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name_n of_o the_o aforesaid_a old_a clime_n and_o that_o you_o may_v also_o see_v without_o calculation_n or_o trouble_v where_o the_o ancient_n place_v they_o i_o have_v set_v down_o the_o first_o syllable_n of_o their_o name_n as_o mer._n sy._n al._n etc._n etc._n according_a to_o their_o respective_a latitude_n to_o find_v then_o in_o what_o clime_n any_o place_n be_v v._n g._n constantinople_n lie_v you_o be_v only_o to_o draw_v your_o string_n from_o the_o pole_n over_o that_o city_n and_o mount_v up_o the_o bead_n thither_o to_o move_v it_o to_o the_o say_v primary_n circle_n of_o longitude_n and_o it_o will_v lie_v on_o the_o clime_n or_o parallel_v require_v but_o if_o you_o will_v know_v what_o place_n be_v suppose_v under_o the_o four_o clime_n throu'out_v the_o world_n i._n e._n what_o place_n have_v their_o long_a day_n just_a 14._o hour_n fix_v the_o bead_n on_o the_o four_o clime_n and_o move_v it_o on_o its_o noose_n from_o the_o pole_n round_o the_o globe_n you_o may_v conclude_v that_o every_o place_n it_o pass_v over_o have_v the_o sun_n exact_o so_o long_o above_o the_o horizon_n when_o the_o day_n be_v at_o the_o long_a and_o in_o the_o same_o manner_n you_o must_v proceed_v on_o the_o south_n of_o the_o aequator_fw-la to_o find_v the_o country_n that_o lie_v under_o the_o four_o southern_a clime_n clime_n in_o short_a here_o we_o have_v beside_o what_o have_v be_v already_o say_v a_o view_n not_o only_o of_o the_o strange_a inequality_n of_o the_o clime_n especial_o between_o the_o first_o and_o last_o but_o also_o of_o their_o exact_a distance_n in_o degree_n and_o consequent_o in_o miles_n by_o help_n of_o our_o table_n of_o reduction_n mention_v in_o the_o first_o 23._o operation_n of_o this_o section_n but_o see_v we_o be_v a_o little_a fall_v into_o speculation_n it_o will_v not_o zone_n be_v perchance_o improper_a to_o proceed_v yet_o further_o and_o to_o consider_v here_o as_o in_o a_o natural_a and_o fit_a place_n the_o bound_n and_o term_n of_o the_o five_o zone_n so_o call_v from_o 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d cingulum_n as_o enclose_v the_o whole_a world_n within_o their_o respective_a district_n it_o be_v with_o the_o torrid_a amphiscii_n one_o we_o will_v then_o begin_v who_o bound_n be_v the_o two_o tropic_n so_o that_o the_o diurnal_a parallel_n not_o only_o remarkable_o distinguish_v it_o from_o the_o other_o zone_n but_o show_v why_o the_o several_a inhabitant_n within_o this_o space_n be_v call_v by_o the_o ancient_n amphiscii_n i._n e._n utrinque_fw-la umbrati_fw-la or_o man_n that_o have_v two_o shadow_n from_o 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d vtrinquè_fw-fr &_o 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d vmbra_fw-la nay_o by_o the_o say_a parallel_n you_o may_v find_v when_o the_o shade_n will_v change_v and_o be_v different_a for_o since_o by_o these_o path_n or_o trace_n the_o sun_n as_o we_o often_o hint_v
happen_v 6_o day_n and_o 16_o hour_n or_o 6_o day_n and_o 20_o hour_n and_o several_a such_o fraction_n and_o deviation_n from_o the_o positive_a term_n prefix_v by_o i_o but_o since_o the_o forementioned_a whole_a and_o half_a day_n will_v bring_v we_o to_o a_o knowledge_n exact_a enough_o of_o the_o hour_n seek_v for_o we_o call_v 6_o day_n and_o 16_o hour_n 6_o day_n and_o a_o ½_o only_o as_o come_v near_o to_o it_o than_o 7_o whole_a one_o in_o like_a manner_n we_o call_v 6_o and_o 20_o hour_n 7_o day_n and_o deal_v in_o this_o proportion_n with_o all_o other_o number_n of_o day_n and_o hour_n which_o the_o ephemerides_n or_o almanac_n give_v we_o concern_v the_o length_n of_o the_o require_v quarter_n and_o here_o you_o may_v be_v please_v to_o remember_v also_o that_o it_o memorandum_n will_v not_o be_v amiss_o in_o case_n you_o exceed_v much_o any_o of_o the_o foresay_a term_n to_o add_v or_o cast_v away_o sometime_o a_o minute_n or_o a_o little_a more_o as_o you_o shall_v see_v cause_n for_o if_o v._n g._n you_o find_v the_o moon_n to_o be_v six_o day_n and_o 17_o hour_n in_o her_o journey_n which_o according_a to_o our_o former_a direction_n be_v to_o be_v repute_v only_o six_o day_n and_o ½_o and_o consequent_o the_o elongation_n 55′½_n you_o may_v then_o cast_v away_o 1′½_n because_o of_o this_o great_a excess_n above_o the_o half_a day_n and_o if_o you_o shall_v find_v she_o at_o another_o time_n to_o be_v 7_o day_n and_o twenty_o hour_n i._n e._n eight_o day_n you_o may_v add_v for_o the_o want_n of_o the_o four_o hour_n a_o minute_n and_o make_v her_o daily_a elongation_n 46_o instead_o of_o the_o forementioned_a 45_o but_o here_o you_o may_v do_v as_o you_o you_o please_v for_o the_o error_n will_v not_o be_v considerable_a these_o particular_n be_v premise_v let_v we_o come_v to_o a_o example_n example_n and_o suppose_v then_o that_o on_o the_o five_o of_o january_n find_v the_o moon_n shadow_n to_o mark_v two_o in_o the_o afternoon_n on_o your_o globe_n for_o the_o lunar_a hour_n you_o shall_v desire_v to_o know_v the_o true_a or_o solar_a hour_n first_o your_o almanac_n can_v tell_v you_o not_o only_o that_o the_o moon_n last_o cardinal_n point_n be_v v_o g._n her_o conjunction_n but_o how_o many_o day_n and_o hour_n she_o spend_v in_o go_v from_o it_o to_o the_o next_o cardinal_n point_n for_o find_v there_o her_o say_a conjunction_n to_o be_v on_o the_o first_o day_n suppose_v at_o seven_o at_o night_n and_o that_o she_o come_v to_o her_o first_o quarter_n on_o the_o nine_o day_n near_o the_o same_o hour_n you_o may_v present_o conclude_v she_o be_v 8_o whole_a day_n in_o this_o voyage_n and_o consequent_o that_o her_o diurnal_a elongation_n from_o the_o sun_n will_v be_v 45_o minute_n now_o because_o the_o say_v five_o day_n be_v the_o 4_o of_o her_o journey_n if_o you_o multiply_v 45_o by_o 4_o or_o lookin_n the_o table_n which_o we_o shall_v present_o show_v you_o belong_v to_o her_o 8_o day_n journey_n you_o will_v have_v three_o hour_n for_o the_o time_n that_o she_o be_v behind_o the_o sun_n so_o that_o the_o solar_a or_o true_a hour_n must_v be_v five_o at_o night_n want_v four_o minute_n for_o you_o be_v always_o careful_o to_o subtract_v two_o minute_n for_o every_o hour_n the_o moon_n want_v of_o complete_n her_o whole_a day_n march_v which_o in_o the_o present_a case_n happen_v not_o before_o seven_o at_o night_n whereas_o you_o must_v have_v add_v they_o have_v the_o solar_a hour_n be_v nine_o at_o night_n because_o than_o her_o elongation_n from_o the_o sun_n will_v have_v be_v 4_o minute_n more_o than_o the_o aforesaid_a three_o hour_n it_o be_v in_o this_o manner_n you_o be_v to_o opperate_a in_o all_o case_n but_o before_o memorandum_n we_o proceed_v take_v these_o two_o memorandum_n with_o you_o first_o that_o by_o the_o moon_n be_v complete_n a_o day_n journey_n i_o mean_v 24_o hour_n after_o the_o time_n let_v it_o happen_v by_o night_n or_o by_o day_n of_o her_o enter_v into_o 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begin_n that_o no_o certain_a number_n of_o minute_n can_v be_v allow_v for_o her_o daily_a elongation_n but_o if_o we_o divide_v 6_o hour_n or_o 360_o minute_n i._n e._n her_o total_a elongation_n from_o one_o cardinal_n point_n to_o another_o by_o the_o day_n and_o half_a day_n she_o spend_v in_o the_o journey_n the_o quotient_n must_v be_v her_o diurnal_a elongation_n at_o least_o to_o sense_n during_o that_o quarter_n now_o since_o the_o diurnal_a elongation_n be_v as_o you_o see_v most_o common_o above_o three_o quarter_n and_o sometime_o almost_o a_o hour_n the_o horary_a one_o must_v be_v as_o i_o say_v considerable_a see_v in_o the_o space_n of_o every_o 7_o hour_n it_o may_v amount_v to_o above_o a_o quarter_n more_o therefore_o this_o inconvenience_n we_o obviate_v by_o allow_v two_o minute_n for_o each_o hour_n after_o her_o complete_a day_n journey_n and_o substract_v they_o from_o what_o she_o want_v of_o it_o here_o i_o confess_v there_o may_v be_v a_o error_n but_o it_o be_v hardly_o worth_a memorandum_n the_o mention_v for_o when_o she_o be_v either_o 8_o day_n or_o 7_o in_o her_o journey_n from_o one_o cardinal_n point_n to_o another_o i._n e._n when_o her_o diurnal_a elongation_n be_v either_o 45′_n or_o 51′_n and_o ½_o the_o difference_n from_o 48_o minute_n a_o day_n or_o 2_o minute_n a_o hour_n can_v be_v but_o 3′_n and_o ½_o in_o a_o whole_a day_n nay_o when_o her_o elongation_n be_v 55′_n and_o ½_o i._o e._n when_o she_o spend_v 6_o day_n and_o ½_o in_o her_o voyage_n the_o difference_n be_v but_o 7′_n and_o ½_o from_o the_o aforesaid_a 48_o minute_n nor_o can_v this_o happen_v till_o the_o end_n of_o every_o complete_a day_n journey_n and_o consequent_o be_v not_o perceivable_a for_o the_o great_a part_n of_o it_o but_o since_o we_o here_o see_v where_o and_o how_o any_o error_n may_v arise_v it_o be_v easy_o remedy_v by_o a_o allowance_n if_o any_o man_n think_v it_o worth_a the_o while_n to_o be_v so_o exact_a as_o for_o the_o reason_n why_o if_o she_o be_v in_o her_o course_n from_o her_o table_n first_o quarter_n to_o her_o full_a or_o from_o her_o last_o quarter_n to_o her_o conjunction_n we_o must_v add_v always_o six_o hour_n to_o the_o elongation_n which_o our_o calculation_n or_o the_o table_n give_v it_o be_v because_o the_o say_a elongation_n be_v only_o the_o precise_a time_n of_o her_o departure_n from_o her_o last_o cardinal_n point_n whereas_o if_o she_o be_v pass_v she_o first_o quarter_n in_o her_o journey_n towards_o her_o full_a she_o be_v so_o much_o and_o six_o hour_n more_o i._n e._n so_o much_o and_o the_o six_o hour_n which_o happen_v from_o her_o conjunction_n
represent_v the_o illumination_n and_o the_o other_o the_o obscurity_n you_o may_v perform_v this_o operation_n at_o any_o time_n whether_o the_o aforesaid_a luminary_n shine_v or_o no._n how_o easy_a therefore_o be_v it_o to_o conceive_v the_o whole_a mystery_n of_o the_o moon_n four_o principal_a change_n and_o what_o man_n mean_v by_o they_o corollary_n for_o first_o we_o see_v that_o as_o she_o be_v call_v new_a by_o a_o astronomer_n from_o her_o be_v with_o the_o sun_n i._n e._n as_o full_o between_o our_o eye_n and_o the_o sun_n as_o she_o then_o course_n permit_v so_o no_o soon_o have_v he_o find_v by_o their_o several_a motion_n that_o she_o be_v get_v 90_o degree_n or_o six_o hour_n from_o the_o sun_n but_o he_o say_v she_o be_v in_o her_o first_o quarter_n and_o when_o they_o be_v asunder_o 180_o degree_n or_o 12_o hour_n to_o wit_n as_o far_o as_o ever_o they_o can_v be_v that_o she_o be_v full_a and_o last_o as_o soon_o as_o they_o be_v distant_a 270_o degree_n or_o 18_o hour_n on_o the_o same_o side_n and_o 90_o degree_n or_o six_o hour_n on_o the_o other_o that_o she_o be_v in_o her_o last_o quarter_n so_o that_o at_o their_o next_o meeting_n she_o become_v new_a again_o operation_n fourteen_o how_o to_o find_v how_o long_o the_o moon_n want_v of_o any_o change_n or_o cardinal_n point_v and_o consequent_o how_o old_a she_o be_v i_o propose_v not_o this_o operation_n as_o a_o thing_n exact_a but_o see_v it_o be_v a_o corollary_n of_o the_o former_a i_o think_v fit_a to_o hint_n it_o therefore_o pray_v take_v it_o for_o better_a for_o worse_a and_o make_v of_o it_o what_o you_o can_v to_o resolve_v then_o these_o question_n by_o the_o globe_n you_o be_v to_o expose_v it_o as_o before_o to_o the_o moon_n when_o she_o shine_v and_o move_v about_o it_o till_o you_o can_v there_o just_a describe_v her_o shape_n and_o by_o the_o way_n you_o will_v come_v near_o the_o mark_n if_o you_o only_o consider_v the_o lunular_a or_o lesser_a portion_n whether_o it_o 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increase_n she_o be_v past_o be_v new_a 40_o degree_n i._n e._n three_o day_n and_o about_o seven_o hour_n see_v her_o hourly_a elongation_n from_o the_o sun_n be_v one_o time_n with_o another_o about_o half_a a_o degree_n and_o half_a a_o minute_n but_o if_o she_o be_v in_o she_o decrease_v she_o want_v so_o many_o day_n and_o hour_n from_o be_v again_o new_a in_o the_o next_o place_n it_o will_v happen_v that_o the_o obscure_a part_n of_o the_o globe_n be_v 140_o degree_n broad_a for_o both_o part_n or_o portion_n make_v up_o the_o apparent_a hemisphere_n the_o say_v obscure_v part_n become_v the_o supplement_n of_o the_o former_a 40_o degree_n so_o that_o 140′_n amount_v to_o about_o 279_o hour_n or_o 11_o day_n and_o 15_o hour_n you_o may_v conclude_v that_o if_o she_o be_v increase_v she_o want_v so_o much_o of_o be_v full_a as_o also_o that_o she_o be_v 50_o degree_n or_o almost_o 100_o hour_n i._n e._n four_o day_n and_o almost_o four_o hour_n past_o her_o first_o quarter_n whereas_o if_o she_o be_v decrease_v she_o will_v want_v eleven_o day_n and_o fifteen_o hour_n from_o her_o next_o conjunction_n and_o be_v four_o day_n and_o almost_o 4_o hour_n beyond_o her_o last_o quarter_n as_o for_o know_v the_o moon_n state_n in_o relation_n to_o her_o wax_a and_o wane_v you_o need_v only_o observe_v on_o what_o side_n of_o she_o discus_fw-la her_z illuminate_v part_n stand_v for_o if_o it_o be_v on_o the_o westside_n of_o it_o she_o be_v in_o a_o wax_a condition_n if_o on_o the_o east-side_n in_o a_o wane_n or_o decline_a one_o and_o here_o also_o remember_v that_o as_o to_o the_o measure_v the_o aforesaid_a portion_n of_o the_o moon_n discus_fw-la represent_v on_o your_o globe_n you_o may_v do_v it_o by_o the_o horizon_n if_o she_o illuminate_v not_o much_o beyond_o the_o zenith_n or_o by_o the_o aequator_fw-la when_o the_o illumination_n reach_v to_o the_o pole_n or_o near_o it_o or_o by_o the_o ecliptic_a when_o it_o extend_v itself_o a_o good_a way_n 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