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Word A Word B Word C Word D Occurrence Frequency Band MI MI Band Prominent
earth_n air_n body_n element_n 4,987 5 9.8633 5 true
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ID Title Author Corrected Date of Publication (TCP Date of Publication) STC Words Pages
A43489 An astrological discourse with mathematical demonstrations proving the powerful and harmonical influence of the planets and fixed stars upon elementary bodies in justification of the validity of astrology : together with an astrological judgment upon the great conjunction of Saturn & Jupiter, 1603 / written by that worthy, learned gentleman, Sir Christopher Heydon, Knight ; and now published by Nicholas Fiske ... Heydon, Christopher, Sir, d. 1623.; Fiske, Nicholas. 1650 (1650) Wing H1663; ESTC R16056 46,071 129

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they_o more_o lift_v up_o above_o the_o superficies_n of_o the_o earth_n then_o 236._o perch_n wherefore_o admit_v g_o f_o which_o be_v the_o part_n of_o the_o perpendicular_a line_n that_o penetrate_v the_o gross_a air_n to_o be_v three_o mile_n and_o f_o c_o the_o semidiamiter_n of_o the_o earth_n to_o be_v 3436_o mile_n and_o the_o summer_n and_o winter_n height_n as_o before_o it_o will_v be_v manifest_a by_o supputation_n that_o whereas_o k_o f_o shall_v pierce_v but_o four_o mile_n or_o thereabouts_o m_o f_o shall_v pass_v twelve_o and_o somewhat_o more_o so_o that_o the_o opposition_n and_o impediment_n which_o the_o sunbeam_n do_v suffer_v in_o winter_n be_v triple_a to_o that_o which_o they_o feel_v in_o their_o summer_n passage_n and_o do_v therefore_o weaken_v the_o sun_n force_n in_o that_o preparation_n and_o be_v add_v to_o the_o rest_n of_o the_o cause_n before_o specify_v do_v demonstrative_o prove_v all_o together_o consider_v that_o the_o heat_n in_o summer_n excel_v 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sun_n
and_o seem_v to_o move_v by_o little_a and_o little_a unto_o the_o centre_n of_o his_o globe_n and_o whereunto_o shall_v we_o refer_v the_o illumination_n and_o extinguish_n of_o the_o comet_n and_o new_a star_n which_o in_o this_o our_o age_n have_v be_v observe_v to_o flame_n in_o heaven_n itself_o do_v they_o not_o all_o demonstrative_o prove_v generation_n and_o corruption_n in_o heaven_n true_a it_o be_v that_o by_o reason_n of_o our_o remote_a distance_n from_o the_o heavenly_a sensible_a sphere_n we_o can_v by_o sense_n attain_v to_o every_o particular_a alteration_n which_o happen_v there_o and_o therefore_o aristotle_n neither_o be_v acquaint_v with_o the_o world_n creation_n nor_o in_o former_a age_n find_v any_o alteration_n in_o heaven_n but_o still_o receive_v by_o tradition_n that_o the_o planet_n the_o fix_a star_n their_o motion_n and_o the_o medium_n in_o which_o they_o be_v remain_v the_o same_o while_o in_o the_o mean_a time_n the_o earth_n and_o element_n be_v daily_o subject_a unto_o divers_a change_n familiar_a to_o our_o eye_n conclude_v from_o experience_n heaven_n to_o be_v privilege_v from_o almutation_n but_o the_o element_n to_o be_v obnoxious_a thereunto_o but_o can_v either_o aristotle_n be_v inform_v that_o now_o this_o latte●_z age_n more_o diligent_a than_o the_o former_a hat●_n observe_v new_a body_n in_o heaven_n or_o be_v it_o possible_a that_o our_o mortal_a eye_n may_v from_o the_o heaven_n behold_v the_o earth_n as_o now_o from_o the_o earth_n we_o behold_v they_o i_o very_o be_o persuade_v that_o both_o the_o philosopher_n will_v change_v his_o opinion_n and_o that_o we_o shall_v from_o heaven_n behold_v as_o little_a alteration_n in_o the_o globe_n of_o the_o earth_n as_o now_o we_o observe_v in_o heaven_n he_o that_o list_v to_o read_v more_o of_o this_o matter_n let_v he_o peruse_v kepler_n himself_o cap._n 23._o de_fw-la nova_fw-la stella_fw-la where_o he_o do_v purposely_o treat_v of_o this_o subject_a and_o prove_v by_o five_o particular_a reason_n that_o the_o matter_n of_o heaven_n be_v alterable_a which_o if_o it_o be_v true_a then_o be_v their_o argument_n from_o the_o consequence_n of_o alteration_n of_o no_o force_n against_o the_o first_o quality_n in_o heaven_n but_o rather_o to_o be_v retort_v upon_o themselves_o in_o this_o manner_n that_o because_o there_o be_v a_o generation_n and_o alteration_n demonstrative_o observe_v ergo_fw-la the_o first_o quality_n may_v likewise_o be_v affirm_v there_o as_o fit_a instrument_n of_o these_o mutation_n but_o nevertheless_o leave_v this_o doctrine_n in_o suspense_n because_o it_o be_v new_a yet_o be_v not_o our_o cause_n so_o needy_a but_o that_o i_o dare_v otherwise_o undertake_v to_o prove_v the_o consequent_a of_o the_o reason_n to_o be_v false_a for_o that_o themselves_o the_o star_n may_v very_o well_o be_v justify_v to_o have_v divers_a and_o contrary_a virtue_n without_o admit_v any_o passion_n in_o the_o heavenly_a body_n for_o astra_fw-la agere_fw-la quod_fw-la in_fw-la seipsis_fw-la non_fw-la est_fw-la be_v no_o rare_a maxim_n among_o the_o learned_a some_o of_o who_o use_v this_o distinction_n between_o the_o differ_a manner_n of_o these_o quality_n in_o the_o star_n otherwise_o then_o in_o the_o element_n by_o suppose_v they_o in_o the_o first_o only_o effective_a and_o in_o the_o latter_a subjective_a because_o as_o they_o will_v have_v it_o the_o star_n be_v not_o actual_o hot_a or_o cold_a but_o virtualiter_fw-la that_o be_v they_o have_v a_o certain_a power_n to_o produce_v heat_n and_o cold_a and_o the_o rest_n of_o the_o quality_n in_o the_o other_o body_n out_o of_o themselves_o which_o nevertheless_o be_v not_o in_o themselves_o but_o for_o my_o own_o part_n i_o free_o confess_v not_o well_o to_o conceive_v this_o subtlety_n though_o it_o be_v scaliger_n how_o the_o sun_n not_o be_v habitual_o hot_a yet_o nevertheless_o can_v burn_v rather_o to_o go_v more_o direct_o to_o the_o work_n matter_n i_o hold_v the_o efficacy_n of_o the_o star_n to_o proceed_v from_o that_o natural_a virtue_n which_o be_v original_o inherent_a in_o themselves_o which_o notwithstanding_o shall_v never_o the_o more_o subject_a these_o excellent_a body_n to_o alteration_n for_o as_o the_o loadstone_n more_o precious_a than_o any_o diamond_n have_v in_o many_o point_n a_o singular_a affinity_n with_o heaven_n so_o it_o do_v not_o fail_v to_o lend_v we_o a_o most_o lively_a example_n how_o contrary_n may_v be_v find_v in_o the_o same_o natural_a body_n without_o destruction_n thereof_o for_o what_o can_v be_v more_o contrary_a than_o attraction_n and_o repulsion_n yet_o if_o the_o needle_n be_v touch_v with_o the_o north_n pole_n of_o the_o loadstone_n it_o be_v certain_a that_o as_o that_o part_n will_v attract_v the_o same_o so_o the_o contrary_a pole_n or_o end_n will_v make_v it_o fly_v away_o yet_o without_o any_o danger_n or_o passion_n in_o the_o stone_n itself_o why_o shall_v we_o not_o therefore_o believe_v that_o as_o heaven_n be_v far_o more_o excellent_a than_o these_o sublunary_a body_n so_o it_o shall_v be_v endow_v with_o all_o the_o virtue_n which_o be_v find_v here_o beneath_o in_o a_o far_o more_o excellent_a manner_n and_o without_o any_o prejudice_n to_o the_o purity_n of_o the_o matter_n whereof_o it_o consist_v for_o if_o the_o matter_n be_v not_o proportion_v unto_o the_o power_n of_o the_o agent_n no_o effect_n can_v follow_v but_o even_o by_o the_o doctrine_n of_o the_o peripatetic_n such_o be_v the_o matter_n of_o heaven_n consist_v of_o a_o simple_a and_o five_o essence_n free_a from_o all_o passion_n ergo_fw-la although_o we_o do_v admit_v contrary_a quality_n to_o flow_v from_o the_o star_n yet_o shall_v this_o work_v no_o alteration_n because_o the_o matter_n of_o heaven_n be_v not_o a_o apt_a subject_n for_o this_o purpose_n and_o for_o this_o reason_n we_o may_v not_o consider_v these_o quality_n as_o they_o be_v find_v in_o the_o element_n or_o mix_v body_n who_o matter_n be_v passive_a but_o rather_o as_o they_o be_v inherent_a in_o a_o simple_a and_o pure_a essence_n privilege_v from_o corruption_n be_v for_o this_o cause_n call_v by_o aristotle_n agentes_fw-la {non-roman}_o {non-roman}_o {non-roman}_o {non-roman}_o {non-roman}_o thereby_o to_o distinguish_v they_o from_o those_o inferior_a thing_n which_o be_v mutual_o subject_a to_o action_n and_o passion_n because_o they_o consist_v of_o elementary_a matter_n i_o doubt_v not_o therefore_o but_o by_o this_o which_o have_v be_v say_v it_o do_v sufficient_o appear_v that_o in_o this_o controversy_n between_o the_o star_n and_o the_o element_n these_o celestial_a and_o pure_a light_n have_v obtain_v priority_n as_o first_o endue_v by_o god_n with_o natural_a power_n by_o their_o motion_n light_n and_o secret_a influence_n to_o excite_v and_o stir_v up_o heat_n cold_a moisture_n and_o siccity_n in_o these_o sublunary_a body_n subordinate_a unto_o they_o according_a to_o their_o several_a virtue_n chap._n xii_o the_o cause_n why_o the_o cold_a in_o winter_n be_v great_a in_o february_n prove_v to_o proceed_v from_o the_o different_a point_n of_o heaven_n who_o diversity_n be_v show_v wherefore_o now_o to_o return_v from_o whence_o i_o digress_v have_v thus_o prepare_v the_o way_n i_o may_v the_o more_o bold_o proceed_v and_o with_o better_a assurance_n according_a to_o the_o rule_n of_o astrology_n ascribe_v this_o increase_n of_o cold_a which_o common_o happen_v about_o february_n partly_o unto_o the_o complexion_n of_o that_o sign_n which_o the_o sun_n then_o pass_v partly_o to_o the_o apparent_a rise_n and_o set_v of_o those_o constellation_n which_o ordinary_o agree_v to_o this_o month_n and_o first_o concerning_o that_o part_n of_o heaven_n which_o the_o sun_n then_o hold_v we_o be_v to_o know_v that_o it_o be_v the_o dominion_n of_o saturn_n who_o influence_n excel_v in_o excite_v cold_a as_o in_o that_o which_o follow_v i_o hope_v infallible_o to_o demonstrate_v the_o same_o be_v diametrical_o opposite_a unto_o the_o royal_a palace_n of_o the_o sun_n which_o alone_o to_o those_o that_o repose_v in_o the_o principle_n deliver_v by_o astrologer_n be_v sufficient_a reason_n in_o this_o case_n but_o if_o any_o there_o be_v that_o do_v doubt_n thereof_o and_o whether_o the_o matter_n of_o heaven_n may_v admit_v variety_n as_o well_o as_o the_o star_n i_o doubt_v not_o but_o to_o satisfy_v he_o also_o partly_o by_o reason_n partly_o by_o undoubted_a exper●ence_n for_o first_o whereas_o we_o see_v the_o form_n of_o divers_a heaven_n thing_n in_o this_o sublunary_a world_n apparent_o to_o consent_n both_o with_o certain_a star_n and_o with_o the_o particular_a region_n of_o heaven_n reason_n teach_v we_o that_o this_o can_v proceed_v from_o no_o other_o probable_a cause_n in_o nature_n then_o from_o the_o sympathy_n or_o agreeable_a temperature_n of_o their_o substance_n and_o that_o one_o or_o two_o example_n may_v stand_v for_o many_o we_o see_v the_o north_n part_n of_o heaven_n particular_o
12._o 7._o oedipus_n or_o a_o resolver_n be_v a_o clew_n that_o lead_v to_o the_o chief_a secret_n and_o true_a resolution_n of_o ammorus_a natural_a moral_a and_o political_a problem_n by_o g._n m._n 12._o 8._o the_o celestial_a lamp_n enlighten_v every_o distress_a soul_n from_o the_o depth_n of_o everlasting_a darkness_n to_o the_o height_n of_o eternal_a light_n by_o tho_n fettisplace_v 12._o choice_n poem_n with_o several_a excellent_a tragedy_n and_o comedy_n 1._o fons_fw-la lachrymarum_fw-la or_o a_o fountain_n of_o tear_n from_o whence_o do_v flow_v england_n complaint_n jeremiah_n lamentation_n with_o a_o elegy_n upon_o that_o son_n of_o valour_n sir_n charles_n lucas_n by_o john_n quarls_n 8._o 2._o nocturnal_a locubration_n or_o meditation_n divine_a and_o moral_a with_o epigram_n and_o epitaph_n by_o robert_n chamberlin_n 3._o the_o unfortunate_a mother_n a_o tragedy_n by_o thomas_n nabbs_n 4._o the_o rebellion_n of_o comedy_n by_o tho_n raulins_n 5._o the_o tragedy_n of_o messalina_n by_o nathaniel_n richards_n 8._o excellent_a piece_n of_o divinity_n of_o certain_a orthodox_a divine_n with_o other_o sermon_n viz._n 1._o the_o remedy_n of_o discontentment_n or_o a_o treatise_n of_o contentation_n in_o whatsoever_o condition_n fit_a for_o these_o sad_a and_o trouble_a time_n by_o the_o right_a reverend_a father_n in_o god_n joseph_n hall_n late_a bishop_n of_o exon_n and_o norwich_n 12._o 2._o the_o grand_a sacrilege_n of_o the_o church_n of_o rome_n in_o take_v away_o the_o sacred_a cup_n from_o the_o laity_n at_o the_o lord_n table_n by_o the_o late_a reverend_a daniel_n feat_n doctor_n in_o divinity_n 4._o 3._o the_o cause_n and_o cure_n of_o ignorance_n error_n enmity_n athiesm_n and_o profaneness_n or_o a_o most_o hopeful_a way_n to_o grace_n and_o salvation_n by_o r._n young_n 8._o 4._o a_o bridle_n for_o the_o time_n tend_v to_o still_o the_o murmur_n to_o settle_v the_o waver_n to_o stay_v the_o wander_v to_o strengthen_v the_o faint_v by_o john_n brinsley_n minister_n of_o god_n word_n at_o yarmouth_n 5._o comfort_n against_o the_o fear_n of_o death_n be_v short_a meditation_n of_o that_o precious_a gentlewoman_n mrs_n anne_n skelton_n of_o norwich_n wherein_o be_v several_a evidence_n of_o the_o work_n of_o grace_n in_o she_o own_o soul_n which_o be_v the_o stay_n of_o her_o heart_n against_o the_o fear_n of_o death_n by_o john_n collings_n of_o norwich_n 6._o jacob_n seed_n or_o the_o excellency_n of_o seek_v god_n by_o prayer_n by_o jeremiah_n burrough_n minister_n of_o the_o gospel_n to_o the_o two_o great_a congregation_n about_o london_n stepney_n and_o cripplegate_n 12._o 10._o the_o zealous_a magistrate_n a_o sermon_n by_o thomas_n trescot_n 11._o britania_n rediviva_fw-la or_o a_o sovereign_a remedy_n to_o cure_v a_o sick_a commonwealth_n in_o a_o sermon_n preach_v in_o the_o minster_n at_o york_n before_o the_o judge_n at_o the_o assize_n aug._n 9_o 1649._o by_o john_n shaw_n min._n of_o hull_n 9_o the_o prince_n royal_a or_o a_o sermon_n preach_v in_o the_o minster_n in_o york_n before_o the_o judge_n march_n 24._o 1650._o by_o john_n shaw_n minister_n of_o hull_n 10._o anatomy_n of_o mortality_n divide_v into_o eight_o head_n 1._o the_o certainty_n of_o death_n 2._o meditation_n of_o death_n 3._o preparation_n for_o death_n 4._o the_o right_a behaviour_n in_o death_n 5._o the_o comfort_n in_o our_o own_o death_n 6._o the_o comfort_n against_o the_o death_n of_o friend_n 7._o the_o case_n wherein_o its_o lawful_a and_o unlawful_a 8._o the_o glorious_a estate_n of_o god_n child_n after_o death_n by_o george_n strand_n errata_fw-la read_v page_n 4._o li._n 2._o be_v above_o a._n p._n 13._o li._n 15._o proportion_n l._n 24._o operation_n p._n 22._o l._n 26._o this_o p._n 23._o l._n 6._o with_o the_o quality_n p._n 24._o l._n 8._o so_o far_o p._n 27._o l._n 5._o operation_n l._n 7._o ardour_n p._n 48._o l._n 7._o the_o general_a p._n 50._o l._n 6._o historiarum_fw-la commentarios_fw-la l._n 23._o sine_fw-la p._n 54._o l._n 8._o this_o p._n 55._o l._n 9_o make_v like_o p._n 58._o l._n 25._o also_o in_o p._n 60._o l._n 12._o of_o these_o l._n 28._o to_o the_o true_a p._n 63._o l._n 23._o the_o same_o l._n 25._o cauda_fw-la cygni_fw-la p._n 66._o l._n 17._o be_v so_o p._n 67._o l._n 14._o passion_n p._n 70._o l._n 26._o by_o r._n of_o p._n 72._o l._n 26._o their_o r._n these_o p._n 74._o l._n 22._o ark_n p._n 75._o l._n 1._o i_o r._n we_o p._n 78._o l._n 4._o of_o r._n as_o l._n 6._o constitute_v p._n 79._o l._n 22._o of_o the_o circum_fw-la p._n 80._o l._n 5._o that_o either_o p._n 99_o l._n 19_o your_o r._n their_o p._n 102._o l._n 22._o happen_v chap._n i._n of_o winter_n not_o without_o great_a judgement_n do_v pliny_n affirm_v 8_o those_o that_o first_o understand_v the_o obliquity_n of_o the_o zodiac_n rerum_fw-la fores_fw-la aperuisse_fw-la for_o beside_o that_o the_o find_v out_o hereof_o prepare_v the_o way_n first_o to_o find_v out_o the_o periodical_a motion_n of_o the_o planet_n the_o philosopher_n himself_o teach_v we_o that_o the_o variety_n generation_n and_o corruption_n of_o all_o thing_n depend_v chief_o hereupon_o and_o common_a experience_n drive_v we_o to_o confess_v the_o access_n and_o recess_n of_o the_o sun_n unto_o the_o four_o cardinal_n point_n of_o this_o circle_n to_o be_v the_o most_o general_a and_o assure_a cause_n of_o the_o year_n successive_a alteration_n upon_o this_o ground_n i_o affirm_v the_o winter_n quarter_n to_o take_v his_o true_a beginning_n at_o what_o time_n the_o sun_n make_v his_o entrance_n into_o the_o tropic_a of_o ♑_o have_v attain_v his_o great_a declination_n southward_o from_o our_o zenith_n or_o vertical_a point_n from_o whence_o divers_a impediment_n evident_a in_o nature_n do_v follow_v which_o bereave_v our_o septentrional_a part_n of_o that_o heat_n and_o vigour_n wherewith_o at_o other_o time_n the_o sun_n be_v near_o and_o more_o elevate_v do_v preserve_v and_o cherish_v the_o element_n and_o all_o thing_n compose_v of_o they_o whether_o vegetable_a or_o sensative_a chap._n ii_o the_o first_o reason_n of_o the_o difference_n between_o the_o heat_n and_o light_n in_o summer_n and_o winter_n draw_v from_o the_o diversity_n of_o stay_n above_o the_o horizon_n winter_n for_o whereas_o first_o of_o all_o continuance_n of_o action_n do_v necessary_o add_v force_n of_o operation_n to_o all_o natural_a agent_n it_o come_v to_o pass_v in_o winter_n by_o reason_n of_o the_o sun_n remote_a position_n that_o his_o continuance_n above_o the_o horizon_n be_v short_a and_o his_o absence_n under_o the_o same_o long_a thereby_o now_o cause_v the_o short_a day_n and_o long_a night_n for_o example_n the_o elevation_n of_o the_o pole_n at_o the_o honourable_a city_n of_o london_n be_v observe_v to_o be_v 51._o g_o 32′_o and_o the_o great_a declination_n of_o the_o sun_n in_o this_o our_o age_n be_v 23._o g_o 31′_n 30″_n therefore_o in_o the_o winter_n solstice_n the_o sun_n finish_v his_o diurnal_a ark_n to_o they_o of_o this_o city_n in_o 7_o hour_n 34_o minute_n and_o for_o this_o consideration_n can_v heat_v the_o air_n here_o but_o a_o little_a while_n see_v the_o same_o be_v not_o one_o three_o of_o a_o natural_a day_n at_o which_o time_n nevertheless_o he_o remain_v hide_v under_o the_o earth_n more_o than_o twice_o so_o long_o and_o so_o cease_v from_o calefaction_n impart_v no_o benefit_n of_o his_o light_n and_o heat_n to_o we_o at_o all_o whereas_o in_o summer_n the_o sun_n persist_v 16_o whole_a hour_n and_o 26_o minute_n in_o operation_n not_o cease_v above_o seven_o hour_n and_o a_o half_a from_o action_n by_o reason_n of_o his_o absence_n under_o the_o horizon_n wherefore_o look_v what_o proportion_n 7_o hour_n 34_o minute_n have_v to_o 16_o how_o 26_o min_fw-fr the_o like_a difference_n there_o shall_v be_v betwixt_o the_o sun_n operation_n in_o summer_n and_o winter_n in_o respect_n of_o his_o diverse_a stay_n above_o the_o horizon_n which_o not_o to_o be_v too_o scrupulous_a be_v a_o double_a proportion_n the_o one_o to_o the_o other_o chap._n iii_o the_o second_o reason_n of_o the_o foresay_a difference_n draw_v from_o the_o difference_n of_o union_n in_o the_o beam_n second_o in_o the_o work_n of_o the_o star_n union_n of_o beam_n be_v a_o thing_n regard_v cause_v as_o of_o special_a consequence_n but_o it_o be_v clear_a to_o they_o that_o have_v any_o insight_n in_o the_o optic_n that_o in_o winter_n the_o union_n of_o the_o beam_n incident_a with_o the_o beam_n reflect_v be_v not_o comparable_a with_o that_o which_o the_o great_a altitude_n of_o the_o sun_n cause_v in_o summer_n and_o therefore_o the_o effect_n depend_v upon_o this_o union_n must_v accordly_n be_v increase_v or_o diminish_v in_o proportion_n that_o this_o be_v true_a diagram_n suppose_v a_o b_o in_o the_o first_o figure_n and_o c_o d_o in_o the_o
second_o to_o be_v two_o equal_a part_n of_o the_o earth_n superficies_n whereupon_o the_o beam_n of_o the_o sun_n e_o a_o in_o winter_n and_o g_o c_o in_o summer_n do_v fall_v e_o a_o in_o the_o winter_n solstice_n make_v a_o angle_n with_o the_o plain_a of_o the_o horizon_n h_o a_o b_o of_o 14._o gr_o 56′_n 30″_n viz._n e_o a_o h_o or_o e_o b_o h_o be_v the_o meridian_n altitude_n of_o the_o sun_n at_o london_n upon_o that_o day_n likewise_o let_v g_o c_o k_o or_o g_o d_o k_o be_v admit_v to_o irradiate_v the_o earth_n at_o the_o high_a meridian_n altitude_n in_o the_o summer_n solstice_n at_o a_o angle_n of_o 61_o gr._n 59′_n 30″_n then_o forasmuch_o as_o by_o the_o principle_n of_o the_o optic_n the_o angle_n of_o incidence_n and_o reflection_n be_v evermore_o equal_a a_o f_o in_o the_o first_o figure_n and_o c_o m_o in_o the_o second_o be_v the_o reflect_a beam_n e_o f_o and_o g_o m_n shall_v be_v reverberate_v from_o a_o b_o and_o c_o d_o at_o like_o angle_n with_o their_o proper_a incident_n which_o be_v true_a it_o be_v also_o evident_a that_o because_o the_o inward_a angle_n at_o c_o and_o d_o be_v great_a than_o the_o inward_a angle_n at_o a_o and_o b_o the_o triangle_n c_o l_o d_o shall_v of_o necessity_n be_v great_a than_o the_o triangle_n a_o i_o b._n and_o forasmuch_o as_o the_o union_n of_o the_o beam_n incident_a with_o the_o reflect_v happen_v within_o the_o limit_n of_o these_o triangle_n therefore_o of_o consequence_n the_o union_n c_o l_o d_o in_o summer_n be_v so_o much_o great_a than_o the_o union_n of_o a_o i_o b_o in_o winter_n as_o the_o area_n of_o the_o one_o do_v exceed_v the_o area_n of_o the_o other_o which_o be_v about_o or_o rather_o somewhat_o above_o six_o to_o one_o and_o be_v join_v to_o the_o former_a difference_n as_o be_v usual_a in_o addition_n of_o proportion_n prove_v that_o this_o difference_n of_o union_n together_o with_o the_o sun_n stay_v in_o summer_n cause_v the_o heat_n to_o exceed_v that_o which_o we_o receive_v in_o winter_n above_o twelve_o time_n chap._n iv._o the_o three_o reason_n of_o the_o former_a diversity_n proceed_v from_o the_o differ_a quantity_n of_o beam_n a_o three_o reason_n of_o the_o difference_n and_o beam_n diminution_n of_o heat_n in_o winter_n proceed_v from_o the_o small_a quantity_n of_o beam_n which_o then_o illustrate_v the_o earth_n superficies_n in_o comparison_n of_o that_o which_o the_o sun_n send_v down_o to_o we_o in_o summer_n for_o as_o the_o specifical_a quality_n of_o the_o rest_n of_o the_o star_n accompany_v their_o light_n so_o it_o be_v also_o true_a that_o the_o heat_n of_o the_o sun_n be_v convey_v unto_o we_o by_o his_o beam_n wherefore_o the_o few_o the_o beam_n be_v which_o fall_n upon_o the_o horizon_n the_o less_o also_o shall_v be_v the_o heat_n and_o forasmuch_o as_o in_o winter_n the_o sun_n dart_v they_o more_o oblique_a than_o in_o summer_n therefore_o it_o be_v evident_a that_o there_o shall_v not_o so_o many_o beam_n fall_v upon_o the_o plain_a of_o the_o horizon_n at_o the_o oblique_a position_n of_o the_o sun_n in_o winter_n as_o when_o he_o approach_v nigh_a to_o a_o perpendicularity_n in_o summer_n to_o demonstrate_v this_o diagram_n suppose_v q_o o_o and_o q_o p_o to_o be_v two_o divers_a superficies_n of_o the_o earth_n upon_o which_o the_o same_o beam_n a_o q_o do_v shine_v diverse_o that_o be_v perpendicular_o upon_o the_o superficies_n q_o o_o but_o oblique_o upon_o the_o superficies_n q_o p._n then_o i_o say_v that_o the_o triangle_n q_o o_o p_o who_o angle_n at_o o_o be_v by_o supposition_n a_o right_a angle_n the_o side_n q_o p_o which_o subtend_v the_o say_a angle_n must_v be_v great_a than_o the_o side_n q_o o_o by_o the_o 18_o of_o the_o first_o of_o euclid_n and_o yet_o from_o hence_o we_o see_v it_o follow_v that_o all_o the_o light_n which_o be_v shed_v upon_o q_o p_o the_o oblique_a but_o great_a super●…cies_n shall_v fall_v notwithstanding_o upon_o q_o o_o the_o less_o but_o direct_o subject_a to_o the_o beam_n a_o q._n if_o moreover_o we_o take_v a_o ●pace_n q_o v_o in_o the_o great_a superficies_n which_o by_o construction_n shall_v be_v equal_a to_o q_o o_o and_o from_o n_o to_o v_o draw_v down_o a_o parallel_n to_o the_o line_n a_o o_o p_o it_o be_v evident_a that_o the_o beam_n n_o q_o wherewith_o the_o superficies_n q_o v_o be_v illuminate_v be_v but_o a_o part_n of_o the_o beam_n a_o q._n for_o which_o reason_n the_o superficies_n q_o v_o shall_v participate_v but_o part_n also_o of_o that_o heat_n which_o be_v communicate_v to_o the_o superficies_n q_o o_o be_v direct_o subject_a to_o the_o beam_n q_o a_o which_o also_o be_v manifest_a enough_o even_o by_o the_o precedent_a figure_n where_o the_o winter_n beam_n e_o a_o compare_v with_o the_o summer_n beam_n g_o d_o be_v next_o hand_n in_o proportion_n but_o as_o one_o to_o four_o by_o reason_n whereof_o the_o sun_n hardly_o impart_v ¼_o of_o that_o light_n and_o heat_n to_o we_o at_o his_o meridional_a height_n in_o the_o winter_n solstice_n which_o we_o feel_v from_o his_o high_a position_n in_o the_o summer_n this_o diminution_n consider_v with_o the_o former_a impediment_n leave_v we_o not_o above_o the_o forty_o eight_o part_n of_o that_o heat_n in_o winter_n which_o we_o receive_v in_o summer_n from_o the_o sun_n chap._n v._o the_o four_o difference_n cause_v by_o the_o depth_n or_o diverse_a crassitude_n of_o the_o air_n by_o which_o the_o beam_n pass_v neither_o can_v we_o be_v right_o say_v to_o air_n have_v the_o full_a fruition_n of_o this_o portion_n of_o heat_n in_o winter_n by_o reason_n that_o the_o crassitude_n or_o thickness_n of_o the_o air_n be_v then_o more_o object_n to_o the_o sun_n oblique_a beam_n then_o in_o summer_n and_o do_v thereby_o resist_v and_o hinder_v they_o more_o now_o then_o in_o summer_n for_o proof_n hereof_o diagram_n let_v d_o f_o h_o represent_v the_o superficies_n of_o the_o earth_n i_o g_o n_o the_o convex_a superficies_n of_o the_o cloudy_a or_o vaporous_a region_n and_o suppose_v the_o sun_n to_o shine_v upon_o f_o the_o place_n of_o our_o habitation_n from_o three_o several_a point_n z_o a_o b_o z_o be_v the_o vertical_a point_n over_o our_o head_n a_o the_o sun_n summer_n height_n b_o his_o altitude_n in_o winter_n as_o before_o be_v express_v so_o z_o f_o a_o f_o and_o b_o f_o shall_v be_v the_o sun_n beam_n part_v whereof_o viz._n g_o f_o k_n f_o and_o m_o f_o we_o see_v be_v in_o a_o sort_n obscure_v hinder_v and_o resist_v by_o the_o vaporous_a air_n but_o now_o for_o as_o much_o as_o by_o the_o 7_o of_o the_o 3_o of_o euclid_n g_o f_o be_v short_a than_o k_n f_o and_o k_n f_o then_o m_n f_o therefore_o the_o sun_n shall_v of_o necessity_n feel_v less_o impediment_n in_o the_o zenith_n at_o z_o then_o at_o a_o and_o by_o consequence_n at_o a_o then_o at_o b._n because_o still_o the_o further_o the_o sun_n be_v remove_v from_o the_o zenith_n the_o long_o be_v the_o passage_n of_o the_o sunbeam_n through_o the_o opposite_a air_n now_o to_o attain_v geometrical_o to_o the_o proportion_n of_o the_o sun_n debilitate_a force_n through_o this_o impediment_n we_o be_v first_o to_o agree_v how_o deep_a or_o thick_o this_o cloudy_a region_n of_o the_o air_n that_o ●efringeth_v the_o sunbeam_n may_v be_v which_o our_o late_a artist_n to_o who_o great_a credit_n be_v to_o be_v give_v as_o they_o have_v be_v more_o conversant_a and_o curious_a in_o the_o observation_n hereof_o than_o their_o predecessor_n do_v all_o agree_v not_o to_o extend_v three_o english_a mile_n in_o the_o perpendicular_a g_o f_o as_o be_v plain_a unto_o live_v they_o that_o be_v acquaint_v with_o the_o disputation_n of_o tycho_n rothman_n kepler_n and_o other_o for_o we_o must_v here_o distinguish_v between_o the_o matter_n of_o the_o crepusculum_fw-la and_o this_o vaporous_a air_n which_o be_v so_o little_o elevate_v above_o the_o earth_n that_o hardly_o we_o may_v live_v upon_o the_o top_n of_o some_o hill_n as_o aristotle_n testify_v of_o olympus_n without_o apply_v a_o sponge_n to_o the_o nostril_n for_o want_n of_o this_o thick_a air_n which_o we_o use_v in_o respiration_n the_o like_a do_v josephus_n acosta_n witness_n unto_o we_o of_o the_o seres_z in_o peru_n which_o be_v hardly_o passable_a by_o such_o as_o labour_v to_o overcome_v their_o height_n because_o the_o air_n before_o they_o come_v to_o the_o top_n of_o these_o hill_n grow_v so_o subtle_a and_o attenuate_v and_o to_o add_v something_o of_o my_o own_o experience_n myself_o have_v make_v some_o trial_n of_o the_o height_n of_o the_o cloud_n as_o well_o in_o the_o heat_n of_o summer_n as_o at_o other_o time_n can_v never_o yet_o find_v