Selected quad for the lemma: cause_n

Word A	Word B	Word C	Word D	Occurrence	Frequency Band	MI	MI Band	Prominent
cause_n	bring_v	good_a	know_v	2,039	5	3.4458	3	true

Text snippets containing the quad

ID	Title	Author	Corrected Date of Publication (TCP Date of Publication)	STC	Words	Pages
A00429	The elements of geometrie of the most auncient philosopher Euclide of Megara. Faithfully (now first) translated into the Englishe toung, by H. Billingsley, citizen of London. Whereunto are annexed certaine scholies, annotations, and inuentions, of the best mathematiciens, both of time past, and in this our age. With a very fruitfull præface made by M. I. Dee, specifying the chiefe mathematicall scie[n]ces, what they are, and wherunto commodious: where, also, are disclosed certaine new secrets mathematicall and mechanicall, vntill these our daies, greatly missed; Elements. English	Euclid.; Dee, John, 1527-1608.; Candale, François de Foix, comte de, 1502-1594.; Billingsley, Henry, Sir, d. 1606.	1570 (1570)	STC 10560; ESTC S106699	1,020,889	884

what_o manly_a virtue_n in_o other_o noble_a man_n flourish_v before_o his_o eye_n he_o sthe_o aspire_v after_o what_o prowess_n he_o purpose_v and_o mean_v to_o achieve_v with_o what_o feat_n and_o art_n he_o begin_v to_o furnish_v and_o fraught_v himself_o for_o the_o better_a service_n of_o his_o king_n and_o country_n both_o in_o peace_n &_o war_n these_o i_o say_v his_o heroical_a meditation_n forecas●inges_n and_o determination_n no_o twain_o i_o think_v beside_o myself_o can_v so_o perfect_o and_o true_o report_v and_o therefore_o in_o conscience_n i_o count_v it_o my_o part_n for_o the_o honour_n preferment_n &_o procure_v of_o virtue_n thus_o brief_o to_o have_v put_v his_o name_n in_o the_o register_n of_o fa●●_n immortal_a to_o our_o purpose_n this_o john_n by_o one_o of_o his_o act_n beside_o many_o other_o both_o in_o england_n and_o france_n by_o i_o in_o he_o note_v do_v dislose_v his_o hearty_a love_n to_o virtuous_a science_n and_o his_o noble_a intent_n to_o excel_v in_o martial_a prowess_n when_o he_o with_o humble_a request_n and_o instant_n solicit_v get_v the_o best_a rule_n either_o in_o time_n pass_v by_o greek_a or_o roman_a or_o in_o our_o time_n use_v and_o new_a stratagem_n therein_o de●ised_v for_o order_v of_o all_o company_n sum_n and_o number●_n of_o man_n many_n or_o few_o with_o one_o kind_n of_o weapon_n or_o more_o appoint_v with_o artillery_n or_o without_o on_o horseback_n or_o on_o foot_n to_o give_v or_o take_v onset_n to_o seem_v many_o be_v few●_n to_o s●em_v few_o be_v many_o to_o march_v in_o battle_n or_o jornay_n with_o many_o such_o feat_n to_o fight_v f●●ld_n skarmoush_n or_o ambush_n appartain_v and_o of_o all_o these_o lively_a desi●nementes_n most_o curious_o to_o be_v in_o velame_n parchment_n describe_v with_o note_n &_o peculiar_a mark_n as_o the_o art_n require_v and_o all_o these_o rules●_n and_o description_n arithmetical_a somerset_n enclose_v in_o a_o rich_fw-fr case_n of_o gold_n he_o use_v to_o wear_v about_o his_o necke●_n as_o his_o jewel_n most_o precious_a and_o counselor_n most_o trusty_a thus_o arithmetic_n of_o he_o be_v shrine_v in_o gold_n of_o number_n fruit_n he_o have_v good_a hope_n now_o number_n therefore_o innumerable_a in_o number_n praise_v his_o sh●●ne_n shall_v find_v what_o need_n i_o for_o far_a proof_n to_o you_o of_o the_o schoolmaster_n of_o justice_n to_o require_v testimony_n how_o needful_a how_o fruitful_a how_o skilful_a a_o thing_n arithmetic_n be_v i_o meane●_n the_o lawyer_n of_o all_o sort_n undoubted_o the_o civilians_n can_v marvelous_o declare_v how_o neither_o the_o ancient_a roman_a law_n without_o good_a knowledge_n of_o number_n art_n can_v be_v perceive_v nor_o justice_n in_o infinite_a case_n without_o due_a proportion_n narrow_o consider_v be_v able_a to_o be_v executed●_n how_o just_o &_o with_o great_a knowledge_n of_o art_n do_v pap●●●●anus_n institute_v a_o law_n of_o partition_n and_o allowance_n between_o man_n and_o wife_n a●●●_n a_o ●●●orce_n but_o how_o acc●rsius_n bald●s_n bartolus_n jason_n alex●nder_n and_o final_o alciat●●_n be_v otherwise_o notable_o well_o learn_v do_v jumble_v guess_v and_o err_v from_o the_o ●quity●●rt_n ●nd_v i●●ent_v of_o the_o lawmaker_n arithmetic_n can_v detect_v and_o convince_v and_o clear_o make_v the_o truth_n to_o shine_v good_a bartolus_n tire_v in_o the_o examine_n &_o proportion_v of_o the_o matter_n ●nd_v with_o accursius_fw-la gloss_n much_o cumber_v burst_v out_o and_o say_v nulla_fw-la est_fw-la i●_z 〈◊〉_d libr●_n 〈◊〉_d glossa_fw-la difficili●r_fw-la evils_n c●mputationem_fw-la nec_fw-la scholas●ici_fw-la ●ec_fw-la doct●res_fw-la intelligent_a etc_n etc_n that_o is●_n in_o the_o whole_a book_n there_o be_v no_o ●losse_n hard_a than_o thi●●_n who_o account_n or_o reckon_n neither_o the_o scholar_n nor_o the_o doctor_n understand_v etc_n etc_n what_o can_v they_o say_v of_o i●lianus_n law_n si_fw-mi ita_fw-la s●ript●m_fw-la etc_n etc_n of_o the_o testator_n will_v just_o perform_v between_o the_o wife_n son_n and_o daughter_n how_o can_v they_o perceive_v the_o ●●●●●tie_n of_o aphricanus_fw-la arithmetical_a reckon_a where_o he_o treat_v of_o lex_n falcid●a●_n ●_z how_o ●●n_fw-la they_o deliver_v he_o from_o his_o reprover_n and_o their_o maintainer_n as_o i●●●●es_n accursius_fw-la hippolytus_n and_o alciatus_fw-la how_o ●ustly_o and_o artificial_o be_v african●s_n reckon_v make_v proportionate_v to_o the_o sum_n bequeath_v the_o contribution_n of_o each_o part_n namely_o for_o the_o hundred_o present_o receive_v 17_o 1_o 7._o and_o for_o the_o hundred_o receive_v after_o ten_o month_n 12_o 6_o 7_o which_o make_v the_o 30_o which_o be_v to_o be_v contribute_v by_o the_o legatari●s_n to_o the_o heir_n for_o what_o proportion_n 100_o have_v to_o 75_o the_o same_o have_v 17_o 1_o 7_o to_o 12_o 6_o 7_o which_o be_v sesquitertia_fw-la that_o be_v as_z 4_o to_o 3._o which_o make_v 7._o wonderful_a many_o place_n in_o the_o civil_a law_n require_v a_o expert_a arithmeticien_fw-fr to_o understand_v the_o deep_a judgement_n &_o just_a determination_n of_o the_o ancient_a roman_a lawmaker_n but_o much_o more_o expert_a aught_o he_o to_o be_v who_o shall_v be_v able_a to_o decide_v with_o equity_n the_o infinite_a variety_n of_o case_n which_o do_v or_o may_v happen_v under_o every_o one_o of_o those_o law_n and_o ordinance_n civil_a hereby_o easy_o you_o may_v now_o conjecture_v that_o in_o the_o canon_n law_n and_o in_o the_o law_n of_o the_o realm_n which_o with_o we_o bear_v the_o chief_a authority_n justice_n and_o equity_n may_v be_v great_o prefer_v and_o skilful_o execute_v through_o due_a skill_n of_o arithmetic_n and_o proportion_n appertain_v the_o worthy_a philosopher_n and_o prudent_a lawmaker_n who_o have_v write_v many_o book_n de_fw-fr republica_n how_o the_o best_a state_n of_o common_a wealth_n may_v be_v procure_v and_o maintain_v have_v very_o well_o determine_v of_o justice_n which_o not_o only_o be_v the_o base_a and_o foundation_n of_o common_a weal_n but_o also_o the_o total_a perfection_n of_o all_o our_o work_n word_n and_o thought_n define_v it_o to_o be_v that_o virtue_n justice._n by_o which_o to_o every_o one_o be_v render_v that_o to_o he_o appertain_v god_n challenge_v this_o at_o our_o hand_n to_o be_v honour_v as_o god_n to_o belove_a as_o a_o father_n to_o be_v fear_v as_o a_o lord_n &_o master_n our_o neighbour_n proportion_n be_v also_o prescribe_v of_o the_o almighty_a lawmaker_n which_o be_v to_o do_v to_o other_o even_o as_o we_o will_v be_v do_v unto_o these_o proportion_n be_v in_o justice_n necessary_a in_o duty_n commendable_a and_o of_o common_a wealth_n the_o life_n strength_n stay_v and_o flourish_a aristotle_n in_o his_o ethic_n to_o fatch_z the_o seed_n of_o justice_n and_o light_n of_o direction_n to_o use_v and_o execute_v the_o sam●_n be_v fain_o to_o fly_v to_o the_o perfection_n and_o power_n of_o number_n for_o proportion_n arithmetical_a and_o geometrical_a 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and_o i_o think_v a_o certain_a god_n rather_o than_o fortune_n to_o have_v give_v we_o this_o gift_n for_o our_o bliss_n for_o why_o shall_v we_o not_o judge_v he_o who_o be_v the_o author_n of_o all_o good_a thing_n to_o be_v also_o the_o cause_n of_o th●_z great_a good_a thing_n namely_o wisdom_n there_o at_o length_n he_o prove_v wisdom_n to_o be_v attain_v by_o good_a skill_n of_o number_n with_o which_o great_a testimony_n and_o the_o manifold_a profess_v and_o reason_n before_o expressed●_n you_o may_v be_v sufficient_o and_o full_o persuade_v of_o the_o perfect_a science_n of_o arithmetic_n to_o make_v this_o account_v that_o of_o all_o science_n ☞_o next_o to_o theologie_n it_o be_v most_o divine_a most_o pure_a most_o ample_a and_o general_a most_o profound_a most_o subtle_a most_o commodious_a and_o most_o necessary_a who_o be_v next_o sister_n be_v the_o absolute_a science_n of_o magnitude_n of_o which_o by_o the_o direction_n and_o aid_n of_o he_o who_o magnitude_n be_v infinite_a and_o of_o we_o incomprehensible_a i_o now_o

again_o of_o thing_n be_v in_o like_a swiftness_n of_o move_v to_o think_v the_o near_a to_o move_v fast_o and_o the_o far_o much_o slow_a nay_o of_o two_o thing_n whereof_o the_o one_o incomparable_o do_v move_v swift_a than_o the_o other_o to_o deem_v the_o slow_a to_o move_v very_o swift_a &_o the_o other_o to_o stand_v what_o a_o error_n be_v this_o of_o our_o eye_n of_o the_o rainbow_n both_o of_o his_o colour_n of_o the_o order_n of_o the_o colour_n of_o the_o bigness_n of_o it_o the_o place_n and_o heith_n of_o it_o etc_o etc_o to_o know_v the_o cause_n demonstrative_a be_v it_o not_o pleasant_a be_v it_o not_o necessary_a of_o two_o or_o three_o son_n appear_v of_o blaze_a star_n and_o such_o like_a thing_n by_o natural_a cause_n bring_v to_o pass_v and_o yet_o nevertheless_o of_o far_a matter_n significative_a be_v it_o not_o commodious_a for_o man_n to_o know_v the_o very_a true_a cause_n &_o occasion_n natural_a yea_o rather_o be_v it_o not_o great_o against_o the_o sovereignty_n of_o man_n nature_n to_o be_v so_o overshoot_v and_o abuse_v with_o thing_n at_o hand_n before_o his_o eye_n as_o with_o a_o peacock_n tail_n and_o a_o dove_n neck_n or_o a_o whole_a ore_n in_o water_n hold_v to_o seem_v break_v thing_n far_o of_o to_o seem_v never_o and_o never_o to_o seem_v far_o of_o small_a thing_n to_o seem_v great_a and_o great_a to_o seem_v small_a one_o man_n to_o seem_v a_o army_n or_o a_o man_n to_o be_v curse_o afraid_a of_o his_o own_o shadow_n yea_o so_o much_o to_o fear_v that_o if_o you_o be_v alone_o near_o a_o certain_a glass_n and_o proffer_n with_o dagger_n or_o sword_n to_o foin_v at_o the_o glass_n you_o shall_v sudden_o be_v move_v to_o give_v back_o in_o manner_n by_o reason_n of_o a_o image_n ☞_o appear_v in_o the_o air_n between_o you_o &_o the_o glass_n with_o like_a hand_n sword_n or_o dagger_n &_o with_o like_a quickness_n foin_a at_o your_o very_a eye_n likewise_o as_o you_o do_v at_o the_o glass_n strange_a this_o be_v to_o hear_v of_o but_o more_o marvellous_a to_o behold_v than_o these_o my_o word_n can_v signify_v and_o nevertheless_o by_o demonstration_n optical_a the_o order_n and_o cause_n thereof_o be_v certify_v even_o so_o as_o the_o effect_n be_v consequent_a yea_o thus_o much_o more_o dare_v i_o take_v upon_o i_o towards_o the_o satisfy_n of_o the_o noble_a courage_n that_o long_v ardent_o for_o the_o wisdom_n of_o cause_n natural_a as_o to_o let_v he_o understand_v that_o in_o london_n he_o may_v wish_v his_o own_o eye_n have_v proof_n of_o that_o which_o i_o have_v say_v herein_o a_o gentleman_n which_o for_o his_o good_a service_n s.w.p._n do_v to_o his_o country_n be_v famous_a and_o honourable_a and_o for_o skill_n in_o the_o mathematical_a science_n and_o language_n be_v the_o odd_a man_n of_o this_o kind_n etc_n etc_n even_o he_o be_v able_a and_o i_o be_o sure_a will_v very_o willing_o let_v the_o glass_n and_o proof_n be_v see_v and_o so_o i_o here_o request_v he_o for_o the_o increase_n of_o wisdom_n in_o the_o honourable_a and_o for_o the_o stop_n of_o the_o mouth_n malicious_a and_o repress_v the_o arrogancy_n of_o the_o ignorant_a you_o may_v easy_o guess_v what_o i_o mean_v this_o art_n of_o perspective_n be_v of_o that_o excellency_n and_o may_v be_v lead_v to_o the_o certify_n and_o execute_v of_o such_o thing_n as_o no_o man_n will_v easy_o believe_v without_o actual_a proof_n perceive_v i_o speak_v nothing_o of_o natural_a philosophy_n which_o without_o perspective_n can_v not_o be_v full_o understand_v nor_o perfect_o attein_v unto_o nor_o of_o astronomy_n which_o without_o perspective_n can_v not_o well_o be_v ground_v nor_o astrology_n natural_o verify_v and_o avouch_v that_o part_n hereof_o which_o deal_v with_o glass_n which_o name_n glass_n be_v a_o general_a name_n in_o this_o art_n for_o any_o thing_n from_o which_o a_o beam_n rebound_v be_v call_v catoptrike_v and_o have_v so_o many_o use_n both_o marvellous_a and_o profitable_a that_o both_o it_o will_v hold_v i_o to_o long_o to_o no●●_n therein_o the_o principal_a conclusion_n all_o ready_a know_v and_o also_o perchance_o some_o thing_n may_v lack_v due_a credit_n with_o you_o and_o i_o thereby_o to_o lose_v my_o labor●_n and_o you_o to_o slip_v into_o light_a judgement_n ☞_o ●_o before_o you_o have_v learn_v sufficient_o the_o power_n of_o nature_n and_o arte._n now_o to_o proceed_v astronomy_n be_v a_o art_n mathematical_a which_o demonstrate_v the_o distance_n magnitude_n and_o all_o natural_a motion_n apparence_n and_o passion_n proper_a to_o the_o planet_n and_o fix_a start_n for_o any_o time_n past_a present_a and_o to_o come_v in_o respect_n of_o a_o certain_a horizon_n or_o without_o respect_n of_o any_o horizon_n by_o this_o art_n we_o be_v certify_v of_o the_o distance_n of_o the_o starry_a sky_n and_o of_o each_o planete_n from_o the_o centre_n of_o the_o earth_n and_o of_o the_o greatness_n of_o any_o fix_a star_n see_v or_o planete_n in_o respect_n of_o the_o earth_n greatness_n as_o we_o be_v sure_a by_o this_o art_n that_o the_o solidity_n massine_n and_o body_n of_o the_o son_n contain_v the_o quantity_n of_o the_o whole_a earth_n and_o sea_n a_o hundred_o three_o score_n and_o two_o time_n less_o by_o 1_o ●_o one_o eight_o part_n of_o the_o earth_n but_o the_o body_n of_o the_o whole_a earthly_a globe_n and_o sea_n be_v big_a than_o the_o body_n of_o the_o moon_n three_o and_o forty_o time_n less_o by_o 1_o ●_o of_o the_o moon_n wherefore_o the_o son_n be_v big_a than_o the_o moon_n 7000_o time_n less_o by_o 59_o ●●_o 164_o that_o be_v precise_o 6940_o ●5_o ●●_o big_a than_o the_o moon_n and_o yet_o the_o unskilful_a man_n will_v judge_v they_o a_o like_a big_a wherefore_o of_o necessity_n the_o one_o be_v much_o far_o from_o we_o than_o the_o other_o the_o son_n when_o he_o be_v far_o from_o the_o earth_n which_o now_o in_o our_o age_n be_v when_o he_o be_v in_o the_o 8._o degree_n of_o cancer_n be_v 1179_o semidiameter_n 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book_n thereof_o to_o the_o emperor_n augustus_n in_o who_o day_n our_o heavenly_a archemaster_n be_v bear_v and_o the_o other_o leo_n baptista_n albertus_n a_o florentine_a who_o also_o publish_v ten_o book_n thereof_o architectura_n say_v vitrwius_fw-la est_fw-la scientia_fw-la pluribus_fw-la disciplinis_fw-la &_o varijs_fw-la eruditionibus_fw-la ornata●_n cvius_fw-la judicio_fw-la probantur_fw-la omni●_n qua_fw-la ab_fw-la cateris_fw-la artificibus_fw-la perficiuntur_fw-la opera_fw-la that_o be_v architecture_n be_v a_o science_n garnish_v with_o many_o doctrine_n &_o diverse_a instruction_n by_o who_o judgement_n all_o work_n by_o other_o workman_n finish_v be_v judge_v it_o follow_v ea_fw-la nascitur_fw-la ex_fw-la fabric_n &_o ratiocinatione_fw-la etc_n etc_n ratiocinatio_fw-la aute●_n est_fw-la quae_fw-la res_fw-la fabricatas_fw-la solertia_fw-la ac_fw-la ratione_fw-la proportionis_fw-la demonstrare_fw-la atque_fw-la explicare_fw-la potest_fw-la architecture_n grow_v of_o 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of_o regular_n and_o mathematical_a music_n that_o he_o may_v temper_v well_o his_o baliste_n catapulte_n and_o scorpion_n etc_n etc_n moreover_o the_o brazen_a vessel_n which_o in_o theatre_n be_v place_v by_o mathematical_a order_n in_o ambry_n under_o the_o step_n and_o the_o diversity_n of_o the_o sound_n which_o the_o grecian_n call_v 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d be_v order_v according_a to_o musical_a symphony_n &_o harmony_n be_v distribute_v in_o the_o circuit_n by_o diatessaron_n diapente_fw-la and_o diapason_n that_o the_o convenient_a voice_n of_o the_o player_n sound_v when_o it_o come_v to_o these_o preparation_n make_v in_o order_n there_o be_v increase_v with_o that_o increase_v may_v come_v more_o clear_a &_o pleasant_a to_o the_o ear_n of_o the_o looker_n on_o etc_n etc_n and_o of_o astronomy_n be_v know_v the_o east_n west_n south_n and_o north._n the_o fashion_n of_o the_o heaven_n the_o aequinox_n the_o solstice_n and_o the_o course_n of_o the_o star_n which_o thing_n unleast_o one_o know_v he_o can_v not_o perceive_v any_o thing_n at_o all_o the_o reason_n of_o horology_n see_v therefore_o this_o ample_a science_n be_v garnish_v beautify_v and_o store_v with_o so_o many_o and_o sundry_a skill_n and_o knowledge_n i_o think_v that_o none_o can_v just_o account_v themselves_o architecte_v of_o the_o sudden_a but_o they_o only_o who_o from_o their_o child_n year_n ascend_v by_o these_o degree_n of_o knowledge_n be_v foster_v up_o with_o the_o attain_v of_o many_o language_n and_o art_n have_v win_v to_o the_o high_a tabernacle_n of_o archicture_n etc_n etc_n and_o to_o who_o nature_n have_v give_v such_o quick_a circumspection_n sharpness_n of_o wit_n and_o memory_n that_o they_o may_v be_v very_o absolute_o skilful_a in_o geometry_n astronomy_n music_n and_o the_o rest_n of_o the_o art_n mathematical_a such_o surmount_v and_o p●sse_v the_o call_n and_o state_n of_o architecte_n and_o be_v become_v mathematician_n mathematicien_n etc_n etc_n and_o they_o be_v find_v seldom_o as_o in_o time_n past_a be_v aristarchus_n samius_n philolaus_n and_o archytas_n tarentyne_n apollonius_n pergeus_n eratosthenes_n cyreneus_n archimedes_n and_o scopas_n syracusian_n who_o also_o leave_v to_o their_o posterity_n many_o engine_n and_o gnomonicall_a work_n by_o number_n and_o natural_a mean_n invent_v and_o declare_v thus_o much_o and_o the_o same_o word_n in_o sense_n in_o one_o only_a chapter_n of_o this_o incomparable_a architect_n vitrunius_n vitrunius_n shall_v you_o find_v and_o if_o you_o shall_v but_o take_v his_o book_n in_o your_o hand_n and_o slight_o look_v through_o it_o you_o will_v say_v straight_a way_n this_o be_v geometry_n arithmetic_n astronomy_n music_n anthropographie_n hydragogie_n horometrie_n etc_n etc_n and_o to_o conclude_v the_o storehouse_n of_o all_o workmanship_n now_o let_v we_o listen_v to_o our_o other_o judge_n our_o florentine_a leo_n baptista_n and_o narrow_o consider_v how_o he_o do_v determine_v of_o architecture_n sed_fw-la anteque_fw-la ultra_fw-la progrediar_fw-la etc_n etc_n but_o before_o i_o proceed_v any_o further_a say_v he_o i_o think_v that_o i_o ought_v to_o express_v what_o man_n i_o will_v have_v to_o be_v allow_v a_o architect_n for_o i_o will_v not_o bring_v in_o place_n a_o carpenter_n as_o though_o you_o may_v compare_v he_o to_o the_o chief_a master●_n of_o other_o artes._n for_o the_o hand_n of_o the_o carpenter_n be_v the_o architecte_n instrument_n architect_n but_o i_o will_v appoint_v the_o architect_n to_o be_v that_o man_n who_o have_v the_o skill_n by_o a_o certain_a and_o marvellous_a mean_n and_o way_n both_o in_o mind_n and_o imagination_n to_o determine_v and_o also_o in_o work_n to_o finish_v what_o work_v so_o ever_o by_o motion_n of_o weight_n and_o cupple_v and_o frame_a together_o of_o body_n may_v most_o apt_o be_v commodious_a for_o the_o worthy_a use_v of_o man_n and_o that_o he_o may_v be_v able_a to_o perform_v these_o thing_n he_o have_v need_n of_o attain_v and_o knowledge_n of_o the_o best_a and_o most_o worthy_a thing_n etc_n etc_n the_o whole_a feat_n of_o architecture_n in_o building_n consist_v in_o lineament_n and_o in_o frame_a and_o the_o whole_a power_n and_o skill_n of_o lineament_n tend_v to_o this_o that_o the_o right_n and_o absolute_a way_n may_v he_o

first_o set_v they_o also_o must_v needs_o be_v at_o the_o least_o commensurable_a in_o power_n the_o one_o to_o the_o other_o for_o forasmuch_o as_o their_o square_n be_v rational_a they_o shall_v be_v commensurable_a to_o the_o square_n of_o the_o rational_a line_n first_o set_v wherefore_o by_o the_o 12._o of_o this_o book_n they_o be_v also_o commensurable_a the_o one_o to_o the_o other_o wherefore_o their_o line_n be_v at_o the_o least_o commensurable_a in_o power_n the_o one_o to_o the_o other_o and_o it_o be_v possible_a also_o that_o they_o may_v be_v commensurable_a in_o length_n the_o one_o to_o the_o other_o for_o suppose_v that_o a_o be_v a_o rational_a li●e_z first_o set_v and_o let_v the_o line_n b_o be_v unto_o the_o same_o rational_a line_n a_o commensurable_a in_o power_n only_o that_o be_v incommensurable_a in_o length_n unto_o it_o let_v there_o be_v also_o a_o other_o line_n c_o commensurable_a in_o length_n to_o the_o line_n b_o which_o be_v possible_a by_o the_o principle_n of_o this_o book_n now_o by_o the_o 13._o of_o the_o ten_o it_o be_v manifest_a that_o the_o line_n c_o be_v incommensurable_a in_o length_n unto_o the_o line_n a._n but_o the_o square_n of_o the_o line_n a_o be_v commensurable_a to_o the_o square_n of_o the_o line_n b_o by_o supposition_n and_o the_o square_a of_o the_o line_n c_o be_v also_o commensurable_a to_o the_o square_n of_o the_o line_n b_o by_o supposition_n wherefore_o by_o the_o 12._o of_o this_o book_n the_o square_a of_o the_o line_n c_o be_v commensurable_a to_o the_o square_n of_o the_o line_n a._n wherefore_o by_o the_o definition_n the_o line_n c_o shall_v be_v rational_a commensurable_a in_o power_n only_o to_o the_o line_n a_o as_o also_o be_v the_o line_n b._n wherefore_o there_o be_v give_v two_o rational_a line_n commensurable_a in_o power_n only_o to_o the_o rational_a line_n first_o set_v and_o commensurable_a in_o length_n the_o one_o to_o the_o other_o here_o be_v to_o be_v note_v which_o thing_n also_o we_o before_o note_v in_o the_o definition_n that_o campane_n and_o other_o which_o follow_v he_o bring_v in_o these_o phrase_n of_o speech_n to_o call_v some_o line_n rational_a in_o power_n only_o cause_n and_o other_o some_o rational_a in_o length_n and_o in_o power_n which_o we_o can_v find_v that_o euclid_n ever_o use_v for_o these_o word_n in_o length_n and_o in_o power_n be_v never_o refer_v to_o rationality_n or_o irrationalitie_n but_o always_o to_o the_o commensurabilitie_n or_o incommensurablitie_n of_o line_n which_o pervert_v of_o word_n as_o be_v there_o declare_v have_v much_o increase_v the_o difficulty_n and_o obscureness_n of_o this_o book_n book_n and_o now_o i_o think_v it_o good_a again_o to_o put_v you_o in_o mind_n that_o in_o these_o proposition_n which_o follow_v we_o must_v ever_o have_v before_o our_o eye_n the_o rational_a line_n first_o set_v note_n unto_o which_o other_o line_n compare_v be_v either_o rational_a or_o irrational_a according_a to_o their_o commensurability_n or_o incommensurabilitie_n ¶_o the_o 16._o theorem_a the_o 19_o proposition_n a_o rectangle_n figure_n comprehend_v under_o right_a line_n commensurable_a in_o length_n be_v rational_a according_a to_o one_o of_o the_o foresay_a way_n be_v rational_a svppose_v that_o this_o rectangle_n figure_n ac_fw-la be_v comprehend_v under_o these_o right_a line_n ab_fw-la and_o bc_o be_v commensurable_a in_o length_n and_o rational_a according_a to_o one_o of_o the_o foresay_a way_n then_o i_o say_v that_o the_o superficies_n ac_fw-la be_v rational_a describe_v by_o the_o 46._o o●_n the_o first_o upon_o the_o line_n ab_fw-la a_o square_a ad._n construction_n wherefore_o that_o square_a ad_fw-la be_v rational_a by_o the_o definition_n demonstration_n and_o forasmuch_o as_o the_o line_n ab_fw-la be_v commensurable_a in_o length_n unto_o the_o line_n bc_o and_o the_o line_n ab_fw-la be_v equal_a unto_o the_o line_n bd_o therefore_o the_o line_n bd_o be_v commensurable_a in_o length_n unto_o the_o line_n bc._n and_o as_o the_o line_n bd_o be_v to_o the_o line_n bc_o so_o be_v the_o square_a dam_n to_o the_o superficies_n ac_fw-la by_o the_o first_o of_o the_o six_o but_o it_o be_v prove_v that_o the_o line_n bd_o be_v commensurable_a unto_o the_o line_n bc_o wherefore_o by_o the_o 10._o of_o the_o ten_o the_o square_a dam_n be_v commensurable_a unto_o the_o rectangle_n superficies_n ac_fw-la but_o the_o square_a dam_n be_v rational_a wherefore_o the_o rectangle_n superficies_n ac_fw-la also_o be_v rational_a by_o the_o definition_n a_o rectangle_n figure_n therefore_o comprehend_v under_o right_a line_n commensurable_a in_o length_n be_v rational_a accord_v to_o one_o of_o the_o foresay_a way_n be_v rational_a which_o be_v require_v to_o be_v prove_v proposition_n where_o as_o in_o the_o former_a demonstration_n the_o square_n be_v describe_v upon_o the_o less_o line_n we_o may_v also_o demonstrate_v the_o proposition_n if_o we_o describe_v the_o square_n upon_o the_o great_a line_n and_o that_o after_o this_o manner_n suppose_v that_o the_o rectangle_n superficies_n bc_o be_v contain_v of_o these_o unequal_a line_n ab_fw-la and_o ac_fw-la which_o let_v be_v rational_a commensurable_a the_o one_o to_o the_o other_o in_o length_n and_o let_v the_o line_n ac_fw-la be_v the_o great_a case_n and_o upon_o the_o line_n ac_fw-la describe_v the_o square_a dc_o then_o i_o say_v that_o the_o parallelogram_n bc_o be_v rational_a length_n for_o the_o line_n ac_fw-la be_v commensurable_a in_o length_n unto_o the_o line_n ab_fw-la by_o supposition_n and_o the_o line_n dam_n be_v equal_a to_o the_o line_n ac_fw-la wherefore_o the_o line_n dam_n be_v commensurable_a in_o length_n to_o the_o line_n ab_fw-la but_o what_o proportion_n the_o line_n dam_n have_v to_o the_o line_n ab_fw-la the_o same_o have_v the_o square_a dc_o to_o the_o para●lelogramme_n c●_n by_o the_o first_o of_o the_o six_o wherefore_o by_o the_o 10._o of_o this_o book_n the_o square_a dc_o be_v commensurable_a to_o the_o parallelogram_n cb._n but_o it_o be_v manifest_a that_o the_o square_a dc_o be_v rational_a for_o that_o it_o be_v the_o square_a of_o a_o rational_a line_n namely_o ac_fw-la wherefore_o by_o the_o definition_n the_o parallelogram_n also_o cb_o be_v rational_a moreover_o forasmuch_o as_o those_o two_o former_a demonstration_n seem_v to_o speak_v of_o that_o parallelogram_n which_o be_v make_v of_o two_o line_n of_o which_o any_o one_o may_v be_v the_o li●e_z first_o set_v which_o be_v call_v the_o first_o rational_a line_n from_o which_o we_o say_v ought_v to_o be_v take_v the_o measure_n of_o the_o other_o line_n compare_v unto_o it_o and_o the_o other_o be_v commensurable_a in_o length_n to_o the_o same_o first_o rational_a line_n length_n which_o be_v the_o first_o kind_n of_o rational_a line_n commensurable_a in_o length_n i_o think_v it_o good_a here_o to_o set_v a_o other_o case_n of_o the_o other_o kind_n of_o rational_a line_n of_o line_n i_o say_v rational_a commensurable_a in_o length_n compare_v to_o a_o other_o rational_a line_n first_o set_v to_o declare_v the_o general_a truth_n of_o this_o theorem_a and_o that_o we_o may_v see_v that_o this_o particle_n according_a to_o any_o of_o the_o foresay_a way_n be_v not_o here_o in_o vain_a put_v now_o then_o suppose_v first_o a_o rational_a line_n ab_fw-la let_v there_o be_v also_o a_o parallelogram_n cd_o contain_v under_o the_o line_n ce_fw-fr and_o ed_z which_o line_n let_v be_v rational_a that_o be_v commensurable_a in_o length_n to_o the_o ●irst_n rational_a line_n propound_v ab_fw-la howbeit_o let_v those_o two_o line_n ce_fw-fr and_o ed_z be_v diverse_a and_o unequal_a line_n unto_o the_o first_o rational_a line_n ab_fw-la then_o i_o say_v that_o the_o parallelogram_n cd_o be_v rational_a case_n describe_v the_o square_a of_o the_o line_n de_fw-fr which_o let_v be_v df._n first_o it_o be_v manifest_a by_o the_o 12._o of_o this_o book_n that_o the_o line_n ce_fw-fr &_o ed_z be_v commensurable_a in_o length_n the_o one_o to_o the_o other_o for_o either_o of_o they_o be_v suppose_v to_o be_v commensurable_a in_o length_n unto_o the_o line_n ab_fw-la but_o the_o line_n ed_z be_v equal_a to_o the_o line_n ef._n wherefore_o the_o line_n ce_fw-fr be_v commensurable_a in_o length_n to_o the_o line_n bf_o but_o 〈◊〉_d the_o line_n ce_fw-fr be_v ●o_o the_o line_n ●_o f_o ●o_o be_v the_o parallelogram_n cd_o to_o the_o square_a df_o by_o the_o first_o of_o the_o six_o wherefore_o by_o the_o 10._o of_o this_o book_n the_o parallelogram_n cd_o shall_v be_v commensurable_a to_o the_o square_a df._n but_o the_o square_a df_o be_v commensurable_a to_o the_o square_n of_o the_o line_n ab_fw-la which_o be_v the_o first_o rational_a line_n propound_v wherefore_o by_o the_o 12._o of_o this_o book_n the_o parallelogram_n cd_o be_v commensurable_a to_o the_o square_n of_o the_o line_n ab_fw-la but_o the_o square_n of_o