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that_o be_v to_o be_v religious_a to_o be_v beneficial_a to_o the_o clergy_n that_o be_v their_o piety_n and_o liberality_n and_o to_o believe_v upon_o their_o word_n that_o which_o a_o man_n know_v in_o his_o conscience_n to_o be_v false_a which_o be_v the_o faith_n they_o require_v i_o can_v name_v a_o great_a many_o more_o such_o point_n of_o their_o moral_n but_o that_o i_o know_v you_o know_v they_o already_o be_v so_o well_o verse_v in_o the_o case_n of_o conscience_n write_v by_o their_o schoolman_n who_o measure_v the_o goodness_n and_o wickedness_n of_o all_o action_n by_o their_o congruity_n with_o the_o doctrine_n of_o the_o roman_a clergy_n b._n but_o what_o be_v the_o moral_a philosophy_n of_o the_o protestant_a clergy_n in_o england_n a._n so_o much_o as_o they_o show_v of_o it_o in_o their_o life_n and_o conversation_n be_v for_o the_o most_o part_n very_o good_a and_o of_o very_o good_a example_n much_o better_a than_o their_o write_n b._n it_o happen_v many_o time_n that_o man_n live_v honest_o for_o fear_n who_o if_o they_o have_v power_n will_v live_v according_a to_o their_o own_o opinion_n that_o be_v if_o their_o opinion_n be_v not_o right_a unrighteous_o a._n do_v the_o clergy_n in_o england_n pretend_v as_o the_o pope_n do_v or_o as_o the_o presbyterian_o do_v to_o have_v a_o right_n from_o god_n immediate_o to_o govern_v the_o king_n and_o his_o subject_n in_o all_o point_n of_o religion_n and_o manner_n if_o they_o do_v you_o can_v doubt_v but_o that_o if_o they_o have_v number_n and_o strength_n which_o they_o be_v never_o like_a to_o have_v they_o will_v attempt_v to_o obtain_v that_o power_n as_o the_o other_o have_v do_v b._n i_o will_v be_v glad_a to_o see_v a_o systeme_n of_o the_o present_a moral_n write_v by_o
force_n to_o make_v he_o consider_v better_o of_o his_o own_o doctrine_n and_o sometime_o bring_v he_o to_o the_o acknowledgement_n of_o the_o truth_n but_o other_o punishment_n they_o can_v inflict_v none_o that_o be_v a_o right_n appropriate_v to_o the_o civil_a power_n so_o that_o all_o the_o punishment_n the_o church_n can_v inflict_v be_v only_o ignominy_n and_o that_o among_o the_o faithful_a consist_v in_o this_o that_o his_o company_n be_v by_o all_o the_o godly_a avoid_v and_o he_o himself_o brand_v with_o the_o name_n of_o heretic_n in_o opposition_n to_o the_o whole_a church_n that_o condemn_v his_o doctrine_n so_o that_o catholic_n and_o heretic_n be_v term_n relative_a and_o here_o it_o be_v that_o heretic_n become_v to_o be_v a_o name_n and_o a_o name_n of_o disgrace_n both_o together_o the_o first_o and_o most_o troublesome_a heresy_n in_o the_o primitive_a church_n be_v about_o the_o trinity_n for_o according_a to_o the_o usual_a curiosity_n of_o natural_a philosopher_n they_o can_v not_o abstain_v from_o dispute_v the_o very_a first_o principle_n of_o christianity_n into_o which_o they_o be_v baptize_v in_o the_o name_n of_o the_o father_n the_o son_n and_o the_o holy_a ghost_n some_o there_o be_v that_o make_v they_o allegorical_a other_o will_v make_v one_o creator_n of_o good_a and_o another_o of_o evil_a which_o be_v in_o effect_n to_o set_v up_o two_o god_n one_o contrary_a to_o another_o suppose_v that_o causation_n of_o evil_n can_v not_o be_v attribute_v to_o god_n without_o impiety_n from_o which_o doctrine_n they_o be_v not_o far_o distant_a that_o now_o make_v the_o first_o cause_n of_o sinful_a action_n to_o be_v every_o man_n as_o to_o his_o own_o sin_n other_o there_o be_v that_o will_v have_v god_n to_o be_v a_o body_n with_o part_n organical_a as_o face_n hand_n forepart_n and_o backpart_n other_o that_o christ_n have_v no_o real_a body_n but_o be_v a_o mere_a phantasm_n for_o phantasm_n be_v take_v then_o and_o have_v be_v ever_o since_o by_o unlearned_a and_o superstitious_a man_n for_o thing_n real_a and_o subsistent_a other_o deny_v the_o divinity_n of_o christ._n other_o that_o christ_n be_v god_n and_o man_n be_v two_o person_n other_o confess_v he_o be_v one_o person_n and_o withal_o that_o he_o have_v but_o one_o nature_n and_o a_o great_a many_o other_o heresy_n arise_v from_o the_o too_o much_o adherence_n to_o the_o philosophy_n of_o those_o time_n whereof_o some_o be_v suppress_v for_o a_o time_n by_o st._n john_n publish_n his_o gospel_n and_o some_o by_o their_o own_o unreasonableness_n vanish_v and_o some_o last_v till_o the_o time_n of_o constantine_n the_o great_a and_o after_z when_o constantine_n the_o great_a make_v so_o by_o the_o assistance_n and_o valour_n of_o the_o christian_a soldier_n have_v attain_v to_o be_v the_o only_a roman_a emperor_n he_o also_o himself_o become_v a_o christian_a and_o cause_v the_o temple_n of_o the_o heathen_a god_n to_o be_v demolish_v and_o authorize_v christian_a religion_n only_o to_o be_v public_a but_o towards_o the_o latter_a end_n of_o his_o time_n there_o arise_v a_o dispute_n in_o the_o city_n of_o alexandria_n between_o alexander_n the_o bishop_n and_o arius_n a_o presbyter_n of_o the_o same_o city_n wherein_o arius_n maintain_v first_o that_o christ_n be_v inferior_a to_o his_o father_n and_o afterward_o that_o he_o be_v no_o god_n allege_v the_o word_n of_o christ_n my_o father_n be_v great_a than_o i_o the_o bishop_n on_o the_o contrary_n allege_v the_o word_n of_o st._n john_n and_o the_o word_n be_v god_n and_o the_o word_n of_o st._n thomas_n my_o lord_n and_o my_o god_n this_o controversy_n present_o among_o the_o inhabitant_n and_o soldier_n of_o alexandria_n become_v a_o quarrel_n and_o be_v the_o cause_n of_o much_o bloodshed_n in_o and_o about_o the_o city_n and_o be_v likely_a then_o to_o spread_v further_o as_o afterward_o it_o do_v this_o so_o far_o concern_v the_o emperor_n civil_a government_n that_o he_o think_v it_o necessary_a to_o call_v a_o general_n council_n of_o all_o the_o bishop_n and_o other_o eminent_a divine_n throughout_o the_o roman_a empire_n to_o meet_v at_o the_o city_n of_o nice_a when_o they_o be_v assemble_v they_o present_v the_o emperor_n with_o libel_n of_o accusation_n one_o against_o another_o when_o he_o have_v receive_v these_o libel_n into_o his_o hand_n he_o make_v a_o oration_n to_o the_o father_n assemble_v exhort_v they_o to_o agree_v and_o to_o fall_v in_o hand_n with_o the_o settlement_n of_o the_o article_n of_o faith_n for_o which_o cause_n he_o have_v assemble_v they_o say_v whatsoever_o they_o shall_v decree_v therein_o he_o will_v cause_v to_o be_v observe_v this_o may_v perhaps_o seem_v a_o great_a indifferency_n than_o will_v in_o these_o day_n be_v approve_v of_o but_o so_o it_o be_v in_o the_o history_n and_o the_o article_n of_o faith_n necessary_a to_o salvation_n be_v not_o think_v then_o to_o be_v so_o many_o as_o afterward_o they_o be_v define_v to_o be_v by_o the_o church_n of_o rome_n when_o constantine_n have_v end_v his_o oration_n he_o cause_v the_o aforesaid_a libel_n to_o be_v cast_v into_o the_o fire_n as_o become_v a_o wise_a king_n and_o a_o charitable_a christian._n this_o do_v the_o father_n fall_v in_o hand_n with_o their_o business_n and_o follow_v the_o method_n of_o a_o former_a creed_n now_o common_o call_v the_o apostle_n creed_n make_v a_o confession_n of_o faith_n viz._n i_o believe_v in_o one_o god_n the_o father_n almighty_n maker_n of_o heaven_n and_o earth_n and_o of_o all_o thing_n visible_a and_o invisible_a in_o which_o be_v condemn_v the_o polytheism_n of_o the_o gentile_n and_o in_o one_o lord_n jesus_n christ_n the_o only_o beget_v son_n of_o god_n against_o the_o many_o son_n of_o the_o many_o god_n of_o the_o heathen_a beget_v of_o his_o father_n before_o all_o world_n god_n of_o god_n against_o the_o arian_n very_a god_n of_o very_a god_n against_o the_o valentinian_o and_o against_o the_o heresy_n of_o apelles_n and_o other_o who_o make_v christ_n a_o mere_a phantasm_n light_n of_o light_n this_o be_v put_v in_o for_o explication_n and_o use_v before_o to_o that_o purpose_n by_o tertullian_n beget_v not_o make_v be_v of_o one_o substance_n with_o the_o father_n in_o this_o again_o they_o condemn_v the_o doctrine_n of_o arius_n for_o this_o word_n of_o one_o substance_n in_o latin_a consubstantialis_fw-la but_o in_o greek_a 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d that_o be_v of_o one_o essence_n be_v put_v as_o a_o touchstone_n to_o discern_v a_o arian_n from_o a_o catholic_n and_o much_o ado_n there_o be_v about_o it_o constantine_n himself_o at_o the_o pass_n of_o this_o creed_n take_v notice_n of_o it_o for_o a_o hard_a word_n but_o yet_o approve_v of_o it_o say_v that_o in_o a_o divine_a mystery_n it_o be_v fit_a to_o use_v divina_fw-la &_o arcana_fw-la verba_fw-la that_o be_v divine_a word_n and_o hide_a from_o humane_a understanding_n call_v that_o word_n 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d divine_a not_o because_o it_o be_v in_o the_o divine_a scripture_n for_o it_o be_v not_o there_o but_o because_o it_o be_v to_o he_o arcanum_n that_o be_v not_o sufficient_o understand_v and_o in_o this_o again_o appear_v the_o indifferency_n of_o the_o emperor_n and_o that_o he_o have_v for_o his_o end_n in_o the_o call_n of_o the_o synod_n not_o so_o much_o the_o truth_n as_o the_o uniformity_n of_o the_o doctrine_n and_o peace_n of_o his_o people_n that_o depend_v on_o it_o the_o cause_n of_o the_o obscurity_n of_o this_o word_n 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d proceed_v chief_o from_o the_o difference_n between_o the_o greek_a and_o roman_a dialect_n in_o the_o philosophy_n of_o the_o peripatetic_n the_o first_o principle_n of_o religion_n in_o all_o nation_n be_v that_o god_n be_v that_o be_v to_o say_v that_o god_n real_o be_v something_o and_o not_o a_o mere_a fancy_n but_o that_o which_o be_v real_o something_o be_v considerable_a alone_o by_o itself_o as_o be_v 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as_o be_v a_o thing_n contrary_n to_o nature_n or_o to_o pay_v they_o any_o reverence_n or_o to_o care_v what_o they_o say_v except_o some_o few_o that_o may_v be_v delight_v with_o their_o jingle_n i_o wish_v with_o all_o my_o heart_n there_o be_v enough_o of_o such_o discreet_a and_o ancient_a man_n as_o may_v suffice_v for_o all_o the_o parish_n of_o england_n and_o that_o they_o will_v undertake_v it_o but_o this_o be_v but_o a_o wish_n i_o leave_v it_o to_o the_o wisdom_n of_o the_o state_n to_o do_v what_o it_o please_v b._n what_o do_v they_o next_o a._n whereas_o the_o king_n have_v send_v prisoner_n into_o place_n remote_a from_o london_n three_o person_n that_o have_v be_v condemn_v for_o publish_v seditious_a doctrine_n some_o in_o writing_n some_o in_o public_a sermon_n the_o parliament_n whether_o with_o his_o majesty_n consent_n or_o no_o i_o have_v forget_v cause_v they_o to_o be_v release_v and_o to_o return_v to_o london_n meaning_n i_o think_v to_o try_v how_o the_o 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his_o majesty_n with_o the_o epistle_n prefix_v in_o the_o year_n 1662._o at_o the_o same_o time_n they_o come_v forth_o in_o latin_n these_o thing_n premise_v there_o remain_v nothing_o but_o to_o wish_v for_o myself_o good_a sale_n to_o the_o buyer_n much_o pleasure_n and_o satisfaction_n your_o humble_a servant_n william_n crook_n behemoth_n or_o the_o epitome_n of_o the_o civil_a war_n of_o england_n part_n i._n a._n if_o in_o time_n as_o in_o place_n there_o be_v degree_n of_o high_a and_o low_a i_o very_o believe_v that_o the_o high_a of_o time_n will_v be_v that_o which_o pass_v between_o 1640._o and_o 1660._o for_o he_o that_o thence_o as_o from_o the_o devil_n mountain_n shall_v have_v look_v upon_o the_o world_n and_o observe_v the_o action_n of_o man_n especial_o in_o england_n may_v have_v have_v a_o prospect_n of_o all_o kind_n of_o injustice_n and_o of_o all_o kind_n of_o folly_n that_o the_o world_n can_v afford_v and_o how_o they_o be_v produce_v by_o their_o hypocrisy_n and_o self-conceit_n whereof_o the_o one_o be_v double_a iniquity_n and_o the_o other_o double_a folly_n b._n i_o shall_v be_v glad_a to_o behold_v that_o prospect_n you_o that_o have_v live_v in_o that_o time_n and_o in_o that_o part_n of_o your_o age_n wherein_o man_n use_v to_o see_v best_a into_o good_a and_o evil_a i_o pray_v you_o set_v i_o that_o can_v not_o see_v so_o well_o upon_o the_o same_o mountain_n by_o the_o relation_n of_o the_o action_n you_o then_o see_v and_o of_o their_o cause_n pretension_n justice_n order_n artifice_n and_o event_n a._n in_o the_o year_n 1640._o the_o government_n of_o england_n be_v monarchical_a and_o the_o king_n that_o reign_v charles_n the_o first_o of_o that_o name_n hold_v the_o sovereignty_n by_o right_a of_o a_o descent_n continue_v above_o 600_o year_n and_o from_o a_o much_o long_a descent_n king_n of_o scotland_n and_o from_o the_o time_n of_o his_o ancestor_n henry_n the_o second_o king_n of_o ireland_n a_o man_n that_o 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to_o the_o people_n god_n ambassador_n pretend_v to_o have_v a_o right_n from_o god_n to_o govern_v every_o one_o his_o parish_n and_o their_o assembly_n the_o whole_a nation_n second_o there_o be_v a_o very_a great_a number_n though_o not_o comparable_a to_o the_o other_o which_o notwithstanding_o that_o the_o pope_n power_n in_o england_n both_o temporal_a and_o ecclesiastical_a have_v be_v by_o act_n of_o parliament_n abolish_v do_v still_o retain_v a_o belief_n that_o we_o ought_v to_o be_v govern_v by_o the_o pope_n who_o they_o pretend_v to_o be_v the_o vicar_n of_o christ_n and_o in_o the_o right_n of_o christ_n to_o be_v the_o governor_n of_o all_o christian_a people_n and_o these_o be_v know_v by_o the_o name_n of_o papist_n as_o the_o minister_n i_o mention_v before_o be_v common_o call_v presbyterian_o three_o there_o be_v not_o a_o few_o who_o in_o the_o begin_n of_o the_o trouble_n be_v not_o discover_v but_o short_o after_o declare_v themselves_o for_o a_o liberty_n in_o 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in_o defence_n of_o the_o civil_a power_n that_o must_v be_v punish_v by_o he_o who_o right_n he_o defend_v like_o vzza_n that_o be_v slay_v because_o he_o will_v needs_o unbidden_a put_v forth_o his_o hand_n to_o keep_v the_o ark_n from_o fall_v but_o what_o if_o a_o whole_a nation_n shall_v revolt_v from_o the_o pope_n at_o once_o what_o effect_n can_v excommunication_n have_v upon_o the_o nation_n a._n why_o they_o shall_v have_v no_o more_o mass_n say_v at_o least_o by_o any_o of_o the_o pope_n priest_n beside_o the_o pope_n will_v have_v no_o more_o to_o do_v with_o they_o but_o cast_v they_o off_o and_o so_o they_o will_v be_v in_o the_o same_o case_n as_o if_o a_o nation_n shall_v be_v cast_v off_o by_o their_o king_n and_o left_a to_o be_v govern_v by_o themselves_o or_o who_o they_o will_v b._n this_o will_v not_o be_v take_v so_o much_o for_o a_o punishment_n to_o the_o people_n as_o to_o the_o king_n and_o therefore_o when_o a_o pope_n excommunicate_v a_o whole_a nation_n methinks_v he_o rather_o excommunicate_v himself_o than_o they_o but_o i_o pray_v you_o tell_v i_o what_o be_v the_o right_n that_o the_o pope_n pretend_v to_o in_o the_o kingdom_n of_o other_o prince_n a._n first_o a_o exemption_n of_o all_o priest_n friar_n and_o monk_n in_o criminal_a cause_n from_o the_o cognizance_n of_o civil_a judge_n second_o collation_n of_o benefice_n on_o who_o he_o please_v native_a or_o stranger_n and_o exaction_n of_o ten_o first_o fruit_n and_o other_o payment_n three_o appeal_v to_o rome_n in_o all_o cause_n where_o the_o church_n can_v pretend_v to_o be_v concern_v four_o to_o be_v the_o supreme_a judge_n concern_v lawfulness_n of_o marriage_n i._n e._n concern_v the_o hereditary_a succession_n of_o king_n and_o to_o have_v the_o cognisance_n of_o all_o cause_n concern_v adultery_n and_o fornication_n b._n good_a a_o monopoly_n of_o woman_n a._n five_o a_o power_n of_o absolve_a subject_n of_o their_o duty_n and_o of_o their_o oath_n of_o fidelity_n to_o their_o lawful_a sovereign_n when_o the_o pope_n shall_v think_v fit_a for_o the_o extirpation_n of_o heresy_n b._n this_o power_n of_o absolve_a subject_n of_o their_o obedience_n as_o also_o that_o other_o of_o be_v judge_n of_o manner_n and_o doctrine_n be_v as_o absolute_a a_o sovereignty_n as_o be_v possible_a to_o be_v and_o consequent_o there_o must_v be_v two_o kingdom_n in_o one_o and_o the_o same_o nation_n and_o no_o man_n be_v able_a to_o know_v which_o of_o his_o master_n he_o must_v obey_v a._n for_o my_o part_n i_o shall_v rather_o obey_v that_o master_n that_o have_v the_o right_n of_o make_v law_n and_o of_o inflict_a punishment_n than_o he_o that_o pretend_v only_o to_o a_o right_n of_o make_v canon_n that_o be_v to_o say_v rule_n and_o no_o right_n of_o co-action_n or_o otherwise_o punish_v but_o by_o excommunication_n b._n but_o the_o pope_n pretend_v also_o that_o his_o canon_n be_v law_n and_o for_o punish_v can_v there_o be_v great_a than_o excommunication_n suppose_v it_o true_a as_o the_o pope_n say_v it_o be_v that_o he_o that_o die_v excommunicate_a be_v damn_v which_o supposition_n it_o seem_v you_o believe_v not_o else_o you_o will_v rather_o have_v choose_v to_o obey_v the_o pope_n that_o will_v cast_v you_o body_n and_o soul_n into_o hell_n than_o the_o king_n that_o can_v only_o kill_v the_o body_n a._n you_o say_v true_a for_o it_o be_v very_o uncharitable_a in_o i_o to_o believe_v that_o all_o english_a man_n except_o a_o few_o papist_n that_o have_v be_v bear_v and_o call_v heretic_n ever_o since_o the_o reformation_n of_o religion_n in_o england_n shall_v be_v damn_v b._n but_o for_o those_o that_o die_v excommunicate_a in_o the_o church_n of_o england_n at_o this_o day_n do_v you_o not_o think_v they_o also_o damn_v a._n doubtless_o he_o that_o die_v in_o sin_n without_o repentance_n be_v damn_v and_o he_o that_o be_v excommunicate_a for_o disobedience_n to_o the_o king_n law_n either_o spiritual_a or_o temporal_a be_v excommunicate_a for_o sin_n and_o therefore_o if_o he_o die_v excommunicate_a and_o without_o desire_n of_o reconciliation_n he_o die_v impenitent_a you_o see_v what_o follow_v but_o to_o die_v in_o disobedience_n to_o the_o precept_n and_o doctrine_n of_o those_o man_n that_o have_v no_o authority_n or_o jurisdiction_n over_o we_o be_v quite_o another_o case_n and_o bring_v no_o such_o danger_n with_o it_o b._n but_o what_o be_v this_o heresy_n which_o the_o church_n of_o rome_n so_o cruel_o persecute_v as_o to_o depose_v king_n that_o do_v not_o when_o they_o be_v bid_v turn_v all_o heretic_n out_o of_o their_o dominion_n a._n heresy_n be_v a_o word_n which_o when_o it_o be_v use_v without_o passion_n signify_v a_o private_a opinion_n so_o the_o different_a sect_n of_o the_o old_a philosopher_n academian_o peripatetic_n epicurean_o stoic_n etc._n etc._n be_v call_v heresy_n but_o in_o the_o christian_a church_n there_o be_v in_o the_o signification_n of_o that_o word_n comprehend_v a_o sinful_a opposition_n to_o he_o that_o be_v chief_a judge_n of_o doctrine_n in_o order_n to_o the_o salvation_n of_o man_n soul_n and_o consequent_o heresy_n may_v be_v say_v to_o bear_v the_o same_o relation_n to_o the_o power_n spiritual_n that_o rebellion_n do_v to_o the_o power_n temporal_a and_o be_v suitable_o to_o be_v persecute_v by_o he_o that_o will_v preserve_v a_o power_n spiritual_a and_o dominion_n over_o man_n conscience_n b._n it_o will_v be_v very_o well_o because_o we_o be_v all_o of_o we_o permit_v to_o read_v the_o holy_a scripture_n and_o bind_v to_o make_v they_o the_o rule_n of_o our_o action_n both_o public_a and_o private_a that_o heresy_n be_v by_o some_o law_n define_v and_o the_o particular_a opinion_n set_v forth_o for_o which_o a_o man_n be_v to_o be_v condemn_v and_o punish_v as_o a_o heretic_n for_o else_o not_o only_o man_n of_o mean_a capacity_n but_o even_o the_o wise_a and_o devout_a christian_n may_v fall_v into_o heresy_n without_o any_o will_n 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that_o they_o fall_v in_o hand_n with_o the_o work_n so_o quick_o for_o the_o first_o rector_n of_o the_o university_n of_o paris_n as_o i_o have_v read_v somewhere_o be_v peter_n lombard_n who_o first_o bring_v in_o they_o the_o learning_n call_v school-divinity_n and_o be_v second_v by_o john_n scot_n of_o duns_n who_o live_v in_o or_o near_o the_o same_o time_n who_o any_o ingenious_a reader_n not_o know_v what_o be_v the_o design_n will_v judge_v to_o have_v be_v two_o the_o most_o egregious_a blockhead_n in_o the_o world_n so_o obscure_a and_o senseless_a be_v their_o write_n and_o from_o these_o the_o schoolman_n that_o succeed_v learn_v the_o trick_n of_o impose_v what_o they_o list_v upon_o their_o reader_n and_o decline_v the_o force_n of_o true_a reason_n by_o verbal_a fork_n i_o mean_v distinction_n that_o signify_v nothing_o but_o serve_v only_o to_o astonish_v the_o multitude_n of_o ignorant_a men._n as_o for_o the_o understand_a reader_n they_o be_v so_o few_o that_o 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and_o draw_v xz_n it_o will_v pass_v through_o t._n and_o the_o four_o line_n tu_fw-la tx_n tie_v and_o tz_n will_v be_v equal_a and_o therefore_o join_v yx_n and_o yz_n the_o figure_n vxyz_n will_v be_v a_o rectangle_n produce_v cd_o to_o p_o so_o as_o dp_v be_v equal_a to_o ad._n now_o if_o yz_n produce_v fall_v on_o p_o there_o will_v be_v three_o rectangle_n equi-angled_n triangle_n dpy_a dyx_n and_o dxv_o and_o consequent_o four_o continual_a proportional_n dp_n die_v dx_o and_o dv_o whereof_o dx_o be_v the_o least_o of_o the_o mean_n and_o therefore_o the_o cube_n of_o dx_o will_v be_v double_a to_o the_o cube_n of_o dv_o a._n that_o be_v true_a and_o the_o cube_n of_o d_o y_fw-fr will_v be_v double_a to_o the_o cube_n of_o dx_o and_o the_o cube_n of_o dp_n double_a to_o the_o cube_n of_o die_v but_o that_o yz_n produce_v fall_v upon_o p_o be_v the_o thing_n they_o deny_v and_o which_o you_o ought_v to_o demonstrate_v b._n if_o yz_n produce_v fall_v not_o on_o p_o then_o draw_v by_a and_o from_o five_o let_v fall_v a_o perpendicular_a upon_o by_a suppose_v at_o v_o divide_v pv_n in_o the_o midst_n at_o a_o and_o join_v au_o which_o do_v au_o will_n be_v equal_a to_o ave_fw-la or_o ap_fw-mi for_o because_o v_n up_o be_v a_o right_a angle_n the_o point_n u._fw-mi will_v be_v in_o the_o semicircle_n whereof_o pv_n be_v the_o diameter_n therefore_o draw_v ur_fw-la the_o angle_n uvr_n will_v be_v a_o right_a angle_n a._n why_o so_o b._n because_o tu_fw-la and_o tie_v be_v equal_a and_o td_v it_o be_v equal_a sv_o will_v also_o be_v equal_a to_o dv_o and_o because_o dp_v and_o r_n be_v equal_a and_o parallel_v ry_o will_v be_v equal_a and_o parallel_v to_o pv_v and_o therefore_o ur_fw-la and_o by_a that_o join_v they_o will_v be_v equal_a and_o parallel_v and_o the_o angle_n p_o uv_n rv_v you_o will_v be_v alternate_a and_o consequent_o equal_a but_o p_o uv_n be_v a_o right_a angle_n therefore_o also_o rv_v you_o will_v be_v a_o right_a angle_n a._n hitherto_o all_o be_v evident_a proceed_v b._n from_o the_o point_n y_fw-fr raise_v a_o perpendicular_a cut_a ur_fw-la wheresoever_o in_o it_o and_o then_o because_o by_a and_o ur_fw-la be_v parallel_n the_o angle_n y_fw-fr tv_n will_v be_v a_o right_a angle_n and_o the_o figure_n uy_fw-fr tv_n a_o rectangle_n and_o ut_fw-la equal_a to_o yu._n but_o yv_n be_v equal_a to_o zx_v and_o therefore_o zx_n be_v equal_a to_o ut_fw-la and_o ut_fw-la must_v pass_v through_o the_o point_n t_o for_o the_o diameter_n of_o any_o rectangle_n divide_v each_o other_o in_o the_o middle_a therefore_o z_o and_o u._fw-mi be_v the_o same_o point_n and_o x_o and_o to_o the_o same_o point_n therefore_o yz_n produce_v fall_v upon_o p._n and_o dx_o be_v the_o lesser_a of_o the_o two_o mean_n between_o ad_fw-la and_o dv_o and_o the_o cube_n of_o dx_o double_a to_o the_o cube_n of_o dv_o which_o be_v to_o be_v demostraten_v a_o i_o can_v imagine_v what_o fault_n there_o can_v be_v in_o this_o demonstration_n and_o yet_o 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