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be_v the_o ark_n of_o the_o meridian_n from_o the_o horizont_n unto_o the_o pole_n raise_v on_o high_a from_o the_o plain_a of_o the_o horizont_n the_o latitude_n of_o a_o place_n be_v the_o ark_n of_o the_o same_o meridian_n place_v between_o the_o equinoctial_a and_o verticiall_a point_n to_o conclude_v the_o latitude_n of_o a_o place_n and_o elevation_n of_o the_o pole_n do_v not_o differ_v in_o the_o magnitude_n or_o largeness_n but_o in_o stand_v only_o by_o the_o former_a figure_n appear_v that_o the_o ark_n of_o the_o longitude_n of_o place_n or_o city_n know_v be_v forthwith_o offer_v at_o the_o first_o sight_n as_o the_o ark_n e._n p._n or_o p._n o._n or_o o._n n._n etc._n etc._n and_o see_v the_o equatour_n be_v in_o compass_n about_o 360._o degree_n do_v whole_o ascend_v in_o 24._o hour_n above_o the_o horizont_n regular_o of_o this_o it_o come_v to_o pass_v while_o in_o each_o hour_n 15._o degree_n of_o the_o equatour_n do_v ascend_v that_o through_o the_o longitude_n of_o city_n it_o be_v easy_o know_v the_o hourly_a distance_n of_o one_o place_n unto_o a_o other_o see_v the_o sun_n come_v late_a to_o the_o meridian_n to_o they_o which_o be_v near_a to_o the_o east_n then_o to_o they_o in_o the_o west_n whereof_o if_o a_o city_n shall_v be_v situate_v in_o l._n and_o a_o other_o in_o k._n the_o ark_n l._n k._n shall_v be_v of_o 30._o degree_n then_o shall_v the_o sun_n come_v soon_o unto_o the_o easterly_a meridian_n k._n by_o two_o hour_n then_o unto_o the_o westerly_a but_o if_o one_o city_n shall_v be_v in_o p._n and_o the_o other_o in_o z._n then_o in_o latitude_n only_o shall_v they_o differ_v and_o shall_v be_v under_o one_o meridian_n which_o be_v declare_v in_o the_o last_o part_n of_o the_o description_n of_o the_o meridian_n what_o the_o office_n and_o utility_n of_o the_o meridiane_a be_v 1_o the_o utility_n and_o use_n of_o this_o circle_n be_v many_o of_o which_o the_o first_o be_v that_o it_o distinguish_v the_o day_n and_o night_n into_o 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thwartnesse_n of_o the_o horizont_n which_o cause_v the_o variety_n &_o notable_a difference_n of_o the_o inclination_n of_o the_o zodiac_n unto_o the_o horizont_n of_o the_o angle_n and_o largeness_n of_o the_o rise_n but_o they_o begin_v to_o account_v from_o noon_n or_o midnight_n the_o sun_n then_o occupy_v the_o meridian_n through_o the_o sun_n which_o congruence_n all_o the_o meridiane_n have_v with_o the_o right_a horizont_n and_o that_o a_o lesser_a variety_n of_o the_o inclination_n of_o the_o zodiac_n happen_v unto_o the_o meridiane_fw-la and_o angle_n which_o it_o make_v with_o the_o meridiane_n also_o in_o this_o circle_n be_v the_o zenith_n or_o direct_a point_n note_v from_o which_o the_o distance_n of_o the_o star_n and_o parallel_v circle_n be_v gather_v 4_o in_o the_o meridiane_n as_o in_o the_o subject_n the_o distance_n of_o the_o star_n from_o the_o equatoure_n the_o latitude_n of_o place_n and_o the_o elevation_n of_o the_o pole_n be_v account_v for_o the_o studious_a and_o skilful_a practisioner_n observe_v the_o latitude_n of_o place_n and_o the_o elevation_n of_o the_o pole_n not_o to_o differ_v in_o the_o quantity_n but_o in_o the_o stand_n only_o for_o the_o elevation_n of_o the_o pole_n be_v the_o ark_n of_o the_o meridiane_n from_o the_o horizont_n raise_v unto_o the_o pole_n the_o latitude_n of_o the_o place_n be_v the_o ark_n of_o the_o same_o meridian_n contain_v between_o the_o equatour_n and_o verticiall_a point_n so_o that_o it_o be_v manifest_a that_o these_o ark_n differ_v in_o the_o stand_n do_v agree_v in_o magnitude_n who_o verticiall_a point_n one_o meridiane_n contain_v but_o not_o one_o parallel_n by_o a_o equal_a space_n from_o the_o west_n be_v unequal_a distant_a from_o the_o equatour_n and_o be_v then_o say_v to_o differ_v in_o the_o latitude_n only_o contrariwise_o to_o who_o top_n one_o and_o the_o same_o parallel_n and_o not_o one_o meridian_n but_o each_o place_n proper_a those_o by_o like_a space_n from_o 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which_o by_o a_o mutual_a section_n do_v make_v a_o angle_n the_o compliment_n of_o the_o latitude_n be_v know_v by_o the_o degree_n abate_v from_o 90._o in_o the_o degree_n of_o the_o latitude_n further_o by_o the_o sun_n meridian_n have_v and_o find_v you_o may_v easy_o conceive_v the_o elevation_n of_o the_o pole_n and_o habitude_n of_o the_o sphere_n for_o the_o whole_a quarter_n be_v of_o 90._o degree_n see_v the_o sun_n meridian_n altitude_n in_o the_o equinoctial_a must_v be_v subtract_v from_o 90._o degree_n the_o rest_n show_v the_o elevation_n of_o the_o pole_n as_o for_o example_n the_o sun_n meridian_n altitude_n of_o viteberge_n in_o germany_n in_o the_o time_n of_o the_o equinoctial_a be_v of_o 38._o degree_n and_o 10._o minute_n the_o rest_n of_o the_o degree_n of_o the_o quarter_n shall_v appear_v to_o be_v 51._o degree_n and_o 50._o minute_n which_o elevation_n of_o the_o pole_n near_o agree_v to_o london_n so_o that_o by_o so_o many_o degree_n be_v the_o pole_n 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two_o quarter_n the_o common_a ark_n be_v abate_v which_o be_v between_o the_o zenith_n and_o pole_n of_o the_o world_n and_o the_o rest_n of_o the_o equal_n remain_v as_o the_o ark_n which_o be_v from_o the_o equinoctial_a unto_o the_o zenith_n and_o call_v the_o latitude_n of_o the_o place_n and_o the_o ark_n which_o be_v from_o the_o pole_n of_o the_o world_n unto_o the_o horizont_a also_o call_v the_o elevation_n of_o the_o pole_n as_o may_v be_v understand_v of_o the_o former_a viteberge_n that_o be_v of_o 51._o degree_n and_o 50._o minute_n yet_o that_o you_o may_v easy_o find_v and_o know_v the_o elevation_n of_o the_o pole_n of_o your_o city_n or_o town_n you_o must_v first_o obtain_v and_o have_v the_o sun_n meridian_n altitude_n which_o workmanly_o may_v be_v have_v and_o observe_v by_o the_o shadow_n as_o when_o the_o sun_n altitude_n in_o the_o time_n of_o the_o equinoctial_a be_v precise_o of_o 45._o degree_n the_o shadow_n than_o be_v like_a to_o the_o gnomone_n which_o be_v at_o venice_n as_o pliny_n write_v also_o of_o milan_n and_o lion_n for_o the_o sun_n to_o they_o be_v in_o the_o time_n of_o the_o equinoctial_a in_o the_o middle_n of_o the_o quarter_n but_o when_o the_o sun_n altitude_n exceed_v 45._o degree_n then_o be_v the_o shadow_n cause_v lesser_a as_o of_o rome_n where_o the_o sun_n meridian_n altitude_n in_o the_o equinoctial_a be_v of_o 42._o degree_n and_o 10._o minute_n so_o that_o the_o shadow_n be_v there_o short_a also_o pliny_n write_v of_o rome_n that_o the_o nine_o part_n of_o the_o gnomon_n in_o the_o equinoctial_a do_v lack_n of_o the_o noon_n shadow_n but_o when_o the_o sun_n altitude_n be_v lesser_a than_o 45._o degree_n the_o shadow_n of_o the_o gnomon_n be_v cause_v long_o the_o like_a be_v with_o we_o through_o all_o winter_n and_o the_o time_n of_o the_o equinoctial_a for_o we_o see_v the_o shadow_n of_o man_n body_n to_o be_v long_o for_o that_o the_o sun_n altitude_n in_o that_o time_n be_v never_o 45._o degree_n 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and_o orchades_n that_o be_v into_o the_o north_n and_o east_n which_o be_v distant_a from_o the_o further_a bind_v of_o scotland_n but_o three_o day_n sail_v if_o prosperous_a wind_n be_v their_o help_n at_o this_o day_n man_n have_v find_v beyond_o thylen_n but_o somewhat_o into_o the_o east_n and_o most_o large_a bound_n stretch_v and_o find_v beyond_o the_o arctic_a or_o northerly_a circle_n &_o these_o be_v whole_a without_o break_v of_o any_o sea_n between_o and_o contain_v suetia_n norway_n iseland_n grunland_n and_o lapeland_n the_o kingdom_n of_o suetia_n appear_v most_o large_a and_o contain_v sundry_a nation_n and_o people_n among_o which_o they_o be_v of_o most_o account_n the_o east_n and_o west_n gutland_n people_n inhabit_v near_o to_o norway_n and_o under_o the_o king_n of_o suetia_n be_v the_o lapeland_n people_n as_o the_o finelapon_n and_o dikilapon_n where_o be_v a_o wild_a and_o fierce_a people_n dwell_v almost_o under_o the_o pole_n arctic_a especial_o the_o 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mile_n be_v wrought_v into_o part_n of_o the_o difference_n of_o longitude_n and_o any_o scruple_n after_o remain_v divide_v those_o by_o 4._o for_o by_o so_o many_o minute_n of_o a_o degree_n do_v a_o german_a mile_n answer_n that_o the_o distance_n shall_v make_v as_o ptolemy_n write_v of_o the_o place_n under_o the_o equatour_n the_o high_a land_n or_o mountain_n of_o the_o satyr_n in_o the_o country_n of_o syna_n who_o longitude_n be_v of_o 175_o degree_n and_o no_o minute_n nor_o have_v any_o latitude_n myrica_fw-la a_o isle_n of_o ethiope_n under_o egypt_n who_o longitude_n be_v of_o 85._o degree_n the_o angle_n of_o the_o difference_n of_o longitude_n between_o the_o meridians_fw-la of_o these_o place_n be_v straight_o or_o right_o and_o contain_v a_o whole_a quarter_n or_o 60._o degree_n the_o like_a be_v these_o place_n stand_v under_o the_o equatour_n colipolis_n a_o city_n of_o india_n beyond_o the_o river_n ganges_n which_o have_v the_o longitude_n 194._o degree_n and_o 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that_o c._n b._n the_o ark_n of_o the_o distance_n of_o place_n which_o reach_v out_o right_a be_v a_o quarter_n of_o the_o great_a circle_n wherefore_o if_o the_o degree_n be_v multiply_v by_o 15._o and_o the_o minute_n divide_v by_o 4._o the_o distance_n than_o shall_v be_v know_v as_o for_o example_n nubarta_n of_o taprobone_n have_v the_o longitude_n 121._o degree_n and_o 20._o minute_n but_o no_o latitude_n the_o city_n pyse_v of_o the_o tuscans_n in_o italy_n have_v the_o longitude_n 31._o degree_n and_o 20._o minute_n almost_o the_o latitude_n of_o 42._o degree_n and_o 11._o minute_n then_o the_o angle_n of_o the_o difference_n of_o longitude_n be_v right_a for_o the_o difference_n be_v of_o 90._o degree_n or_o a_o whole_a quadrant_a these_o then_o multiply_v by_o 15._o do_v procreate_v or_o bring_v forth_o the_o distance_n to_o be_v of_o 13_o 50._o german_a mile_n essina_fw-la a_o mart-towne_n or_o principal_a â—itty_n of_o aethiope_n under_o the_o government_n of_o egypt_n 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97._o degree_n and_o 20._o minute_n the_o quadrant_a be_v abate_v there_o remain_v 7._o degree_n and_o 20._o minute_n the_o complement_n of_o the_o latitude_n of_o tyrus_n be_v of_o 56._o degree_n and_o 40._o minute_n if_o of_o two_o place_n give_v either_o stand_v without_o the_o equatoure_n towards_o some_o one_o of_o the_o opposite_a quarter_n and_o the_o other_o under_o the_o equatoure_n then_o be_v the_o reason_n of_o the_o stand_v consider_v and_o the_o angle_n of_o the_o difference_n of_o longitude_n for_o the_o one_o differ_v either_o by_o like_a space_n from_o each_o bound_n and_o be_v near_a to_o the_o pole_n the_o other_o to_o the_o equatoure_n the_o same_o appear_v by_o the_o compare_v latitude_n which_o like_a top_n of_o either_o place_n contain_v the_o same_o parallel_n the_o unlike_a be_v distant_a and_o the_o parallel_n by_o a_o space_n separate_v towards_o each_o place_n do_v argue_v peculiar_a and_o proper_a top_n but_o the_o angle_n of_o the_o difference_n of_o longitude_n either_o it_o be_v right_a blunt_a or_o sharp_a this_o of_o the_o place_n and_o diversity_n of_o the_o angle_n do_v much_o vary_v or_o alter_v the_o reason_n &_o method_n of_o the_o search_n of_o these_o if_o two_o place_n give_v have_v equal_a ark_n of_o the_o latitude_n and_o from_o the_o middle_n or_o half_a of_o the_o equatoure_n be_v alike_o distant_a and_o how_o much_o so_o ever_o the_o angle_n of_o the_o difference_n of_o longitude_n be_v as_o here_o under_o the_o difference_n of_o longitude_n be_v in_o the_o first_o of_o the_o example_n teach_v yet_o be_v the_o arke_n of_o the_o latitude_n agree_v and_o equal_o find_v so_o that_o in_o this_o example_n appear_v no_o difference_n but_o in_o the_o only_a longitude_n of_o the_o place_n offer_v as_o for_o example_n the_o longitude_n of_o dansk_a be_v of_o 39_o degree_n and_o twoe_o scruple_n or_o minute_n the_o latitude_n of_o the_o same_o have_v 54_o degree_n and_o 48._o minute_n the_o longitude_n of_o lubeck_n be_v 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both_o appear_v to_o contain_v 1077._o german_a mile_n and_o a_o half_a if_o of_o two_o place_n give_v the_o one_o be_v further_a distant_a from_o the_o equatour_n than_o the_o other_o and_o the_o greatness_n of_o the_o compliment_n of_o either_o latitude_n differ_v as_o that_o the_o arke_n of_o the_o latitude_n be_v unequal_a so_o that_o the_o diversity_n of_o the_o angle_n include_v with_o the_o ark_n of_o the_o compliment_n shall_v vary_v the_o method_n or_o reason_n of_o the_o search_n for_o that_o the_o one_o give_v and_o form_v a_o right_a angle_n another_o a_o sharp_a another_o a_o blunt_a angle_n yet_o to_o these_o the_o angle_n of_o the_o difference_n of_o longitude_n be_v right_a the_o example_n of_o two_o place_n differ_v alike_o both_o in_o the_o longitude_n and_o latitude_n here_o appear_v the_o city_n tacola_n which_o at_o this_o day_n be_v call_v malchaia_n or_o magna_n a_o place_n of_o much_o resort_n of_o merchant_n this_o from_o the_o west_n have_v the_o longitude_n of_o 160._o degree_n and_o 30._o minute_n of_o latitude_n from_o the_o equatour_n it_o be_v 4._o degree_n and_o 15._o scruple_n distant_a the_o other_o city_n and_o place_n in_o the_o country_n of_o pontus_n name_v trapezus_n be_v a_o head_n city_n of_o cappadocia_n and_o be_v the_o ancient_a seat_n of_o the_o emperor_n this_o have_v the_o longitude_n of_o 70._o degree_n and_o 30._o minute_n and_o the_o latitude_n of_o the_o same_o be_v of_o 43._o degree_n and_o 5._o scruple_n the_o difference_n of_o longitude_n between_o the_o one_o and_o the_o other_o be_v of_o 90._o degree_n the_o ark_n of_o distance_n between_o both_o place_n be_v of_o 87._o degree_n and_o 6._o minute_n to_o which_o 1306._o &_o a_o half_a german_a mile_n answer_v if_o the_o unequal_a arke_n of_o the_o latitude_n and_o angle_v of_o the_o difference_n of_o longitude_n be_v lesser_a than_o the_o right_n it_o canse_v a_o diverse_a reason_n of_o the_o search_n by_o which_o the_o ark_n of_o the_o complement_n of_o the_o great_a latitude_n do_v vary_v three_o way_n as_o it_o be_v great_a or_o lesser_a and_o as_o with_o the_o ark_n by_o the_o second_o in_o quisition_n sure_o know_v and_o be_v join_v form_n either_o more_o or_o less_o a_o quarter_n of_o the_o circle_n or_o thus_o that_o the_o angle_n which_o the_o unequal_a compliment_n of_o the_o unequal_a latitude_n include_v be_v sharp_a that_o be_v and_o if_o the_o ark_n of_o the_o latitude_n of_o either_o place_n be_v unequal_a and_o the_o difference_n of_o longitude_n be_v lesser_a than_o the_o quadrant_a as_o in_o this_o example_n more_o plain_a appear_v of_o twoe_o place_n be_v of_o sundry_a longitude_n that_o worthy_a city_n trapezus_n of_o cappadocia_n who_o longitude_n be_v of_o 70._o degree_n and_o 30._o minute_n the_o latitude_n 43._o degree_n and_o 5._o minute_n the_o longitude_n of_o that_o well_o know_a city_n of_o rome_n have_v 39_o degree_n and_o 8._o scruple_n the_o latitude_n 41._o degree_n and_o 8._o minute_n the_o difference_n of_o longitude_n between_o the_o one_o and_o the_o other_o be_v of_o 33._o degree_n and_o 22._o minute_n another_o example_n not_o unlike_o the_o former_a and_o not_o much_o vary_v from_o the_o former_a as_o the_o longitude_n of_o jerusalem_n which_o be_v of_o 66._o degree_n and_o no_o minute_n the_o latitude_n of_o 31._o degree_n and_o 40._o scruple_n the_o longitude_n of_o viteberge_n be_v of_o 30._o degree_n and_o 30._o minute_n the_o latitude_n 51._o degree_n and_o 50._o scruple_n the_o difference_n between_o the_o one_o and_o the_o other_o of_o longitude_n be_v of_o 35._o degree_n and_o 50._o scruple_n if_o in_o place_n unequal_o distant_a from_o the_o equatoure_n the_o angle_n of_o the_o difference_n of_o longitude_n be_v blunt_a by_o which_o the_o difference_n of_o longitude_n shall_v appear_v great_a than_o the_o quadrant_a or_o thus_o that_o
the_o angle_n of_o the_o difference_n of_o longitude_n be_v blunt_a see_v the_o place_n be_v further_a distant_a than_o a_o whole_a quarter_n and_o thereby_o cause_v a_o diverse_a reason_n and_o way_n of_o search_n from_o the_o former_a which_o semblable_o the_o diverse_a quantity_n of_o the_o complement_n of_o the_o great_a latitude_n do_v three_o manner_n of_o way_n vary_v as_o in_o the_o same_o ark_n which_o perfect_o know_v by_o the_o second_o be_v either_o great_a or_o lesser_a the_o example_n of_o this_o appear_v of_o these_o two_o place_n the_o noble_a city_n antiochia_n in_o syria_n which_o be_v after_o call_v seleucia_n have_v the_o longitude_n of_o 106._o degree_n and_o no_o minute_n the_o latitude_n be_v of_o 40._o degree_n and_o 40._o scruple_n the_o other_o of_o toletum_n who_o longitude_n be_v of_o 7._o degree_n and_o 4._o scruple_n the_o latitude_n have_v 37._o degree_n and_o 50._o minute_n the_o difference_n of_o longitude_n be_v of_o 98._o degree_n and_o 56._o scruple_n which_o deduct_v from_o the_o half_a circle_n or_o 180._o degree_n the_o difference_n that_o remain_v unto_o the_o half_a circle_n be_v of_o 81._o degree_n and_o 4._o minute_n the_o like_a example_n not_o much_o vary_v from_o the_o former_a of_o these_o two_o place_n as_o the_o noble_a city_n of_o portugal_n name_v lysebone_n who_o longitude_n be_v of_o 4._o degree_n and_o 18._o scruple_n the_o latitude_n have_v 39_o degree_n and_o 38._o scruple_n the_o other_o name_v calecute_v although_o the_o latitude_n differ_v have_v the_o longitude_n of_o 112._o degree_n and_o no_o minute_n the_o latitude_n be_v of_o 5._o degree_n and_o no_o minute_n the_o difference_n of_o longitude_n contain_v 107._o degree_n and_o 42._o scruple_n more_o than_o the_o quadrant_a the_o same_o deduct_v from_o the_o half_a circle_n do_v express_v the_o difference_n remain_v unto_o the_o half_a circle_n to_o be_v of_o 72._o degree_n and_o 18._o minute_n the_o complement_n of_o the_o great_a latitude_n be_v of_o 50._o degree_n and_o 22._o scruple_n the_o complement_n of_o the_o lesser_a latitude_n be_v of_o 85._o degree_n and_o no_o scruple_n another_o example_n of_o two_o place_n distant_a from_o the_o equatour_n of_o which_o the_o one_o be_v distant_a from_o the_o middle_n of_o the_o equatour_n into_o the_o north_n and_o the_o other_o into_o the_o south_n as_o this_o example_n further_o instruct_v the_o one_o be_v the_o will_v of_o thilen_n which_o in_o ptholomiesâ—â—me_n â—â—me_z be_v the_o uttermost_a bond_n of_o the_o earth_n know_v northward_o that_o have_v the_o longitude_n of_o 33._o degree_n the_o latitude_n northerly_a of_o 63._o degree_n the_o other_o call_v the_o will_v of_o s._n thomas_n have_v the_o longitude_n of_o 27_o degree_n and_o 20._o minute_n the_o latitude_n southerly_a of_o 16._o degree_n the_o difference_n of_o longitude_n be_v of_o 5â—_n degree_n â—nd_v 40._o minute_n the_o complement_n of_o the_o latitude_n northerly_a be_v of_o 26._o degree_n a_o three_o example_n of_o the_o difference_n of_o other_o two_o place_n as_o basâ—a_o of_o taprobane_n which_o ptolemy_n affirm_v to_o be_v in_o longitude_n 126._o degree_n and_o in_o latitude_n towards_o the_o south_n 6._o degree_n and_o 30._o scruple_n the_o other_o name_v stocholma_n in_o the_o realm_n of_o suecia_n have_v the_o longitude_n of_o 42._o degree_n and_o 38._o scruple_n and_o the_o latitude_n of_o 60._o degree_n &_o 30._o scruple_n the_o complement_n of_o the_o latitude_n boreal_a be_v 29._o degree_n and_o 30._o minute_n the_o common_a way_n of_o measure_v of_o place_n with_o their_o space_n by_o the_o rule_n of_o longitude_n and_o latitude_n here_o before_o i_o have_v somewhat_o write_v of_o sundry_a habitable_a place_n on_o the_o earth_n who_o sundry_a point_n differ_v between_o the_o one_o and_o the_o other_o either_o in_o the_o only_a longitude_n or_o in_o the_o only_a latitude_n or_o in_o the_o longitude_n and_o latitude_n both_o together_o those_o place_n which_o do_v differ_v in_o the_o only_a longitude_n be_v distant_a by_o equal_a space_n from_o the_o equatoure_n towards_o either_o of_o the_o pole_n of_o the_o world_n the_o verticiall_a point_n of_o those_o place_n end_v by_o the_o same_o parallel_n join_v next_o the_o same_o space_n between_o yet_o each_o have_v their_o own_o proper_a meridians_fw-la be_v not_o distant_a by_o a_o like_a space_n from_o the_o westerly_a bind_v the_o distance_n of_o these_o be_v always_o gather_v and_o note_v in_o the_o same_o parallel_n which_o common_o belong_v to_o either_o place_n stand_v or_o hang_v right_o over_o the_o top_n of_o they_o those_o place_n which_o do_v differ_v in_o the_o only_a latitude_n be_v stand_v â—â—der_o the_o same_o meridiane_n but_o they_o have_v diverse_a parallel_n use_v each_o proper_a and_o those_o continual_o distant_a unequal_o either_o toward_o one_o pole_n from_o the_o middle_n of_o the_o equatour_n if_o either_o place_n decline_v unto_o one_o and_o the_o same_o quarter_n or_o otherwise_o from_o the_o middle_n of_o the_o equatoure_n sever_v and_o distant_a into_o the_o contrary_a quarter_n by_o equal_a or_o unequal_a space_n if_o that_o one_o of_o the_o place_n look_v into_o the_o south_n and_o the_o other_o into_o the_o north_n the_o distance_n of_o these_o be_v always_o account_v in_o the_o common_a meridian_n those_o place_n which_o do_v differ_v both_o in_o the_o longitude_n and_o latitude_n together_o or_o both_o decline_n toward_o one_o pole_n of_o the_o world_n or_o separate_v and_o distant_a from_o the_o midst_n of_o the_o equatoure_n toward_o the_o opposite_a pole_n as_o the_o one_o look_v into_o y_fw-fr â—_o north_n and_o the_o other_o into_o the_o south_n or_o else_o by_o equal_a parallel_n distant_a from_o the_o equatour_n of_o which_o two_o only_a be_v in_o the_o sphere_n if_o they_o be_v reduce_v and_o apply_v unto_o one_o great_a circle_n per_fw-la 3._o secundi_fw-la theodosij_n or_o else_o be_v under_o by_o unequal_a parallel_n and_o by_o a_o unequal_a space_n the_o difference_n of_o the_o longitude_n of_o those_o which_o either_o be_v toward_o they_o or_o towards_o the_o pole_n equal_o distant_a be_v always_o gather_v in_o the_o middle_a parallel_n between_o either_o of_o the_o bond_n by_o arithmetical_a proportion_n as_o afore_o teach_v but_o in_o those_o place_n which_o have_v equal_a parallel_n and_o equal_o dastant_a unto_o the_o opposite_a quarter_n the_o difference_n of_o longitude_n be_v imagine_v &_o note_v in_o either_o of_o the_o equal_a parallel_n therefore_o the_o ark_n have_v the_o distance_n of_o the_o place_n stand_v by_o the_o next_o space_n draw_v overthwart_o by_o the_o point_n of_o those_o place_n which_o with_o the_o ark_n of_o the_o difference_n of_o either_o both_o of_o the_o longitude_n and_o latitude_n do_v form_n and_o make_v a_o spherical_a tryangle_n right_a corner_a always_o in_o the_o upper_a face_n of_o the_o globe_n if_o that_o two_o meridiane_n meet_v and_o end_v at_o the_o pole_n of_o the_o world_n and_o be_v cut_v by_o the_o overthwart_a cyrcumference_n of_o the_o parallel_n do_v make_v with_o the_o include_v arke_n of_o they_o right_a corner_a tryangle_n through_o the_o four_o right_o lesser_a angle_n but_o the_o angle_n be_v not_o right_a the_o ark_n of_o the_o distance_n of_o the_o place_n do_v divide_v they_o into_o two_o right_a corner_a tryangle_n one_o of_o those_o tryangle_n be_v use_v in_o the_o common_a account_n for_o the_o right_a corner_a because_o in_o place_n not_o far_o distant_a from_o the_o equatoure_n the_o angle_n contain_v between_o the_o mutual_a section_n of_o the_o meridians_fw-la and_o parallel_n do_v not_o so_o much_o vary_v from_o the_o right_a angle_n but_o in_o place_n far_o distant_a from_o the_o equatour_n they_o vary_v very_o much_o now_o the_o rule_n for_o the_o diverse_a stand_n of_o place_n shall_v be_v teach_v in_o a_o easy_a and_o common_a manner_n if_o place_n do_v differ_v in_o the_o only_a longitude_n to_o the_o search_a and_o know_v of_o this_o like_v as_o in_o the_o former_a be_v the_o longitude_n and_o latitude_n of_o place_n give_v require_v by_o which_o they_o be_v find_v see_v in_o the_o latitude_n there_o be_v no_o diversity_n the_o difference_n of_o longitude_n be_v only_o to_o be_v consider_v by_o deduct_v the_o lesser_a longitude_n out_o of_o the_o great_a and_o then_o howemany_a mile_n by_o proportion_n of_o the_o parallel_n under_o which_o the_o place_n stand_v or_o lie_v to_o the_o equatoure_n answer_v to_o one_o degree_n of_o the_o same_o the_o same_o do_v that_o rule_n set_v forth_o in_o the_o form_n of_o a_o table_n here_o follow_v declare_v be_v draw_v and_o make_v unto_o this_o use_n by_o the_o learned_a in_o which_o the_o mile_n that_o answer_v to_o one_o degree_n of_o each_o parallel_n be_v there_o find_v and_o note_v unto_o one_o degree_n of_o the_o distance_n of_o the_o parallel_n from_o the_o equatour_n if_o to_o the_o whole_a
degree_n of_o the_o distance_n of_o the_o parallel_n do_v minute_n depend_v then_o from_o the_o difference_n of_o the_o two_o next_o number_n to_o one_o degree_n may_v the_o proportional_a part_n be_v deduct_v or_o draw_v which_o from_o the_o number_n of_o the_o mile_n express_v unto_o a_o whole_a degree_n be_v abate_v that_o the_o parallel_n succeed_v may_v be_v little_a &_o little_o be_v cause_v to_o stretch_n &_o appear_v narower_n to_o be_v brief_a the_o mile_n with_o the_o scruple_n or_o quarter_n if_o any_o be_v adjoin_v let_v they_o be_v reduce_v into_o the_o whole_a ark_n of_o the_o difference_n of_o longitude_n which_o then_o shall_v manifest_o show_v and_o express_v the_o measure_a space_n by_o the_o german_a mile_n ptolemy_n when_o he_o have_v learn_v the_o longitude_n and_o latitude_n of_o certain_a notable_a place_n he_o can_v extract_v and_o gather_v by_o they_o the_o other_o unknown_a place_n by_o the_o distance_n true_o learn_v from_o traveller_n for_o by_o the_o longitude_n and_o latitude_n know_v of_o two_o circle_n and_o the_o distance_n also_o of_o they_o from_o any_o three_o place_n there_o be_v then_o offer_v and_o give_v to_o know_v as_o well_o the_o longitude_n as_o the_o latitude_n of_o the_o three_o place_n further_o in_o any_o two_o place_n lie_v and_o be_v in_o the_o upper_a face_n of_o the_o earth_n be_v five_o note_n common_o learn_v the_o distance_n of_o they_o convert_v into_o degree_n the_o latitude_n of_o the_o one_o and_o the_o latitude_n of_o the_o other_o the_o difference_n of_o longitude_n the_o angle_n under_o the_o circumferencial_a distance_n and_o the_o meridians_fw-la contain_v by_o the_o other_o of_o the_o which_o five_o if_o three_o only_o be_v know_v it_o be_v certain_a that_o the_o other_o two_o may_v easy_o come_v to_o knowledge_n by_o the_o practice_n and_o skill_n of_o the_o spherical_a tryangle_n a_o example_n of_o these_o former_a word_n as_o touch_v the_o difference_n of_o longitude_n of_o two_o place_n the_o latitude_n be_v alike_o as_o the_o city_n byzantium_n now_o call_v constantinople_n who_o longitude_n be_v 55._o degree_n and_o no_o minute_n the_o latitude_n have_v 43._o degree_n and_o 5._o minute_n the_o other_o city_n trapezus_n have_v the_o longitude_n of_o 70._o degree_n and_o 50._o minute_n the_o latitude_n of_o 43._o degree_n and_o 5._o minute_n the_o difference_n of_o longitude_n be_v of_o 15._o degree_n and_o 50._o minute_n to_o one_o degree_n of_o the_o common_a parallel_n and_o to_o each_o place_n do_v 10._o german_a mile_n with_o 29_o 30._o answer_n or_o agree_v these_o now_o bring_v into_o the_o difference_n of_o longitude_n do_v cause_n &_o make_v 174._o german_a mile_n almost_o the_o like_a example_n to_o the_o former_a be_v arbela_n of_o assiria_n which_o have_v the_o longitude_n of_o 80_o and_o no_o minute_n the_o latitude_n of_o 37._o and_o 15._o minute_n the_o other_o athens_n who_o longitude_n be_v of_o 52._o degree_n and_o 15._o minute_n the_o latitude_n 37._o degree_n and_o 15._o minute_n the_o difference_n be_v of_o 27._o degree_n and_o 45._o minute_n other_o brief_a example_n  _fw-fr lon._n lati._n areca_n in_o comagena_n be_v a_o part_n of_o syria_n 70._o 10._o 37._o 15._o megara_n the_o country_n of_o euclid_n 52._o 0._o 37._o 15._o the_o difference_n be_v of_o 18._o 10._o  _fw-fr lon._n lat._n philippi_n a_o city_n in_o thracia_n or_o country_n of_o alexandria_n 50._o 45._o 41._o 50._o the_o royal_a city_n of_o room_n 36._o 20._o 41._o 50._o the_o difference_n be_v of_o 14._o 25._o longitude_n lipsia_n 29._o 58._o 51._o 24._o the_o difference_n of_o long_a be_v 9_o degr_n &_o 42._o min._n the_o difference_n of_o long_a be_v 6._o degree_n &_o 4._o min._n antwerp_n 20._o 16._o 51._o 28._o vratislavia_n 34._o 34_o 51._o 10._o erphordia_fw-la 28._o 30._o 51._o 10._o if_o place_n do_v differ_v in_o the_o only_a latitude_n or_o that_o both_o be_v place_v towards_o one_o pole_n or_o either_o distant_a from_o the_o middle_n of_o the_o equatour_n so_o that_o in_o the_o only_o latitude_n the_o place_n differ_v when_o the_o longitude_n be_v like_a the_o standing_z of_o the_o place_n be_v to_o be_v consider_v toward_o either_o pole_n whether_o either_o place_n decline_v towards_o one_o pole_n or_o that_o the_o one_o be_v southerly_a and_o the_o other_o northerly_a if_o they_o decline_v unto_o one_o place_n and_o quarter_n then_o deduct_v the_o lesser_a latitude_n out_o of_o the_o more_o and_o the_o difference_n of_o latitude_n shall_v appear_v if_o either_o be_v distant_a from_o the_o middle_n of_o the_o equatoure_n the_o latitude_n join_v do_v show_v the_o difference_n the_o degree_n of_o the_o difference_n wrought_v by_o 15._o and_o the_o scruple_n divide_v by_o 4._o shall_v offer_v &_o give_v the_o estimate_n distance_n in_o german_a mile_n as_o in_o this_o example_n the_o city_n of_o noriberge_n have_v 28._o degree_n and_o 20._o minute_n of_o longitude_n the_o latitude_n be_v of_o 49._o degree_n and_o 24._o minute_n the_o other_o be_v mylayne_v who_o longitude_n be_v of_o 28._o degree_n and_o 20._o minute_n the_o latitude_n have_v 45._o degree_n and_o 6._o minute_n the_o difference_n of_o latitude_n be_v of_o 4._o degree_n and_o 18._o minute_n the_o space_n between_o be_v 64._o mile_n and_o a_o half_a like_a example_n be_v these_o trapezus_n 70._o 15._o 43._o 5._o the_o difference_n of_o latit_fw-la be_v 5._o degree_n &_o 45._o min._n the_o difference_n of_o latit_fw-la be_v 6._o degree_n &_o 44._o min._n antioch_n 70._o 15._o 37._o 20._o padua_n 31._o 50._o 51._o 0._o budissina_fw-la 31._o 50._o 44._o 16._o if_o two_o differ_v together_o in_o the_o longitude_n and_o latitude_n and_o that_o either_o decline_v toward_o one_o pole_n then_o in_o either_o towards_o the_o place_n differ_v as_o in_o the_o longitude_n and_o latitude_n be_v the_o difference_n of_o the_o space_n from_o either_o bound_n of_o the_o latitude_n and_o longitude_n gather_v the_o half_a difference_n of_o the_o latitude_n add_v to_o the_o lesser_a altitude_n shall_v show_v the_o parallel_n in_o which_o the_o difference_n of_o longitude_n be_v account_v with_o that_o parallel_n by_o this_o rule_n be_v the_o mile_n gather_v and_o know_v which_o answer_n or_o agree_v to_o one_o degree_n these_o find_v reduce_v into_o the_o whole_a difference_n of_o the_o longitude_n and_o that_o which_o proceed_v agréeable_o of_o the_o same_o that_o be_v multiply_v in_o itself_o or_o arise_v of_o the_o multiplication_n keep_v after_o the_o degree_n of_o the_o difference_n of_o longitude_n reduce_v into_o 15._o and_o the_o minute_n annex_v if_o any_o such_o be_v distribute_v or_o divide_v by_o four_o that_o which_o arise_v of_o either_o work_n reduce_v joint_o one_o to_o the_o other_o and_o add_v to_o the_o number_n keep_v afore_o for_o of_o the_o whole_a gather_a may_v the_o square_a root_n be_v attain_v which_o show_v the_o distance_n of_o place_n as_o by_o a_o like_a example_n the_o city_n of_o witeberge_n have_v the_o 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latitude_n of_o the_o other_o as_o the_o former_a example_n show_v in_o such_o sort_n that_o the_o degree_n of_o the_o other_o and_o likewise_o the_o minute_n under_o the_o minute_n after_o seek_v the_o difference_n as_o well_o of_o the_o longitude_n and_o latitude_n in_o this_o manner_n subtract_v the_o lesser_a longitude_n from_o the_o great_a the_o remainder_n be_v call_v the_o difference_n of_o the_o longitude_n after_o deduct_v the_o lesser_a latitude_n out_o of_o the_o more_o and_o the_o difference_n of_o the_o latitude_n shall_v remain_v by_o the_o difference_n of_o the_o longitude_n and_o latitude_n shall_v the_o distance_n of_o city_n give_v be_v gather_v but_o in_o that_o there_o be_v three_o manner_n difference_n of_o place_n as_o that_o there_o be_v certain_a place_n which_o differ_v in_o the_o only_a latitude_n that_o be_v under_o one_o meridiane_n and_o yet_o lie_v under_o diverse_a parallel_n and_o certain_a that_o differ_v in_o the_o only_a longitude_n that_o be_v 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minute_n the_o latitude_n of_o viteberge_n be_v of_o 51._o degree_n and_o 50._o minute_n these_o now_o differ_v in_o the_o only_a latitude_n which_o difference_n of_o the_o latitude_n be_v of_o 6._o degree_n and_o 36._o minute_n that_o be_v 99_o german_a mile_n so_o much_o be_v the_o distance_n almost_o between_o trydent_n and_o viteberge_n another_o the_o longitude_n of_o thunis_n be_v of_o â—6_n degree_n and_o 50._o minute_n the_o longitude_n of_o salerne_n in_o a_o manner_n the_o same_o the_o latitude_n of_o thunis_n be_v of_o 32._o degree_n and_o 30._o minute_n the_o latitude_n of_o salerne_n be_v of_o 40._o degree_n and_o 30._o minute_n the_o difference_n of_o latitude_n be_v of_o 〈◊〉_d degree_n &_o 〈◊〉_d minute_n that_o be_v 120._o mile_n and_o somuch_o be_v the_o distance_n between_o thunis_n and_o salerne_n another_o the_o city_n of_o york_n and_o the_o town_n of_o berwick_n agree_v in_o longitude_n for_o the_o longitude_n of_o either_o place_n be_v of_o 17._o degree_n and_o no_o minute_n but_o they_o differ_v in_o latitude_n in_o that_o the_o latitude_n of_o york_n be_v of_o 54._o degree_n &_o no_o minute_n the_o latitude_n of_o berwick_n be_v of_o 56._o degree_n &_o 50._o minute_n the_o difference_n of_o the_o latitude_n be_v of_o 2._o degree_n and_o 50._o minute_n that_o be_v 210._o english_a mile_n so_o much_o in_o a_o manner_n be_v the_o distance_n between_o the_o city_n of_o york_n and_o berwick_n another_o the_o city_n of_o london_n and_o northampton_n in_o a_o manner_n be_v of_o like_a longitude_n for_o the_o longitude_n of_o london_n be_v of_o 16._o degree_n and_o 30._o minute_n approve_v but_o they_o differ_v in_o latitude_n in_o that_o london_n have_v the_o latitude_n of_o 51._o degree_n and_o 34._o minute_n the_o latitude_n of_o northampton_n be_v of_o 52._o degree_n and_o 50._o minute_n the_o difference_n of_o the_o latitude_n be_v of_o 1._o degree_n and_o 16._o minute_n that_o be_v 7â—_n english_a mile_n so_o much_o in_o a_o manner_n be_v the_o distance_n between_o london_n and_o northampton_n another_o this_o example_n differ_v both_o in_o the_o longitude_n and_o latitude_n somewhat_o for_o the_o longitude_n of_o colchester_n be_v 18._o degree_n and_o 30._o minute_n the_o longitude_n of_o oxeforde_n have_v 15._o degree_n and_o no_o minute_n the_o difference_n of_o longitude_n between_o the_o one_o and_o the_o other_o be_v of_o 3._o degree_n 38_o minute_n that_o be_v 109._o english_a mile_n the_o latitude_n of_o colchester_n have_v 51._o degree_n and_o 59_o minute_n the_o difference_n of_o latitude_n be_v no_o degree_n and_o 16._o minute_n so_o that_o 16._o english_a mile_n be_v the_o distance_n between_o the_o one_o and_o the_o other_o after_o their_o stand_n northward_o another_o cygnea_n and_o ratisbone_n agree_v in_o longitude_n for_o either_o be_v of_o 29._o degree_n and_o 51._o minute_n but_o they_o differ_v in_o latitude_n in_o that_o the_o latitude_n of_o cygnea_n have_v 50._o degree_n and_o 46._o minute_n the_o 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how_o much_o near_o they_o be_v to_o the_o pole_n so_o much_o the_o lesser_a they_o be_v and_o how_o further_a of_n they_o be_v from_o the_o â—nâ—â—s_n so_o much_o the_o great_a they_o be_v whereof_o it_o be_v manifeâ—e_a mile_n aswell_o the_o great_a as_o the_o less_o circle_n of_o the_o parallel_n â—â—tes_n stribute_v or_o divide_v into_o 360._o degree_n and_o that_o those_o degree_n according_a to_o the_o distance_n of_o those_o parallel_n from_o the_o pole_n be_v great_a or_o lesser_a for_o the_o same_o cause_n shall_v you_o here_o find_v in_o the_o table_n follow_v how_o many_o german_a mile_n answer_v in_o each_o elevation_n to_o the_o degree_n of_o the_o parallel_n a_o table_n contain_v the_o degree_n of_o the_o difference_n of_o each_o parallel_n from_o the_o equator_fw-la unto_o the_o proper_a pole_n by_o whole_a degree_n of_o the_o latitude_n convert_v into_o miles_n degree_n miles_n scruple_n degree_n miles_n scruple_n degree_n miles_n scruple_n degree_n miles_n scruple_n degree_n miles_n scruple_n 1_o 14_o 59_o 19_o 14_o 11_o 37_o 11_o 59_o 55_o 8_o 30_o 73_o 4_o 23_o 2_o 14_o 59_o 20_o 14_o 6_o 38_o 11_o 49_o 56_o 8_o 23_o 74_o 4_o 8_o 3_o 14_o 58_o 21_o 14_o 0_o 39_o 11_o 39_o 57_o 8_o 10_o 75_o 3_o 53_o 4_o 14_o 58_o 22_o 13_o 54_o 40_o 11_o 29_o 58_o 7_o 57_o 76_o 3_o 38_o 5_o 14_o 56_o 23_o 13_o 48_o 41_o 11_o 19_o 59_o 7_o 43_o 77_o 3_o 22_o 6_o 14_o 55_o 24_o 13_o 42_o 42_o 11_o 9_o 60_o 7_o 30_o 78_o 3_o 7_o 7_o 14_o 53_o 25_o 13_o 36_o 43_o 10_o 58_o 61_o 7_o 16_o 79_o 2_o 52_o 8_o 14_o 51_o 26_o 13_o 29_o 44_o 10_o 47_o 62_o 7_o 2_o 80_o 2_o 36_o 9_o 14_o 48_o 27_o 13_o 22_o 45_o 10_o 36_o 63_o 6_o 48_o 81_o 2_o 21_o 10_o 14_o 46_o 28_o 13_o 15_o 46_o 10_o 25_o 64_o 6_o 34_o 82_o 2_o 5_o 11_o
14_o 43_o 29_o 13_o 7_o 47_o 10_o 14_o 65_o 6_o 20_o 83_o 1_o 50_o 12_o 14_o â—â—_o â—0_n 12_o 59_o 48_o 10_o 2_o 66_o 6_o 6_o 84_o 1_o 34_o 13_o â—â—_o â—â—_o 31_o 12_o 51_o 40_o 9_o 50_o 67_o 5_o 52_o 85_o 1_o 18_o 14_o â—4_n 33_o 32_o 12_o 43_o 50_o 9_o 38_o 68_o 5_o 37_o 86_o 1_o 3_o 15_o 14_o 29_o 33_o 12_o 35_o 51_o 9_o 26_o 69_o 5_o 23_o 87_o 0_o 47_o 16_o 14_o 25_o 34_o 12_o 26_o 52_o 9_o â—4_n 70_o 5_o 8_o 88_o 0_o 31_o 17_o 14_o 21_o 35_o 12_o 17_o 53_o 9_o 12_o 71_o 4_o 53_o 89_o 0_o 16_o 18_o 14_o 26_o 36_o 12_o 8_o 54_o 8_o 49_o 72_o 4_o 38_o 90_o 0_o 0_o a_o example_n for_o the_o use_n of_o this_o table_n lvneburgum_n and_o stetinum_n have_v the_o elevation_n of_o the_o pole_n precise_o of_o 54._o degree_n to_o know_v how_o many_o german_a mile_n answer_v to_o one_o degree_n of_o the_o parallel_n pass_v by_o the_o zenith_n of_o either_o city_n enter_v your_o table_n and_o there_o diligent_o look_v you_o shall_v find_v by_o the_o degree_n of_o that_o latitude_n 54._o note_v eight_o mile_n and_o 49._o scruple_n of_o a_o mile_n for_o so_o many_o mile_n in_o that_o parallel_n answer_v to_o a_o degree_n that_o be_v eight_z a_o half_a and_o the_o three_o part_n almost_o of_o a_o german_a mile_n and_o this_o be_v easy_o find_v if_o the_o elevation_n do_v only_o consist_v in_o whole_a degree_n for_o in_o each_o elevation_n be_v certain_a mile_n and_o the_o scruple_n of_o a_o mile_n answer_v to_o each_o degree_n assign_v but_o if_o the_o place_n or_o city_n have_v minute_n depend_v to_o the_o latitude_n as_o viteberge_n who_o latitude_n be_v of_o 51._o degree_n and_o 50._o minute_n then_o seek_v in_o this_o table_n how_o many_o mile_n and_o scruple_n of_o a_o mile_n be_v atribute_v to_o the_o whole_a degree_n and_o you_o shall_v find_v by_o the_o degree_n of_o the_o latitude_n of_o 51._o note_v 9_o mile_n and_o 26._o scruple_n of_o a_o german_a mile_n after_o seek_v the_o mile_n and_o minute_n that_o next_o join_v to_o the_o elevation_n follow_v be_v 52._o 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