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 latteâ—_z age_n more_o diligent_a than_o the_o former_a hatâ—_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 experâ—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
censure_n if_o they_o know_v not_o their_o error_n before_o but_o forasmuch_o as_o those_o that_o be_v supputate_v to_o one_o particular_a orison_n place_n will_v not_o agree_v the_o same_o day_n to_o every_o horizon_n let_v none_o from_o hence_o take_v occasion_n to_o calumniate_v astrology_n if_o the_o effect_n do_v likewise_o differ_v in_o divers_a orison_n but_o rather_o let_v they_o learn_v for_o this_o cause_n the_o more_o to_o admire_v the_o art_n for_o that_o from_o hence_o chief_o the_o true_a reason_n do_v grow_v why_o in_o several_a elevation_n the_o weather_n be_v oft_o time_n differ_v upon_o the_o same_o day_n see_v that_o in_o a_o small_a difference_n of_o latitude_n both_o the_o emersion_n and_o occultation_n may_v vary_v divers_a day_n wherefore_o the_o effect_n must_v according_o follow_v the_o cause_n the_o reason_n why_o the_o apparent_a rise_n and_o set_n be_v prefer_v by_o antiquity_n before_o the_o true_a be_v not_o express_v by_o they_o but_o lean_v simple_o upon_o observation_n and_o experience_n they_o commend_v the_o same_o in_o their_o monument_n to_o posterity_n neither_o in_o truth_n be_v it_o necessary_a regard_v see_v the_o reason_n be_v evident_a in_o itself_o for_o who_o doubt_v that_o the_o substraction_n or_o addition_n of_o light_n may_v beget_v such_o a_o new_a degree_n of_o temperature_n in_o the_o air_n as_o be_v sufficient_a to_o mutation_n as_o we_o see_v it_o often_o to_o happen_v in_o distillation_n where_o the_o alteration_n though_o of_o a_o very_a small_a heat_n do_v either_o perfect_a or_o give_v impediment_n to_o the_o work_n but_o moist_a whereas_o for_o the_o most_o part_n this_o mutation_n turn_v unto_o moisture_n this_o be_v purposely_o to_o be_v impute_v to_o the_o great_a quantity_n of_o borrow_a light_n wherewith_o they_o shine_v for_o as_o it_o be_v hold_v in_o the_o perspective_n there_o be_v no_o doubt_n but_o that_o the_o star_n do_v as_o well_o reflect_v unto_o we_o the_o light_n of_o the_o sun_n as_o shine_v with_o their_o own_o proper_a light_n wherefore_o the_o sun_n light_n be_v debilitate_a by_o reflection_n do_v heat_n imperfect_o be_v for_o that_o cause_n fit_a to_o resolve_v and_o cause_n moisture_n to_o flow_v then_o to_o consume_v the_o same_o be_v stir_v and_o here_o be_v further_a to_o be_v note_v that_o ptolemy_n do_v not_o require_v the_o apparent_a rise_n and_o set_v of_o all_o the_o fix_a star_n for_o it_o be_v clear_a in_o that_o tractate_n of_o their_o signification_n that_o he_o neglect_v all_o but_o those_o of_o the_o first_o and_o star_n second_o magnitude_n whereof_o he_o give_v two_o reason_n one_o because_o the_o exact_a emersion_n and_o occultation_n of_o the_o lesser_a star_n can_v be_v observe_v by_o reason_n that_o their_o weak_a light_n be_v not_o able_a to_o overcome_v the_o twilight_n whereby_o the_o ark_n of_o their_o apparition_n be_v uncertain_a the_o apparition_n itself_o can_v be_v calculate_v the_o other_o reason_n be_v because_o these_o more_o notable_a star_n be_v for_o the_o most_o part_n so_o convenient_o situate_v as_o the_o appearance_n of_o the_o lesser_a happen_v much_o about_o the_o same_o time_n be_v not_o so_o to_o be_v regard_v as_o these_o that_o be_v more_o illustrious_a and_o thus_o for_o example_n he_o think_v it_o enough_o to_o observe_v the_o apparent_a rise_n and_o set_n of_o arcturus_n and_o spica_fw-la though_o we_o pass_v vindimiatricks_n in_o silence_n neither_o care_v he_o much_o for_o the_o haedi_fw-la or_o the_o vergiliae_fw-la or_o hyades_n so_o he_o observe_v hircus_fw-la and_o the_o bright_a of_o the_o hyades_n wherefore_o ptolemy_n have_v not_o supputate_v these_o apparition_n ptolemy_n for_o above_o 30._o myself_o come_v short_a of_o he_o by_o 6._o for_o more_o of_o the_o first_o and_o second_o magnitude_n do_v not_o rise_v and_o set_v to_o we_o because_o the_o declination_n of_o divers_a do_v exceed_v the_o compliment_n of_o our_o pole_n and_o therefore_o if_o the_o sun_n be_v septenâ—rional_a they_o never_o set_v as_o lyra_n lucida_n persei_fw-la dexter_n humerus_fw-la aurigae_fw-la conâ—a_n cygni_fw-la and_o the_o like_a or_o if_o this_o excess_n be_v austral_a than_o they_o do_v never_o â—ise_v of_o which_o kind_n canobus_n and_o pes_fw-la dexter_n centauri_fw-la be_v which_o be_v never_o see_v above_o our_o horizon_n chap._n xvii_o intention_n and_o remission_n by_o configuration_n of_o the_o star_n the_o cause_n hitherto_o mention_v although_o they_o be_v very_o divine_a and_o contain_v much_o excellency_n in_o they_o yet_o they_o come_v all_o near_o the_o nature_n of_o matter_n than_o this_o which_o follow_v for_o the_o manner_n of_o their_o operation_n do_v consist_v chief_o in_o a_o certain_a flux_n and_o emission_n of_o light_n continue_v down_o to_o these_o sublunary_a body_n which_o although_o it_o be_v common_o think_v without_o matter_n or_o time_n yet_o it_o be_v not_o without_o the_o dimension_n of_o quantity_n handle_v for_o it_o be_v make_v by_o a_o right_a line_n it_o be_v attenuate_v by_o the_o distance_n thereof_o from_o the_o star_n it_o increase_v or_o decrease_v with_o the_o face_n of_o the_o planet_n itself_o it_o be_v hinder_v by_o opposition_n of_o a_o shady_a body_n and_o last_o the_o visible_a presence_n of_o the_o star_n admit_v it_o be_v necessary_o presuppose_v also_o neither_o be_v this_o find_v in_o one_o and_o the_o same_o single_a star_n consider_v by_o itself_o but_o in_o comparison_n also_o with_o other_o as_o because_o the_o sun_n and_o moon_n excel_v all_o other_o star_n in_o their_o visible_a magnitude_n therefore_o their_o action_n be_v most_o evident_a but_o in_o the_o rest_n who_o visible_a diameter_n be_v not_o comparable_a to_o the_o sun_n or_o moon_n their_o efficacy_n be_v hardly_o sensible_a and_o not_o to_o be_v attain_v without_o long_a experience_n this_o cause_n therefore_o which_o follow_v and_o belong_v equal_o to_o the_o planet_n and_o fix_a star_n be_v more_o noble_a and_o to_o be_v admire_v then_o the_o other_o for_o this_o savore_v nothing_o of_o matter_n but_o have_v only_o consideration_n cause_n of_o form_n not_o so_o much_o respect_v the_o straight_a beam_n of_o light_n which_o flow_v from_o every_o star_n as_o value_v and_o esteem_v how_o their_o beam_n meet_v at_o the_o earth_n between_o we_o and_o their_o light_n but_o both_o when_o they_o be_v hide_v under_o the_o horizon_n and_o seem_v above_o the_o same_o it_o make_v the_o efficacy_n of_o the_o star_n more_o notable_a over_o all_o the_o world_n then_o at_o other_o time_n which_o kind_n of_o operation_n if_o the_o star_n be_v swift_a in_o motion_n be_v in_o a_o manner_n but_o momentany_a for_o that_o the_o geometrical_a angle_n be_v change_v into_o another_o angle_n that_o be_v improportionable_a and_o improper_a immediate_o or_o not_o long_o after_o this_o efficacy_n also_o cease_v though_o the_o light_n of_o the_o star_n at_o that_o time_n chance_n to_o increase_v for_o which_o cause_n i_o give_v not_o so_o much_o regard_n to_o the_o aspect_n of_o the_o moon_n with_o other_o planet_n in_o the_o alteration_n of_o the_o weather_n as_o unto_o the_o configuration_n of_o the_o planet_n among_o themselves_o or_o with_o the_o fix_a star_n who_o motion_n be_v but_o slow_a in_o respect_n of_o the_o moon_n do_v not_o so_o sudden_o vary_v the_o angle_n of_o their_o configuration_n at_o the_o earth_n from_o hence_o it_o be_v therefore_o that_o those_o ark_n or_o portion_n of_o the_o heaven_n allot_v unto_o the_o aspect_n be_v not_o so_o much_o esteem_v above_o all_o other_o cause_n in_o astrological_a judgement_n for_o although_o it_o be_v true_a that_o in_o all_o situation_n the_o star_n send_v forth_o their_o beam_n unto_o all_o the_o part_n of_o heaven_n and_o earth_n which_o they_o behold_v as_o may_v be_v argue_v out_o of_o vitellio_n his_o demonstration_n 22._o by_o mean_n whereof_o the_o beam_n and_o line_n of_o true_a motion_n in_o every_o two_o star_n do_v retain_v a_o mutual_a respect_n one_o to_o another_o and_o so_o do_v evermore_o intercept_v some_o ark_n of_o heaven_n and_o concur_v at_o some_o angle_n of_o the_o earth_n which_o may_v seem_v to_o make_v a_o aspect_n among_o themselves_o yet_o nevertheless_o all_o the_o ancient_a and_o modern_a astronomer_n follow_v nature_n for_o their_o guide_n have_v heretofore_o regard_v these_o few_o configuration_n only_o be_v but_o five_o in_o all_o namely_o the_o ☌_o âš¹_o â–¡_o â–³_o and_o â˜_o among_o which_o although_o the_o first_o do_v not_o common_o go_v for_o a_o aspect_n because_o every_o aspect_n be_v repute_v a_o proportion_a distance_n between_o two_o or_o more_o star_n yet_o nevertheless_o see_v a_o certain_a position_n of_o the_o star_n in_o the_o zodiac_n be_v rather_o consider_v in_o this_o position_n than_o any_o diversity_n of_o place_n and_o that_o the_o enumeration_n of_o the_o aspect_n ever_o begin_v from_o the_o conjunction_n therefore_o as_o well_o in_o respect_n of_o this_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 superâ—…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 â—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 â—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
the_o rest_n of_o the_o aspect_n either_o the_o â–³_o be_v place_v between_o the_o â˜_o and_o the_o â–¡_o or_o the_o â–¡_o between_o the_o â˜_o and_o the_o âš¹_o we_o shall_v find_v either_o way_n three_o number_n which_o admit_v all_o the_o law_n of_o harmoniacal_a proportion_n as_o in_o these_o figure_n follow_v be_v evident_a 80._o diagram_n where_o to_o let_v the_o rest_n pass_v as_o plain_a enough_o of_o itself_o by_o that_o which_o be_v before_o speak_v we_o be_v further_a to_o note_v that_o the_o â˜_o compare_v in_o the_o last_o figure_n of_o those_o two_o with_o the_o âš¹_o have_v a_o triple_a proportion_n to_o the_o same_o compound_v of_o a_o double_a and_o sesquialter_fw-la proportion_n as_o diapente_fw-la with_o diapason_n in_o music_n be_v and_o so_o be_v find_v no_o simple_a or_o perfect_a aspect_n but_o exact_o aspect_n answerable_a to_o b_o flat_n the_o first_o imperfect_a or_o compound_a concord_n in_o music_n be_v a_o six_o from_o g_o sol_fw-la re_fw-la ut_fw-la which_o nevertheless_o in_o some_o respect_n be_v after_o a_o sort_n esteem_v perfect_a because_o it_o use_v the_o same_o division_n compare_v to_o d_o sol_fw-mi re_fw-it that_o the_o perfect_a concord_n do_v for_o it_o be_v half_o a_o five_o and_o situate_a in_o the_o middle_n between_o γ_n ut_fw-la and_o d_o sol_fw-mi re_fw-it as_o also_o the_o âš¹_o compare_v with_o the_o â–³_o be_v a_o just_a half_a thereof_o which_o before_o have_v be_v show_v to_o be_v in_o a_o sesquialter_fw-la proportion_n to_o the_o â˜_o as_o d_o sol_fw-mi re_fw-it be_v to_o γ_n ut_fw-la and_o therefore_o exact_o agreeable_a to_o a_o diapente_fw-la in_o music_n which_o the_o rather_o i_o here_o note_v because_o we_o shall_v have_v some_o use_n thereof_o afterward_o in_o speak_v handle_v of_o the_o new_a aspect_n and_o thus_o much_o shall_v short_o serve_v for_o the_o theory_n or_o philosophical_a speculation_n of_o they_o that_o ascribe_v the_o efficacy_n of_o these_o irradiation_n to_o the_o harmonical_a proportion_n which_o be_v sound_a between_o they_o wherefore_o see_v they_o carry_v the_o same_o mutual_a respect_n one_o towards_o another_o which_o the_o foresay_a harmonical_a concord_n do_v retain_v between_o themselves_o what_o wonder_n be_v it_o if_o nature_n in_o her_o operation_n as_o well_o by_o light_n as_o by_o sound_n admit_v no_o other_o symmetry_n but_o that_o which_o be_v derive_v from_o these_o proportion_n reject_v all_o other_o as_o irrational_a and_o discordant_a yet_o all_o this_o hitherto_o do_v rather_o illustrate_v another_o a_o simili_fw-la and_o do_v more_o and_o more_o express_a unto_o we_o that_o nature_n indeed_o have_v adorn_v these_o proportion_n with_o singular_a privilege_n above_o any_o other_o then_o satisfy_v we_o with_o the_o true_a reason_n why_o in_o the_o infinite_a variety_n of_o sound_n and_o light_n these_o only_a shall_v consent_v most_o sweet_o in_o music_n and_o be_v effectual_a in_o the_o operation_n of_o nature_n neither_o have_v any_o man_n herein_o endeavour_v with_o more_o probability_n to_o give_v satisfaction_n unto_o the_o learned_a than_o kepler_n who_o have_v witty_o labour_v to_o demonstrate_v that_o god_n in_o the_o creation_n of_o the_o world_n have_v observe_v the_o same_o proportion_n in_o the_o magnitude_n and_o distance_n of_o the_o heavenly_a sphere_n which_o be_v find_v in_o the_o regular_a solides_n which_o as_o geometry_n teach_v have_v their_o original_a from_o the_o ordinate_a playn_v in_o the_o end_n conclude_v with_o good_a probability_n that_o the_o heavenly_a motion_n shall_v then_o consent_v sweet_o and_o cooperate_v strong_o together_o when_o the_o nature_n of_o these_o sublunary_a thing_n endue_v as_o he_o suppose_v with_o a_o sensitive_a or_o know_a faculty_n apprehend_v the_o beam_n of_o the_o star_n to_o observe_v that_o respect_n in_o their_o concurrence_n at_o the_o centre_n of_o the_o earth_n which_o answer_v unto_o the_o ordinate_a playn_v from_o whence_o the_o regularity_n of_o these_o proportion_n be_v derive_v as_o the_o impress_a character_n of_o that_o symmetry_n which_o god_n be_v say_v to_o have_v use_v in_o the_o creation_n of_o the_o world_n itself_o so_o imagine_v that_o as_o often_o as_o the_o nature_n of_o any_o thing_n meet_v with_o these_o proportion_n it_o exercise_v itself_o as_o it_o be_v by_o this_o idea_n which_o it_o retain_v still_o and_o that_o in_o such_o sort_n as_o what_o it_o do_v but_o ordinary_o and_o slack_o at_o other_o time_n it_o perform_v now_o much_o more_o effectual_o and_o as_o it_o be_v with_o extraordinary_a diligence_n not_o say_v he_o that_o these_o proportion_n work_v any_o thing_n of_o their_o own_o virtue_n for_o in_o music_n it_o be_v neither_o the_o sound_n neither_o the_o proportion_n of_o the_o concord_n that_o work_v any_o thing_n of_o themselves_o or_o beget_v any_o delightful_a humour_n in_o a_o man_n but_o the_o soul_n approach_v to_o the_o instrument_n of_o sense_n first_o there_o entertain_v the_o sound_n inward_o than_o value_v their_o proportion_n and_o find_v the_o same_o good_a and_o geometrical_a last_o exhilarate_v itself_o and_o move_v the_o body_n wherein_o it_o be_v as_o with_o a_o object_n wherein_o it_o take_v delight_n and_o sure_o be_v these_o proportion_n set_v unsatisfied_a down_o by_o kepler_n exact_o find_v in_o the_o symmetry_n of_o the_o world_n than_o i_o can_v the_o better_o give_v ear_n unto_o he_o and_o believe_v this_o mystery_n to_o rest_v in_o that_o which_o he_o have_v say_v but_o he_o himself_o have_v inscribe_v the_o several_a sphere_n of_o the_o planet_n within_o the_o regular_a body_n in_o the_o end_n find_v their_o distance_n from_o the_o centre_n of_o the_o world_n to_o differ_v very_o much_o both_o in_o jupiter_n the_o earth_n which_o he_o suppose_v to_o occupy_v the_o sun_n place_n and_o mercury_n from_o that_o which_o copernicus_n and_o other_o astronomer_n do_v set_v down_o by_o observation_n i_o love_v not_o after_o the_o expectance_n of_o geometrical_a demonstration_n though_o he_o come_v near_o in_o some_o to_o feed_v myself_o with_o fancy_n in_o the_o rest_n neither_o can_v i_o well_o conceive_v in_o that_o poor_a understanding_n which_o i_o have_v in_o philosophy_n how_o configuration_n consist_v only_o of_o intelligible_a angle_n shall_v be_v object_n to_o any_o sensitive_a power_n or_o how_o the_o sensitive_a power_n which_o he_o do_v imagine_v in_o the_o element_n and_o all_o elementary_a thing_n shall_v apprehend_v without_o organical_a instrument_n yet_o nevertheless_o beam_n leave_v this_o conceit_n of_o kepler_n without_o prejudice_n of_o his_o conceit_n or_o judgement_n unto_o other_o of_o ripe_a judgement_n than_o myself_o i_o will_v as_o perspicuous_o as_o i_o can_v deliver_v that_o which_o myself_o have_v further_o consider_v as_o the_o reason_n why_o these_o beam_n shall_v be_v more_o effectual_a than_o other_o and_o first_o concerning_o the_o ☌_o and_o â˜_o i_o hold_v myself_o abundant_o satisfy_v with_o the_o union_n of_o beam_n which_o therefore_o be_v the_o most_o potent_a and_o powerful_a configuration_n of_o all_o other_o as_o be_v evident_a in_o this_o figure_n where_o we_o see_v the_o beam_n as_o well_o incident_a as_o reflect_v to_o be_v unite_v diagram_n for_o let_v a_o be_v in_o ☌_o here_o with_o b_o it_o be_v first_o manifest_a that_o all_o the_o beam_n flow_v from_o g_o and_o e_o the_o point_n of_o touch_n in_o the_o circumference_n of_o a_o shall_v unite_v themselves_o with_o the_o beam_n that_o be_v send_v from_o b_o to_o c_o the_o earth_n or_o centre_n of_o the_o world_n second_o we_o be_v also_o to_o observe_v that_o in_o this_o case_n only_o the_o beam_n a_o c_o or_o b_o c_o come_v from_o the_o centre_n of_o the_o star_n reflect_v into_o itself_o as_o be_v only_o perpendicular_a whereas_o those_o beam_n which_o be_v send_v from_o the_o point_n e_o and_o g_o make_v a_o acute_a angle_n at_o c_o and_o do_v therefore_o reflect_v the_o one_o into_o the_o other_o at_o equal_a angle_n as_o g_o c_o reflect_v from_o c_o to_o e_o and_o e_o c_o from_o c_o to_o g_o last_o of_o all_o the_o union_n that_o happen_v in_o â˜_o be_v manifest_a without_o more_o circumstance_n where_o the_o beam_n send_v from_o the_o opposite_a point_n make_v but_o one_o straight_a line_n as_o g_o f_o and_o e_o h_o in_o this_o figure_n except_o in_o case_n where_o the_o earth_n hinder_v be_v big_a than_o the_o star_n in_o opposition_n for_o there_o without_o latitude_n the_o union_n of_o their_o beam_n must_v needs_o be_v hinder_v by_o interposition_n of_o the_o earth_n for_o which_o cause_n it_o be_v special_o here_o to_o be_v remember_v perigaeo_n in_o the_o ☌_o of_o the_o two_o inferior_a planet_n with_o the_o sun_n that_o if_o this_o hap_n in_o the_o apogaeon_fw-mi of_o their_o epicycle_n their_o ☌_o shall_v not_o be_v of_o that_o efficacy_n or_o force_n as_o when_o they_o be_v in_o perigaeo_n because_o according_a to_o the_o hypothesis_n of_o tycho_n
and_o copernicus_n they_o be_v above_o the_o sun_n and_o the_o sun_n much_o big_a than_o they_o the_o sun_n shall_v return_v all_o their_o beam_n to_o themselves_o from_o the_o earth_n so_o that_o their_o union_n by_o this_o mean_n shall_v be_v interrupt_v and_o frustrate_a in_o like_a manner_n in_o my_o contemplation_n for_o help_v in_o the_o configuration_n of_o the_o âš¹_o and_o â–³_o i_o find_v that_o which_o do_v reasonable_o give_v i_o contentment_n because_o in_o the_o concurrence_n of_o their_o beam_n at_o the_o earth_n i_o find_v a_o mutual_a reflection_n of_o the_o one_o into_o the_o other_o and_o so_o a_o union_n by_o reflection_n diagram_n for_o admit_v a_o b_o c_o to_o be_v three_o star_n a_o and_o b_o in_o a_o âš¹_o configuration_n a_o c_o in_o a_o â–³_o then_o for_o so_o much_o as_o b_o f_o the_o beam_n incident_a of_o the_o âš¹_o fall_v oblique_o in_o respect_n of_o a_o f_o and_o make_v a_o acute_a angle_n therewith_o it_o be_v evident_a to_o those_o that_o have_v any_o mean_a understanding_n in_o the_o optic_n that_o b_o f_o shall_v reflect_v to_o c_o and_o so_o be_v unite_v to_o c_o f_o the_o incident_a of_o the_o star_n declare_v c_o which_o be_v in_o a_o â–³_o configuration_n with_o a_o as_o also_o c_o f_o shall_v for_o the_o same_o reason_n reflect_v to_o the_o star_n in_o b_o and_o be_v likewise_o unite_v with_o b_o f_o the_o incident_a of_o the_o star_n at_o b._n behold_v here_o by_o the_o way_n the_o ground_n of_o that_o familiarity_n which_o ptolemy_n note_v in_o these_o ark_n of_o heaven_n when_o he_o consider_v the_o position_n apt_a for_o the_o aphaeta_fw-la of_o life_n or_o the_o house_n of_o the_o figure_n and_o thus_o far_o i_o think_v i_o pursue_v the_o reason_n of_o that_o virtue_n which_o be_v find_v in_o the_o aspect_n with_o good_a encouragement_n that_o i_o shall_v have_v find_v their_o force_n to_o depend_v upon_o union_n or_o reflection_n but_o when_o i_o come_v to_o consider_v of_o the_o quartile_n who_o beam_n only_o cut_v each_o other_o ad_fw-la angulos_fw-la rectos_fw-la and_o so_o reflect_v into_o themselves_o after_o much_o deliberation_n with_o myself_o find_v all_o aid_n of_o the_o optic_n to_o fail_v i_o i_o be_v force_v to_o say_v with_o offusius_fw-la ingenué_fw-fr fatebimur_fw-la causam_fw-la talis_fw-la union_n effectus_fw-la nos_fw-la demonstrare_fw-la non_fw-la posse_fw-la id_fw-la tamen_fw-la verissimum_fw-la esse_fw-la tam_fw-la diuturna_fw-la observatione_fw-la compertum_fw-la habemus_fw-la ut_fw-la ea_fw-la de_fw-la re_fw-la dubitare_fw-la puderet_fw-la wherefore_o recount_v with_o myself_o some_o of_o those_o speculation_n before_o remember_v and_o special_o that_o theorem_n which_o prove_v the_o angle_n of_o the_o âš¹_o â–¡_o and_o â–³_o to_o be_v only_o proportionable_a in_o take_v up_o the_o centre_n of_o the_o world_n the_o more_o i_o consider_v thereof_o the_o more_o i_o find_v myself_o confirm_v that_o the_o mystery_n or_o secret_a of_o these_o configuration_n rest_v chief_o in_o this_o that_o these_o only_a irradiation_n and_o those_o that_o be_v derive_v from_o these_o be_v proportional_a unto_o all_o patille_a matter_n and_o therefore_o more_o effectual_a for_o that_o these_o irradiation_n only_o be_v every_o way_n proportionable_a be_v before_o abundant_o influence_n prove_v whether_o we_o respect_v the_o take_n up_o of_o the_o circumference_n the_o power_n and_o proportion_n oftheir_o subtense_n unto_o the_o diameter_n or_o last_o and_o principal_o the_o occupy_n of_o place_n at_o the_o centre_n of_o the_o world_n which_o prerogative_n see_v no_o other_o ark_n subtense_n or_o angle_n do_v enjoy_v therefore_o i_o conclude_v these_o above_o all_o other_o to_o be_v proportional_a unto_o the_o whole_a system_n of_o the_o world_n for_o that_o be_v true_o say_v proportionable_a which_o be_v neither_o defective_a interrupt_v nor_o redundant_fw-la but_o such_o be_v the_o ark_n subtense_n and_o angle_n of_o those_o irradiation_n and_o none_o other_o ergo_fw-la these_o and_o none_o other_o be_v proportionable_a now_o as_o that_o which_o be_v defective_a and_o want_v proportion_n leave_v the_o action_n frustrate_v and_o without_o effect_n so_o that_o which_o on_o the_o other_o side_n offend_v in_o excess_n must_v needs_o incur_v the_o contrary_a fault_n and_o overcharge_v that_o which_o either_o nature_n or_o art_n intend_v whereby_o of_o necessity_n it_o will_v follow_v that_o there_o be_v no_o defect_n nor_o excess_n but_o a_o equal_a and_o just_a mixture_n of_o the_o influence_n of_o the_o star_n in_o these_o irradiation_n these_o only_a shall_v be_v apt_a and_o convenient_a to_o produce_v agreeable_a effect_n in_o the_o matter_n of_o all_o sublunary_a thing_n for_o it_o fare_v in_o these_o effect_n which_o be_v produce_v by_o the_o mixture_n of_o light_n and_o influence_n as_o with_o chemical_a operation_n where_o the_o defect_n of_o heat_n produce_v nothing_o as_o on_o the_o other_o side_n excess_n do_v either_o by_o sublimation_n eruption_n vitrification_n break_v the_o vessel_n and_o the_o like_a destroy_v the_o work_n and_o to_o make_v it_o yet_o clear_a how_o the_o beam_n of_o any_o such_o star_n do_v proportional_o take_v up_o the_o centre_n of_o the_o world_n whereas_o in_o that_o which_o go_v before_o i_o have_v only_o show_v how_o the_o point_n of_o those_o ordinate_a playn_v whereunto_o these_o configuration_n have_v be_v compare_v often_o reiterate_v do_v take_v up_o place_n opposite_a now_o will_v i_o set_v forth_o how_o the_o beam_n of_o any_o two_o star_n in_o any_o one_o of_o the_o former_a configuration_n shall_v take_v up_o more_o space_n then_o that_o which_o be_v comprehend_v between_o their_o incident_n or_o beam_n of_o true_a motion_n and_o how_o by_o their_o beam_n either_o incident_a reflect_v or_o opposite_a they_o do_v possess_v and_o take_v up_o the_o whole_a centre_n of_o the_o world_n at_o one_o instant_a with_o proportionable_a angle_n for_o evident_a demonstration_n whereof_o concerning_o ☌_o and_o â˜_o who_o force_n rather_o depend_v upon_o union_n than_o proportion_n i_o need_v no_o further_a labour_n then_o to_o refer_v the_o reader_n to_o the_o view_n of_o the_o last_o figure_n but_o one_o where_o he_o see_v the_o unite_a beam_n of_o such_o star_n as_o be_v in_o ☌_o and_o â˜_o to_o surround_v the_o centre_n and_o all_o elementary_a matter_n whatsoever_o subject_n unto_o the_o action_n of_o heaven_n and_o so_o for_o the_o â–¡_o who_o beam_n incident_a and_o opposite_a traverse_v the_o centre_n of_o the_o world_n at_o four_o right_a angle_n viz._n afg_o gfi_n afh_n and_o hfi_o see_v four_o point_n of_o a_o rectangle_n quadrilater_n figure_n have_v be_v before_o prove_v to_o occupy_v place_n i_o likewise_o need_v no_o other_o proof_n then_o that_o the_o reader_n will_v in_o the_o last_o figure_n consider_v how_o these_o four_o right_a angle_n make_v by_o one_o quartile_n take_v up_o the_o centre_n of_o the_o world_n but_o concerning_o the_o â–³_o and_o âš¹_o although_o the_o like_a be_v evident_a enough_o to_o any_o of_o mean_a skill_n yet_o nevertheless_o there_o be_v some_o other_o speculation_n which_o require_v a_o word_n or_o two_o more_o for_o in_o the_o last_o figure_n suppose_v two_o star_n a_o and_o birradiate_v the_o earth_n with_o their_o âš¹_o beam_n although_o it_o be_v true_a that_o by_o the_o protract_n of_o the_o opposite_a beam_n from_o f_o to_o d_o the_o centre_n of_o the_o whole_a world_n seem_v occupy_v with_o proportionable_a angle_n bfa_o be_v subtend_v by_o the_o ark_n of_o 60._o which_o be_v before_o declare_v to_o be_v the_o angle_n of_o a_o ordinate_a aequilater_n triangle_n and_o so_o leave_v the_o outward_a angle_n bfi_o equal_a to_o the_o angle_n of_o a_o ordinate_a hexagon_n subtend_v hereby_o the_o ark_n 120_o which_o be_v the_o ark_n of_o a_o â–³_o the_o like_a be_v also_o to_o be_v understand_v of_o the_o angle_n make_v by_o the_o opposite_a beam_n ad_fw-la verticem_fw-la yet_o nevertheless_o we_o be_v here_o further_o to_o consider_v how_o the_o incident_a beam_n of_o b_o viz._n bf_o reflect_v unto_o c_o and_o so_o take_v up_o the_o whole_a semicircle_n abci_o with_o three_o âš¹_o viz._n afb_o bfc_o and_o cfi_o in_o like_a manner_n if_o we_o consider_v c_o to_o be_v in_o a_o triangular_a configuration_n with_o a_o we_o see_v that_o as_o the_o opposite_a beam_n of_o a_o viz._n fi_o make_v a_o âš¹_o with_o the_o incident_a beam_n of_o a_o star_n at_o c_o viz._n cf_o so_o cf_o be_v the_o beam_n incident_a of_o the_o star_n c_o reflect_v also_o to_o the_o point_n b_o and_o so_o make_v the_o same_o three_o âš¹_o wherewith_o the_o aforesaid_a whole_a semicircle_n be_v take_v up_o as_o be_v before_o demonstrate_v wherefore_o this_o may_v satisfy_v the_o indifferent_a how_o any_o two_o star_n in_o any_o of_o these_o configuration_n do_v proportionable_o ocupy_v the_o whole_a centre_n of_o the_o world_n in_o the_o same_o moment_n without_o reiterate_v the_o same_o angle_n and_o