_o another_o time_n not_o the_o same_o it_o be_v former_o for_o example_n whether_o a_o man_n grow_v old_a be_v the_o same_o man_n he_o be_v while_o he_o be_v young_a or_o another_o man_n or_o whether_o a_o city_n be_v in_o different_a age_n the_o same_o or_o another_o city_n some_o place_n individuity_n in_o the_o unity_n of_o matter_n other_o in_o the_o unity_n of_o form_n and_o one_o say_v it_o consist_v in_o the_o unity_n of_o the_o aggregate_v of_o all_o the_o accident_n together_o for_o matter_n it_o be_v plead_v that_o a_o lump_n of_o wax_n whether_o it_o be_v spherical_a or_o cubical_a be_v the_o same_o wax_n because_o the_o same_o matter_n for_o form_n that_o when_o a_o man_n be_v grow_v from_o a_o infant_n to_o be_v a_o old_a man_n though_o his_o matter_n be_v change_v yet_o he_o be_v still_o the_o same_o numerical_a man_n for_o that_o identity_n which_o can_v be_v attribute_v to_o the_o matter_n ought_v probable_o to_o be_v ascribe_v to_o the_o form_n for_o the_o aggregate_v of_o accident_n no_o instance_n can_v be_v make_v but_o because_o
touch_v a_o spiral_n at_o the_o end_n of_o its_o first_o conversion_n for_o upon_o the_o centre_n a_o in_o the_o six_o figure_n let_v the_o circle_n bcde_v be_v describe_v and_o in_o it_o let_v archimedes_n his_o spiral_n afghb_n be_v draw_v beginning_z at_z a_o and_o end_n at_o b._n through_o the_o centre_n a_o let_v the_o straight_a line_n ce_fw-fr be_v draw_v cut_v the_o diameter_n bd_o at_o right_n angle_n and_o let_v it_o be_v produce_v to_o i_o so_o that_o ai_fw-fr be_v equal_a to_o the_o perimeter_n bcdeb_fw-mi therefore_o ib_n be_v draw_v will_v touch_v the_o spiral_n afghb_n in_o b_o which_o be_v demonstrate_v by_o archimedes_n in_o his_o book_n de_fw-fr spiralibus_fw-la and_o for_o a_o straight_a line_n equal_a to_o the_o give_v spiral_n afghb_n it_o may_v be_v find_v thus_o let_v the_o straight_a line_n a_z which_o be_v equal_a to_o the_o perimeter_n bcde_v be_v bisect_v in_o k_o and_o take_v kl_n equal_a to_o the_o radius_fw-la ab_fw-la let_v the_o rectangle_n il_fw-fr be_v complete_v let_v ml_o be_v understand_v to_o be_v the_o axis_fw-la and_o kl_n the_o base_a of_o a_o parabola_fw-la and_o let_v mk_n be_v the_o crooked_a line_n thereof_o now_o if_o the_o point_n m_o be_v conceive_v to_o be_v so_o move_v by_o the_o concourse_n of_o two_o movent_n the_o one_o from_o in_o to_o kl_n with_o velocity_n increase_a continual_o in_o the_o same_o proportion_n with_o the_o time_n the_o other_o from_o ml_o to_o ik_fw-mi uniform_o that_o both_o those_o motion_n begin_v together_o in_o m_n and_o end_n in_o k_o galilaeus_fw-la have_v demonstrate_v that_o by_o such_o motion_n of_o the_o point_n m_o the_o crooked_a line_n of_o a_o parabola_fw-la will_v be_v describe_v again_o if_o the_o point_n a_o be_v conceive_v to_o be_v move_v uniform_o in_o the_o straight_a line_n ab_fw-la and_o in_o the_o same_o time_n to_o be_v carry_v round_o upon_o the_o centre_n a_o by_o the_o circular_a motion_n of_o all_o the_o point_n between_o a_o and_o b_o archimedes_n have_v demonstrate_v that_o by_o such_o motion_n will_v be_v describe_v a_o spiral_n line_n and_o see_v the_o circle_n of_o all_o these_o motion_n be_v concentric_a in_o a_o and_o the_o interior_a circle_n be_v always_o less_o than_o the_o exterior_a in_o the_o proportion_n of_o the_o time_n in_o which_o ab_fw-la be_v pass_v over_o with_o uniform_a motion_n the_o velocity_n also_o of_o the_o circular_a motion_n of_o the_o point_n a_o will_v continual_o increase_v proportional_o to_o the_o time_n and_o thus_o far_o the_o generation_n of_o the_o parabolical_a line_n mk_n and_o of_o the_o spiral_n line_n afghb_n be_v like_a but_o the_o uniform_a motion_n in_o ab_fw-la concur_v with_o circular_a motion_n in_o the_o perimeter_n of_o all_o the_o concentric_a circle_n describe_v that_o circle_n who_o centre_n be_v a_o and_o perimeter_n bcde_v and_o therefore_o that_o circle_n be_v by_o the_o coral_n of_o the_o first_o article_n of_o the_o 16_o chapter_n the_o aggregate_v of_o all_o the_o velocity_n together_o take_v of_o the_o point_n a_o whilst_o it_o describe_v the_o spiral_n afghb_n also_o the_o rectangle_n iklm_n be_v the_o aggregate_v of_o all_o the_o velocity_n together_o take_v of_o the_o point_n m_o while_o it_o describe_v the_o crooked_a line_n mk_n and_o therefore_o the_o whole_a velocity_n by_o which_o the_o parabolicall_a line_n mk_n be_v describe_v be_v to_o the_o whole_a velocity_n with_o which_o the_o spiral_n line_n afghb_n be_v describe_v in_o the_o same_o time_n as_o the_o rectangle_n iklm_n be_v to_o the_o circle_n bcde_v that_o be_v to_o the_o triangle_n aib_n but_o because_o a_z be_v bisect_v in_o k_o &_o the_o straight_a line_n in_o &_o ab_fw-la be_v equal_a therefore_o the_o rectangle_n iklm_n and_o the_o triangle_n aib_n be_v also_o equal_a wherefore_o the_o spiral_n line_n afghb_n and_o the_o parabolical_a line_n mk_n be_v describe_v with_o equal_a velocity_n and_o in_o equal_a time_n be_v equal_a to_o one_o another_o now_o in_o the_o first_o article_n of_o the_o 18_o chapter_n a_o straight_a line_n be_v find_v out_o equal_a to_o any_o parabolical_a line_n wherefore_o also_o a_o straight_a line_n be_v find_v out_o equal_a to_o a_o give_v spiral_n line_n of_o the_o first_o revolution_n describe_v by_o archimedes_n which_o be_v to_o be_v do_v 6_o in_o the_o six_o chapter_n which_o be_v of_o method_n that_o which_o i_o shall_v there_o have_v speak_v of_o the_o analytic_n of_o geometrician_n i_o think_v fit_a to_o defer_v because_o i_o can_v not_o there_o have_v be_v understand_v as_o not_o have_v then_o so_o much_o as_o name_v line_n superficies_n solid_n equal_a and_o unequal_a etc._n etc._n wherefore_o i_o will_v in_o this_o place_n set_v down_o my_o thought_n concern_v it_o analysis_n be_v continual_a reason_v from_o the_o definition_n of_o the_o term_n of_o a_o proposition_n we_o suppose_v true_a and_o again_o from_o the_o definition_n of_o the_o term_n of_o those_o definition_n and_o so_o on_o till_o we_o come_v to_o some_o thing_n know_v the_o composition_n whereof_o be_v the_o demonstration_n of_o the_o truth_n or_o falsity_n of_o the_o first_o supposition_n and_o this_o composition_n or_o demonstration_n be_v that_o we_o call_v synthesis_n analytica_n therefore_o be_v that_o art_n by_o which_o our_o reason_n proceed_v from_o something_o suppose_v to_o principle_n that_o be_v to_o prime_a proposition_n or_o to_o such_o as_o be_v know_v by_o these_o till_o we_o have_v so_o many_o know_a proposition_n as_o be_v sufficient_a for_o the_o demonstration_n of_o the_o truth_n or_o falsity_n of_o the_o thing_n suppose_v synthetica_fw-la be_v the_o art_n itself_o of_o demonstration_n synthesis_n therefore_o and_o analysis_n differ_v in_o nothing_o but_o in_o proceed_v forward_o or_o backward_o and_o logistica_fw-la comprehend_v both_o so_o that_o in_o the_o analysis_n or_o synthesis_n of_o any_o question_n that_o be_v to_o say_v of_o any_o problem_n the_o term_n of_o all_o the_o proposition_n ought_v to_o be_v convertible_a or_o if_o they_o be_v enunciate_v hypothetical_o the_o truth_n of_o the_o consequent_a ought_v not_o only_o to_o follow_v out_o of_o the_o truth_n of_o its_o antecedent_n but_o contrary_o also_o the_o truth_n of_o the_o antecedent_n must_v necessary_o be_v infer_v from_o the_o truth_n of_o the_o consequent_a for_o otherwise_o when_o by_o resolution_n we_o be_v arrive_v at_o principle_n we_o can_v by_o composition_n return_v direct_o back_o to_o the_o thing_n seek_v for_o for_o those_o term_n which_o be_v the_o first_o in_o analysis_n will_v be_v the_o last_o in_o synthesis_n as_o for_o example_n when_o in_o resolve_v we_o say_v these_o two_o rectangle_v be_v equal_a and_o therefore_o their_o side_n be_v reciprocal_o proportional_a we_o must_v necessary_o in_o compound_v say_v the_o side_n of_o these_o rectangle_v be_v reciprocal_o proportional_a and_o therefore_o the_o rectangle_v themselves_o be_v equal_a which_o we_o can_v not_o say_v â—…ss_n rectangle_v have_v their_o side_n reciprocal_o proportional_a and_o rectangle_v be_v equal_a be_v term_n convertible_a now_o in_o every_o analysis_n that_o which_o be_v seek_v be_v the_o proportion_n of_o two_o quantity_n by_o which_o proportion_n a_o figure_n be_v describe_v the_o quantity_n seek_v for_o may_v be_v expose_v to_o sense_n and_o this_o exposition_n be_v the_o end_n and_o solution_n of_o the_o question_n or_o the_o construction_n of_o the_o problem_n and_o see_v analysis_n be_v reason_v from_o something_o suppose_v till_o we_o come_v to_o principle_n that_o be_v to_o definition_n or_o to_o theorem_n former_o know_v and_o see_v the_o same_o reason_n tend_v in_o the_o last_o place_n to_o some_o equation_n we_o can_v therefore_o make_v no_o end_n of_o resolve_v till_o we_o come_v at_o last_o to_o the_o cause_n themselves_o of_o equality_n and_o inequality_n or_o to_o theorem_n former_o demonstrate_v from_o those_o cause_n and_o so_o have_v a_o sufficient_a number_n of_o those_o theorem_n for_o the_o demonstration_n of_o the_o thing_n seek_v for_o and_o see_v also_o that_o the_o end_n of_o the_o analytic_n be_v either_o the_o construction_n of_o such_o a_o problem_n as_o be_v possible_a or_o the_o detection_n of_o the_o impossibility_n thereof_o whensoever_o the_o problem_n may_v be_v solve_v the_o analyst_n must_v not_o stay_v till_o he_o come_v to_o those_o thing_n which_o contain_v the_o efficient_a cause_n of_o that_o whereof_o he_o be_v to_o make_v construction_n but_o he_o must_v of_o necessity_n stay_v when_o he_o come_v to_o prime_a proposition_n and_o these_o be_v definition_n these_o definition_n therefore_o must_v contain_v the_o efficient_a cause_n of_o his_o construction_n i_o say_v of_o his_o construction_n not_o of_o the_o conclusion_n which_o he_o demonstrate_v for_o the_o cause_n of_o the_o conclusion_n be_v contain_v in_o the_o premise_a proposition_n that_o be_v to_o say_v the_o truth_n of_o the_o proposition_n he_o prove_v be_v
end_n that_o the_o reader_n may_v know_v that_o those_o axiom_n be_v not_o indemonstrable_a &_o therefore_o not_o principle_n of_o demonstration_n and_o from_o hence_o learn_v to_o be_v wary_a how_o he_o admit_v any_o thing_n for_o a_o principle_n which_o be_v not_o at_o least_o as_o evident_a as_o these_o be_v great_a be_v define_v to_o be_v that_o who_o part_n be_v equal_a to_o the_o whole_a of_o another_o now_o if_o we_o suppose_v any_o whole_a to_o be_v a_o and_o a_o part_n of_o it_o to_o be_v b_o seeing_z the_o whole_a b_o be_v equal_a to_o itself_o and_o the_o same_o b_o be_v a_o part_n of_o a_o therefore_o a_o part_n of_o a_o will_v be_v equal_a to_o the_o whole_a b._n wherefore_o by_o the_o definition_n above_o a_o be_v great_a than_o b_o which_o be_v to_o be_v prove_v chap._n ix_o of_o cause_n and_o effect_n 1_o action_n and_o passion_n what_o they_o be_v 2_o action_n and_o passion_n mediate_v and_o immediate_a 3_o cause_n simple_o take_v cause_o without_o which_o no_o effect_n follow_v or_o cause_o necessary_a by_o supposition_n 4_o cause_n efficient_a and_o material_a 5_o a_o entire_a cause_n be_v always_o sufficient_a to_o produce_v its_o effect_n at_o the_o same_o instant_n that_o the_o cause_n be_v entire_a the_o effect_n be_v produce_v every_o effect_n have_v a_o necessary_a cause_n 6_o the_o generation_n of_o effect_n be_v continual_a what_o be_v the_o beginning_n in_o causation_n 7_o no_o cause_n of_o motion_n but_o in_o a_o body_n contiguous_a and_o move_v 8_o the_o same_o agent_n and_o patient_n if_o alike_o dispose_v produce_v like_o effect_n though_o at_o different_a time_n 9_o all_o mutation_n be_v motion_n 10_o contingent_a accident_n what_o they_o be_v 1_o a_o body_n be_v say_v to_o work_n upon_o or_o act_n that_o be_v to_o say_v do_v some_o thing_n to_o another_o body_n when_o it_o either_o generate_v or_o destroy_v some_o accident_n in_o it_o and_o the_o body_n in_o which_o a_o accident_n be_v generate_v or_o destroy_v be_v say_v to_o suffer_v that_o be_v to_o have_v something_o do_v to_o it_o by_o another_o body_n as_o when_o one_o body_n by_o put_v forward_o another_o body_n generate_v motion_n in_o it_o it_o be_v call_v the_o agent_n and_o the_o body_n in_o which_o motion_n be_v so_o generate_v be_v call_v the_o patient_n so_o fire_n that_o warm_v the_o hand_n be_v the_o agent_n and_o the_o hand_n which_o be_v warm_v be_v the_o patient_n that_o accident_n which_o be_v generate_v in_o the_o patient_n be_v call_v the_o effect_n 2_o when_o a_o agent_n and_o patient_n be_v contiguous_a to_o one_o another_o their_o action_n and_o reason_n be_v then_o say_v to_o be_v immediate_a otherwise_o mediate_v and_o when_o another_o body_n lie_v betwixt_o the_o agent_n and_o patient_n be_v contiguous_a to_o they_o both_o it_o be_v then_o itself_o both_o a_o agent_n and_o a_o patient_n a_o agent_n in_o respect_n of_o the_o body_n next_o after_o it_o upon_o which_o it_o work_v and_o a_o patient_n in_o respect_n of_o the_o body_n next_o before_o it_o from_o which_o it_o suffer_v also_o if_o many_o body_n be_v so_o order_v that_o every_o two_o which_o be_v next_o to_o one_o another_o be_v contiguous_a than_o all_o those_o that_o be_v betwixt_o the_o first_o and_o the_o last_o be_v both_o agent_n and_o patient_n and_o the_o first_o be_v a_o agent_n only_o and_o the_o last_o a_o patient_n only_o 3_o a_o agent_n be_v understand_v to_o produce_v its_o determine_a or_o certain_a effect_n in_o the_o patient_n according_a to_o some_o certain_a accident_n or_o accident_n with_o which_o both_o it_o and_o the_o patient_n be_v affect_v that_o be_v to_o say_v the_o agent_n have_v its_o effect_n precise_o such_o not_o because_o it_o be_v a_o body_n but_o because_o such_o a_o body_n or_o so_o move_v for_o otherwise_o all_o agent_n see_v they_o be_v all_o body_n alike_o will_v produce_v like_o effect_n in_o all_o patient_n and_o therefore_o the_o fire_n for_o example_n do_v not_o warm_a because_o it_o be_v a_o body_n but_o because_o it_o be_v hot_a nor_o do_v one_o body_n put_v forward_o another_o body_n because_o it_o be_v a_o body_n but_o because_o it_o be_v move_v into_o the_o place_n of_o that_o other_o body_n the_o cause_n therefore_o of_o all_o effect_n consist_v in_o certain_a accident_n both_o in_o the_o agent_n and_o in_o the_o patient_n which_o when_o they_o be_v all_o present_a the_o effect_n be_v produce_v but_o if_o any_o one_o of_o they_o be_v want_v it_o be_v not_o produce_v and_o that_o accident_n either_o of_o the_o agent_n or_o patient_n without_o which_o the_o effect_n can_v be_v produce_v be_v call_v causa_fw-la sine_fw-la qua_fw-la non_fw-la or_o cause_o necessary_a by_o supposition_n as_o also_o the_o cause_n requisite_a for_o the_o production_n of_o the_o effect_n but_o a_o cause_n simple_o or_o a_o entire_a cause_n be_v the_o aggregate_v of_o all_o the_o accident_n both_o of_o the_o agent_n how_o many_o soever_o they_o be_v and_o of_o the_o patient_n put_v together_o which_o when_o they_o be_v all_o suppose_a to_o be_v present_a it_o can_v be_v understand_v but_o that_o the_o effect_n be_v produce_v at_o the_o same_o instant_n and_o if_o any_o one_o of_o they_o be_v want_v it_o can_v be_v understand_v but_o that_o the_o effect_n be_v not_o produce_v 4_o the_o aggregate_v of_o accident_n in_o the_o agent_n or_o agent_n requisite_a for_o the_o production_n of_o the_o effect_n the_o effect_n be_v produce_v be_v call_v the_o efficient_a cause_n thereof_o and_o the_o aggregate_v of_o accident_n in_o the_o patient_n the_o effect_n be_v produce_v be_v usual_o call_v the_o material_a cause_n i_o say_v the_o effect_n be_v produce_v for_o where_o there_o be_v no_o effect_n there_o can_v be_v no_o cause_n for_o nothing_o can_v be_v call_v a_o cause_n where_o there_o be_v nothing_o that_o can_v be_v call_v a_o effect_n but_o the_o efficient_a and_o material_a cause_n be_v both_o but_o partial_a cause_n or_o part_n of_o that_o cause_n which_o in_o the_o next_o precedent_n article_n i_o call_v a_o entire_a cause_n and_o from_o hence_o it_o be_v manifest_a that_o the_o effect_v we_o expect_v though_o the_o agent_n be_v not_o defective_a on_o their_o part_n may_v nevertheless_o be_v frustrate_v by_o a_o defect_n in_o the_o patient_n and_o when_o the_o patient_n be_v sufficient_a by_o a_o defect_n in_o the_o agent_n 5_o a_o entire_a cause_n be_v always_o sufficient_a for_o the_o production_n of_o its_o effect_n if_o the_o effect_v be_v at_o all_o possible_a for_o let_v any_o effect_n whatsoever_o be_v propound_v to_o be_v produce_v if_o the_o same_o be_v produce_v it_o be_v manifest_a that_o the_o cause_n which_o produce_v it_o be_v a_o sufficient_a cause_n but_o if_o it_o be_v not_o produce_v and_o yet_o be_v possible_a it_o be_v evident_a that_o something_o be_v want_v either_o in_o some_o agent_n or_o in_o the_o patient_n without_o which_o it_o can_v not_o be_v produce_v that_o be_v that_o some_o accident_n be_v want_v which_o be_v requisite_a for_o its_o production_n and_o therefore_o that_o cause_n be_v not_o entire_a which_o be_v contrary_a to_o what_o be_v suppose_v it_o follow_v also_o from_o hence_o that_o in_o whatsoever_o instant_n the_o cause_n be_v entire_a in_o the_o same_o instant_n the_o effect_n be_v produce_v for_o if_o it_o be_v not_o produce_v something_o be_v still_o want_v which_o be_v requisite_a for_o the_o production_n of_o it_o and_o therefore_o the_o cause_n be_v not_o entire_a as_o be_v suppose_v and_o see_v a_o necessary_a cause_n be_v define_v to_o be_v that_o which_o be_v suppose_v the_o effect_n can_v but_o follow_v this_o also_o may_v be_v collect_v that_o whatsoever_o effect_n be_v produce_v at_o any_o time_n the_o same_o be_v produce_v by_o a_o necessary_a cause_n for_o whatsoever_o be_v produce_v in_o as_o much_o as_o it_o be_v produce_v have_v a_o entire_a cause_n that_o be_v have_v all_o those_o thing_n which_o be_v suppose_v it_o can_v be_v understand_v but_o that_o the_o effect_n follow_v that_o be_v it_o have_v a_o necessary_a cause_n and_o in_o the_o same_o manner_n it_o may_v be_v show_v that_o whatsoever_o effect_n be_v hereafter_o to_o be_v produce_v shall_v have_v a_o necessary_a cause_n so_o that_o all_o the_o effect_n that_o have_v be_v or_o shall_v be_v produce_v have_v their_o ne_n cessity_n in_o thing_n antecedent_n 6_o and_o from_o this_o that_o whensoever_o the_o cause_n be_v entire_a the_o effect_n be_v produce_v in_o the_o same_o instant_n it_o be_v manifest_a that_o causation_n and_o the_o production_n of_o effect_n consist_v in_o a_o certain_a continual_a progress_n so_o that_o as_o there_o be_v a_o continual_a mutation_n in_o the_o agent_n or_o agent_n by_o the_o work_n of_o other_o agent_n upon_o they_o so_o also_o the_o patient_n upon_o
which_o they_o work_v be_v continual_o alter_v and_o change_v for_o example_n as_o the_o heat_n of_o the_o fire_n increase_v more_o and_o more_o so_o also_o the_o effect_n thereof_o namely_o the_o heat_n of_o such_o body_n as_o be_v next_o to_o it_o &_o again_o of_o such_o other_o body_n as_o be_v next_o to_o they_o increase_v more_o &_o more_o according_o which_o be_v already_o no_o little_a argument_n that_o all_o mutation_n consist_v in_o motion_n only_o the_o truth_n whereof_o shall_v be_v further_o demonstrate_v in_o the_o nine_o article_n but_o in_o this_o progress_n of_o causation_n that_o be_v of_o action_n and_o passion_n if_o any_o man_n comprehend_v in_o his_o imagination_n a_o part_n thereof_o and_o divide_v the_o same_o into_o part_n the_o first_o part_n or_o beginning_n of_o it_o can_v be_v consider_v otherwise_o then_o as_o action_n or_o cause_n for_o if_o it_o shall_v be_v consider_v as_o effect_v or_o passion_n than_o it_o will_v be_v necessary_a to_o consider_v something_o before_o it_o for_o its_o cause_n or_o action_n which_o can_v be_v for_o nothing_o can_v be_v before_o the_o beginning_n and_o in_o like_a manner_n the_o last_o part_n be_v consider_v only_o as_o effect_v for_o it_o can_v be_v call_v cause_n if_o nothing_o follow_v it_o but_o after_o the_o last_o nothing_o follow_v and_o from_o hence_o it_o be_v that_o in_o all_o action_n the_o beginning_n and_o cause_n be_v take_v for_o the_o same_o thing_n but_o every_o one_o of_o the_o intermediate_v part_n be_v both_o action_n and_o passion_n and_o cause_n and_o effect_v according_a as_o they_o be_v compare_v with_o the_o antecedent_n or_o subsequent_a part_n 7_o there_o can_v be_v no_o cause_n of_o motion_n except_o in_o a_o body_n contiguous_a and_o move_v for_o let_v there_o be_v any_o two_o body_n which_o be_v not_o contiguous_a and_o betwixt_o which_o the_o intermediate_v space_n be_v empty_a or_o if_o fill_v fill_v with_o another_o body_n which_o be_v at_o rest_n and_o let_v one_o of_o the_o propound_a body_n be_v suppose_v to_o be_v at_o rest_n i_o say_v it_o shall_v always_o be_v at_o rest._n for_o if_o it_o shall_v be_v move_v the_o cause_n of_o that_o motion_n by_o the_o 8_o chapter_n 19_o article_n will_v be_v in_o some_o external_a body_n and_o therefore_o if_o between_o it_o and_o that_o external_a body_n there_o be_v nothing_o but_o empty_a space_n than_o whatsoever_o the_o disposition_n be_v of_o that_o external_a body_n or_o of_o the_o patient_n itself_o yet_o if_o it_o be_v suppose_v to_o be_v now_o at_o rest_n we_o may_v conceive_v it_o will_v continue_v so_o till_o it_o be_v touch_v by_o some_o other_o body_n but_o see_v cause_n by_o the_o definition_n be_v the_o aggregate_v of_o all_o such_o accident_n which_o be_v suppose_v to_o be_v present_a it_o can_v be_v conceive_v but_o that_o the_o effect_n will_v follow_v those_o accident_n which_o be_v either_o in_o external_a body_n or_o in_o the_o patient_n itself_o can_v be_v the_o cause_n of_o future_a motion_n and_o in_o like_a manner_n see_v we_o may_v conceive_v that_o whatsoever_o be_v at_o rest_n will_v still_o be_v at_o rest_n though_o it_o be_v touch_v by_o some_o other_o body_n except_o that_o other_o body_n be_v move_v therefore_o in_o a_o contiguous_a body_n which_o be_v at_o rest_n there_o can_v be_v no_o cause_n of_o motion_n wherefore_o there_o be_v no_o cause_n of_o motion_n in_o any_o body_n except_o it_o be_v contiguous_a and_o move_v the_o same_o reason_n may_v serve_v to_o prove_v that_o whatsoever_o be_v move_v will_v always_o be_v move_v on_o in_o the_o same_o way_n and_o with_o the_o same_o velocity_n except_o it_o be_v hinder_v by_o some_o other_o contiguous_a and_o move_v body_n and_o consequent_o that_o no_o body_n either_o when_o they_o be_v at_o rest_n or_o when_o there_o be_v a_o interposition_n of_o vacuum_n can_v generate_v or_o extinguish_v or_o lesson_n motion_n in_o other_o body_n there_o be_v one_o that_o have_v write_v that_o thing_n move_v be_v more_o resist_v by_o thing_n at_o rest_n then_o by_o thing_n contrary_o move_v for_o this_o reason_n that_o he_o conceive_v motion_n not_o to_o be_v so_o contrary_a to_o motion_n as_o rest._n that_o which_o deceive_v he_o be_v that_o the_o word_n rest_v and_o motion_n be_v but_o contradictory_n name_n whereas_o motion_n indeed_o be_v not_o resist_v by_o rest_n but_o by_o contrary_a motion_n 8_o but_o if_o a_o body_n work_v upon_o another_o body_n at_o one_o time_n and_o afterward_o the_o same_o body_n work_v upon_o the_o same_o body_n at_o another_o time_n so_o that_o both_o the_o agent_n and_o patient_n and_o all_o their_o part_n be_v in_o all_o thing_n as_o they_o be_v and_o there_o be_v no_o difference_n except_o only_o in_o time_n that_o be_v that_o one_o action_n be_v former_a the_o other_o late_a in_o time_n it_o be_v manifest_a of_o itself_o that_o the_o effect_n will_v be_v equal_a and_o like_a as_o not_o differ_v in_o any_o thing_n beside_o time_n and_o as_o effect_n themselves_o proceed_v from_o their_o cause_n so_o the_o diversity_n of_o they_o depend_v upon_o the_o diversity_n of_o their_o cause_n also_o 9_o this_o be_v true_a it_o be_v necessary_a that_o mutation_n can_v be_v nothing_o else_o but_o motion_n of_o the_o part_n of_o that_o body_n which_o be_v change_v for_o first_o we_o do_v not_o say_v any_o thing_n be_v change_v but_o that_o which_o appear_v to_o our_o sense_n otherwise_o than_o it_o appear_v former_o second_o both_o those_o appearance_n be_v effect_n produce_v in_o the_o sentient_a &_o therefore_o if_o they_o be_v different_a it_o be_v necessary_a by_o the_o precede_a article_n that_o either_o some_o part_n of_o the_o agent_n which_o be_v former_o at_o rest_n be_v now_o move_v and_o so_o the_o mutation_n consist_v in_o this_o motion_n or_o some_o part_n which_o be_v former_o move_v be_v now_o otherwise_o move_v and_o so_o also_o the_o mutation_n consist_v in_o this_o new_a motion_n or_o which_o be_v former_o move_v be_v now_o at_o rest_n which_o as_o i_o have_v show_v above_o can_v come_v to_o pass_v without_o motion_n and_o so_o again_o mutation_n be_v motion_n or_o last_o it_o happen_v in_o some_o of_o these_o manner_n to_o the_o patient_n or_o some_o of_o its_o part_n so_o that_o mutation_n howsoever_o it_o be_v make_v will_v consist_v in_o the_o motion_n of_o the_o part_n either_o of_o the_o body_n which_o be_v perceive_v or_o of_o the_o sentient_a body_n or_o of_o both_o mutation_n therefore_o be_v motion_n namely_o of_o the_o part_n either_o of_o the_o agent_n or_o of_o the_o patient_n which_o be_v to_o be_v demonstrate_v and_o to_o this_o it_o be_v consequent_a that_o rest_n can_v be_v the_o cause_n of_o any_o thing_n nor_o can_v any_o action_n proceed_v from_o it_o see_v neither_o motion_n nor_o mutation_n can_v be_v cause_v by_o it_o 10_o accident_n in_o respect_n of_o other_o accident_n which_o precede_v they_o or_o be_v before_o they_o in_o time_n &_o upon_o which_o they_o do_v not_o depend_v as_o upon_o their_o cause_n be_v call_v contingent_a accident_n i_o say_v in_o respect_n of_o those_o accident_n by_o which_o they_o be_v not_o generate_v for_o in_o respect_n of_o their_o cause_n all_o thing_n come_v to_o pass_v with_o equal_a necessity_n for_o otherwise_o they_o will_v have_v no_o cause_n at_o all_o which_o of_o thing_n generate_v be_v not_o intelligible_a chap._n x._o of_o power_n and_o act._n 1_o power_n and_o cause_n be_v the_o same_o thing_n 2_o a_o act_n be_v produce_v at_o the_o same_o instant_n in_o which_o the_o power_n be_v plenary_a 3_o active_a and_o passive_a power_n be_v part_n only_o of_o plenary_a power_n 4_o a_o act_n when_o say_v to_o be_v possible_a 5_o a_o act_n necessary_a and_o contingent_a what_o 6_o active_a power_n consist_v in_o motion_n 7_o cause_v formal_n and_o final_a what_o they_o be_v 1correspondent_a to_o cause_n and_o effect_n be_v power_n and_o act_n nay_o those_o and_o these_o be_v the_o same_o thing_n though_o for_o divers_a consideration_n they_o have_v divers_a name_n forwhensoever_o any_o agent_n have_v all_o those_o accident_n which_o be_v necessary_o requisite_a for_o the_o production_n of_o some_o effect_n in_o the_o patient_n than_o we_o say_v that_o agent_n have_v power_n to_o produce_v that_o effect_n if_o it_o be_v apply_v to_o a_o patient_n but_o as_o i_o have_v show_v in_o the_o precedent_a chapter_n those_o accident_n constitute_v the_o efficient_a cause_n and_o therefore_o the_o same_o accident_n which_o constitute_v the_o efficient_a cause_n constitute_v also_o the_o power_n of_o the_o agent_n wherefore_o the_o power_n of_o the_o agent_n and_o the_o efficient_a cause_n be_v the_o same_o thing_n but_o they_o be_v consider_v with_o this_o difference_n that_o cause_o be_v so_o call_v in_o respect_n of_o the_o effect_n already_o
same_o chapter_n i_o have_v show_v that_o whatsoever_o be_v at_o rest_n will_v always_o be_v at_o rest_n unless_o there_o be_v some_o other_o body_n beside_o it_o which_o by_o get_v into_o its_o place_n suffer_v it_o no_o long_o to_o remain_v at_o rest._n and_o that_o whatsoever_o be_v move_v will_v always_o be_v move_v unless_o there_o be_v some_o other_o body_n beside_o it_o which_o hinder_v its_o motion_n ten_o in_o the_o 9_o chapter_n and_o 7_o article_n i_o have_v demonstrate_v that_o when_o any_o body_n be_v move_v which_o be_v former_o at_o rest_n the_o immediate_a efficient_a cause_n of_o that_o motion_n be_v in_o some_o other_o move_v and_o contiguous_a body_n eleven_o i_o have_v show_v in_o the_o same_o place_n that_o whatsoever_o be_v move_v will_v always_o be_v move_v in_o the_o same_o way_n and_o with_o the_o same_o swiftness_n if_o it_o be_v not_o hinder_v by_o some_o other_o move_v and_o contiguous_a body_n 2_o to_o which_o principle_n i_o shall_v here_o add_v these_o that_o follow_v first_o i_o define_v endeavour_n to_o be_v motion_n make_v in_o less_o space_n and_o time_n then_o can_v be_v give_v that_o be_v less_o than_o can_v be_v determine_v or_o assign_v by_o exposition_n or_o number_n that_o be_v motion_n make_v through_o the_o length_n of_o a_o point_n and_o in_o a_o instant_a or_o point_n of_o time_n for_o the_o explayn_v of_o which_o definition_n it_o must_v be_v remember_v that_o by_o a_o point_n be_v not_o to_o be_v understand_v that_o which_o have_v no_o quantity_n or_o which_o can_v by_o any_o mean_n be_v divide_v for_o there_o be_v no_o such_o thing_n in_o nature_n but_o that_o who_o quantity_n be_v not_o at_o all_o consider_v that_o be_v whereof_o neither_o quantity_n nor_o any_o part_n be_v compute_v in_o demonstration_n so_o that_o a_o point_n be_v not_o to_o be_v take_v for_o a_o indivisible_a but_o for_o a_o undivided_a thing_n as_o also_o a_o instant_a be_v to_o be_v take_v for_o a_o undivided_a and_o not_o for_o a_o indivisible_a time_n in_o like_a manner_n endeavour_n be_v to_o be_v conceive_v as_o motion_n but_o so_o as_o that_o neither_o the_o quantity_n of_o the_o time_n in_o which_o nor_o of_o the_o line_n in_o which_o it_o be_v make_v may_v in_o demonstration_n be_v at_o all_o bring_v into_o comparison_n with_o the_o quantity_n of_o that_o time_n or_o of_o that_o line_n of_o which_o it_o be_v a_o part_n and_o yet_o as_o a_o point_n may_v be_v compare_v with_o a_o point_n so_o one_o endeavour_n may_v be_v compare_v with_o another_o endeavour_n and_o one_o may_v be_v find_v to_o be_v great_a or_o less_o than_o another_o for_o if_o the_o vertical_a point_n of_o two_o angle_n be_v compare_v they_o will_v be_v equal_a or_o unequal_a in_o the_o same_o proportion_n which_o the_o angle_n themselves_o have_v to_o one_o another_o or_o if_o a_o straight_a line_n cut_v many_o circumference_n of_o concentric_a circle_n the_o inequality_n of_o the_o point_n of_o intersection_n will_v be_v in_o the_o same_o proportion_n which_o the_o perimeter_n have_v to_o one_o another_o and_o in_o the_o same_o manner_n if_o two_o motion_n begin_v and_o end_n both_o together_o their_o endeavour_n will_v be_v equal_a or_o unequal_a according_a to_o the_o proportion_n of_o their_o velocity_n as_o we_o see_v a_o bullet_n of_o lead_n descend_v with_o great_a endeavour_n than_o a_o ball_n of_o wool_n second_o i_o define_v impetus_fw-la or_o quickness_n of_o motion_n to_o be_v the_o swiftness_n or_o velocity_n of_o the_o body_n move_v but_o consider_v in_o the_o several_a point_n of_o that_o time_n in_o which_o it_o be_v move_v in_o which_o sense_v impetus_fw-la be_v nothing_o else_o but_o the_o quantity_n or_o velocity_n of_o endeavour_n but_o consider_v with_o the_o whole_a time_n it_o be_v the_o whole_a velocity_n of_o the_o body_n move_v take_v together_o throughout_o all_o the_o time_n and_o equal_a to_o the_o product_n of_o a_o line_n represent_v the_o time_n multiply_v into_o a_o line_n represent_v the_o arithmetical_o mean_v impetus_fw-la or_o quickness_n which_o arithmetical_a mean_n what_o it_o be_v be_v define_v in_o the_o 29_o article_n of_o the_o 13_o chapter_n and_o because_o in_o equal_a time_n the_o way_n that_o be_v pass_v be_v as_o the_o velocity_n and_o the_o impetus_fw-la be_v the_o velocity_n they_o go_v withal_o reckon_v in_o all_o the_o several_a point_n of_o the_o time_n it_o follow_v that_o during_o any_o time_n whatsoever_o howsoever_o the_o impetus_fw-la be_v increase_v or_o decrease_v the_o length_n of_o the_o way_n pass_v over_o shall_v be_v increase_v or_o decrease_v in_o the_o same_o proportion_n and_o the_o same_o line_n shall_v represent_v both_o the_o way_n of_o the_o body_n move_v and_o the_o several_a impetus_fw-la or_o degree_n of_o swiftness_n wherewith_o the_o way_n be_v pass_v over_o and_o if_o the_o body_n move_v be_v not_o a_o point_n but_o a_o straight_a line_n move_v so_o as_o that_o every_o point_n thereof_o make_v a_o several_a straight_a line_n the_o plain_a describe_v by_o its_o motion_n whether_o uniform_a accelerate_a or_o retard_v shall_v be_v great_a or_o less_o the_o time_n be_v the_o same_o in_o the_o same_o proportion_n with_o that_o of_o the_o impetus_fw-la reckon_v in_o one_o motion_n to_o the_o impetus_fw-la reckon_v in_o the_o other_o for_o the_o reason_n be_v the_o same_o in_o parallellogram_n and_o their_o side_n for_o the_o same_o cause_n also_o if_o the_o body_n move_v be_v a_o plain_a the_o solid_a describe_v shall_v be_v still_o great_a or_o less_o in_o the_o proportion_n of_o the_o several_a impetus_fw-la or_o quickness_n reckon_v through_o one_o line_n to_o the_o several_a impetus_fw-la reckon_v through_o another_o this_o understand_v let_v abcd_v in_o the_o first_o figure_n of_o the_o 17_o chapter_n be_v a_o parallelogram_n in_o which_o suppose_v the_o side_n ab_fw-la to_o be_v move_v parallel_o to_o the_o opposite_a side_n cd_o decrease_v all_o the_o way_n till_o it_o vanish_v in_o the_o point_n c_o and_o so_o describe_v the_o figure_n abefc_n the_o point_n b_o as_o ab_fw-la decrease_v will_v therefore_o describe_v the_o line_n befc_n and_o suppose_v the_o time_n of_o this_o motion_n design_v by_o the_o line_n cd_o and_o in_o the_o same_o time_n cd_o suppose_v the_o side_n ac_fw-la to_o be_v move_v parallelly_n and_o uniform_o to_o bd._n from_o the_o point_n o_o take_v at_o adventure_n in_o the_o line_n cd_o draw_v or_o parallel_v to_o bd_o cut_v the_o line_n befc_n in_o e_o and_o the_o side_n ab_fw-la in_o r._n and_o again_o from_o the_o point_n qui_fw-fr take_v also_o at_o adventure_n in_o the_o line_n cd_o draw_v q_n parallel_v to_o bd_o cut_v the_o line_n befc_n in_o f_o and_o the_o side_n ab_fw-la in_o saint_n and_o draw_v eglantine_n and_o fh_n parallel_n to_o cd_o cut_v ac_fw-la in_o g_z and_o h._n last_o suppose_v the_o same_o construction_n do_v in_o all_o the_o point_n possible_a of_o the_o line_n befc_n i_o saâ—_n that_o as_o the_o proportion_n of_o the_o swiftness_n wherewith_o qf_n oe_o db_n and_o all_o the_o rest_n supopse_v to_o be_v draw_v parallel_n to_o db_n and_o terminate_v in_o the_o line_n befc_n be_v to_o the_o proportion_n of_o their_o several_a time_n design_v by_o the_o several_a parallel_n hf_n ge_n ab_fw-la and_o all_o the_o rest_n suppose_v to_o be_v draw_v parallel_n to_o the_o line_n of_o time_n cd_o and_o terminate_v in_o the_o line_n befc_n the_o aggregate_v to_o the_o aggregate_v so_o be_v the_o area_n or_o plain_a dbefc_n to_o the_o area_n or_o plain_a acfeb_n for_o as_o ab_fw-la decrease_v continual_o by_o the_o line_n befc_n vanish_v in_o the_o time_n cd_o into_o the_o point_n c_o so_o in_o the_o same_o time_n the_o line_n dc_o continual_o decrease_v vanish_v by_o the_o same_o line_n cfeb_n into_o the_o point_n b_o and_o the_o point_n d_o describe_v in_o that_o decrease_a motion_n the_o line_n db_n equal_a to_o the_o line_n ac_fw-la describe_v by_o the_o point_n a_o in_o the_o decrease_a motion_n of_o a_o 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draw_v from_o the_o proposition_n which_o prove_v the_o same_o but_o the_o cause_n of_o his_o construction_n be_v in_o the_o thing_n themselves_o and_o consist_v in_o motion_n or_o in_o the_o concourse_n of_o motion_n wherefore_o those_o proposition_n in_o which_o analysis_n end_v be_v definition_n but_o such_o as_o signify_v in_o what_o manner_n the_o construction_n or_o generation_n of_o the_o thing_n proceed_v for_o otherwise_o when_o he_o go_v back_o by_o synthesis_n to_o the_o proof_n of_o his_o problem_n he_o will_v come_v to_o no_o demonstration_n at_o all_o there_o be_v no_o true_a demonstration_n but_o such_o as_o be_v scientifical_a and_o no_o demonstration_n be_v scientifical_a but_o that_o which_o proceed_v from_o the_o knowledge_n of_o the_o cause_n from_o which_o the_o construction_n of_o the_o problem_n be_v draw_v to_o collect_v therefore_o what_o have_v be_v say_v into_o few_o word_n analysis_n be_v ratiocination_n from_o the_o suppose_a construction_n or_o 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multiplication_n division_n addition_n and_o substraction_n as_o also_o by_o the_o extraction_n of_o the_o root_n of_o those_o power_n or_o by_o find_v where_o straight_o line_n of_o the_o same_o proportion_n terminate_v for_o example_n when_o any_o number_n of_o straight_a line_n how_o many_o soever_o be_v draw_v from_o a_o straight_a line_n and_o pass_v all_o through_o the_o same_o point_n look_v what_o proportion_n they_o have_v and_o if_o their_o part_n continue_v from_o the_o point_n retain_v every_o where_o the_o same_o proportion_n they_o shall_v all_o terminate_v in_o a_o straight_a line_n and_o the_o same_o happen_v if_o the_o point_n be_v take_v between_o two_o circle_n so_o that_o the_o place_n of_o all_o their_o point_n of_o termination_n make_v either_o straight_a line_n or_o circumference_n of_o circle_n and_o be_v call_v plain_a place_n so_o also_o when_o straight_o parallel_a line_n be_v apply_v to_o one_o straight_a line_n if_o the_o part_n of_o the_o straight_a line_n to_o which_o they_o be_v apply_v be_v to_o one_o another_o in_o proportion_n duplicate_v to_o that_o of_o the_o contiguous_a apply_v line_n they_o will_v all_o terminate_v in_o a_o conical_a section_n which_o section_n be_v the_o place_n of_o their_o termination_n be_v call_v a_o solid_a place_n because_o it_o serve_v for_o the_o find_v out_o of_o the_o quantity_n of_o any_o equation_n which_o consist_v of_o three_o dimension_n there_o be_v therefore_o three_o way_n of_o find_v out_o the_o cause_n of_o equality_n or_o inequality_n between_o two_o give_v quantity_n namely_o first_o by_o the_o computation_n of_o motion_n for_o by_o equal_a motion_n &_o equal_a time_n equal_a space_n be_v describe_v and_o ponderation_n be_v motion_n second_o by_o indivisibles_n because_o all_o the_o part_n together_o take_v be_v equal_a to_o the_o whole_a and_o three_o by_o the_o power_n for_o when_o they_o be_v equal_a their_o root_n also_o be_v equal_a and_o contrary_o the_o power_n be_v equal_a when_o 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geometrician_n without_o vieta_n though_o vieta_n be_v a_o most_o admirable_a geometrician_n but_o he_o that_o have_v vieta_n for_o his_o master_n not_o so_o without_o euclid_n and_o as_o for_o that_o part_n of_o analysis_n which_o work_v by_o the_o power_n though_o it_o be_v esteem_v by_o some_o geometrician_n not_o the_o chief_a to_o be_v the_o best_a way_n of_o solve_v all_o problem_n yet_o it_o be_v a_o thing_n of_o no_o great_a extent_n it_o be_v all_o contain_v in_o the_o doctrine_n of_o rectangle_v and_o rectangle_v solid_n so_o that_o although_o they_o come_v to_o a_o equation_n which_o determine_v the_o quantity_n seek_v yet_o they_o can_v sometime_o by_o art_n exhibit_v that_o quantity_n in_o a_o plain_a but_o in_o some_o conique_a section_n that_o be_v as_o geometrician_n say_v not_o geometrical_o but_o mechanical_o now_o such_o problem_n as_o these_o they_o call_v solid_a and_o when_o they_o can_v exhibit_v the_o quantity_n seek_v for_o with_o the_o help_n of_o a_o conique_n section_n they_o call_v it_o a_o lineary_a problem_n and_o therefore_o in_o the_o quantity_n of_o angle_n and_o of_o the_o arch_n of_o circle_n there_o be_v no_o use_n at_o all_o of_o the_o analytic_n which_o proceed_v by_o the_o power_n so_o that_o the_o ancient_n pronounce_v it_o impossible_a to_o exhibit_v in_o a_o plain_a the_o division_n of_o angles_n except_o bisection_n and_o the_o bisection_n of_o the_o bisected_a part_n otherwise_o then_o mechanical_o for_o pappus_n before_o the_o 31_o proposition_n of_o his_o four_o book_n distinguish_v and_o define_v the_o several_a kind_n of_o problem_n say_v that_o some_o be_v plain_a other_o solid_a and_o other_o lineary_a those_o therefore_o which_o may_v be_v solve_v by_o straight_a line_n and_o the_o circumference_n of_o circle_n that_o be_v which_o may_v be_v describe_v with_o the_o rule_n and_o compass_n without_o any_o other_o instrument_n be_v fit_o call_v plain_a for_o the_o line_n by_o which_o such_o problem_n be_v find_v out_o have_v their_o generation_n in_o a_o plain_n but_o those_o which_o be_v solve_v by_o the_o use_n of_o some_o one_o or_o more_o conique_a section_n in_o their_o construction_n be_v call_v solid_a because_o their_o construction_n can_v be_v make_v without_o use_v the_o superficies_n of_o solid_a figure_n namely_o of_o cones_n there_o remain_v the_o three_o kind_n which_o be_v call_v lineary_a because_o other_o line_n beside_o those_o already_o mention_v be_v make_v use_n of_o in_o their_o construction_n etc._n etc._n and_o a_o little_a after_o he_o say_v of_o this_o kind_n be_v the_o spiral_n line_n the_o quadratrice_n the_o conchoeides_n and_o the_o cissoeides_n and_o geometrician_n think_v it_o no_o small_a fault_n when_o for_o the_o find_v out_o of_o a_o plain_a problem_n any_o man_n make_v use_v of_o conique_n or_o new_a line_n now_o he_o rank_n the_o trisection_n of_o a_o angle_n among_o solid_a problem_n and_o the_o quinquesection_n among_o lineary_a but_o what_o be_v the_o ancient_a geometrician_n
be_v so_o stretch_v as_o that_o there_o be_v leave_v in_o it_o no_o boâ—ome_n at_o all_o for_o otherwise_o the_o straight_a line_n lp_v mq_n &_o bk_n will_v not_o be_v perpendicular_a to_o the_o plain_a of_o the_o sail_n but_o fall_v below_o p_o q_o and_o k_o will_v drive_v the_o ship_n backward_o but_o by_o make_v use_n of_o a_o small_a board_n for_o a_o sail_n a_o little_a wagon_n with_o wheel_n for_o the_o ship_n and_o of_o a_o smooth_a pavement_n for_o the_o sea_n i_o have_v by_o experience_n find_v this_o to_o be_v so_o true_a that_o i_o can_v scarce_o oppose_v the_o board_n to_o the_o wind_n in_o any_o obliquity_n though_o never_o so_o small_a but_o the_o wagon_n be_v carry_v forward_o by_o it_o by_o the_o same_o 6_o theorem_a it_o may_v be_v find_v how_o much_o a_o stroke_n which_o fall_v oblique_o be_v weak_a than_o a_o stroke_n fall_v perpendicular_o they_o be_v like_a and_o equal_a in_o all_o other_o respect_n let_v a_o stroke_n fall_n upon_o the_o wall_n ab_fw-la oblique_o as_o for_o example_n in_o the_o straight_a line_n ca_n in_o the_o 3d_o figure_n let_v ce_fw-fr be_v draw_v parallel_n to_o ab_fw-la &_o da_fw-la perpendicular_a to_o the_o same_o ab_fw-la &_o equal_a to_o ca_n &_o let_v both_o the_o velocity_n &_o time_n of_o the_o motion_n in_o ca_n be_v equal_a to_o the_o velocity_n &_o time_n of_o the_o motion_n in_o da._n i_o say_v the_o stroke_n in_o ca_n will_v be_v weak_a than_o that_o in_o da_fw-la in_o the_o proportion_n of_o ea_fw-la to_o da._n for_o produce_v da_fw-la howsoever_o to_o f_o the_o endeavour_n of_o both_o the_o stroke_n will_v by_o the_o 6_o art_n proceed_v from_o a_o in_o the_o perpendicular_a af._n but_o the_o stroke_n in_o ca_n be_v make_v by_o the_o concourse_n of_o two_o motion_n in_o ce_fw-fr and_o ea_fw-la of_o which_o that_o in_o ce_fw-fr contribute_v nothing_o to_o the_o stroke_n in_o a_o because_o ce_fw-fr and_o basilius_n be_v parallel_n and_o therefore_o the_o stroke_n in_o ca_n be_v make_v by_o the_o motion_n which_o be_v in_o ea_fw-la only_o but_o the_o velocity_n or_o force_n of_o the_o perpendicular_a stroke_n in_o ea_fw-la to_o the_o velocity_n or_o force_n of_o the_o stroke_n in_o da_fw-la be_v as_o ea_z to_o da._n wherefore_o the_o oblique_a stroke_n in_o ca_n be_v weak_a than_o the_o perpendicular_a stroke_n in_o da_fw-la in_o the_o proportion_n of_o ea_fw-la to_o dam_fw-la or_o ca_n which_o be_v to_o be_v prove_v 9_o in_o a_o full_a medium_fw-la all_o endeavour_n proceed_v as_o far_o as_o the_o medium_fw-la itself_o reach_v that_o be_v to_o say_v if_o the_o medium_fw-la be_v infinite_a the_o endeavour_n will_v proceed_v infinite_o for_o whatsoever_o endeavour_v be_v move_v and_o therefore_o whatsoever_o stand_v in_o its_o way_n it_o make_v it_o yield_v at_o least_o a_o little_a namely_o so_o far_o as_o the_o movent_fw-la itself_o be_v move_v forward_o but_o that_o which_o yield_v be_v also_o move_v and_o consequent_o make_v that_o to_o yield_v which_o be_v in_o its_o way_n and_o so_o on_o successive_o as_o long_o as_o the_o medium_fw-la be_v full_a that_o be_v to_o say_v infinite_o if_o the_o full_a medium_fw-la be_v infinite_a which_o be_v to_o be_v prove_v now_o although_o endeavour_v thus_o perpetual_o propagate_v do_v not_o always_o appear_v to_o the_o sense_n as_o motion_n yet_o it_o appear_v as_o action_n or_o as_o the_o efficient_a cause_n of_o some_o mutation_n for_o if_o there_o be_v place_v before_o our_o eye_n some_o very_a little_a object_n as_o for_o example_n a_o small_a grain_n of_o sand_n which_o at_o a_o certain_a distance_n be_v visible_a it_o be_v manifest_a that_o it_o may_v be_v remove_v to_o such_o a_o distance_n as_o not_o to_o be_v any_o long_o see_v though_o by_o its_o action_n it_o still_o work_v upon_o the_o organ_n of_o sight_n as_o be_v manifest_a from_o that_o which_o be_v last_o prove_v that_o all_o endeavour_n proceed_v infinite_o let_v it_o be_v conceive_v therefore_o to_o be_v remove_v from_o our_o eye_n to_o any_o distance_n how_o great_a soever_o and_o a_o sufficient_a number_n of_o other_o grain_n of_o sand_n of_o the_o same_o bigness_n add_v to_o it_o it_o be_v evident_a that_o the_o aggregate_v of_o all_o those_o sand_n will_v be_v visible_a and_o though_o none_o of_o they_o can_v be_v see_v when_o it_o be_v single_a and_o sever_v from_o the_o rest_n yet_o the_o whole_a heap_n or_o hill_n which_o they_o make_v will_v manifest_o appear_v to_o the_o sight_n which_o will_v be_v impossible_a if_o some_o action_n do_v not_o proceed_v from_o each_o several_a part_n of_o the_o whole_a heap_n 10_o between_o the_o degree_n of_o hard_a and_o soft_a be_v those_o thing_n which_o we_o call_v tough_a tough_n be_v that_o which_o may_v be_v bend_v without_o be_v alter_v from_o what_o it_o be_v and_o the_o bend_v of_o a_o line_n be_v either_o the_o adduction_n or_o diduction_n of_o the_o extreme_a part_n that_o be_v a_o morion_n from_o straightness_n to_o crookedness_n or_o contrary_o while_o the_o line_n remain_v still_o the_o same_o it_o be_v for_o by_o draw_v out_o the_o extreme_a point_n of_o a_o line_n to_o their_o great_a distance_n the_o line_n be_v make_v straight_o which_o otherwise_o be_v crooked_a so_o also_o the_o bend_v of_o a_o superficies_n be_v the_o diduction_n or_o adduction_n of_o its_o extreme_a line_n that_o be_v their_o dilatation_n and_o contraction_n 11_o dilatation_n and_o contraction_n as_o also_o all_o flexion_n suppose_v necessary_o that_o the_o internal_a part_n of_o the_o body_n bow_v do_v either_o come_v near_o to_o the_o external_a part_n or_o go_v further_o from_o they_o for_o though_o flexion_n be_v consider_v only_o in_o the_o length_n of_o a_o body_n yet_o when_o that_o body_n be_v bow_v the_o line_n which_o be_v make_v on_o one_o side_n will_v be_v convex_a and_o the_o line_n on_o the_o other_o side_n will_v be_v concave_a of_o which_o the_o concave_a be_v the_o interior_a line_n will_v unless_o something_o be_v take_v from_o it_o and_o add_v to_o the_o convex_a line_n be_v the_o more_o crooked_a that_o be_v the_o great_a of_o the_o two_o but_o they_o be_v equal_a and_o therefore_o in_o flexion_n there_o be_v a_o accession_n make_v from_o the_o interior_a to_o the_o exterior_a part_n and_o on_o the_o contrary_a in_o tension_n from_o the_o exterior_a to_o the_o interior_a part_n and_o as_o for_o those_o thing_n which_o do_v not_o easy_o suffer_v such_o transposition_n of_o their_o part_n they_o be_v call_v brittle_a and_o the_o great_a force_n they_o require_v to_o make_v they_o yield_v make_v they_o also_o with_o sudden_a motion_n to_o leap_v asunder_o and_o break_v in_o piece_n 12_o also_o motion_n be_v distinguish_v into_o pulsion_n and_o traction_n and_o pulsion_n as_o i_o have_v already_o define_v it_o be_v when_o that_o which_o be_v move_v go_v before_o that_o which_o move_v it_o but_o contrary_o in_o traction_n the_o movent_fw-la go_v before_o that_o which_o be_v move_v nevertheless_o consider_v it_o with_o great_a attention_n it_o seem_v to_o be_v the_o same_o with_o pulsion_n for_o of_o two_o part_n of_o a_o hard_a body_n when_o that_o which_o be_v foremost_a drive_v before_o it_o the_o medium_fw-la in_o which_o the_o motion_n be_v make_v at_o the_o same_o time_n that_o which_o be_v thrust_v forward_o thrust_v the_o next_o and_o this_o again_o the_o next_o and_o so_o on_o successive_o in_o which_o action_n if_o we_o suppose_v that_o there_o be_v no_o place_n void_a it_o must_v needs_o be_v that_o by_o continual_a pulsion_n namely_o when_o that_o action_n have_v go_v round_o the_o movent_fw-la will_v be_v behind_o that_o part_n which_o at_o the_o first_o seem_v not_o to_o be_v thrust_v forward_o but_o to_o be_v draw_v so_o that_o now_o the_o body_n which_o be_v draw_v go_v before_o the_o body_n which_o give_v it_o motion_n and_o its_o motion_n be_v no_o long_a traction_n but_o pulsion_n 13_o such_o thing_n as_o be_v remove_v from_o their_o place_n by_o forcible_a compression_n or_o extension_n and_o as_o soon_o as_o the_o force_n be_v take_v away_o do_v present_o return_v and_o restore_v themselves_o to_o their_o former_a situation_n have_v the_o beginning_n of_o their_o restitution_n within_o themselves_o namely_o a_o certain_a motion_n in_o their_o internal_a part_n which_o be_v there_o when_o before_o the_o take_v away_o of_o the_o force_n they_o be_v compress_v or_o extend_v for_o that_o restitution_n be_v motion_n and_o that_o which_o be_v at_o rest_n can_v be_v move_v but_o by_o a_o move_v and_o a_o contiguous_a movent_fw-la nor_o do_v the_o cause_n of_o their_o restitution_n proceed_v from_o the_o take_n away_o of_o the_o force_n by_o which_o they_o be_v compress_v or_o extend_v for_o the_o remove_n of_o impediment_n have_v not_o the_o efficacy_n of_o a_o cause_n as_o have_v
be_v show_v at_o the_o end_n of_o the_o 3d_o article_n of_o the_o 15_o chapter_n the_o cause_n therefore_o of_o their_o restitution_n be_v some_o motion_n either_o of_o the_o part_n of_o the_o ambient_fw-la or_o of_o the_o part_n of_o the_o body_n compress_v or_o extend_v but_o the_o part_n of_o the_o ambient_fw-la have_v no_o endeavour_v which_o contribute_v to_o their_o compression_n or_o extension_n nor_o to_o the_o set_n of_o they_o at_o liberty_n or_o restitution_n it_o remain_v therefore_o that_o from_o the_o time_n of_o their_o compression_n or_o extension_n there_o be_v leave_v some_o endeavour_n or_o motion_n by_o which_o the_o impediment_n be_v remove_v every_o part_n resume_v its_o former_a place_n that_o be_v to_o say_v the_o whole_a restore_v itself_o 14_o in_o the_o carriage_n of_o body_n if_o that_o body_n which_o carry_v another_o hit_v upon_o any_o obstacle_n or_o be_v by_o any_o mean_n sudden_o stop_v and_o that_o which_o be_v carry_v be_v not_o stop_v it_o will_v go_v on_o till_o its_o motion_n be_v by_o some_o external_a impediment_n take_v away_o for_o i_o have_v demonstrate_v in_o the_o 8_o chapter_n at_o the_o 19_o article_n that_o motion_n unless_o it_o be_v hinder_v by_o some_o external_a resistance_n will_v be_v continue_v eternal_o with_o the_o same_o celerity_n and_o in_o the_o seven_o article_n of_o the_o 9th_o chap._n that_o the_o action_n of_o a_o external_a agent_n be_v of_o no_o effect_n without_o contact_n when_o therefore_o that_o which_o carry_v another_o thing_n be_v stop_v that_o stop_n do_v not_o present_o take_v away_o the_o motion_n of_o that_o which_o be_v carry_v it_o will_v therefore_o proceed_v till_o its_o motion_n be_v by_o little_a and_o little_o extinguish_v by_o some_o external_a resistance_n which_o be_v to_o be_v prove_v though_o experience_n alone_o have_v be_v sufficient_a to_o prove_v this_o in_o like_a manner_n if_o that_o body_n which_o carry_v another_o be_v put_v from_o rest_n into_o sudden_a motion_n that_o which_o be_v carry_v will_v not_o be_v move_v forward_o together_o with_o it_o but_o will_v be_v leave_v behind_o for_o the_o contiguous_a part_n of_o the_o body_n carry_v have_v almost_o the_o same_o motion_n with_o the_o body_n which_o carry_v it_o and_o the_o remote_a part_n will_v receive_v different_a velocity_n according_a to_o their_o different_a distance_n from_o the_o body_n that_o carry_v they_o namely_o the_o more_o remote_a the_o part_n be_v the_o less_o will_v be_v their_o degree_n of_o velocity_n it_o be_v necessary_a therefore_o that_o the_o body_n which_o be_v carry_v be_v leave_v according_o more_a or_o less_o behind_o and_o this_o also_o be_v manifest_a by_o experience_n when_o at_o the_o start_n forward_o of_o the_o horse_n the_o rider_n fall_v backward_o 15_o in_o percussion_n therefore_o when_o one_o hard_a body_n be_v in_o some_o small_a â—art_n of_o it_o strike_v by_o another_o with_o great_a force_n it_o be_v not_o necessary_a that_o the_o whole_a body_n shall_v yield_v to_o the_o stroke_n with_o the_o same_o celerity_n with_o which_o the_o strike_a part_n yield_v for_o the_o rest_n of_o the_o part_n receive_v their_o motion_n from_o the_o motion_n of_o the_o part_n strike_v and_o yield_a which_o motion_n be_v less_o propagate_v every_o way_n towards_o the_o side_n than_o it_o be_v direct_o forward_o and_o hence_o it_o be_v that_o sometime_o very_o hard_a body_n which_o be_v erect_v can_v hardly_o be_v make_v to_o stand_v be_v more_o easy_o break_v then_o throw_v down_o by_o a_o violent_a stroke_n when_o nevertheless_o if_o all_o their_o part_n together_o be_v by_o any_o weak_a motion_n thrust_v forward_o they_o will_v easy_o be_v cast_v down_o 16_o though_o the_o difference_n between_o trusion_n and_o percussion_n consist_v only_o in_o this_o that_o in_o trusion_n the_o motion_n both_o of_o the_o movent_fw-la and_o moved_n body_n begin_v both_o together_o in_o their_o very_a contact_n and_o in_o percussion_n the_o strike_a body_n be_v first_o move_v and_o afterward_o the_o body_n strike_v yet_o their_o effect_n be_v so_o different_a that_o it_o seem_v scarce_o possible_a to_o compare_v their_o force_n with_o one_o another_o i_o say_v any_o effect_n of_o percussion_n be_v propound_v as_o for_o example_n the_o stroke_n of_o a_o beetle_n of_o any_o weight_n assign_v by_o which_o a_o pile_n of_o any_o give_a length_n be_v to_o be_v drive_v into_o earth_n of_o any_o tenacity_n give_v it_o seem_v to_o i_o very_o hard_o if_o not_o impossible_a to_o define_v with_o what_o weight_n or_o with_o what_o stroke_n and_o in_o what_o time_n the_o same_o pile_n may_v be_v drive_v 〈◊〉_d a_o depth_n assign_v into_o the_o same_o earth_n the_o cause_n of_o which_o difficulty_n be_v this_o that_o the_o velocity_n of_o the_o percutient_fw-la be_v to_o be_v compare_v with_o the_o magnitude_n of_o the_o ponderant_fw-la now_o velocity_n see_v it_o be_v compute_v by_o the_o length_n of_o space_n transmit_v be_v to_o be_v account_v but_o as_o one_o dimension_n but_o weight_n be_v as_o a_o solid_a thing_n be_v measure_v by_o the_o dimension_n of_o the_o whole_a body_n and_o there_o be_v no_o comparison_n to_o be_v make_v of_o a_o solid_a body_n with_o a_o length_n that_o be_v with_o a_o line_n 17_o if_o the_o internal_a part_n of_o a_o body_n be_v at_o rest_n or_o retain_v the_o same_o situation_n with_o one_o another_o for_o any_o time_n how_o little_a soever_o there_o can_v in_o those_o part_n be_v generate_v any_o new_a motion_n or_o endeavour_v whereof_o the_o efficient_a cause_n be_v not_o without_o the_o body_n of_o which_o they_o be_v part_n for_o if_o any_o small_a part_n which_o be_v comprehend_v within_o the_o superficies_n of_o the_o whole_a body_n be_v suppose_v to_o be_v now_o at_o rest_n and_o by_o and_o by_o to_o be_v move_v that_o part_n must_v of_o necessity_n receive_v its_o motion_n from_o some_o move_v and_o contiguous_a body_n but_o by_o supposition_n there_o be_v no_o such_o move_v and_o contiguous_a part_n within_o the_o body_n wherefore_o if_o there_o be_v any_o endeavour_n or_o motion_n or_o change_v of_o situation_n in_o the_o internal_a part_n of_o that_o body_n it_o must_v needs_o arise_v from_o some_o efficient_a cause_n that_o be_v without_o the_o body_n which_o contain_v they_o which_o be_v to_o be_v prove_v 18_o in_o hard_a body_n therefore_o which_o be_v compress_v or_o extend_v if_o that_o which_o compress_v or_o extend_v they_o be_v take_v away_o they_o restore_v themselves_o to_o their_o former_a place_n or_o situation_n it_o must_v needs_o be_v that_o that_o endeavour_v or_o motion_n of_o their_o internal_a part_n by_o which_o they_o be_v able_a to_o recover_v their_o former_a place_n or_o situation_n be_v not_o extinguish_v when_o the_o force_n by_o which_o they_o be_v compress_v or_o extend_v be_v take_v away_o therefore_o when_o the_o lath_n of_o a_o cross-bow_n bend_v do_v as_o soon_o as_o it_o be_v at_o liberty_n restore_v itself_o though_o to_o he_o that_o judge_n by_o sense_n both_o it_o and_o all_o its_o part_n seem_v to_o be_v at_o rest_n yet_o he_o that_o judge_v by_o reason_n do_v not_o account_v the_o take_v away_o of_o impediment_n for_o a_o efficient_a cause_n nor_o conceive_v that_o without_o a_o efficient_a cause_n any_o thing_n can_v pass_v from_o rest_n to_o motion_n will_v conclude_v that_o the_o part_n be_v already_o in_o motion_n before_o they_o begin_v to_o restore_v themselves_o 19_o action_n and_o reaction_n proceed_v in_o the_o same_o line_n but_o from_o opposite_a term_n for_o see_v reaction_n be_v nothing_o but_o endeavour_n in_o the_o patient_n to_o restore_v itself_o to_o that_o situation_n from_o which_o it_o be_v force_v by_o the_o agent_n the_o endeavour_n or_o motion_n both_o of_o the_o agent_n and_o patient_n or_o reagent_n will_v be_v propagate_v between_o the_o same_o term_n yet_o so_o as_o that_o in_o action_n the_o term_n from_o which_o be_v in_o reaction_n the_o term_n to_o which_o and_o see_v all_o action_n proceed_v in_o this_o manner_n not_o only_o between_o the_o opposite_a term_n of_o the_o whole_a line_n in_o which_o it_o be_v propagate_v but_o also_o in_o all_o the_o part_n of_o that_o line_n the_o term_n from_o which_o and_o to_o which_o both_o of_o the_o action_n and_o reaction_n will_v be_v in_o the_o same_o line_n wherefore_o action_n and_o reaction_n proceed_v in_o the_o same_o line_n etc._n etc._n 20_o to_o what_o have_v be_v say_v of_o motion_n i_o will_v add_v what_o i_o have_v to_o say_v concern_v habit._n habit_n therefore_o be_v a_o generation_n of_o motion_n not_o of_o motion_n simple_o but_o a_o easy_a conduct_v of_o the_o move_v body_n in_o a_o certain_a and_o design_a way_n and_o see_v it_o be_v attain_v by_o the_o weaken_n of_o such_o endeavour_n as_o divert_v its_o motion_n therefore_o such_o endeavour_n be_v to_o be_v
sometime_o aversion_n to_o the_o same_o thing_n as_o they_o think_v it_o will_v either_o be_v for_o their_o good_a or_o their_o hurt_n while_o that_o vicissitude_n of_o appetite_n and_o aversion_n remain_v in_o they_o they_o have_v that_o series_n of_o thought_n which_o be_v call_v deliberation_n which_o last_v as_o long_o as_o they_o have_v it_o in_o their_o power_n to_o obtain_v that_o which_o please_v or_o to_o avoid_v that_o which_o displease_v they_o appetite_n therefore_o and_o aversion_n be_v simple_o so_o call_v as_o long_o as_o they_o follow_v not_o deliberation_n but_o if_o deliberation_n have_v go_v before_o than_o the_o last_o act_n of_o it_o if_o it_o be_v appetite_n be_v call_v will_n if_o aversion_n unwillingness_n so_o that_o the_o same_o thing_n be_v call_v both_o will_n and_o appetite_n but_o the_o consideration_n of_o they_o namely_o before_o and_o after_o deliberation_n be_v divers_a nor_o be_v that_o which_o be_v do_v within_o a_o man_n while_o he_o will_v any_o thing_n different_a from_o that_o which_o be_v do_v in_o other_o live_a creature_n while_o deliberation_n have_v precede_v they_o have_v appetite_n neither_o be_v the_o freedom_n of_o willing_a or_o not_o will_v great_a in_o man_n then_o in_o other_o live_a creature_n for_o where_o there_o be_v appetite_n the_o entire_a cause_n of_o appetite_n have_v precede_v and_o consequent_o the_o act_n of_o appetite_n can_v not_o choose_v but_o follow_v that_o be_v have_v of_o necessity_n follow_v as_o be_v show_v chapt._n 9th_o article_n 5._o and_o therefore_o such_o a_o liberty_n as_o be_v free_a from_o necessity_n be_v not_o to_o be_v find_v in_o the_o will_v either_o of_o man_n or_o beast_n but_o if_o by_o liberty_n we_o understand_v the_o faculty_n or_o power_n not_o of_o willing_a but_o of_o do_v what_o they_o will_v then_o certain_o that_o liberty_n be_v to_o be_v allow_v to_o both_o and_o both_o may_v equal_o have_v it_o whensover_v it_o be_v to_o be_v have_v again_o when_o appetite_n and_o aversion_n do_v with_o celerity_n succeed_v one_o another_o the_o whole_a series_n make_v by_o they_o have_v its_o name_n sometime_o from_o one_o sometime_o from_o the_o other_o for_o the_o same_o deliberation_n while_o it_o incline_v sometime_o to_o one_o sometime_o to_o the_o other_o be_v from_o appetite_n call_v hope_n and_o from_o aversion_n fear_v for_o where_o there_o be_v no_o hope_n it_o be_v not_o to_o be_v call_v fear_n but_o hate_v and_o where_o no_o fear_n not_o hope_n but_o desire_v to_o conclude_v all_o the_o passion_n call_v passion_n of_o the_o mind_n consist_v of_o appetite_n and_o aversion_n except_o pure_a pleasure_n and_o pain_n which_o be_v a_o certain_a fruition_n of_o good_a or_o evil_a as_o anger_n be_v aversion_n from_o some_o imminent_a evil_n but_o such_o as_o be_v join_v with_o appetite_n of_o avoid_v that_o evil_a by_o force_n but_o because_o the_o passion_n and_o perturbation_n of_o the_o mind_n be_v innumerable_a and_o many_o of_o they_o not_o to_o be_v discern_v in_o any_o creature_n beside_o man_n i_o will_v speak_v of_o they_o more_o at_o large_a in_o that_o section_n which_o be_v concern_v man._n as_o for_o those_o object_n if_o there_o be_v any_o such_o which_o do_v not_o at_o all_o stir_v the_o mind_n we_o be_v say_v to_o contemn_v they_o and_o thus_o much_o of_o sense_n in_o general_n in_o the_o next_o place_n i_o shall_v speak_v of_o sensible_a object_n chap._n xxvi_o of_o the_o world_n and_o of_o the_o star_n 1_o the_o magnitude_n and_o duration_n of_o the_o world_n inscrutable_a 2_o no_o place_n in_o the_o world_n empty_a 3_o the_o argument_n of_o lucretius_n for_o vacuum_n invalid_a 4_o other_o argument_n for_o the_o establish_n of_o vacuum_n invalid_a 5_o six_o supposition_n for_o the_o salve_v of_o the_o phaenomena_n of_o nature_n 6_o possible_a cause_n of_o the_o motion_n annual_a and_o diurnal_a and_o of_o the_o apparent_a direction_n station_n and_o retrogradation_n of_o the_o planet_n 7_o the_o supposition_n of_o simple_a motion_n why_o likely_a 8_o the_o cause_n of_o the_o excentricity_n of_o the_o annual_a motion_n of_o the_o earth_n 9_o the_o cause_n why_o the_o moon_n have_v always_o one_o and_o the_o same_o face_n turn_v towards_o the_o earth_n 10_o the_o cause_n of_o the_o tide_n of_o the_o ocean_n 11_o the_o cause_n of_o the_o praecession_n of_o the_o equinox_n 1_o consequent_a to_o the_o contemplation_n of_o sense_n be_v the_o contemplation_n of_o body_n which_o be_v the_o efficient_a cause_n or_o object_n of_o sense_n now_o every_o object_n be_v either_o a_o part_n of_o the_o whole_a world_n or_o a_o aggregate_v of_o part_n the_o great_a of_o all_o body_n or_o sensible_a object_n be_v the_o world_n itself_o which_o we_o behold_v when_o we_o look_v round_o about_o we_o from_o this_o point_n of_o the_o same_o which_o we_o call_v the_o earth_n concern_v the_o world_n as_o it_o be_v one_o aggregate_v of_o many_o part_n the_o thing_n that_o fall_v under_o inquiry_n be_v but_o few_o and_o those_o we_o can_v determine_v none_o of_o the_o whole_a world_n we_o may_v inquire_v what_o be_v its_o magnitude_n what_o its_o duration_n and_o how_o many_o there_o be_v but_o nothing_o else_o for_o as_o for_o place_n and_o time_n that_o be_v to_o say_v magnitude_n and_o duration_n they_o be_v only_o our_o own_o fancy_n of_o a_o body_n simple_o so_o call_v that_o be_v to_o say_v of_o a_o body_n indefinite_o take_v as_o i_o have_v show_v before_o in_o the_o 7_o chapter_n all_o other_o phantasm_n be_v of_o body_n or_o object_n as_o they_o be_v distinguish_v from_o one_o another_o as_o colour_n the_o phantasm_n of_o colour_a body_n sound_v of_o body_n that_o move_v the_o sense_n of_o hear_v etc._n etc._n the_o question_n concern_v the_o magnitude_n of_o the_o world_n be_v whether_o it_o be_v finite_a or_o infinite_a full_a or_o not_o full_a concern_v its_o duration_n whether_o it_o have_v a_o beginning_n or_o be_v eternal_a and_o concern_v the_o number_n whether_o there_o be_v one_o or_o many_o though_o as_o concern_v the_o number_n if_o it_o be_v of_o infinite_a magnitude_n there_o can_v be_v no_o controversy_n at_o all_o also_o if_o it_o have_v a_o beginning_n then_o by_o what_o cause_n and_o of_o what_o matter_n it_o be_v make_v and_o again_o from_o whence_o that_o cause_n and_o that_o matter_n have_v their_o be_v will_v be_v new_a question_n till_o at_o last_o we_o come_v to_o one_o or_o many_o eternal_a cause_n or_o cause_n and_o the_o determination_n of_o all_o these_o thing_n belong_v to_o he_o that_o profess_v the_o universal_a doctrine_n of_o philosophy_n in_o case_n as_o much_o can_v be_v know_v as_o can_v be_v seek_v but_o the_o knowledge_n of_o what_o be_v infinite_a can_v never_o be_v attain_v by_o a_o finite_a inquirer_n whatsoever_o we_o know_v that_o be_v man_n we_o learn_v it_o from_o our_o phantasm_n and_o of_o infinite_a whether_o magnitude_n or_o time_n there_o be_v no_o phantasm_n at_o all_o so_o that_o it_o be_v impossible_a either_o for_o a_o man_n or_o any_o other_o creature_n to_o have_v any_o conception_n of_o infinite_a and_o though_o a_o man_n may_v from_o some_o effect_n proceed_v to_o the_o immediate_a cause_n thereof_o &_o from_o that_o to_o a_o more_o remote_a cause_n and_o so_o ascend_v continual_o by_o right_a ratiocination_n from_o cause_n to_o cause_n yet_o he_o will_v not_o be_v able_a to_o proceed_v eternal_o but_o weary_v will_v at_o last_o give_v over_o without_o know_v whether_o it_o be_v possible_a for_o he_o to_o proceed_v to_o a_o end_n or_o not_o but_o whether_o we_o suppose_v the_o world_n to_o be_v finite_a or_o infinite_a no_o absurdity_n will_v follow_v for_o the_o same_o thing_n which_o now_o appear_v may_v appear_v whether_o the_o creator_n have_v please_v it_o shall_v be_v finite_a or_o infinite_a beside_o though_o from_o this_o that_o nothing_o can_v move_v itself_o it_o may_v right_o be_v infer_v that_o there_o be_v some_o first_o eternal_a movent_fw-la yet_o it_o can_v never_o be_v infer_v though_o some_o use_n to_o make_v such_o inference_n that_o that_o movent_fw-la be_v eternal_o immovable_a but_o rather_o eternal_o move_v for_o as_o it_o be_v true_a that_o nothing_o be_v move_v by_o itself_o so_o it_o be_v true_a also_o that_o nothing_o be_v move_v but_o by_o that_o which_o be_v already_o move_v the_o question_n therefore_o about_o the_o magnitude_n and_o beginning_n of_o the_o world_n be_v not_o to_o be_v determine_v by_o philosopher_n but_o by_o those_o that_o be_v lawful_o authorise_v to_o order_v the_o worship_n of_o god_n for_o as_o almighty_a god_n when_o he_o have_v bring_v his_o people_n into_o judaea_n allow_v the_o priest_n the_o first_o fruit_n reserve_v to_o himself_o so_o when_o he_o have_v deliver_v up_o the_o world_n to_o the_o disputation_n of_o man_n it_o be_v his_o pleasure_n that_o
will_v remain_v no_o cause_n at_o all_o why_o the_o water_n shall_v be_v force_v out_o wherefore_o the_o assertion_n of_o vacuum_n be_v repugnant_a to_o the_o very_a experiment_n which_o be_v here_o bring_v to_o establish_v it_o many_o other_o phaenomena_n be_v usual_o bring_v for_o vacuum_n as_o those_o of_o weather-glass_n aeolipile_n wind-gun_n etc._n etc._n which_o will_v all_o be_v very_o hard_a to_o be_v salve_v unless_o water_n be_v penetrable_a by_o air_n without_o the_o intermixture_n of_o empty_a space_n but_o now_o see_v air_n may_v with_o no_o great_a endeavour_n pass_v through_o not_o only_a water_n but_o any_o other_o fluid_a body_n though_o never_o so_o stubborn_a as_o quicksilver_n these_o phaenomena_n prove_v nothing_o nevertheless_o it_o may_v in_o reason_n be_v expect_v that_o he_o that_o will_v take_v away_o vacuum_n shall_v without_o vacuum_n show_v we_o such_o cause_n of_o these_o phaenomena_n as_o shall_v be_v at_o least_o of_o equal_a if_o not_o great_a probability_n this_o therefore_o shall_v be_v do_v in_o the_o follow_a discourse_n when_o i_o come_v to_o speak_v of_o these_o phaenomena_n in_o their_o proper_a place_n but_o first_o the_o most_o general_a hypothesis_n of_o natural_a philosophy_n be_v to_o be_v premise_v and_o see_v that_o supposition_n be_v put_v for_o the_o true_a cause_n of_o apparent_a effect_n every_o supposition_n except_o such_o as_o be_v absurd_a must_v of_o necessity_n consist_v of_o some_o suppose_a possible_a motion_n for_o rest_n can_v never_o be_v the_o essicient_a cause_n of_o any_o thing_n &_o motion_n suppose_v body_n movable_a of_o which_o there_o be_v three_o kind_n fluid_a consistent_a and_o mix_v of_o both_o fluid_fw-la be_v those_o who_o part_n may_v by_o very_o weak_a endeavonr_n be_v separate_v from_o one_o another_o and_o consistent_a those_o for_o the_o separation_n of_o who_o part_n great_a force_n be_v to_o be_v apply_v there_o be_v therefore_o degree_n of_o consistency_n which_o degree_n by_o comparison_n with_o more_o or_o less_o consistent_a have_v the_o name_n of_o hardness_n or_o softness_n wherefore_o a_o fluid_a body_n be_v always_o divisible_a into_o body_n equal_o fluid_a as_o quantity_n into_o quantity_n and_o soft_a body_n of_o whatsoever_o degree_n of_o softness_n into_o soft_a body_n of_o the_o same_o degree_n and_o though_o many_o man_n seem_v to_o conceive_v no_o other_o difference_n of_o fluidity_n but_o such_o as_o arise_v from_o the_o different_a magnitude_n of_o the_o part_n in_o which_o sense_n dust_n though_o of_o diamond_n may_v be_v call_v fluid_a yet_o i_o understand_v by_o fluidity_n that_o which_o be_v make_v such_o by_o nature_n equal_o in_o every_o part_n of_o the_o fluid_a body_n not_o as_o dust_n be_v fluid_a for_o so_o a_o house_n which_o be_v fall_v in_o piece_n may_v be_v call_v fluid_fw-la but_o in_o such_o manner_n as_o water_n seem_v fluid_a and_o to_o divide_v itself_o into_o part_n perpetual_o fluid_a and_o this_o be_v well_o understand_v i_o come_v to_o my_o supposition_n 5_o first_o therefore_o i_o suppose_v that_o the_o immense_a space_n which_o we_o call_v the_o world_n be_v the_o aggregate_v of_o all_o body_n which_o be_v either_o consistent_a &_o visible_a as_o the_o earth_n and_o the_o star_n or_o invisible_a as_o the_o small_a atom_n which_o be_v disseminated_a through_o the_o whole_a space_n between_o the_o earth_n and_o the_o star_n and_o last_o that_o most_o fluid_a aether_n which_o so_o fill_v all_o the_o rest_n of_o the_o universe_n as_o that_o it_o leave_v in_o it_o no_o empty_a place_n at_o all_o second_o i_o suppose_v with_o copernicus_n that_o the_o great_a body_n of_o the_o world_n which_o be_v both_o consistent_a and_o permanent_a have_v such_o order_n among_o themselves_o as_o that_o the_o sun_n have_v the_o first_o place_n mercury_n the_o second_o venus_n the_o three_o the_o earth_n with_o the_o moon_n go_v about_o it_o the_o four_o mars_n the_o five_o jupiter_n with_o his_o attendant_n the_o six_o saturn_n the_o seven_o and_o after_o these_o the_o fix_a star_n have_v their_o several_a distance_n from_o the_o sun_n three_o i_o suppose_v that_o in_o the_o sun_n &_o the_o rest_n of_o the_o planet_n there_o be_v and_o always_o have_v be_v a_o simple_a circular_a motion_n four_o i_o suppose_v that_o in_o the_o body_n of_o the_o air_n there_o be_v certain_a other_o body_n intermingle_v which_o be_v not_o fluid_a but_o withal_o that_o they_o be_v so_o small_a that_o they_o be_v not_o preceptible_a by_o sense_n and_o that_o these_o also_o have_v their_o proper_a simple_a motion_n and_o be_v some_o of_o they_o more_o some_o less_o hard_a or_o consistent_a five_o i_o suppose_v with_o kepler_n that_o as_o the_o distance_n between_o the_o sun_n and_o the_o earth_n be_v to_o the_o distance_n between_o the_o moon_n and_o the_o earth_n so_o the_o distance_n between_o the_o moon_n and_o the_o earth_n be_v to_o the_o semidiameter_n of_o the_o earth_n as_o for_o the_o magnitude_n of_o the_o circle_n and_o the_o time_n in_o which_o they_o be_v describe_v by_o the_o body_n which_o be_v in_o they_o i_o will_v suppose_v they_o to_o be_v such_o as_o shall_v seem_v most_o agreeable_a to_o the_o phaenomena_n in_o question_n 6_o the_o cause_n of_o the_o different_a season_n of_o the_o year_n and_o of_o the_o several_a variation_n of_o day_n and_o night_n in_o all_o the_o part_n of_o the_o superficies_n of_o the_o earth_n have_v be_v demonstrate_v first_o by_o copernicus_n and_o since_o by_o kepler_n galilaeus_fw-la and_o other_o from_o the_o supposition_n of_o the_o earth_n diurnal_a revolution_n about_o its_o own_o axis_n together_o with_o its_o annual_a motion_n about_o the_o sun_n in_o the_o ecliptic_a according_a to_o the_o order_n of_o the_o sign_n and_o three_o by_o the_o annual_a revolution_n of_o the_o same_o earth_n about_o its_o own_o centre_n contrary_a to_o the_o order_n of_o the_o sign_n i_o suppose_v with_o copernicus_n that_o the_o diurnal_a revolution_n be_v from_o the_o motion_n of_o the_o earth_n by_o which_o the_o aequinoctial_a circle_n be_v describe_v about_o it_o and_o as_o for_o the_o other_o two_o annual_a motion_n they_o be_v the_o efficient_a cause_n of_o the_o earth_n be_v carry_v about_o in_o the_o ecliptic_a in_o such_o manner_n as_o that_o its_o axis_n be_v always_o keep_v parallel_n to_o itself_o which_o parallelisme_n be_v for_o this_o reason_n introduce_v lest_o by_o the_o earth_n annual_a revolution_n its_o pole_n shall_v seem_v to_o be_v necessary_o carry_v about_o the_o sun_n contrary_a to_o experience_n i_o have_v in_o the_o 10_o artic._n of_o the_o â—â—th_v chap._n demonstrate_v from_o the_o supposition_n of_o simple_a circular_a motion_n in_o the_o sun_n that_o the_o earth_n be_v so_o carry_v about_o the_o sun_n as_o that_o its_o axis_n be_v thereby_o keep_v always_o parallel_v to_o itself_o wherefore_o from_o these_o two_o suppose_a motion_n in_o the_o sun_n the_o one_o simple_a circular_a motion_n the_o other_o circular_a motion_n about_o it_o own_v centre_n it_o may_v be_v demonstrate_v that_o the_o year_n have_v both_o the_o same_o variation_n of_o day_n and_o night_n as_o have_v be_v demonstrate_v by_o copernicus_n for_o if_o the_o circle_n abcd_v in_o the_o 3d_o figure_n be_v the_o ecliptic_a who_o centre_n be_v e_o and_o diameter_n aec_fw-la and_o the_o earth_n be_v place_v in_o a_o &_o the_o sun_n be_v move_v in_o the_o little_a circle_n fghi_fw-la namely_o according_a to_o the_o order_n f_o g_o h_o &_o i_o it_o have_v be_v demonstrate_v that_o a_o body_n place_v in_o a_o will_v be_v move_v in_o the_o same_o order_n through_o the_o point_n of_o the_o ecliptic_a a_o b_o c_o &_o d_o and_o will_v always_o keep_v its_o axis_n parallel_n to_o its_o self_n but_o if_o as_o i_o have_v suppose_v the_o earth_n also_o be_v move_v with_o simple_a circular_a motion_n in_o a_o plain_a that_o pass_v through_o a_o cut_v the_o plain_a of_o the_o ecliptic_a so_o as_o that_o the_o common_a section_n of_o both_o the_o plain_n be_v in_o ac_fw-la thus_o also_o the_o axis_n of_o the_o earth_n will_v be_v keep_v always_o parallel_v to_o itself_o for_o let_v the_o centre_n of_o the_o earth_n be_v move_v about_o in_o the_o circumference_n of_o the_o epicycle_n who_o diameter_n be_v lak_a which_o be_v a_o part_n of_o the_o straight_a line_n lac_fw-la therefore_o lak_a the_o diameter_n of_o the_o epicycle_n pass_v through_o the_o centre_n of_o the_o earth_n will_v be_v in_o the_o plain_a of_o the_o ecliptic_a wherefore_o see_v that_o by_o reason_n of_o the_o earth_n simple_a motion_n both_o in_o the_o ecliptic_a and_o in_o its_o epicycle_n the_o straight_a line_n lak_a be_v keep_v always_o parallel_v to_o itself_o every_o other_o straight_o line_n also_o take_v in_o the_o body_n of_o the_o earth_n and_o consequent_o its_o axis_n will_v in_o like_a manner_n be_v keep_v always_o parallel_v
a_o syringe_n into_o the_o space_n fgb_n in_o that_o injection_n the_o air_n but_o pure_a air_n go_v with_o the_o same_o force_n out_o of_o the_o vessel_n through_o the_o injected_a water_n but_o as_o for_o those_o small_a body_n which_o former_o i_o suppose_v to_o be_v intermingle_v with_o air_n &_o to_o be_v move_v with_o simple_a motion_n they_o can_v not_o together_o with_o the_o our_o air_n penetrate_v the_o water_n but_o remain_v behind_o be_v necessary_o thrust_v together_o into_o a_o narrow_a place_n namely_o into_o the_o space_n which_o be_v above_o the_o water_n fg._n the_o motion_n therefore_o of_o those_o small_a body_n will_v be_v less_o and_o less_o free_a by_o how_o much_o the_o quantity_n of_o the_o injected_a water_n be_v great_a and_o great_a so_o that_o by_o their_o motion_n fall_v upon_o one_o another_o the_o same_o small_a body_n will_v mutual_o compress_v each_o other_o and_o have_v a_o perpetual_a endeavour_n of_o regayn_v their_o liberty_n and_o of_o depress_v the_o water_n that_o hinder_v they_o wherefore_o as_o soon_o as_o the_o orifice_n above_o be_v open_v the_o water_n which_o be_v next_o it_o will_v have_v a_o endeavour_n to_o ascend_v and_o will_v therefore_o necessary_o go_v out_o but_o it_o can_v go_v out_o unless_o at_o the_o same_o time_n there_o enter_v in_o as_o much_o air_n and_o therefore_o both_o the_o water_n will_v go_v out_o and_o the_o air_n enter_v in_o till_o those_o small_a body_n which_o be_v leave_v within_o the_o vessel_n have_v recover_v their_o former_a liberty_n of_o motion_n that_o be_v to_o say_v till_o the_o vessel_n be_v again_o fill_v with_o air_n and_o no_o water_n be_v leave_v of_o sufficient_a height_n to_o stop_v the_o passage_n at_o b._n wherefore_o i_o have_v show_v a_o possible_a cause_n of_o this_o phaenomenon_n namely_o the_o same_o with_o that_o of_o thunder_n for_o as_o in_o the_o generation_n of_o thunder_n the_o small_a body_n enclose_v within_o the_o cloud_n by_o be_v too_o close_o pen_v together_o do_v by_o their_o motion_n break_v the_o cloud_n and_o restore_v themselves_o to_o their_o natural_a liberty_n so_o here_o also_o the_o small_a body_n enclose_v within_o the_o space_n which_o be_v above_o the_o straight_a line_n fg_v do_v by_o their_o own_o motion_n expel_v the_o water_n as_o soon_o as_o the_o passage_n be_v open_v above_o and_o if_o the_o passage_n be_v keep_v stop_v and_o these_o small_a body_n be_v more_o vehement_o compress_v by_o the_o perpetual_a force_n in_o of_o more_o water_n they_o will_v at_o last_o break_v the_o vessel_n itself_o with_o great_a noise_n 10_o if_o aire_n be_v blow_v into_o a_o hollow_a cylinder_n or_o into_o a_o bladder_n it_o will_v increase_v the_o weight_n of_o either_o of_o they_o a_o little_a as_o many_o have_v find_v by_o experience_n who_o with_o great_a accurateness_n have_v try_v the_o same_o and_o it_o be_v no_o wonder_n see_v as_o i_o have_v suppose_v there_o be_v intermingle_v with_o the_o common_a air_n a_o great_a number_n of_o small_a hard_a body_n which_o be_v heavy_a than_o the_o pure_a air_n for_o the_o aethereal_a substance_n be_v on_o all_o side_n equal_o agitate_a by_o the_o motion_n of_o the_o sun_n have_v a_o equal_a endeavour_n towards_o all_o the_o part_n of_o the_o universe_n and_o therefore_o it_o have_v no_o gravity_n at_o all_o 11_o we_o find_v also_o by_o experience_n that_o by_o the_o force_n of_o air_n enclose_v in_o a_o hollow_a canon_n a_o bullet_n of_o lead_n may_v with_o considerable_a violence_n be_v shoot_v out_o of_o a_o gun_n of_o late_a invention_n call_v the_o windgun_n in_o the_o end_n of_o this_o canon_n there_o be_v two_o hole_n with_o their_o valve_n on_o the_o inside_n to_o shut_v they_o close_o one_o of_o they_o serve_v for_o the_o admission_n of_o air_n and_o the_o other_o for_o the_o let_n of_o it_o out_o also_o to_o that_o end_n which_o serve_v for_o the_o receive_n in_o of_o air_n there_o be_v join_v another_o canon_n of_o the_o same_o metal_n and_o bigness_n in_o which_o there_o be_v fit_v a_o rammer_n which_o be_v perforate_v and_o have_v also_o a_o valve_n open_v towards_o the_o former_a canon_n by_o the_o help_n of_o this_o valve_n the_o rammer_n be_v easy_o draw_v back_o and_o let_v in_o air_n from_o without_o and_o be_v often_o draw_v back_o and_o return_v again_o with_o violent_a stroke_n it_o force_v some_o part_n of_o that_o air_n into_o the_o former_a canon_n so_o long_o till_o at_o last_o the_o resistance_n of_o the_o enclose_a air_n be_v great_a than_o the_o force_n of_o the_o stroke_n and_o by_o this_o mean_n man_n think_v there_o be_v now_o a_o great_a quantity_n of_o air_n in_o the_o canon_n then_o there_o be_v former_o though_o it_o be_v full_a before_o also_o the_o air_n thus_o force_v in_o how_o much_o soever_o it_o be_v be_v hinder_v from_o get_v out_o again_o by_o the_o foresay_a valve_n which_o the_o very_a endeavour_n of_o the_o air_n to_o get_v out_o do_v necessary_o shut_v last_o that_o valve_n be_v open_v which_o be_v make_v for_o the_o let_v out_o of_o the_o air_n it_o present_o break_v out_o with_o violence_n &_o drive_v the_o bullet_n before_o it_o with_o great_a force_n and_o velocity_n as_o for_o the_o cause_n of_o this_o i_o can_v easy_o attribute_v it_o as_o most_o man_n do_v to_o condensation_n and_o think_v that_o the_o air_n which_o have_v at_o the_o first_o but_o its_o ordinary_a degree_n of_o rarity_n be_v afterward_o by_o the_o force_n in_o of_o more_o air_n condense_v and_o last_o of_o all_o rarefy_v again_o by_o be_v let_v out_o and_o restore_v to_o its_o natural_a liberty_n but_o i_o can_v imagine_v how_o the_o same_o place_n can_v be_v always_o full_a and_o nevertheless_o contain_v sometime_o a_o great_a sometime_o a_o less_o quantity_n of_o matter_n that_o be_v to_o say_v that_o it_o can_v be_v full_a than_o full_a nor_o can_v i_o conceive_v how_o fullness_n can_v of_o itself_o be_v a_o efficient_a cause_n of_o motion_n for_o both_o â—hese_n be_v impossible_a wherefore_o we_o must_v seek_v out_o some_o other_o possible_a cause_n of_o this_o phaenomenon_n whilst_o therefore_o the_o valve_n with_o ch_n serve_v for_o the_o let_n in_o of_o air_n be_v open_v by_o the_o first_o stroke_n of_o the_o rammer_n the_o air_n within_o do_v with_o equal_a force_n resist_v the_o enter_n of_o the_o air_n from_o without_o so_o that_o the_o endeavour_n between_o the_o internal_a and_o external_a air_n be_v opposite_a that_o be_v there_o be_v two_o opposite_a motion_n while_o the_o one_o go_v in_o and_o the_o other_o come_v out_o but_o no_o augmentation_n at_o all_o of_o air_n within_o the_o canon_n for_o there_o be_v drive_v out_o by_o the_o stroke_n as_o much_o pure_a air_n which_o pass_v between_o the_o rammer_n and_o the_o side_n of_o the_o canon_n as_o there_o be_v force_v in_o of_o air_n impure_a by_o the_o same_o stroke_n and_o thus_o by_o many_o forcible_a stroke_n the_o quantity_n of_o small_a hard_a body_n will_v be_v increase_v within_o the_o canon_n and_o their_o motion_n also_o will_v grow_v strong_a and_o strong_a as_o long_a as_o the_o matter_n of_o the_o canon_n be_v able_a to_o endure_v their_o force_n by_o which_o if_o it_o be_v not_o break_v it_o will_v at_o least_o be_v urge_v every_o way_n by_o their_o endeavour_n to_o free_v themselves_o and_o as_o soon_o as_o the_o valve_n which_o serve_v to_o let_v they_o out_o be_v open_v they_o will_v fly_v out_o with_o violent_a motion_n and_o carry_v with_o they_o the_o bullet_n which_o be_v in_o their_o way_n wherefore_o i_o have_v give_v a_o possible_a cause_n of_o this_o phaenomenon_n 12_o water_n contrary_a to_o the_o custom_n of_o heavy_a body_n ascend_v in_o the_o weatherglass_n but_o it_o do_v it_o when_o the_o air_n be_v cold_a for_o when_o it_o be_v warm_v it_o descend_v again_o and_o this_o organ_n be_v call_v a_o thermometer_n or_o thermoscope_n because_o the_o degree_n of_o heat_n and_o cold_a be_v measure_v and_o mark_v by_o it_o it_o be_v make_v in_o this_o manner_n let_v a_o b_o c_o d_o in_o the_o 5_o figure_n be_v a_o vessel_n full_a of_o water_n and_o e_o f_o g_o a_o hollow_a cylinder_n of_o glass_n close_v at_o e_o and_o open_a at_o g._n let_v it_o be_v heat_v and_o set_v upright_o within_o the_o water_n to_o f_o and_o let_v the_o open_a end_n reach_v to_o g._n this_o be_v do_v as_o the_o air_n by_o little_a and_o little_o grow_v cold_a the_o water_n will_v ascend_v slow_o within_o the_o cylinder_n from_o f_o towards_o e_z till_o at_o last_o the_o external_a and_o internal_a air_n come_v to_o be_v both_o of_o the_o same_o temper_n it_o will_v neither_o ascend_v high_a nor_o descend_v low_o till_o the_o temper_n of_o the_o air_n be_v change_v suppose_v it_o therefore_o