and_o the_o verse_v sine_fw-la of_o the_o distance_n from_o the_o meridian_n for_o the_o better_a understanding_n of_o the_o premise_n i_o have_v set_v down_o this_o figure_n follow_v and_o wish_v the_o reader_n to_o consider_v of_o the_o same_o with_o the_o 4._o pro._n of_o the_o 6._o of_o euclid_n let_v amt_v be_v the_o meridian_n circle_n bdq._n the_o common_a section_n of_o the_o meridian_n and_o equinoctial_a their_o plain_n which_o be_v also_o the_o diameter_n of_o both_o circle_n adt._n the_o plain_a of_o the_o horizon_n lhp._n the_o parallel_n of_o the_o sun_n which_o be_v describe_v upon_o the_o centre_n f._n at_o the_o distance_n fl._n which_o be_v the_o sine_fw-la of_o the_o complement_n of_o the_o declination_n ab_fw-la the_o ark_n of_o the_o elevation_n of_o the_o equinoctial_a boy_n the_o first_o right_a sine_z thereof_o al._n the_o ark_n of_o the_o meridian_n altitude_n lx._n the_o sine_fw-la thereof_o an._n the_o ark_n of_o the_o sun_n elevation_n at_o the_o time_n of_o the_o observation_n n_o c._n the_o sine_fw-la thereof_o b_o d._n the_o whole_a sine_fw-la in_o respect_n of_o the_o former_a arke_n and_o sin_n l_o r._n the_o semidiurnall_a ark_n of_o the_o parallel_n r_o s._n the_o first_o right_a sine_z thereof_o s_o l._n the_o verse_v sine_fw-la of_o the_o same_o l_o i._n the_o ark_n of_o the_o sun_n distance_n from_o the_o meridian_n i_o k._n the_o first_o right_a sine_z thereof_o i_o g._n the_o second_o right_a sine_fw-la which_o be_v equal_a to_o k_o f._n k_o l._n the_o verse_v sine_fw-la n_o e._n which_o be_v equal_a to_o k_o s._n the_o difference_n of_o the_o 2._o verse_v sin_n l_o s._n and_o l_o k._n l_o f._n the_o whole_a sine_fw-la in_o respect_n of_o the_o ark_n and_o sin_n of_o the_o parallel_n now_o as_o b_o o._n be_v to_o l_o x._o so_o be_v b_o d._n to_o l_o s._n and_o as_o l_o x._o to_z n_o c._n so_o be_v l_o s._n to_o n_o e._n or_o else_o thus_o as_o b_o o._n to_o n_n c._n so_o be_v b_o d._n to_o n_o e._n example_n the_o 16._o october_n 1580._o in_o lymehouse_n the_o elevation_n of_o the_o pole_n artik_a 51._o d._n 32′_n the_o declination_n of_o ehe_fw-ge sun_n 12._o d._n 30′_n the_o elevation_n of_o the_o sun_n observe_v in_o the_o fornoone_n 17._o d._n 0′_n the_o variation_n of_o the_o shadow_n upon_o the_o instrument_n 52._o d._n 35′_n from_o north_n to_o west_n 38._o 28′_n 90._o 0′_n 25._o 58′_n  _fw-fr b_o o._n b_o d._n l_o x._o l_o s_o if._n 62205._o give_v 100000._o then_o 43784._o give_v 70386._o 38._o 28′_n 90._o 0′_n 17._o 0′_n  _fw-fr b_o o._n b_o d._n n_o c._n n_o e._n again_o if_o 62205._o give_v 100000._o 29237._o shall_v give_v 47001._o now_o out_o of_o l_o s_o 70386._o take_v n_o e._n 47001._o rest_n l_o k._n 23385._o then_o if_o l_o f._n 97629._o the_o sine_fw-la of_o 77._o d._n 30′_n the_o complement_n of_o the_o declination_n give_v l_o f._n 100000._o then_o l_o k._n 23385._o give_v l_o k._n 23952._o the_o verse_v sine_fw-la of_o the_o ark_n i_o l._n in_o his_o due_a part_n the_o same_o subtract_v from_o l_o f._n 100000._o the_o whole_a sine_fw-la leve_v k_o f._n or_o i_o g._n 76048._o the_o second_o right_a sine_fw-la of_o the_o same_o ark_n which_o be_v the_o first_o right_a sine_z of_o the_o ark_n i_o h._n which_o ark_n you_o shall_v find_v in_o the_o table_n of_o sin_n to_o be_v 49._o d._n 30′_n 24″_n the_o complement_n whereof_o to_o the_o quadrant_a be_v 40._o d._n 29′_n 36″_n the_o ark_n i_o l._n of_o the_o parallel_n between_o the_o sun_n and_o the_o meridian_n who_o correspondent_a ark_n in_o the_o equinoctial_a be_v the_o ark_n that_o be_v seek_v now_o ha_v 〈…〉_o f_o the_o equinoctial_a you_o must_v work_v 〈…〉_o 〈…〉_o thereof_o by_o the_o sine_fw-la of_o the_o complement_n the_o declination_n and_o divide_v the_o product_n by_o the_o whole_a sine_fw-la the_o quotient_n be_v the_o sine_fw-la of_o a_o ark_n contain_v between_o the_o sun_n and_o the_o meridian_n make_v right_a angle_n with_o the_o meridian_n this_o sine_fw-la multiply_v by_o the_o whole_a sine_fw-la the_o product_n divide_v by_o the_o the_o sine_fw-la of_o the_o complement_n of_o the_o sun_n elevation_n at_o the_o time_n of_o the_o observation_n the_o quotient_n be_v the_o sine_fw-la of_o the_o ark_n of_o the_o horizon_n contain_v between_o the_o azimuth_n of_o the_o sun_n and_o the_o meridian_n which_o be_v the_o ark_n that_o be_v propose_v to_o be_v find_v let_v d_o h_n n_o p._n be_v the_o meridian_n d_o a_o k._n the_o horizon_n e_o a_o n._n the_o equinoctial_a m._n the_o place_n of_o the_o sun_n in_o the_o heaven_n at_o the_o time_n of_o the_o observation_n l_o m_o o._n the_o parallel_n h_o m_o b._n the_o azimuth_n or_o vertical_a circle_n pass_v by_o the_o sun_n a_o m_o g._n a_o great_a circle_n imagine_v to_o pass_v by_o the_o sun_n &_o to_o cross_v the_o meridian_n at_o right_a angle_n i_o m_o p._n a_o great_a circle_n pass_a by_o the_o pole_n of_o the_o world_n and_o place_n of_o the_o sun_n at_o the_o time_n of_o the_o observation_n common_o call_v the_o citcle_n of_o hour_n or_o circle_n of_o declination_n c_o m._n the_o south_n declination_n of_o the_o sun_n 〈◊〉_d the_o complement_n thereof_o to_o the_o quadrant_a mâ—â—â—_n the_o ark_n between_o the_o sun_n and_o the_o â—â—â—_o of_o the_o former_a imagine_a circle_n a_o m_o g_o in_o this_o figure_n the_o reader_n be_v to_o consider_v the_o manner_n of_o the_o spherical_a triangle_n and_o to_o compare_v the_o sin_n of_o their_o side_n according_a to_o the_o doctrine_n of_o copernicus_n in_o the_o 14._o chapter_n of_o his_o first_o book_n and_o of_o regiomontanus_n his_o 25._o and_o 27._o proposition_n of_o his_o 4._o book_n of_o triangle_n as_o p_o c._n be_v to_o c_o e._n so_o be_v p_o m._n to_o m_o g._n but_o 3._o of_o they_o be_v give_v therefore_o the_o four_o shall_v be_v know_v and_o as_o h_n m._n be_v to_o m_o g._n so_o be_v h_n b._n to_o b_o d._n the_o ark_n that_o be_v seek_v which_o by_o the_o three_o first_o give_v be_v likewise_o give_v ¶_o the_o second_o part_n of_o the_o example_n 90._o 0′_n 40._o 29′_n 36″_n 77._o 30′_n  _fw-fr p_o c._o e_o c._n p_o m._n m_o g._n if._n 100000._o give_v 64935._o then_o 97629._o give_v 63395._o  _fw-fr 73._o 0′_n  _fw-fr 90._o 0′_n 41._o 31′_n 22″_n  _fw-fr h_n m._n m_o g._n h_o b._n b_o d._n again_o if_o 956_o 〈…〉_o give_v 63395._o 100000._o give_v 66291._o who_o 〈…〉_o b_o d._n 41._o d._n 31′_n 22″_n be_v the_o horizontall_a distance_n of_o the_o join_a 〈…〉_o we_fw-mi of_o the_o sun_n from_o the_o meridian_n the_o thing_n that_o which_o 〈…〉_o ught_v now_o compare_v the_o same_o with_o the_o variation_n find_v upon_o the_o instrument_n at_o the_o instant_n of_o 17._o d._n elevation_n which_o be_v 52._o d._n 35′_n i_o find_v it_o to_o be_v less_o and_o therefore_o subtract_v it_o and_o so_o have_v i_o the_o difference_n 11._o d._n 3′_n 38″_n and_o because_o the_o observation_n be_v in_o the_o fornoone_n and_o the_o variation_n upon_o the_o instrument_n great_a than_o the_o ark_n of_o the_o horizon_n between_o the_o sun_n azimuth_n and_o the_o meridian_n therefore_o i_o conclude_v that_o the_o variation_n be_v 11._o d._n 3′_n 38″_n from_o south_n to_o west_n or_o north_n to_o east_n which_o be_v the_o thing_n promise_v to_o be_v show_v but_o compare_v the_o same_o ark_n of_o the_o horizon_n 41._o d._n 31′_n 22″_n with_o the_o variation_n find_v at_o the_o correspondent_a elevation_n in_o the_o afternoon_n which_o be_v 30._o d._n 0′_n i_o subtract_v the_o lesser_a from_o the_o great_a and_o find_v the_o excess_n 11._o d._n 31′_n 22″_n which_o shall_v be_v the_o variation_n and_o because_o the_o variation_n find_v upon_o the_o instrument_n be_v less_o than_o the_o ark_n of_o the_o azimuth_n upon_o the_o horizon_n i_o account_v the_o variation_n on_o the_o same_o side_n of_o the_o meridian_n which_o be_v from_o south_n to_o west_n or_o north_n to_o east_n this_o variety_n between_o the_o observation_n make_v in_o the_o fornoone_n and_o that_o in_o the_o afternoon_n proceed_v either_o of_o the_o imperfection_n of_o the_o instrument_n or_o negligence_n of_o the_o observer_n for_o in_o the_o rule_n there_o can_v be_v no_o error_n be_v ground_v upon_o geometrical_a demonstration_n than_o which_o nothing_o can_v be_v more_o certain_a the_o former_a precept_n and_o example_n do_v serve_v when_o the_o sun_n do_v decline_v from_o the_o equinoctial_a either_o northwards_o or_o southwards_o but_o if_o the_o sun_n be_v in_o the_o equinoctial_a than_o the_o manner_n of_o the_o work_n be_v more_o easy_a and_o brief_a for_o if_o you_o multiply_v the_o sine_fw-la of_o the_o sun_n elevation_n at_o the_o time_n of_o observation_n by_o the_o
be_v the_o complement_n of_o the_o declination_n and_o set_v one_o end_n upon_o g._n the_o point_n of_o the_o great_a elevation_n describe_v with_o the_o other_o end_n a_o ark_n or_o piece_n of_o a_o circle_n at_o h._n this_o do_v set_v one_o foot_n of_o the_o cumpas_n unaltred_a in_o e._n the_o lesser_a elevation_n and_o with_o the_o other_o end_n describe_v a_o piece_n of_o a_o circle_n cross_v the_o former_a ark_n at_o h._n this_o intersection_n shall_v be_v the_o elevate_v pole_n then_o set_v the_o quadrant_a of_o altitude_n unto_o the_o point_n h._n and_o it_o will_v show_v the_o meridian_n to_o cross_v the_o horizon_n at_o k._n so_o shall_v you_o have_v the_o elevation_n of_o the_o pole_n k_n h._n 51._o d._n ½_n or_o there_o about_o and_o the_o true_a meridian_n kai_n and_o from_o k._n to_o d._n the_o horizontall_a distance_n 90._o d._n ¾_n which_o subtract_v from_o k_o i._n 180._o d._n the_o semicircle_n of_o the_o horizon_n rest_v the_o ark_n d_o i._n 89._o d._n ¼_n the_o distance_n of_o the_o azimuth_n of_o the_o first_o observation_n from_o the_o meridian_n i._n which_o distance_n compare_v with_o the_o variation_n find_v upon_o the_o instrument_n at_o the_o first_o elevation_n 100_o d._n 30′_n and_o deduct_v from_o the_o same_o rest_v 11._o d._n ¼_n therefore_o i_o say_v the_o true_a meridian_n show_v the_o pole_n artik_a be_v 11._o d._n ¼_n to_o the_o westward_n of_o the_o magnetical_a meridian_n show_v by_o the_o needle_n and_o consequent_o the_o variation_n of_o the_o needle_n 11._o d._n ¼_n from_o the_o north_n to_o the_o east_n in_o this_o example_n the_o declination_n be_v subtract_v from_o the_o quadrant_a because_o the_o sun_n be_v between_o the_o equinoctial_a and_o the_o elevate_v pole_n but_o if_o the_o equinoctial_a be_v between_o the_o elevate_v pole_n and_o the_o sun_n than_o shall_v you_o add_v the_o declination_n to_o the_o quadrant_a and_o with_o that_o distance_n take_v upon_o the_o equinoctial_a with_o your_o cumpass_n proceed_v as_o in_o the_o former_a example_n these_o example_n that_o i_o have_v show_v and_o such_o like_a experiment_n to_o be_v do_v upon_o the_o globe_n be_v easy_a to_o be_v conceive_v and_o the_o reason_n very_o manifest_a but_o the_o truth_n of_o the_o matter_n consist_v in_o the_o exactness_n of_o the_o instrument_n and_o the_o orderly_a application_n and_o handle_n of_o they_o i_o may_v here_o have_v annex_v the_o manner_n how_o upon_o two_o observation_n of_o the_o sun_n elevation_n in_o fornoone_n or_o afternoon_n and_o difference_n of_o the_o azimuth_n to_o calculate_v the_o premise_n more_o exact_o by_o the_o table_n of_o sines_n and_o doctrine_n of_o spherical_a triangle_n but_o that_o it_o be_v a_o very_a tedious_a way_n and_o my_o meaning_n be_v rather_o to_o give_v the_o reader_n a_o proof_n of_o the_o pleasant_a use_n of_o these_o calculation_n which_o i_o think_v i_o have_v sufficient_o do_v in_o the_o former_a chapter_n then_o to_o cloy_v he_o at_o the_o first_o with_o the_o hard_a and_o painful_a practice_n of_o many_o example_n notwithstanding_o for_o the_o satisfaction_n of_o some_o i_o will_v brief_o set_v down_o the_o ground_n and_o sum_n of_o the_o work_n which_o be_v this_o the_o compliment_n of_o your_o two_o elevation_n be_v two_o side_n of_o a_o spherical_a triangle_n not_o rectangle_n the_o angle_n by_o these_o two_o know_v side_n contain_v at_o the_o zenith_n be_v give_v by_o the_o difference_n of_o the_o azimuth_n or_o variation_n upon_o the_o instrument_n wherefore_o by_o the_o 28._o of_o the_o 4._o of_o regiomontanus_n the_o three_o side_n which_o be_v the_o ark_n comprehend_v between_o the_o two_o elevation_n and_o the_o other_o angle_n may_v be_v give_v then_o have_v you_o a_o other_o like_o triangle_n who_o three_o side_n be_v these_o the_o first_o one_o of_o the_o foresay_v compliment_n of_o elevation_n the_o second_o the_o ark_n of_o the_o circle_n of_o declination_n between_o the_o sun_n at_o the_o instant_n of_o the_o same_o elevation_n and_o the_o elevate_v pole_n the_o three_o side_n be_v a_o ark_n of_o the_o meridian_n between_o the_o zenith_n and_o the_o pole_n which_o be_v the_o complement_n of_o the_o elevation_n of_o the_o pole_n or_o latitude_n of_o the_o place_n the_o two_o first_o side_n be_v always_o give_v for_o find_v the_o three_o side_n it_o be_v necessary_a to_o know_v the_o angle_n that_o the_o two_o give_v side_n contain_v which_o be_v the_o difference_n of_o two_o angle_n whereof_o one_o be_v a_o angle_n of_o the_o first_o triangle_n give_v the_o other_o a_o angle_n contain_v between_o the_o ark_n of_o the_o circle_n of_o declination_n and_o the_o three_o side_n of_o the_o first_o triangle_n which_o angle_n be_v diverse_o find_v and_o be_v find_v and_o subtract_v from_o the_o other_o angle_n or_o that_o from_o it_o the_o difference_n be_v the_o angle_n of_o this_o other_o triangle_n and_o so_o have_v you_o in_o the_o spherical_a triangle_n two_o side_n and_o the_o angle_n by_o the_o same_o two_o side_n contain_v give_v and_o by_o the_o same_o 28._o of_o the_o fowerth_o of_o regiomontanus_n the_o third_o side_n be_v find_v the_o complement_n whereof_o be_v the_o elevation_n of_o the_o pole_n and_o the_o elevation_n of_o the_o pole_n and_o declination_n of_o the_o sun_n be_v give_v the_o fowerth_o chapter_n show_v by_o one_o observation_n to_o find_v the_o variation_n of_o the_o needle_n of_o the_o pole_n of_o the_o magnes_n ¶_o the_o eight_o chapter_n first_o it_o be_v to_o be_v understand_v that_o by_o experience_n of_o traveller_n it_o be_v find_v and_o confirm_v that_o the_o meridian_n common_a to_o the_o pole_n of_o the_o world_n and_o the_o pole_n of_o the_o magnes_n that_o be_v to_o say_v where_o the_o compass_n or_o needle_n touch_v with_o the_o magnes_n show_v the_o pole_n of_o the_o world_n direct_o pass_v at_o the_o island_n of_o the_o açore_n or_o never_o there_o about_o but_o i_o find_v by_o great_a probability_n that_o it_o be_v somewhat_o to_o the_o eastwarde_n of_o those_o island_n and_o not_o to_o the_o westward_n from_o which_o meridian_n i_o account_v the_o beginning_n of_o longitude_n and_o find_v our_o meridian_n of_o london_n to_o be_v from_o the_o same_o 23._o d._n ½_n our_o latitude_n as_o before_o say_v 51._o d._n 32′_n and_o the_o veriation_n of_o the_o compass_n or_o needle_n 11._o d._n ¼_n from_o the_o north_n to_o the_o eastwarde_n now_o upon_o these_o ground_n i_o find_v by_o calculation_n the_o pole_n of_o the_o magnes_n or_o the_o intersection_n of_o the_o two_o magnetical_a meridians_fw-la upon_o the_o superficies_n of_o the_o earth_n to_o be_v from_o the_o pole_n arctic_a 25._o d._n 44′_n and_o in_o longitude_n 180._o d._n that_o be_v to_o say_v 25._o d._n 44′_n in_o the_o former_a common_a meridian_n on_o the_o other_o side_n of_o the_o pole_n it_o may_v be_v happy_o that_o some_o of_o you_o will_v be_v desirous_a to_o know_v the_o manner_n how_o this_o magnetical_a pole_n be_v find_v out_o that_o you_o may_v apply_v the_o same_o to_o like_a purpose_n hereafter_o therefore_o i_o think_v good_a to_o set_v down_o a_o example_n of_o the_o former_a calculation_n let_v a._n be_v the_o pole_n artik_a pef._n the_o equinoctial_a dag_n the_o common_a meridian_n of_o the_o pole_n artik_a and_o pole_n of_o the_o magnes_n eaf_a the_o meridian_n of_o london_n make_v out_o the_o quadrant_n ihk_v and_o lnk_v so_o shall_v they_o cross_v themselves_o with_o the_o quadrant_a oak_n at_o the_o point_n k._n now_o have_v you_o abc_n a_o spherical_a triangle_n two_o angle_n whereof_o and_o the_o common_a contain_v side_n of_o they_o be_v give_v abc_n 11._o d._n ¼_n the_o angle_n of_o variation_n at_o london_n bac_n 156._o d._n 30′_n the_o complement_n of_o the_o angle_n dae_n the_o difference_n of_o the_o longitude_n to_o two_o right_a angle_n and_o the_o side_n ab_fw-la 38._o d._n 28′_n the_o complement_n of_o the_o latitude_n of_o london_n and_o in_o a_o spherical_a triangle_n not_o rectangle_n who_o two_o angle_n be_v give_v and_o their_o common_a contain_v side_n the_o other_o angle_n and_o side_n be_v know_v by_o the_o 31_o of_o the_o 4._o of_o regiomontanus_n wherefore_o the_o ark_n ac_fw-la the_o distance_n of_o the_o two_o pole_n be_v give_v which_o be_v the_o thing_n require_v for_o as_o the_o sine_fw-la of_o bh_n be_v to_o the_o sine_fw-la of_o he_o so_o be_v the_o sine_fw-la of_o basilius_n to_o the_o sine_fw-la of_o ao_o and_o three_o of_o they_o be_v give_v the_o 4._o be_v find_v 90_o 0′_n 11_o 15′_n 38_o 28′_n 6_o 58′_n bh_n he_o basilius_n ao_o if._n 100000._o give_v 19509._o then_o 62205._o give_v 12135._o now_o as_o ak_v be_v to_o ah_o the_o sin_n i_o mean_v so_o be_v quoth_fw-mi to_z oi_o but_o the_o three_o first_o be_v know_v ak_a and_o ah_o by_o their_o compliment_n
meridian_n ¶_o the_o elevation_n of_o the_o pole_n and_o place_n of_o the_o sun_n give_v how_o upon_o the_o globe_n to_o find_v the_o variation_n of_o the_o needle_n by_o any_o one_o observation_n either_o in_o fornoone_n or_o afternoon_n ¶_o the_o four_o chapter_n in_o the_o former_a declaration_n the_o only_a way_n to_o try_v the_o variation_n be_v by_o compare_v of_o the_o several_a correspondent_a observation_n of_o the_o sun_n elevation_n in_o the_o fornoone_n with_o those_o of_o the_o afternoon_n so_o that_o if_o the_o sun_n shall_v be_v obscure_v or_o by_o any_o other_o occasion_n like_o observation_n can_v not_o be_v make_v in_o the_o afternoon_n than_o the_o former_a rule_n give_v not_o the_o desire_a purpose_n therefore_o i_o think_v good_a to_o show_v how_o by_o any_o one_o observation_n in_o the_o fore_n or_o afternoon_n the_o elevation_n of_o the_o pole_n and_o place_n of_o the_o sun_n give_v you_o may_v know_v the_o true_a meridian_n and_o the_o variation_n of_o the_o 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for_o the_o commeditie_n of_o all_o such_o as_o shall_v have_v occasion_n to_o use_v the_o same_o for_o navigation_n and_o cosmography_n ¶_o to_o find_v the_o elevation_n of_o the_o pole_n situation_n of_o the_o meridian_n and_o variation_n of_o the_o needle_n at_o any_o place_n by_o the_o sun_n upon_o two_o observation_n either_o in_o forenoon_n or_o afternoon_n ¶_o the_o seven_o chapter_n whereas_o in_o the_o three_o last_o chapter_n the_o ground_n of_o the_o calculation_n consist_v in_o the_o elevation_n of_o the_o pole_n to_o be_v give_v which_o thing_n to_o know_v be_v no_o less_o difficuit_fw-la than_o the_o chief_a matter_n that_o be_v by_o they_o require_v for_o the_o common_a precept_n which_o as_o yet_o have_v chief_o be_v give_v for_o the_o find_v thereof_o depend_v only_o upon_o the_o observation_n of_o the_o meridian_n altitude_n of_o the_o sun_n or_o star_n or_o else_o upon_o certain_a false_a and_o gross_a rule_n of_o the_o guard_n and_o pole_n star_n therefore_o i_o 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and_o quoth_fw-mi the_o quadrant_a therefore_o the_o 4._o be_v give_v 83_o 2′_n 51_o 32′_n 90_o 0′_n 52_o 4′_n ka_o ah_o quoth_fw-mi oi_o if._n 99261._o give_v 78297._o then_o 100000._o give_v 78879._o and_o as_o basilius_n be_v to_o boy_n the_o complement_n of_o the_o ark_n oi_o last_o find_v so_o be_v ae_n to_o em_n the_o quantity_n of_o the_o angle_n bao_n 38_o 28′_n 37_o 56′_n 90_o 0′_n 81.12_o ab_fw-la boy_n ae_n em_n if._n 62205._o give_v 61474._o then_o 100000._o give_v 98824._o sohave_v em_n 81._o d._n 12′_n the_o quantity_n of_o the_o angle_n bao_n i_o subtract_v the_o same_o from_o eglantine_n 156._o d._n 30′_n the_o quantity_n of_o the_o whole_a angle_n bac_n rest_v mg_n 75._o d._n 18′_n the_o quantity_n of_o the_o angle_n cao_n to_o the_o which_o be_v equal_a the_o opposite_a angle_n pad_n and_o as_o ap._n be_v to_o pd_v so_o be_v ak_v to_o kn._n 90_o 0′_n 75_o 18′_n 83_o 2′_n 73_o 46′_n ap._n pd_v ak_v kn._n if._n 100000._o give_v 96726._o then_o 99261._o give_v 96011._o the_o complement_n of_o which_o ark_n kn._n be_v nl_n 16._o d._n 14′_n the_o quantity_n of_o the_o angle_n acb_n and_o as_o nl_n be_v to_o nc_n so_o be_v ao_o to_o ac_fw-la wherefore_o i_o say_v 16_o 14′_n 90_o 0′_n 6_o 58′_n 25_o 44′_n nl_n nc_n ao_o ac_fw-la if._n 27954._o give_v 100000._o then_o 12135._o give_v 43410._o which_o be_v the_o distance_n of_o the_o pole_n of_o the_o magnes_n from_o the_o pole_n artik_a the_o thing_n that_o be_v seek_v ¶_o of_o the_o point_n respective_a ¶_o the_o nine_o chapter_n have_v show_v in_o the_o former_a chapter_n upon_o the_o ground_n therein_o specify_v the_o place_n of_o the_o pole_n of_o the_o magnes_n upon_o the_o superificies_n of_o the_o earth_n there_o rest_v now_o to_o be_v declare_v of_o the_o point_n respective_a where_o it_o shall_v be_v by_o the_o new_a property_n find_v of_o the_o decline_v of_o the_o needle_n at_o this_o place_n for_o london_n 71._o d._n 50′_n first_o it_o be_v to_o be_v consider_v that_o as_o the_o magnetical_a 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then_o qa_n the_o axis_fw-la of_o the_o world_n qc_fw-la the_o common_a section_n of_o the_o magnetical_a plain_n bz_n the_o line_n of_o the_o needle_n declination_n cross_v the_o say_v common_a section_n at_o r._n which_o be_v the_o point_n respective_a qt_fw-la a_o straight_a line_n cross_v bz_n at_o right_a angle_n in_o x._o qr_n the_o distance_n of_o the_o point_n respective_a from_o the_o centre_n of_o the_o earth_n rs._n the_o distance_n there_o of_o from_o the_o axis_fw-la now_o as_o qu._n be_v to_o qc_n so_o be_v qx._n to_o qr_n but_o the_o three_o first_o be_v know_v qu._n the_o second_o right_n sine_fw-la of_o the_o ark_n et_fw-la 9_o d._n 4′_n the_o difference_n of_o the_o ark_n bt_n 71._o d._n 50′_n and_o bc._n 62._o d._n 46′_n then_o qc_a the_o semidiameter_n or_o whole_a sine_fw-la and_o qx._n the_o second_o right_a sine_fw-la of_o the_o ark_n bt_n wherefore_o qr_n be_v give_v by_o the_o 4._o of_o the_o sixth_o of_o euclid_n 30_o 56′_n 90_o 0′_n 18_o 10′_n  _fw-fr qu._n qc_fw-la qx._n qr_n if._n 98750._o give_v 100000._o then_o 31178._o give_v 31572._o so_o have_v iqr._n in_o such_o part_n as_o the_o semidiameter_n of_o the_o earth_n qc_n be_v 100000._o which_o be_v reduce_v into_o mile_n account_v 3436_o 4_o 11._o for_o the_o semidiameter_n of_o the_o earth_n do_v give_v 1084._o mile_n and_o 10_o 11._o which_o be_v the_o distance_n of_o the_o point_n respective_a r._n from_o the_o centre_n of_o the_o earth_n q._n again_o as_o qc_a be_v to_o cy_n so_o be_v qr_n to_o rs._n wherefore_o qc_n and_o qr_n be_v give_v as_o before_o &_o cy_n the_o sine_fw-la of_o the_o ark_n ca._n likewise_o know_v rs._n be_v give_v  _fw-fr 25_o 44′_n  _fw-fr  _fw-fr qc_fw-fr cy_n qr_n rs._n if._n 100000._o give_v 43410._o then_o 31572._o give_v 13705._o which_o be_v in_o the_o part_n of_o the_o sin_n i_o reduce_v into_o mile_n as_o before_o and_o find_v the_o same_o 470._o mile_n and_o 10_o 11._o which_o be_v the_o distance_n of_o the_o point_n respective_a r._n from_o the_o axis_fw-la of_o the_o world_n qa_n ¶_o of_o the_o inconvenience_n and_o defect_n in_o sail_v and_o in_o description_n of_o country_n cause_v by_o the_o variation_n of_o the_o cumpas_n ¶_o the_o ten_o chapter_n in_o all_o sea_n chartes_n general_o which_o be_v make_v without_o consideration_n of_o the_o variation_n be_v commit_v great_a error_n and_o confusion_n for_o either_o the_o part_n in_o they_o contain_v be_v frame_v to_o agree_v in_o their_o latitude_n by_o the_o scale_n thereof_o and_o so_o wrest_v from_o the_o true_a course_n that_o one_o place_n bear_v from_o a_o other_o by_o the_o cumpas_n or_o else_o in_o set_v the_o part_n to_o agree_v in_o their_o due_a course_n they_o have_v place_v they_o in_o false_a latitude_n or_o abridge_v or_o over_o stretch_v the_o true_a distance_n between_o they_o in_o the_o marine_a platte_n make_v for_o newfoundlande_n the_o course_n set_v down_o from_o silly_a to_o cape_n raso_n be_v due_a wi_v which_o be_v find_v to_o be_v so_o by_o our_o common_a sail_v cumpasse_n who_o wire_n be_v set_v at_o ½_n a_o point_n from_o north_n to_o east_n notwithstanding_o silly_a be_v in_o latitude_n 50._o d._n little_a more_o cape_n raso_n in_o newfoundland_n be_v find_v to_o be_v but_o in_o 46._o d._n ⅓_n which_o be_v 3._o d._n ⅔_n less_o than_o the_o latitude_n of_o silly_a to_o make_v a_o show_n of_o reformation_n of_o this_o error_n cause_v by_o the_o variation_n and_o set_n of_o the_o wire_n in_o the_o cumpasse_n or_o to_o give_v a_o light_n of_o that_o difference_n in_o latitude_n they_o have_v place_v in_o the_o plat_n against_o that_o coast_n a_o new_a scale_n of_o latitude_n some_o upon_o the_o line_n of_o south_n and_o north_n and_o some_o other_o have_v place_v the_o same_o upon_o the_o line_n of_o north_n northeast_n &_o south_n south-weste_a because_o that_o point_n of_o the_o cumpasse_n show_v the_o pole_n nearest_o in_o that_o place_n and_o have_v furnish_v the_o degree_n thereof_o agreeable_o to_o the_o latitude_n of_o cape_n raso_n and_o by_o that_o mean_n have_v have_v a_o double_a scale_n of_o latitude_n one_o for_o the_o easter_n cost_v the_o other_o for_o that_o west_n but_o how_o far_o the_o same_o have_v be_v from_o reform_v the_o error_n or_o give_v any_o help_n to_o navigation_n you_o may_v easy_o judge_v other_o to_o avoid_v that_o error_n of_o the_o difference_n in_o latitude_n in_o that_o voyage_n and_o course_n have_v use_v cumpass_n who_o wire_n have_v be_v set_v direct_o under_o the_o north_n point_n and_o thereby_o sait_v west_n from_o silly_a have_v fall_v to_o the_o northwards_o of_o cape_n raso_n about_o 50._o league_n and_o in_o latitude_n near_o 49._o d._n some_o other_o have_v use_v in_o the_o same_o voyage_n to_o place_v a_o blank_a fly_n upon_o their_o sail_v cumpasse_n which_o they_o have_v remoove_v from_o time_n to_o time_n as_o they_o have_v judge_v the_o variation_n have_v alter_v by_o which_o way_n albeit_o they_o may_v seem_v to_o keep_v themselves_o near_o the_o parallel_n yet_o the_o same_o in_o navigation_n work_v the_o great_a confusion_n of_o all_o other_o and_o therefore_o be_v to_o be_v utter_o abolish_v in_o our_o voyage_n from_o hence_o eastwardes_o to_o s._n nicolas_n in_o russia_n and_o to_o the_o narue_v in_o livonia_n etc._n etc._n the_o marine_a platte_n of_o the_o coast_n be_v describe_v by_o our_o common_a sail_v cumpas_n with_o consideration_n of_o the_o variation_n at_o diverse_a place_n whereby_o the_o true_a meridians_fw-la reform_o set_v down_o decline_v from_o y_z e_z parallel_n meridians_fw-la of_o the_o plat_n do_v necessary_o widen_v northwards_o and_o straighten_v to_o the_o southwards_o contrary_a to_o the_o true_a form_n and_o nature_n
of_o meridians_fw-la and_o yet_o notwithstanding_o that_o be_v the_o best_a mean_n hitherto_o know_v to_o reform_v in_o plat_n the_o error_n that_o else_o will_v grow_v by_o the_o strange_a variation_n that_o way_n and_o albeit_o these_o platte_n serve_v very_o well_o for_o those_o navigation_n yet_o by_o mean_n of_o the_o variation_n consider_v the_o sorme_n of_o those_o coast_n be_v so_o distort_v from_o the_o right_a shape_n it_o shall_v bear_v be_v true_o describe_v upon_o the_o globe_n or_o otherwise_o in_o plain_a accord_v to_o the_o true_a latitude_n and_o longitude_n that_o whereas_o the_o narue_v be_v in_o latitude_n 59_o d._n ¼_n and_o in_o longitude_n from_o the_o meridian_n of_o london_n 26._o d._n 10′_n shall_v be_v from_o s._n nicolas_n 9_o d._n 40′_n in_o longitude_n to_o the_o westward_n s._n nicolas_n be_v in_o latitude_n 64._o d._n 35′_n and_o in_o longitude_n from_o london_n 35._o d._n 50′_n in_o the_o sail_v plat_n it_o be_v bring_v to_o be_v in_o the_o meridian_n of_o colmogorod_n which_o be_v in_o latitude_n 64._o d._n 20′_n and_o in_o longitude_n from_o london_n 37._o d._n 45′_n which_o be_v 1._o d._n 55′_n to_o the_o eastwarde_n of_o the_o meridian_n of_o s._n nicolas_n in_o the_o mediterranean_a sea_n and_o in_o the_o coast_n thereof_o where_o in_o great_a reason_n shall_v be_v the_o perfect_a description_n of_o the_o world_n for_o that_o in_o those_o part_n have_v be_v the_o seat_n &_o abode_n of_o the_o most_o famous_a and_o learned_a man_n in_o all_o age_n we_o see_v notwithstanding_o in_o the_o marine_a platte_n of_o those_o part_n gross_a error_n commit_v through_o want_n of_o knowledge_n of_o the_o variation_n and_o the_o use_n thereof_o in_o which_o they_o have_v not_o account_v of_o 3._o 4._o or_o 5._o degree_n error_n in_o the_o latitude_n of_o place_n but_o those_o defect_n of_o the_o latitude_n have_v be_v very_o well_o reform_v by_o the_o famous_a and_o learned_a gerardus_n mercator_n who_o i_o honour_v and_o esteem_v as_o the_o chief_a cosmographer_n of_o the_o world_n in_o his_o universal_a map_n which_o though_o he_o have_v make_v with_o sail_v line_n and_o dedicate_v to_o the_o use_n of_o seaman_n yet_o for_o want_v of_o consideration_n of_o the_o variation_n and_o partly_o by_o angment_v his_o degree_n of_o latitude_n towards_o the_o pole_n the_o same_o be_v more_o fit_n for_o such_o to_o behold_v as_o study_v in_o cosmographie_n by_o read_v author_n upon_o the_o land_n then_o to_o be_v use_v in_o navigation_n at_o the_o sea_n there_o be_v also_o in_o the_o same_o universal_a map_n and_o likewise_o in_o all_o other_o modern_a map_n of_o the_o north_n part_n of_o europe_n a_o great_a fault_n by_o place_v two_o wardhouses_n distant_a one_o from_o the_o other_o above_o 20._o d._n in_o longitude_n whereas_o indeed_o they_o be_v but_o one_o thing_n and_o no_o such_o distance_n between_o they_o this_o error_n have_v grow_v by_o take_v wardhouse_n and_o the_o sea_n coast_n from_o thence_o to_o s._n nicolas_n vaigat_n and_o the_o ob_fw-la etc._n etc._n out_o of_o the_o map_n of_o anthony_n jenkinsons_n travail_n to_o boghar_n and_o persia_n in_o the_o which_o i_o place_v that_o border_n of_o the_o sea_n coast_n and_o for_o some_o cause_n go_v no_o further_o in_o that_o description_n than_o wardhouse_n which_o be_v in_o latitude_n 70._o d._n ⅓_n and_o in_o longitude_n from_o london_n 29._o d._n wherefore_o to_o accomplish_v the_o whole_a border_n of_o that_o coast_n he_o be_v force_v to_o seek_v some_o other_o description_n to_o join_v with_o it_o &_o take_v as_o appear_v the_o map_n of_o olaus_n magnus_n of_o the_o north_n country_n wherein_o he_o find_v likewise_o wardhouse_n but_o false_o place_v in_o latitude_n about_o 19_o d._n too_o much_o and_o in_o longitude_n as_o much_o too_o little_a the_o which_o although_o he_o may_v take_v to_o be_v the_o same_o specify_v in_o master_n jenkinsons_n map_n yet_o he_o be_v constrain_v to_o separate_v they_o the_o say_v distance_n of_o 20._o d._n in_o longitude_n or_o to_o leave_v there_o so_o much_o superfluous_a room_n otherwise_o he_o shall_v have_v thrust_v the_o south_n part_n of_o those_o country_n together_o and_o confound_v the_o whole_a description_n and_o albeit_o he_o have_v have_v the_o entire_a sail_v plat_n that_o we_o use_v for_o those_o part_n yet_o if_o he_o have_v not_o know_v the_o secret_a effect_n of_o the_o variation_n in_o the_o make_v thereof_o he_o may_v have_v fall_v into_o the_o like_a absurdity_n or_o worse_o but_o of_o those_o coast_n and_o of_o the_o inward_a part_n of_o the_o country_n russia_n muscovia_n etc._n etc._n i_o have_v make_v a_o perfect_a plat_n and_o description_n by_o my_o own_o experience_n in_o sundry_a voyage_n and_o travail_n both_o by_o sea_n and_o land_n to_o and_o fro_o in_o those_o part_n which_o i_o give_v to_o her_o majesty_n in_o anno_fw-la 1578._o beside_o these_o and_o like_a imperfection_n procead_v of_o the_o variation_n there_o be_v yet_o a_o other_o inconvenience_n which_o oftentimes_o increase_v the_o former_a error_n and_o that_o be_v the_o diverse_a place_n of_o the_o wire_n fix_v to_o the_o fly_n of_o the_o cumpasse_n this_o variety_n ofset_v the_o wire_n have_v cause_v great_a confusion_n in_o navigation_n and_o in_o other_o account_n of_o sea_n cause_n for_o when_o it_o be_v say_v that_o from_o such_o a_o headlande_n to_o such_o a_o place_n be_v such_o a_o course_n or_o at_o such_o a_o place_n the_o moon_n upon_o such_o a_o point_n of_o the_o compass_n make_v the_o full_a sea_n it_o be_v requisite_a to_o be_v demand_v by_o what_o cumpasse_n the_o observation_n be_v make_v whereas_o if_o the_o wire_n have_v not_o be_v alter_v from_o the_o north_n point_n of_o the_o fly_n which_o i_o wish_v have_v never_o be_v any_o where_n these_o doubt_n have_v be_v avoid_v it_o behove_v therefore_o all_o man_n that_o will_v make_v hydrographical_a description_n for_o the_o use_n of_o sail_a to_o have_v special_a regard_n of_o the_o cumpas_n by_o which_o 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of_o the_o time_n of_o the_o day_n by_o any_o one_o observation_n in_o any_o place_n beside_o that_o it_o be_v of_o all_o other_o that_o hitherto_o have_v be_v use_v at_o sea_n the_o most_o tedious_a and_o unfit_a for_o that_o purpose_n it_o be_v also_o by_o reason_n of_o the_o variation_n not_o consider_v â—iere_v false_a and_o erroneous_a for_o the_o true_a meridian_n which_o be_v the_o ground_n of_o his_o purpose_n be_v as_o far_o to_o seek_v as_o the_o thing_n he_o promise_v to_o give_v by_o the_o same_o the_o like_a may_v be_v say_v of_o all_o other_o instrument_n make_v upon_o the_o same_o ground_n whether_o they_o serve_v for_o the_o sea_n or_o land_n the_o same_o author_n in_o the_o 4._o chapter_n of_o his_o book_n entreat_v of_o sail_a upon_o the_o point_n of_o the_o cumpas_n say_v that_o in_o sail_a south_n or_o north_n he_o shall_v pass_v by_o the_o pole_n of_o the_o world_n and_o keep_v under_o one_o meridian_n till_o he_o come_v to_o the_o place_n from_o whence_o he_o 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with_o the_o axis_n shall_v describe_v the_o plain_a of_o the_o equinoctial_a equidistant_n from_o the_o pole_n of_o the_o world_n and_o at_o right_a angle_n with_o the_o axis_n and_o the_o point_n of_o the_o same_o line_n at_o the_o centre_n of_o the_o cumpas_n the_o circumference_n of_o the_o equinoctial_a upon_o the_o superficies_n of_o the_o sea_n so_o be_v from_o the_o equinoctial_a on_o either_o side_n imagine_v the_o line_n of_o south_n &_o north_n in_o your_o cumpas_n to_o represent_v always_o the_o axis_n of_o the_o world_n and_o to_o lie_v parallel_n with_o it_o the_o line_n of_o east_n and_o west_n most_o cross_a the_o same_o axis_n always_o at_o right_a angle_n and_o suppose_v a_o line_n to_o fall_v from_o the_o centre_n of_o your_o cumpas_n to_o the_o axis_n of_o the_o world_n make_v right_a angle_n with_o the_o same_o axis_n in_o sail_a east_n or_o west_n that_o imagine_a line_n be_v carry_v about_o with_o the_o cumpas_n always_o at_o right_a angle_n with_o the_o axis_n 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always_o the_o pole_n of_o the_o world_n but_o vari_v from_o the_o same_o diverse_o and_o in_o sail_v describe_v circle_n accordyng_o which_o thing_n if_o petrus_n nonius_n and_o the_o rest_n that_o have_v write_v of_o navigation_n have_v joint_o consider_v in_o the_o tractation_n of_o their_o rule_n and_o instrument_n than_o may_v they_o have_v be_v more_o available_a to_o the_o use_n of_o navigation_n but_o they_o perceive_v the_o difficulty_n of_o the_o thing_n and_o that_o if_o they_o have_v deal_v therewith_o it_o will_v have_v utter_o overwhelm_v their_o former_a plausible_a conceit_n with_o pedro_n de_fw-fr medina_n who_o as_o it_o appear_v have_v some_o small_a suspicion_n of_o the_o matter_n reason_v very_o clerkly_o that_o it_o be_v not_o necessary_a that_o such_o a_o absurdity_n as_o the_o variation_n shall_v be_v admit_v in_o such_o a_o excellent_a art_n as_o navigation_n be_v they_o have_v all_o thought_n best_a to_o pass_v it_o over_o with_o silence_n but_o i_o hope_v such_o as_o intend_v hereafter_o to_o write_v of_o navigation_n will_v either_o frame_v their_o rule_n precept_n and_o instrument_n with_o regard_n of_o the_o variation_n as_o herein_o i_o have_v show_v or_o else_o ease_v themselves_o of_o that_o travail_n for_o as_o good_a none_o as_o unprofitable_a ¶_o of_o the_o application_n of_o the_o variation_n to_o the_o use_n of_o navigation_n ¶_o the_o twelve_o chapter_n upon_o the_o hypothesis_n of_o the_o pole_n of_o the_o magnes_n on_o the_o superficies_n of_o the_o earth_n and_o the_o point_n respective_a in_o the_o body_n thereof_o accord_v to_o the_o former_a calculation_n may_v be_v infer_v many_o pleasant_a conclusion_n both_o for_o the_o longitude_n and_o latitude_n of_o place_n but_o touch_v the_o point_n respective_a by_o the_o decline_v of_o the_o needle_n see_v this_o be_v the_o first_o and_o only_a experiment_n that_o have_v be_v make_v of_o it_o i_o can_v not_o infer_v any_o further_a matter_n thereof_o then_o that_o which_o i_o have_v already_o set_v down_o until_o by_o observation_n in_o other_o place_n we_o find_v how_o it_o will_v hold_v and_o as_o for_o the_o variation_n if_o it_o be_v general_o regular_a and_o certain_a as_o in_o some_o part_n it_o seem_v to_o be_v that_o be_v to_o say_v from_o hence_o west_n ward_n to_o meta_fw-la incognita_fw-la new_a foundland_n florida_n and_o that_o part_n of_o the_o coast_n of_o america_n then_o may_v there_o be_v give_v by_o it_o general_a rule_n most_o certain_a and_o commodious_a for_o the_o use_n of_o navigation_n and_o by_o the_o same_o hypothesis_n of_o the_o pole_n of_o the_o magnes_n at_o 25._o 44′_n from_o the_o pole_n of_o the_o world_n the_o great_a variation_n of_o the_o needle_n in_o the_o equinoctial_a shall_v be_v at_o 90._o d._n of_o longitude_n 25._o 44′_n from_o north_n to_o east_n and_o consequent_o the_o great_a variation_n in_o the_o parallel_n of_o 70._o d._n shall_v be_v at_o the_o longitude_n of_o 128._o d._n 51′_n from_o north_n to_o 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upon_o his_o observation_n make_v at_o that_o place_n which_o confirm_v the_o retrograde_a quality_n in_o the_o variation_n from_o hence_o eastwardes_o as_o aforesaid_a which_o strange_a variety_n i_o have_v here_o plain_o propose_v to_o the_o end_n that_o the_o learned_a sort_n may_v consider_v thereof_o and_o sharpen_v their_o wit_n see_v what_o probable_a cause_n and_o ground_n they_o can_v assign_v for_o the_o same_o for_o consider_v it_o remain_v always_o constant_a without_o alteration_n in_o every_o several_a place_n there_o be_v hope_v it_o may_v be_v reduce_v into_o method_n and_o rule_n as_o for_o that_o westward_n because_o it_o carry_v proportion_n and_o have_v some_o apparent_a regularitie_n i_o will_v apply_v the_o same_o to_o the_o general_a commodity_n of_o all_o such_o as_o shall_v travail_v that_o way_n which_o if_o i_o shall_v here_o particular_o decipher_v it_o will_v require_v a_o volume_n whereby_o contrary_a to_o my_o first_o intent_n i_o shall_v far_o exceed_v the_o bound_n of_o a_o addition_n i_o will_v therefore_o abridge_v it_o to_o a_o hydrographical_a plat_v wherein_o all_o such_o error_n and_o defect_n as_o have_v be_v hither_o to_o use_v be_v reform_v which_o shall_v be_v easy_a for_o the_o mean_a capacity_n to_o conceive_v and_o serve_v more_o effectual_o in_o use_n then_o if_o i_o shall_v have_v express_v the_o same_o by_o multitude_n of_o rule_n in_o writing_n therefore_o for_o this_o matter_n i_o refer_v you_o to_o the_o same_o the_o which_o you_o shall_v look_v for_o very_o short_o ¶_o a_o new_a instrument_n for_o the_o variation_n because_o i_o have_v find_v some_o imperfection_n in_o the_o first_o instrument_n for_o the_o variation_n which_o notwithstanding_o do_v far_o excel_v the_o cumpass_n of_o variation_n heretofore_o use_v for_o that_o purpose_n i_o have_v here_o set_v down_o the_o form_n of_o a_o new_a instrument_n wherein_o all_o scruple_n of_o doubt_n and_o defect_n that_o may_v grow_v by_o the_o other_o be_v quite_o 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