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their_o fame_n among_o the_o modern_n they_o be_v dia-meroes_a dia-syenes_a dia-alexandrias_a dia-rhodou_a dia-romes_n dia-boristheneos_a and_o dia-riphoeon_a be_v all_o name_n make_v by_o the_o addition_n of_o the_o greek_a preposition_n 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d i._n e._n per_fw-la to_o some_o remarkable_a town_n river_n or_o place_n through_o which_o the_o middle_a of_o each_o clime_n past_o so_o that_o the_o middle_n of_o the_o first_o go_v through_o meroe_n a_o ethiopian_a city_n on_o the_o nile_n where_o according_a to_o some_o queen_n candace_n reign_v the_o second_o through_o syene_n in_o egypt_n lie_v just_a under_o the_o tropic_a the_o three_o through_o alexandria_n the_o four_o through_o the_o isle_n of_o rhodes_n the_o five_o through_o rome_n the_o six_o through_o the_o mouth_n of_o boristhenes_n now_o call_v nieper_n by_o the_o cossack_n and_o the_o other_o inhabitant_n and_o the_o seven_o and_o last_o through_o the_o riphoean_a hill_n part_n of_o which_o lie_v 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therefore_o begin_v at_o the_o very_a aequator_fw-la my_o first_o parallel_n or_o middle_a of_o my_o first_o clime_n be_v suppose_v to_o run_v over_o the_o place_n that_o enjoy_v 12._o hour_n and_o a_o quarter_n of_o day_n and_o the_o end_n of_o it_o note_v on_o the_o primary_n circle_n of_o longitude_n or_o 2_o a_o clock_n hour_n circle_n with_o the_o figure_n i._o over_o the_o place_n that_o have_v 12._o and_o 1_o 2_o and_o thus_o we_o proceed_v to_o the_o polar_a circle_n to_o wit_n where_o the_o 24_o clime_n or_o 48th_o parallel_n terminate_v so_o that_o from_o thence_o we_o come_v to_o the_o devision_n on_o the_o say_a circle_n of_o longitude_n which_o show_v where_o the_o day_n be_v as_o long_o as_o a_o ordinary_a week_n where_o as_o long_o as_o a_o month_n and_o where_o as_o two_o arrive_v at_o last_o at_o the_o pole_n themselves_o where_o there_o be_v a_o constant_a half_a year_n of_o light_n and_o as_o much_o of_o darkness_n and_o to_o give_v you_o a_o remembrance_n of_o the_o 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
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 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further_o for_o the_o say_a portion_n of_o the_o moon_n discus_fw-la be_v measure_v at_o first_o sight_n by_o that_o great_a circle_n which_o lie_v equal_o distant_a from_o each_o horn_n of_o the_o lunula_n on_o the_o globe_n i._n e._n by_o that_o great_a circle_n which_o cross_v it_o as_o we_o say_v in_o the_o middle_n at_o right_a angle_n and_o when_o no_o great_a circle_n do_v so_o you_o have_v best_o measure_v it_o exact_o with_o your_o compass_n see_v that_o on_o the_o knowledge_n of_o its_o breadth_n the_o resolution_n of_o all_o the_o former_a question_n depend_v many_o thing_n of_o great_a use_n may_v be_v draw_v from_o know_v the_o true_a proportion_n of_o the_o illuminate_v and_o obscure_a part_n of_o the_o moon_n orb_n but_o this_o i_o leave_v to_o they_o that_o have_v exacter_n instrument_n than_o the_o globe_n and_o more_o time_n to_o make_v deduction_n the_o end_n of_o the_o three_o section_n sect_n iv._o show_v the_o proportion_n between_o perpendicular_o and_o their_o shade_n see_v there_o be_v the_o same_o proportion_n between_o all_o shade_n and_o their_o perpendicular_o at_o least_o to_o sense_n and_o see_v the_o several_a almucantars_n of_o the_o two_o great_a luminary_n be_v the_o chief_a cause_n of_o the_o lengthen_v or_o shorten_v of_o they_o i_o have_v here_o adjoin_v a_o few_o by_o operation_n even_o in_o altimetry_n itself_o as_o belong_v natural_o to_o our_o globe_n since_o it_o not_o only_o show_v we_o several_a way_n of_o find_v from_o time_n to_o time_n the_o say_a almucantars_n but_o give_v we_o also_o at_o the_o same_o instant_n without_o trouble_n as_o appear_v by_o the_o ensue_a operation_n the_o abovementioned_a proportion_n and_o consequent_o the_o height_n of_o all_o thing_n perpendicular_a to_o the_o horizon_n operation_n i._n how_o to_o find_v the_o proportion_n between_o the_o perpendicular_a and_o its_o shade_n consider_v the_o northern_a or_o back_o part_n of_o the_o globe_n meridian_n which_o we_o will_v call_v hereafter_o the_o quadrant_n of_o proportion_n and_o which_o be_v not_o only_o divide_v like_o the_o southern_a or_o forepart_n into_o degree_n but_o mark_v also_o in_o relation_n to_o the_o affair_n in_o hand_n with_o several_a figure_n of_o which_o that_o next_o the_o zenith_n be_v 17_o and_o the_o remote_a 188._o and_o by_o the_o way_n you_o must_v take_v notice_n that_o when_o you_o see_v a_o cross_n behind_o any_o figure_n it_o signify_v half_o a_o integer_fw-la memorandum_n more_fw-it so_o that_o 17_o +_o be_v 17_o degree_n and_o a_o half_a 26_o +_o be_v 26_o and_o a_o half_a etc._n etc._n when_o you_o will_v therefore_o operate_v turn_v the_o southern_a or_o forepart_n of_o the_o meridian_n towards_o the_o sun_n till_o they_o be_v both_o in_o the_o same_o plane_n i._n e._n till_o the_o shade_n of_o the_o pin_n in_o the_o zenith_n fall_v direct_o upon_o the_o quadrant_n of_o proportion_n and_o what_o figure_n soever_o suppose_n 25_o the_o shade_n of_o extuberancy_n cut_v that_o will_v be_v the_o then_o proportion_n between_o perpendicular_o and_o their_o shade_n for_o here_o you_o may_v take_v notice_n that_o we_o ever_o suppose_v the_o shade_n to_o be_v 100_o nay_o if_o find_v by_o any_o of_o the_o 5._o former_a way_n the_o sun_n height_n to_o be_v suppose_v 14_o degree_n you_o rectify_v your_o bead_n to_o 76_o degree_n or_o the_o compliment_n of_o it_o you_o need_v only_o clap_v back_o your_o string_n that_o be_v to_o say_v draw_v it_o from_o the_o zenith_n over_o the_o devision_n of_o the_o aforementioned_a quadrant_n and_o then_o the_o figure_n under_o the_o bead_n to_o wit_n 25_o will_v show_v you_o the_o require_a proportion_n in_o short_a take_v but_o the_o sun_n height_n any_o how_v and_o reckon_v from_o the_o zenith_n as_o many_o degree_n on_o
only_o a_o glimpse_n or_o faint_a sight_n of_o the_o sun_n then_o stand_v the_o globe_n be_v compose_v on_o the_o obumbrated_a or_o other_o side_n of_o it_o and_o let_v your_o string_n hang_v down_o on_o that_o side_n also_o aim_n or_o look_v along_o it_o with_o one_o by_o towards_o the_o sun_n and_o role_n the_o string_n gentle_o with_o your_o finger_n backward_o or_o forward_o till_o it_o lie_v exact_o in_o the_o same_o plane_n as_o the_o sun_n do_v or_o if_o the_o cloud_n suffer_v you_o not_o clear_o to_o see_v he_o till_o it_o lie_v in_o the_o plane_n of_o its_o suppose_a place_n and_o the_o degree_n under_o your_o string_n reckon_v the_o contrary_a way_n that_o be_v to_o say_v from_o the_o northern_a or_o back_o part_n of_o the_o meridian_n be_v the_o require_v azimuth_n therefore_o by_o the_o by_o if_o the_o sun_n shine_v out_o it_o be_v but_o draw_v the_o string_n through_o the_o shade_n of_o the_o zenith-pin_n and_o it_o will_v reckon_v thus_o answer_v the_o question_n way_n 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be_v the_o 10_o of_o april_n you_o have_v his_o parallel_n because_o it_o be_v mark_v with_o the_o say_a day_n now_o since_o the_o colurus_n aequinoctiorum_fw-la or_o 6_o a_o clock_n hour_n circle_n be_v as_o we_o say_v gradual_o divide_v from_o the_o aequator_fw-la to_o the_o pole_n and_o that_o the_o say_a parallel_n pass_v almost_a throu_fw-fr '_o its_o 12_o degree_n you_o have_v his_o declension_n as_o also_o his_o place_n in_o his_o parallel_n if_o you_o have_v his_o almucantar_n or_o azimuth_n as_o you_o will_v find_v by_o the_o second_o or_o follow_a way_n if_o now_o you_o know_v not_o the_o day_n of_o the_o month_n take_v the_o sun_n be_v way_n 6._o almucantar_n and_o 10_o azimuth_n by_o some_o of_o the_o forego_n way_n and_o rectify_v your_o bead_n to_o the_o height_n draw_v your_o string_n from_o the_o zenith_n on_o the_o horizon_n according_a to_o the_o azimuth_n find_v and_o your_o bead_n will_v lie_v on_o his_o true_a place_n and_o consequent_o show_v his_o declension_n 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fall_v at_o the_o horizon_n a_o little_a beyond_o the_o character_n of_o sebe_n for_o his_o bear_v according_a to_o the_o point_n of_o the_o compass_n operation_n viii_o to_o find_v when_o the_o sun_n come_v to_o true_a east_n or_o west_n or_o any_o other_o bear_v have_v find_v the_o parallel_n of_o the_o day_n viz._n that_o of_o the_o 10_o of_o april_n and_o put_v your_o string_n over_o the_o zenith_n bring_v it_o straight_o to_o the_o east_n point_n that_o be_v to_o say_v to_o the_o point_n of_o the_o globe_n where_o the_o horizon_n and_o 6_o a_o clock_n circle_n intersect_v and_o you_o will_v find_v the_o say_a string_n to_o cut_v the_o say_a parallel_n about_o 20_o minute_n before_o 7_o in_o the_o morning_n which_o be_v the_o exact_a time_n of_o the_o sun_n be_v then_o come_v to_o full_a east_n now_o if_o the_o string_n be_v lay_v on_o the_o western_a intersection_n it_o will_v cut_v the_o say_a parallel_n at_o 20_o minute_n or_o thereabouts_o after_o 5_o in_o the_o evening_n for_o the_o time_n of_o the_o sun_n be_v come_v to_o full_a west_n in_o like_a manner_n if_o you_o will_v know_v when_o he_o come_v v._n g._n to_o s._n w._n you_o be_v only_o to_o draw_v your_o string_n as_o before_o over_o that_o bear_v and_o you_o will_v find_v by_o the_o intersection_n of_o your_o say_a string_n and_o parallel_n that_o at_o a_o quarter_n past_o 2_o of_o the_o clock_n in_o the_o afternoon_n or_o thereabouts_o he_o will_v have_v that_o bear_v operation_n ix_o to_o find_v what_o sign_n and_o degree_n of_o it_o the_o sun_n be_v in_o at_o any_o time_n seek_v out_o the_o parallel_n of_o the_o day_n viz._n that_o of_o the_o 10_o of_o april_n and_o you_o will_v find_v it_o to_o cross_v the_o ecliptic_a in_o two_o place_n to_o wit_n at_o the_o first_o of_o taurus_n and_o the_o first_o of_o leo_n now_o because_o in_o april_n the_o sun_n be_v still_o ascend_v that_o be_v to_o say_v the_o day_n increase_n you_o may_v conclude_v that_o the_o first_o of_o taurus_n be_v his_o then_o true_a place_n in_o the_o ecliptic_a for_o be_v he_o in_o leo_n he_o will_v descend_v towards_o the_o aequator_fw-la and_o consequent_o shorten_v the_o day_n operation_n x._o to_o find_v the_o hour_n of_o the_o day_n by_o the_o sun_n together_o with_o a_o second_o way_n of_o compose_v the_o globe_n and_o find_v the_o globe_n and_o find_v the_o day_n of_o the_o month_n many_o be_v the_o way_n to_o perform_v this_o operation_n as_o to_o the_o hour_n but_o now_o we_o will_v insist_v on_o four_o only_a each_o of_o which_o have_v some_o peculiar_a propriety_n belong_v to_o it_o for_o the_o first_o give_v we_o the_o hour_n by_o the_o help_n of_o the_o natural_a style_n the_o second_o by_o a_o artificial_a one_o the_o three_o without_o any_o style_n at_o all_o and_o the_o four_o together_o with_o the_o say_a hour_n the_o contemplation_n of_o several_a please_a operation_n at_o a_o time_n and_o among_o the_o rest_n this_o of_o compose_v the_o globe_n by_o the_o shade_n i._o have_v 8._o 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carry_v away_o the_o bell_n some_o st._n nicholas_n but_z other_o st._n vincent_n as_o appear_v by_o hondius_n globe_n now_o langrenius_n in_o his_o begin_v from_o st._n mary_n and_o st._n michael_n in_o the_o azore_n johnsonius_n in_o his_o universal_a map_n count_v from_o corvo_n and_o flores_n whereas_o the_o learned_a dudley_n the_o late_a titular_a duke_n of_o northumberland_n give_v the_o honour_n to_o pico_n and_o have_v as_o much_o reason_n for_o it_o as_o the_o rest_n nor_o be_v there_o less_o do_v about_o the_o canary_n for_o the_o french_a fix_v it_o at_o ferro_fw-la several_a of_o the_o hollander_n at_o teneriffa_n and_o many_o other_o nation_n at_o palma_n which_o be_v the_o place_n i_o will_v willing_o choose_v since_o the_o great_a ptolemy_n think_v fit_a at_o last_o to_o assign_v it_o there_o be_v it_o as_o convenient_a for_o my_o present_a purpose_n as_o st._n vincent_n it_o be_v st._n vincent_n then_o i_o here_o pitch_n upon_o for_o this_o meridian_n to_o meridian_n pace_v throu_fw-fr '_o because_o it_o differ_v in_o longitude_n from_o london_n within_o less_o than_o 20_o minute_n of_o just_a 30_o degree_n or_o 2_o hour_n so_o that_o the_o 2_o a_o clock_n circle_n will_v represent_v it_o within_o almost_o a_o minute_n in_o time_n without_o need_n of_o draw_v a_o particular_a one_o and_o the_o say_a meridian_n be_v as_o i_o tell_v you_o in_o the_o beginning_n distinguish_v from_o the_o rest_n by_o prick_n which_o be_v distant_a from_o each_o other_o a_o quarter_n of_o a_o degree_n be_v useful_a on_o several_a occasion_n have_v thus_o fix_v our_o grand_a meridian_n or_o first_o longitude_n place_n that_o of_o other_o place_n follow_v we_o with_o ease_n for_o if_o you_o will_v know_v the_o longitude_n of_o constantinople_n draw_v but_o your_o string_n from_o the_o pole_n over_o it_o and_o it_o will_v cut_v the_o aequator_fw-la near_o the_o 62._o degree_n for_o the_o longitude_n require_v as_o you_o may_v ready_o perceive_v by_o the_o low_a little_o aequinoctial_a figure_n operation_n iii_o how_o to_o find_v out_o any_o place_n the_o longitude_n and_o latitude_n be_v give_v this_o operation_n be_v not_o only_o useful_a for_o the_o find_v out_o of_o town_n express_v on_o the_o globe_n when_o you_o can_v guess_v whereabout_o they_o be_v situate_v but_o also_o for_o the_o place_v they_o true_o in_o case_n they_o shall_v chance_v not_o to_o be_v set_v down_o suppose_v then_o constantinople_n be_v the_o town_n seek_v for_o and_o that_o you_o find_v its_o latitude_n to_o be_v 43_o g._n 5′_n and_o longitude_n 61_o g._n 46′_n in_o some_o book_n or_o geographical_a table_n i_o say_v suppose_v this_o you_o have_v nothing_o to_o do_v after_o have_v mount_v your_o bead_n by_o the_o help_n of_o the_o divide_v colurus_n 43_o g._n 5′_n above_o the_o aequator_fw-la but_o to_o move_v your_o string_n on_o its_o noose_n from_o the_o pole_n to_o 61._o 46._o in_o the_o say_fw-la aequator_fw-la and_o constantinople_n will_v be_v just_a under_o your_o bead_n and_o if_o in_o case_n of_o omission_n it_o shall_v not_o you_o may_v then_o if_o you_o please_v mark_v it_o out_o yourself_o for_o that_o be_v its_o exact_a place_n but_o by_o the_o way_n if_o the_o geographical_a table_n agree_v not_o with_o memorandum_n the_o longitude_n of_o your_o globe_n as_o tell_v you_o that_o v._n g._n constantinople_n have_v but_o 54_o g._n 36′_n you_o be_v then_o to_o look_v from_o whence_o the_o say_v table_n begin_v and_o find_v their_o commencement_n suppose_v at_o palma_n and_o that_o palma_n according_a to_o the_o former_a operation_n have_v by_o your_o globe_n 7_o g._n 10′_n of_o longitude_n you_o must_v add_v this_o number_n to_o your_o table_n and_o then_o you_o will_v agree_v operation_n iv._o to_o find_v the_o situation_n of_o any_o place_n according_a to_o the_o angle_n of_o position_n or_o point_n of_o the_o compass_n draw_v the_o string_n from_o the_o zenith_n over_o v_o g._n constantinople_n and_o it_o will_v cut_v the_o horizon_n 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