the_o distance_n 3268_o m._n l_o b_o 351428_o be_v to_o the_o radius_fw-la 90_o d._n l_o a_o b_o 1000000_o so_o be_v the_o logarithm_n of_o the_o difference_n of_o longitude_n 3093_o m._n a_o b_o 349037_o to_o the_o sine_fw-la of_o the_o rumb_n 997609_o a_o l_o b_o 71_o d._n 10_o m._n add_v the_o radius_fw-la to_o the_o logarithm_n of_o the_o difference_n of_o longitude_n and_o subtract_v the_o logarithm_n of_o the_o distance_n and_o you_o have_v the_o sine_fw-la of_o the_o rumb_n 997609_o a_o l_o b_o 71_o d._n 10_o m._n so_o that_o the_o difference_n of_o longitude_n and_o the_o distance_n be_v in_o proportion_n to_o the_o rumb_n in_o the_o common_a chart._n seven_o i_o shall_v give_v the_o difference_n of_o longitude_n 3093_o m._n a_o b_o and_o the_o distance_n 3268_o m._n l_o b_o and_o demand_v the_o difference_n of_o latitude_n l_o a._n to_o find_v the_o difference_n of_o latitude_n the_o proportion_n arithmetical_a add_v the_o difference_n of_o longitude_n 3093_o m._n to_o the_o distance_n 3268_o m._n and_o you_o have_v 6361_o mil._n for_o the_o sum_n of_o the_o side_n then_o subtract_v the_o difference_n of_o longitude_n from_o the_o distance_n and_o you_o hauâ—_n 175_o mile_n for_o the_o difference_n of_o thâ—_n side_n so_o take_v the_o logarithm_n of_o thâ—_n sum_n of_o the_o side_n a_o b_o l_o b_o 6361_o mileâ—_n 380352_o and_o the_o logarithm_n of_o thâ—_n difference_n of_o the_o side_n 175_o mile_n 224303_o add_v they_o together_o anâ—_n you_o have_v 604655_o the_o half_a be_v 302327_o which_o be_v the_o logarithm_n of_o the_o difference_n of_o latitude_n 1055_o m._n l_o a._n sâ—_n that_o the_o difference_n of_o longitude_n anâ—_n the_o distance_n be_v in_o proportion_n in_o a_o right_o line_v triangle_n in_o the_o common_a chart_n eight_o i_o shall_v give_v the_o differencâ—_n of_o latitude_n l_o a_o 1055_o m._n and_o thâ—_n distance_n l_o b_o 3268_o m._n and_o demand_v thâ—_n difference_n of_o longitude_n to_o find_v the_o difference_n of_o longitude_n the_o proportion_n arithmetical_a adâ—_n the_o difference_n of_o latitude_n 1055_o m._n to_o the_o distance_n 3268_o m._n and_o you_o have_v 4323_o mile_n for_o the_o sum_n of_o the_o side_n than_o subtract_v the_o difference_n of_o latitude_n from_o the_o distance_n and_o you_o have_v 2213_o mile_n for_o the_o difference_n of_o the_o side_n so_o take_v the_o logarithm_n of_o the_o sum_n of_o the_o side_n 4323_o mile_n l_o a_o l_o b_o 363578_o and_o the_o logarithm_n of_o the_o difference_n of_o the_o side_n 2213_o 334498_o add_v they_o together_o and_o you_o have_v 698076_o the_o half_a be_v 349038_o which_o be_v the_o logarithm_n of_o the_o difference_n of_o longitude_n 3093_o miles_n a_o b_o so_o that_o the_o difference_n of_o latitude_n and_o the_o distance_n be_v in_o proportion_n in_o a_o rightlined_n triangle_n in_o the_o common_a chart._n i_o have_v prove_v by_o the_o forego_n question_n that_o the_o rumb_n and_o the_o right-line_n of_o the_o magnetic_a compass_n agree_v with_o the_o rumb_n and_o the_o right-line_n of_o the_o common_a chart_n from_o hence_o may_v arise_v a_o objection_n how_o the_o right-line_n of_o the_o magnetic_a compass_n can_v measure_v the_o superficies_n of_o the_o globe_n which_o be_v spherical_a to_o answer_v this_o objection_n i_o will_v grant_v you_o to_o be_v in_o any_o meridian_n and_o parallel_n of_o the_o world_n wherein_o you_o must_v see_v 180_o d._n of_o heaven_n for_o it_o be_v 90_o d._n from_o your_o zenith_n every_o way_n to_o the_o horizon_n than_o the_o circulation_n of_o the_o horizon_n must_v contain_v 360_o d._n to_o this_o i_o compare_v tâ—â—_n magnetic_a compass_n which_o contain_v 360_o d._n and_o be_v horizontal_n to_o the_o horizon_n always_o in_o all_o meridian_n anâ—_n parallel_n of_o the_o world_n so_o that_o thâ—_n north_n and_o south_n and_o the_o east_n anâ—_n west_n point_v of_o the_o magnetic_a compass_n point_n to_o the_o celestial_a pole_n oâ—_n north_n and_o south_n and_o to_o the_o celestiaâ—_n pole_n of_o east_n and_o west_n in_o all_o meridian_n and_o parallel_n of_o the_o earth_n and_o sea_n without_o give_v any_o difference_n of_o observation_n for_o the_o semidiameter_n of_o the_o earth_n and_o sea_n theâ—_n the_o meridian_n of_o the_o magnetic_a compass_n must_v run_v parallel_n to_o the_o pole_n of_o east_n and_o west_n as_o the_o parallel_n of_o latitude_n run_v parallel_n to_o the_o pole_n of_o north_n and_o south_n therefore_o the_o magnetic_a compass_n be_v of_o right-line_n measure_n the_o superficies_n of_o the_o globe_n by_o right-line_n as_o if_o the_o superficies_n of_o the_o globe_n be_v always_o a_o plain_a to_o the_o horizon_n so_o that_o whatever_o position_n do_v disagree_v with_o the_o rumb_n and_o the_o right-line_n of_o the_o magnetic_a compass_n must_v be_v a_o false_a position_n in_o navigation_n for_o the_o work_n of_o navigation_n must_v be_v perform_v by_o the_o magnetic_a compass_n and_o the_o latitude_n â—_o place_n by_o observation_n by_o which_o â—eans_v all_o the_o know_a part_n of_o the_o â—orld_n have_v be_v discover_v and_o lay_v â—own_v in_o a_o plain_a in_o the_o common_a chart_n therefore_o i_o shall_v show_v you_o â—ow_o the_o difference_n of_o latitude_n and_o the_o difference_n of_o longitude_n and_o the_o distance_n of_o place_n in_o the_o common_a chart_n be_v transfer_v in_o proportion_n to_o the_o difference_n of_o latitude_n and_o the_o distance_n of_o place_n upon_o the_o globe_n wherein_o i_o shall_v prove_v by_o demonstration_n that_o the_o meridian_n of_o the_o magnetic_a compass_n do_v differ_v from_o the_o meridian_n of_o the_o globe_n as_o they_o be_v draw_v to_o prove_v how_o the_o difference_n of_o latitude_n and_o the_o distance_n of_o place_n and_o the_o difference_n of_o longitude_n in_o the_o common_a chart_n be_v transfer_v from_o the_o common_a chart_n to_o be_v in_o proportion_n by_o demonstration_n to_o the_o difference_n of_o latitude_n and_o the_o distance_n of_o place_n upon_o the_o globe_n in_o the_o forego_n question_n by_o thâ—_n common_a chart_n the_o lizard_n be_v in_o thâ—_n latitude_n of_o 50_o d._n 00_o m._n the_o bermuduâ—_n be_v in_o the_o latitude_n of_o 32_o d._n 25_o m._n theiâ—_n difference_n of_o latitude_n be_v 1055_o m_o or_o 17_o d._n 35_o m._n and_o the_o difference_n oâ—_n longitude_n be_v 3093_o m._n or_o 51_o d._n 33_o m._n and_o the_o distance_n be_v 3268_o m._n or_o 54_o d._n 28_o m._n before_o i_o proceed_v to_o the_o demonstration_n upon_o the_o globe_n you_o may_v observe_v the_o difference_n of_o longitude_n in_o all_o rightlined_n triangle_n be_v in_o proportion_n to_o the_o difference_n of_o longitude_n in_o the_o middle_a parallel_n of_o the_o globe_n between_o such_o place_n differ_v in_o longitude_n and_o latitude_n in_o all_o meridian_n and_o parallel_v of_o the_o world_n pag_n 19_o to_o prove_v how_o the_o difference_n of_o latitude_n and_o the_o distance_n of_o place_n and_o the_o difference_n of_o longitude_n in_o the_o common_a chart_n be_v transfer_v by_o demonstration_n to_o be_v in_o proportion_n to_o the_o difference_n of_o latitude_n and_o the_o distance_n of_o place_n upon_o the_o globe_n example_n the_o lizard_n be_v in_o the_o latitude_n of_o 50_o d._n 00_o m._n l._n bermudus_n be_v in_o the_o latitude_n of_o 32_o d._n 25_o m._n b_o their_o difference_n of_o latitude_n be_v a_o l_o 17_o d._n 35_o m._n the_o half_a thereof_o be_v 08_o d._n 47_o m._n 30_o sec_fw-la which_o be_v add_v to_o d_o a_o 32_o d._n 25_o m._n the_o latitude_n of_o bermudus_n you_o have_v d_o e_o 41_o d._n 12_o m._n 30_o sec_fw-la the_o latitude_n of_o the_o middle_a parallel_n between_o the_o lizard_n and_o bermudus_n then_o reduce_v the_o diâ—rence_n of_o longitude_n find_v by_o the_o foâ—_n go_v rightlined_n triangle_n between_o the_o meridian_n and_o parallel_n of_o the_o lyzaâ—_n and_o the_o meridian_n and_o parallel_n of_o bâ—mudus_n 3093_o m._n into_o degree_n of_o tâ—_n aequinoctial_a by_o divide_v 3093_o by_o 60_o m._n and_o you_o have_v 51_o d._n 33_o which_o distance_n be_v take_v by_o you_o compass_n from_o the_o aequinoctial_a paâ—_n of_o the_o globe_n and_o measure_v thâ—_n distance_n in_o the_o middle_a parallel_n e_o â—_o 41_o d._n 12_o m._n 30_o sec_fw-la you_o will_v find_v thaâ—_n distance_n 51_o d._n 33_o m._n to_o reach_v from_o thâ—_n meridian_n of_o the_o lizard_n to_o the_o meridian_n of_o the_o bermudus_n in_o the_o parallel_n of_o 41_o d._n 12_o m._n 30_o sec_fw-la which_o be_v thâ—_n same_o distance_n in_o the_o common_a chart_n so_o that_o the_o lizard_n must_v be_v lay_v down_o upon_o the_o globe_n in_o the_o meridian_n oâ—_n the_o middle_a parallel_n d_o e_o p_o and_o in_o the_o latitude_n of_o 50_o d._n 00_o m._n at_o l_o and_o bermudus_n must_v be_v lay_v down_o upon_o the_o globe_n in_o the_o meridian_n of_o the_o middle_a parallel_n c_o e_o p_o
349037_o so_o the_o radius_fw-la 90_o d._n oh_o m._n p_o d_o 100000â—_n to_o the_o logarithm_n of_o 356394_o aâ—_n the_o logarithm_n of_o the_o difference_n longitude_n in_o the_o middle_a parallel_n the_o radius_fw-la and_o subtract_v the_o co-siâ—â—_a of_o the_o latitude_n and_o you_o have_v tâ—â—_n logarithm_n of_o 356394_o then_o add_v the_o logarithm_n of_o 36823_o find_v in_o proportion_n to_o 3093_o m._n longitude_n in_o the_o parallel_n of_o 50_o d._n 00_o m_o to_o the_o logarithm_n of_o 356394_o find_v 〈◊〉_d proportion_n to_o 3093_o m._n of_o longitude_n 〈◊〉_d the_o parallel_n of_o 32_o d._n 25_o m._n and_o yoâ—_n have_v 724625_o the_o half_a be_v 362312_o which_o be_v the_o logarithm_n of_o the_o difference_n of_o longitude_n in_o the_o aequinoctiaâ—_n part_n of_o the_o globe_n 4200_o m._n d_o c_o demand_v so_o that_o the_o proportion_n arithmetical_a agree_v with_o the_o proportion_n geometrical_a therefore_o the_o difference_n of_o longitude_n in_o the_o middle_a parallel_n of_o the_o globe_n be_v the_o proper_a difference_n of_o longitude_n 3093_o m._n in_o proportion_n to_o the_o rumb_n by_o the_o magâ—etick_a compass_n i_o have_v do_v with_o first_o questionn_n in_o the_o common_a chart_n between_o place_n differ_v in_o longitude_n and_o latitude_n wherein_o i_o have_v prove_v how_o the_o meridian_n and_o parallel_v of_o the_o common_a chart_n differ_v in_o longitude_n and_o latitude_n be_v transfer_v by_o demonstration_n in_o proportion_n to_o the_o difference_n of_o latitude_n and_o the_o distance_n of_o place_n upon_o the_o globe_n last_o of_o all_o i_o shall_v show_v you_o how_o to_o transferr_v the_o difference_n of_o longitude_n in_o one_o and_o the_o same_o latitude_n in_o the_o common_a chart_n into_o the_o meridian_n and_o parallel_v of_o the_o globe_n example_n in_o the_o common_a chart_n in_o the_o latitude_n of_o 50_o d._n 00_o m._n the_o difference_n of_o longitude_n be_v 3093_o m._n l_o t_o i_o demand_v the_o difference_n of_o meridian_n in_o tâ—_n aequinoctial_a part_n of_o the_o globe_n to_o find_v the_o difference_n of_o longitude_n in_o the_o aequinoctial_a part_n of_o the_o gloâ—â—_n the_o proportion_n arithmetrical_a as_o tâ—_n cousin_a of_o the_o latitude_n 40_o d._n 00_o m._n p_o 980806_o be_v to_o the_o logarithm_n of_o the_o difference_n of_o longitude_n in_o the_o parallel_n 50_o d._n 00_o m._n l_o t_o 3093_o m._n 349037_o so_o be_v the_o radius_fw-la 90_o d._n p_o d_o 1000000_o to_o the_o logarithm_n of_o 368231_o which_o the_o logarithm_n of_o d_o h_n 4812_o mile_n â—_o 80_o d._n 12_o m._n the_o difference_n of_o meridian_n in_o the_o aequinoctial_a part_n of_o the_o globâ—_n be_v oblique_a do_v differ_v from_o thâ—_n meridian_n of_o the_o common_a chart_n thaâ—_n be_v rightlined_n but_o the_o distance_n oâ—_n place_n in_o the_o globe_n be_v the_o same_o in_o the_o common_a chart_n in_o regard_n the_o distance_n of_o place_n be_v transfer_v from_o the_o common_a chart_n to_o the_o globe_n therefore_o the_o superficies_n of_o the_o common_a chart_n in_o all_o meridian_n and_o parallel_v be_v in_o proportion_n to_o the_o superficies_n of_o the_o globe_n in_o all_o meridian_n and_o parallel_n and_o whereas_o all_o writer_n in_o navigation_n have_v condemn_v the_o â—ommon_a chart_n to_o be_v pester_v with_o notorious_a error_n it_o prove_v a_o great_a mistake_n therefore_o i_o shall_v answer_v the_o principal_a objection_n and_o in_o that_o i_o answer_v all_o the_o rest_n mr._n edward_n wright_n in_o his_o correction_n of_o error_n in_o the_o common_a chart_n fol._n 5._o â—aith_n in_o show_v the_o distance_n of_o place_n there_o be_v as_o great_a a_o error_n commit_v as_o in_o any_o of_o the_o former_a for_o example_n if_o you_o imagine_v two_o ship_n to_o be_v under_o the_o aequinoctial_a 100_o league_n asunder_o and_o that_o each_o of_o they_o shall_v sail_v from_o thence_o due_a north_n or_o south_n under_o his_o meridian_n until_o they_o come_v to_o the_o parallel_n of_o 60_o d._n latitude_n they_o shall_v be_v there_o but_o only_o 50_o league_n distant_a because_o at_o that_o parallel_n the_o meridian_n be_v distant_a but_o half_a so_o much_o one_o from_o another_o as_o they_o be_v at_o the_o aequinoctial_a as_o it_o may_v most_o manifest_o appear_v by_o the_o globe_n and_o that_o the_o chart_n will_v show_v that_o those_o tâ—â—_n ship_n have_v the_o selfsame_a distance_n 100_o league_n be_v under_o the_o parallel_n of_o 60_o degree_n which_o they_o haâ—_n before_o when_o they_o be_v under_o tâ—â—_n aequinoctial_a it_o be_v grant_v that_o the_o difference_n 〈◊〉_d meridian_n in_o the_o common_a chart_n 100_o league_n in_o the_o equinoctial_a anâ—_n 100_o league_n in_o the_o parallel_n of_o 6â—_n degree_n in_o regard_v it_o appear_v by_o observation_n by_o the_o magnetic_a compass_n that_o thâ—_n east_n and_o west_n point_n of_o the_o magnetic_n compass_n as_o it_o be_v horizontal_n do_v always_o point_n to_o the_o pole_n of_o east_n and_o w._n in_o the_o celestial_a sphere_n likewise_o the_o north_n and_o south_n point_n of_o the_o magnetic_a compass_n as_o it_o be_v horizontal_n do_v always_o point_n to_o the_o pole_n of_o north_n and_o south_n in_o the_o celestial_a sphere_n in_o all_o meridian_n and_o parallel_n of_o the_o terrestrial_a sphere_n without_o make_v any_o difference_n of_o observation_n for_o the_o semi-diameter_n of_o the_o earth_n and_o whereas_o it_o appear_v by_o observation_n that_o the_o magnetic_a compass_n in_o its_o true_a pole_n â—ill_v direct_v your_o the_o circulation_n of_o the_o â—arth_n and_o sea_n in_o any_o parallel_n of_o latitude_n keep_v a_o equal_a distance_n â—om_n the_o pole_n of_o north_n and_o south_n â—_o likewise_o it_o must_v be_v grant_v that_o the_o meridian_n of_o the_o magnetic_a compass_n â—ust_z run_z parallel_n to_o the_o pole_n of_o â—ast_n and_o west_n the_o circulation_n of_o the_o â—arth_n in_o all_o parallel_n meridian_n in_o â—egard_n the_o magnetic_a compass_n as_o it_o be_v horizontal_n make_v the_o same_o position_n to_o the_o pole_n of_o north_n and_o south_n in_o the_o celestial_a sphere_n and_o to_o the_o â—oles_n of_o east_n and_o west_n in_o the_o celestial_a sphere_n in_o all_o meridian_n and_o parallel_n of_o the_o terrestrial_a sphere_n without_o make_v any_o difference_n of_o observation_n for_o the_o semi-diameter_n of_o the_o earth_n so_o that_o the_o meridian_n do_v cross_v the_o parallel_n of_o the_o magnetic_a compass_n at_o right-angle_n in_o all_o meridian_n and_o parallel_n of_o the_o earth_n and_o sea_n as_o it_o be_v by_o demonstration_n in_o the_o common_a chart._n therefore_o the_o magnetic_a compass_n as_o it_o be_v horizontal_n must_v measure_v the_o superficies_n of_o the_o terrestrial_a sphere_n by_o right-line_n as_o if_o tâ—_n superficies_n of_o the_o terrestrial_a spheâ—â—_n be_v a_o plain_a to_o the_o horizon_n so_o that_o you_o imagine_v two_o ship_n to_o be_v under_o tâ—â—_n aequinoctial_a 100_o league_n asunder_o aâ—_n that_o each_o of_o they_o shall_v sail_v froâ—_n thence_o due_a north_n or_o due_a south_n undâ—â—_n his_o meridian_n until_o they_o come_v to_o thâ—_n parallel_v of_o 60_o d._n latitude_n they_o muâ—â—_n be_v 100_o league_n distant_a in_o regard_n thâ—_n meridian_n of_o the_o magnetic_a compasâ—_n must_v run_v parallel_n to_o the_o pole_n oâ—_n east_n and_o west_n as_o the_o east_n and_o weâ—â—_n point_v of_o the_o magnetic_a compass_n ruâ—â—_n parallel_n to_o the_o pole_n of_o north_n anâ—_n south_n i_o shall_v treat_v more_o at_o large_a oâ—_n this_o in_o its_o due_a place_n i_o have_v give_v you_o the_o geometrical_a demonstration_n and_o the_o arithmetical_a rule_n how_o all_o place_n in_o the_o common_a chart_n be_v transfer_v into_o the_o meridian_n and_o parallel_n of_o the_o globe_n therefore_o you_o can_v resolve_v any_o question_n in_o navigaton_n from_o the_o globe_n without_o you_o have_v such_o proportion_n from_o the_o globe_n as_o be_v in_o proportion_n to_o the_o rumb_n and_o the_o right-line_n of_o the_o magnetic_a compass_n the_o same_o question_n resolve_v by_o mercator_n projection_n mr._n edward_n wright_n in_o his_o projection_n of_o mercators_n plain-sphere_n do_v make_v the_o superficies_n of_o the_o globe_n as_o a_o â—lain_n to_o the_o horizon_n and_o do_v measure_n â—l_o the_o parallel_n of_o the_o globe_n in_o proportion_n to_o the_o degree_n of_o the_o aequinoctial_a â—o_o the_o north_n and_o south_n pole_n so_o that_o â—ll_o the_o parallel_n in_o mercator_n plain-â—phere_a be_v of_o equal_a diameter_n to_o the_o pole_n then_o mercator_n divide_v the_o meridian_n line_n into_o unequal_a part_n and_o do_v increase_v the_o degree_n and_o minute_n of_o latitude_n from_o the_o aequinoctial_a to_o the_o pole_n to_o almost_o a_o endless_a proportion_n therefore_o at_o every_o point_n of_o latitude_n in_o his_o plain-sphere_n the_o difference_n of_o meridian_n do_v so_o increase_v that_o take_v half_o a_o degree_n above_o a_o point_n of_o latitude_n and_o half_a a_o degree_n below_o the_o
of_o the_o terrestrial_a sphere_n example_n by_o observation_n if_o the_o sun_n be_v upon_o the_o horizon_n in_o the_o aequinoctial_a the_o suns-amplitude_n shall_v be_v east_n or_o west_n of_o you_o by_o the_o magnetic_a compass_n as_o it_o be_v horizontal_n in_o all_o meridian_n and_o parallel_n of_o the_o terrestrial_a sphere_n but_o if_o i_o be_v in_o the_o latitude_n 32_o d._n 25_o m._n or_o in_o any_o other_o latitude_n and_o i_o be_v to_o sail_v by_o the_o magnetic_a compass_n east_n or_o west_n the_o circulation_n of_o the_o earth_n and_o sea_n i_o shall_v find_v i_o have_v not_o alter_v my_o latitude_n by_o observation_n therefore_o the_o east_n and_o west_n course_n of_o the_o magnetic_a compass_n agree_v with_o the_o parallel_n of_o latitude_n upon_o the_o terrestrial_a sphere_n by_o observation_n this_o position_n can_v be_v prove_v but_o from_o the_o latitude_n of_o place_n by_o observation_n which_o agree_v with_o the_o east_n and_o west_n course_n of_o the_o magnetic_a compass_n so_o that_o the_o parallel_n of_o latitude_n upon_o the_o globe_n be_v of_o equal_a distance_n from_o the_o pole_n of_o north_n and_o south_n and_o in_o proportion_n to_o the_o rumb_n by_o the_o magnetic_a compass_n in_o the_o next_o place_n i_o shall_v prove_v the_o north_n and_o south_n point_v of_o the_o magnetic_a compass_n point_n to_o the_o pole_n of_o north_n and_o south_n in_o the_o celestial_a sphere_n in_o all_o meridian_n and_o parallel_n of_o the_o terrestrial_a sphere_n then_o i_o shall_v prove_v the_o north_n and_o south_n point_v of_o the_o magnetic_a compass_n must_v run_v parallel_n to_o the_o pole_n of_o east_n and_o west_n in_o all_o meridian_n and_o parallel_n of_o the_o terrestrial_a sphere_n example_n by_o observation_n if_o the_o sun_n or_o star_n be_v upon_o their_o meridian_n in_o my_o meridian_n and_o parallel_n of_o the_o terrestrial_a sphere_n the_o sun_n be_v or_o star_n azimuth_n musâ—_n be_v north_n or_o south_n by_o the_o horizontaâ—_n bear_v of_o the_o magnetic_a compass_n to_o the_o celestial_a pole_n so_o that_o the_o magnetic_a compass_n as_o it_o be_v horizontal_n point_n to_o the_o celestial_a pole_n of_o north_n and_o south_n and_o to_o the_o celestial_a pole_n of_o east_n and_o west_n in_o all_o meridian_n and_o parallel_n of_o the_o earth_n and_o sea_n without_o give_v any_o difference_n of_o observation_n for_o the_o semi-diameter_n of_o the_o earth_n and_o sea_n and_o notwithstanding_o the_o magnetic_a compass_n point_v to_o the_o celestial_a pole_n of_o north_n and_o south_n and_o to_o the_o celestial_a pole_n of_o east_n and_o west_n in_o all_o meridian_n and_o parallel_n of_o the_o terrestrial_a sphere_n it_o be_v prove_v by_o observation_n that_o you_o may_v run_v the_o circulation_n of_o the_o earth_n by_o the_o magnetic_a compass_n in_o any_o parallel_n of_o latitude_n therefore_o the_o magnetic_a compass_n must_v run_v parallel_n to_o the_o pole_n of_o east_n and_o west_n as_o the_o magnetic_a compass_n run_v parallel_n to_o the_o pole_n of_o north_n and_o south_n in_o the_o terrestrial_a sphere_n in_o regard_n the_o magnetic_a compass_n make_v the_o same_o position_n to_o the_o pole_n of_o east_n and_o west_n and_o to_o the_o pole_n of_o north_n and_o south_n in_o the_o celestial_a sphere_n so_o that_o the_o difference_n of_o meridian_n by_o the_o magnetic_a compass_n as_o it_o be_v horrizontal_n upon_o the_o terrestrial_a sphere_n be_v of_o equal_a distance_n from_o the_o pole_n of_o east_n and_o west_n as_o the_o difference_n of_o the_o parallel_n of_o latitude_n by_o the_o magnetic_a compass_n as_o it_o be_v horizontal_n be_v of_o equal_a distance_n from_o the_o pole_n of_o north_n and_o south_n this_o position_n must_v be_v infallible_a for_o by_o observation_n the_o magnetic_a compass_n as_o it_o be_v horizontal_n point_n to_o the_o celestial_a pole_n so_o that_o the_o north_n and_o south_n point_v of_o the_o magnetic_a compass_n do_v across_o the_o east_n and_o west_n point_v of_o the_o magnetic_a compass_n at_o right-angle_n in_o all_o meridian_n and_o parallel_n of_o the_o earth_n and_o sea_n therefore_o the_o magnetic_a compass_n do_v measure_v the_o superficies_n of_o the_o globâ—_n by_o right-line_n as_o if_o the_o superficies_n oâ—_n the_o globe_n be_v a_o plain_a to_o the_o orison_n in_o the_o next_o place_n if_o the_o sun_n be_v iâ—_n the_o aequinoctial_a and_o that_o you_o be_v iâ—_n the_o latitude_n of_o 60_o d._n or_o 70_o d._n or_o 80_o d_o of_o north_n or_o south_n latitude_n the_o suâ—_n upon_o the_o horizon_n shall_v be_v east_n of_o you_o in_o the_o morning_n and_o west_n of_o you_o iâ—_n the_o afternoon_n by_o the_o magnetic_a compass_n in_o its_o true_a pole_n as_o if_o you_o be_v in_o the_o aequinoctial_a part_n of_o the_o earth_n or_o sea_n the_o reason_n of_o this_o observation_n be_v this_o the_o terrestrial_a sphere_n be_v spacious_a to_o we_o that_o be_v upon_o it_o but_o it_o appear_v to_o be_v no_o other_o than_o a_o centre_n to_o the_o body_n of_o the_o sun_n or_o star_n in_o regard_n the_o magnetic_a compass_n run_v atwhart_n the_o parallel_n of_o latitude_n in_o the_o terrestrial_a sphere_n to_o the_o pole_n of_o east_n and_o west_n in_o the_o celestial_a sphere_n without_o give_v any_o difference_n of_o observation_n for_o the_o semi-diameter_n of_o the_o earth_n and_o sea_n therefore_o it_o have_v be_v impossible_a to_o find_v the_o magnetic_a compass_n shall_v run_v parallel_n to_o the_o pole_n of_o north_n and_o south_n in_o the_o terrestrial_a sphere_n if_o the_o meridian_n altitude_n of_o the_o sun_n or_o star_n by_o observation_n do_v not_o produce_v the_o same_o latitude_n or_o parallel_n with_o the_o magnetic_a compass_n the_o circulation_n of_o the_o earth_n in_o regard_n the_o magnetic_a compass_n as_o it_o be_v horinzontal_n point_n to_o the_o pole_n of_o east_n and_o west_n in_o the_o celestial_a sphere_n as_o the_o magnetic_a compass_n point_v to_o the_o pole_n of_o north_n and_o south_n in_o the_o celestial_a sphere_n then_o observe_v there_o be_v no_o reason_n in_o navigation_n to_o suppose_v the_o meridian_n or_o the_o north_n and_o south_n point_v of_o the_o magnetic_a compass_n as_o it_o be_v horizontal_n to_o the_o meridian_n altitude_n of_o the_o sun_n or_o star_n in_o the_o celestial_a sphere_n to_o run_v to_o the_o north_n and_o south_n pole_n as_o it_o be_v in_o the_o terrestrial_a sphere_n but_o that_o you_o may_v likewise_o suppose_v meridian_n or_o the_o east_n and_o west_n point_v of_o the_o magnetic_a compass_n as_o it_o be_v horizontal_n to_o the_o sun_n amplitude_n in_o the_o aequinoctial_a to_o run_v to_o the_o pole_n of_o east_n and_o west_n in_o the_o terrestrial_a sphere_n in_o regard_n the_o magnetic_a compass_n make_v the_o same_o position_n to_o the_o pole_n of_o east_n and_o west_n as_o it_o have_v to_o the_o pole_n of_o north_n and_o south_n in_o the_o celestial_a sphere_n in_o the_o next_o place_n it_o must_v be_v grant_v if_o the_o east_n and_o west_n point_v of_o the_o magnetic_a compass_n in_o the_o parallel_n oâ—_n 80_o d._n point_n to_o the_o pole_n of_o east_n and_o west_n in_o the_o celestial_a sphere_n without_o give_v any_o difference_n of_o observation_n for_o almost_o the_o semi-diameter_n of_o the_o earth_n in_o the_o terrestrial_a sphere_n than_o the_o north_n and_o south_n point_v of_o the_o magnetic_a compass_n in_o the_o meridian_n of_o 80_o d._n must_v point_n to_o the_o pole_n of_o north_n and_o south_n in_o the_o celestial_a sphere_n without_o give_v any_o difference_n of_o observation_n for_o almost_o the_o semi-diameter_n of_o the_o earth_n in_o the_o terrestrial_a sphere_n therefore_o the_o meridian_n of_o the_o magnetic_a compass_n have_v the_o same_o position_n in_o the_o terrestrial_a sphere_n and_o must_v run_v parallel_n to_o the_o pole_n of_o east_n and_o west_n as_o the_o parallel_n of_o latitude_n run_v parallel_n by_o the_o magnetic_a compass_n to_o the_o pole_n of_o north_n and_o south_n then_o observe_v the_o magnetic_a compass_n be_v always_o horizontal_n to_o the_o horizon_n it_o do_v measure_v the_o superficies_n of_o the_o earth_n and_o sea_n by_o right-line_n in_o the_o parallel_n meridian_n to_o the_o pole_n of_o east_n and_o west_n and_o in_o the_o parallel_n to_o the_o pole_n of_o north_n and_o south_n as_o if_o the_o superficies_n of_o the_o globe_n be_v a_o plain_a to_o the_o horizon_n this_o position_n you_o have_v at_o large_a in_o the_o common_a chart_n wherein_o you_o have_v the_o difference_n of_o meridian_n and_o the_o difference_n of_o latitude_n and_o the_o distance_n of_o place_n in_o proportion_n to_o the_o rumb_n and_o the_o right-line_n of_o the_o magnetic_a compass_n if_o the_o position_n of_o the_o common_a chart_n be_v not_o the_o only_a truth_n in_o navigation_n there_o be_v no_o geometrical_a demonstration_n in_o proportion_n to_o the_o rumb_n and_o the_o right-line_n of_o the_o magnetic_a
compass_n therefore_o it_o have_v be_v a_o great_a mistake_n in_o all_o writer_n to_o suppose_v the_o magnetic_a compass_n to_o agree_v with_o the_o meridian_n of_o the_o globe_n as_o they_o be_v draw_v whereas_o there_o be_v no_o observation_n or_o demonstration_n to_o prove_v iâ—_n only_o the_o meridian_n of_o the_o magnetic_n compass_n as_o it_o be_v horizontal_n to_o thâ—_n meridian_n of_o the_o sun_n and_o star_n poinâ—_n to_o the_o pole_n of_o the_o celestial_a sphere_n â—_o to_o this_o i_o must_v reply_v that_o the_o eaâ—â—_n and_o west_n point_v of_o the_o magnetic_n compass_n as_o it_o be_v horizontal_n poinâ—_n to_o the_o east_n and_o west_n pole_n of_o the_o celestial_a sphere_n from_o all_o meridian_n anâ—_n parallel_n of_o the_o terrestrial_a sphere_n sâ—_n that_o you_o may_v as_o well_o draw_v meridianâ—_n in_o navigation_n by_o the_o magnetic_a compass_n from_o the_o pole_n of_o east_n and_o west_n as_o from_o the_o pole_n of_o north_n and_o south_n in_o the_o terrestrial_a sphere_n therefore_o the_o work_n of_o navigation_n can_v be_v perform_v by_o the_o oblique_a line_n of_o the_o globe_n i_o have_v prove_v by_o observation_n that_o the_o east_n and_o west_n point_v of_o the_o magnetic_a compass_n run_v parallel_n to_o the_o pole_n of_o north_n and_o south_n in_o the_o terrestrial_a sphere_n therefore_o the_o north_n and_o south_n point_v of_o the_o magnetic_a compass_n must_v run_v parallel_n to_o the_o pole_n of_o east_n and_o west_n in_o the_o terrestrial_a sphere_n in_o regard_n those_o pole_n do_v cross_a at_o right-angle_n in_o all_o meridian_n and_o parallel_n of_o the_o earth_n and_o sea_n last_o of_o all_o i_o shall_v show_v you_o the_o error_n that_o attend_v mercator_n i_o have_v prove_v that_o mercator_n do_v grant_v the_o difference_n of_o latitude_n and_o the_o distance_n of_o place_n to_o be_v of_o equal_a part_n and_o to_o be_v in_o proportion_n to_o the_o rumb_n by_o the_o magnetic_a compass_n in_o a_o rightlined_n triangle_n so_o that_o mercator_n have_v grant_v three_o part_n in_o four_o in_o a_o rightlined_n triangle_n then_o if_o the_o difference_n of_o longitude_n in_o a_o rightlined_n triangle_n be_v not_o the_o true_a difference_n of_o meridian_n according_a to_o the_o rumb_n by_o the_o magnetic_a compass_n we_o have_v no_o geometrical_a demonstration_n in_o navigation_n therefore_o i_o shall_v proceed_v to_o find_v the_o distance_n between_o the_o meridian_n and_o parallel_n of_o bermudus_n and_o the_o meridian_n and_o parallel_n of_o the_o lizard_n in_o a_o rightlined_n triangle_n from_o the_o rumb_n sound_n by_o the_o brief_a rule_n of_o mercator_n and_o the_o difference_n of_o latitude_n and_o last_o of_o all_o i_o shall_v show_v you_o the_o disproportion_n between_o the_o meridian_n of_o the_o common_a chart_n and_o the_o meridian_n of_o mercator_n and_o the_o globe_n as_o they_o be_v draw_v so_o that_o whoever_o pretend_v to_o keep_v account_n of_o the_o ship_n way_n according_a to_o the_o difference_n of_o meridian_n in_o mercator_n plani-sphere_n or_o according_a to_o the_o difference_n of_o meridian_n upon_o the_o globe_n they_o must_v commit_v gross_a error_n example_n i_o sail_v from_o the_o meridian_n and_o parallel_n of_o the_o lizard_n in_o the_o latitude_n of_o 50_o d._n 00_o m._n in_o a_o angle_n of_o 71_o d._n 21_o m._n southwestward_a as_o the_o rumb_n be_v find_v by_o the_o brief_a rule_n of_o mercator_n into_o the_o meridian_n and_o parallel_n of_o bermudus_n in_o the_o latitude_n of_o 32_o d._n 25_o m._n i_o demand_v the_o distance_n and_o the_o difference_n of_o longitude_n between_o the_o meridian_n and_o parallel_n of_o bermudus_n and_o the_o meridian_n and_o parallel_n of_o the_o lizard_n in_o a_o rightlined_n triangle_n pag_n 61_o the_o angle_n of_o position_n by_o mercator_n brief_a rule_n do_v differ_v from_o the_o angle_n of_o position_n by_o the_o common_a chart_n 11_o m._n however_o the_o distance_n between_o the_o lizard_n and_o bermudus_n can_v be_v know_v but_o by_o a_o rightlined_n triangle_n the_o angle_n follow_v be_v a_o rightlined_n triangle_n be_v in_o like_a proportion_n to_o the_o common_a chart_n so_o be_v l_o the_o meridian_n and_o parallel_n of_o the_o lizard_n and_o b_o be_v the_o meridian_n and_o parallel_n of_o bermudus_n then_o be_v l_o a_o the_o difference_n of_o latitude_n 1055_o m._n and_o c_o l_o d_o be_v the_o rumb_n or_o angle_n of_o position_n between_o the_o meridian_n and_o parallel_n of_o the_o lizard_n and_o the_o meridian_n and_o parallel_n of_o bermudus_n then_o be_v a_o b_o and_o l_o t_o the_o difference_n of_o longitude_n between_o the_o meridian_n of_o the_o lizard_n and_o the_o meridian_n of_o bermudus_n and_o l_o b_o be_v the_o distance_n between_o the_o lizard_n and_o bermudus_n then_o be_v b_o h_n and_o l_o q_o the_o difference_n of_o longitude_n in_o mercators_n plani-sphere_n and_o upon_o the_o globe_n which_o differ_v from_o the_o meridian_n of_o the_o common_a chart_n 419_o m._n and_o 426_o mile_n to_o find_v the_o distance_n between_o the_o meridian_n and_o parallel_n of_o the_o lizard_n and_o bermudus_n l_o b_o the_o proportion_n arithmetical_a as_o the_o cousin_a of_o the_o rumb_n 71_o d._n 21_o m._n a_o b_o l_o 950485_o be_v to_o the_o logarithm_n of_o the_o difference_n of_o latitude_n 1055_o m._n l_o a_o 302325_o so_o be_v the_o radius_fw-la 90_o d._n labernele_n 1000000_o to_o the_o logarithm_n of_o the_o distance_n 3299_o m._n l_o b_o 351840_o demand_v add_v the_o logarithm_n of_o the_o difference_n of_o latitude_n to_o the_o radius_fw-la and_o subtract_v the_o cousin_a of_o the_o rumb_n and_o you_o have_v the_o logarithm_n of_o the_o distance_n 351840_o l_o b_o 3299_o m._n thus_o you_o see_v when_o mercator_n have_v weary_v himself_o with_o find_v brief_a rule_n to_o be_v in_o proportion_n between_o the_o difference_n of_o longitude_n in_o the_o aequinoctial_a and_o the_o difference_n of_o latitude_n in_o meridional_a part_n to_o find_v the_o rumb_n by_o the_o magnetic_a compass_n then_o mercator_n do_v grant_v that_o the_o distance_n of_o place_n differ_v in_o longitude_n and_o latitude_n can_v be_v find_v by_o any_o geometrical_a demonstration_n to_o be_v in_o proportion_n to_o the_o rumb_n by_o the_o magnetic_a compass_n and_o the_o difference_n of_o latitude_n but_o by_o a_o rightlined_n triangle_n therefore_o mercator_n do_v grant_v three_o part_n in_o four_o in_o a_o rightlined_n triangle_n then_o if_o the_o difference_n of_o longitude_n in_o a_o rightlined_n triangle_n be_v not_o the_o true_a difference_n of_o meridian_n there_o be_v no_o geometrical_a demonstration_n in_o navigation_n to_o find_v the_o difference_n of_o meridian_n in_o proportion_n to_o the_o rumb_n by_o the_o magnetic_a compass_n in_o the_o next_o place_n i_o shall_v proceed_v to_o find_v the_o difference_n of_o longitude_n in_o a_o rightlined_n triangle_n from_o the_o difference_n of_o latitude_n and_o the_o rumb_n find_v by_o mercator_n brief_a rule_n example_n i_o sail_v from_o the_o meridian_n and_o parallel_n of_o the_o lizard_n in_o the_o latitude_n of_o 50_o d._n 00_o m._n in_o a_o angle_n of_o 71_o d._n 21_o m._n southwestward_a as_o the_o rumb_n be_v find_v by_o the_o brief_a rule_n of_o mercator_n into_o the_o meridian_n and_o parallel_n of_o bermudus_n in_o the_o latitude_n of_o 32_o d._n 25_o m._n i_o demand_v the_o difference_n of_o longitude_n in_o a_o rightlined_n triangle_n to_o find_v the_o difference_n of_o longitude_n the_o proportion_n arithmetical_a as_o the_o radius_fw-la 90_o d._n a_o b_o l_o 1000000_o be_v to_o the_o logarithm_n of_o the_o difference_n of_o latitude_n 1055_o m._n l_o a_o 302325_o so_o be_v the_o tangent_fw-la of_o the_o rumb_n 71_o d._n 21_o m._n a_o l_o b_o 1047171_o to_o the_o logarithm_n of_o the_o difference_n of_o longitude_n 349496_o a_o b_o 3126_o m._n add_v the_o logarithm_n of_o the_o difference_n of_o latitude_n to_o the_o tangent_fw-la of_o the_o rumb_n and_o subtract_v the_o radius_fw-la and_o you_o have_v the_o logarithm_n of_o the_o difference_n of_o longitude_n in_o proportion_n to_o the_o rumb_n by_o the_o magnetic_a compass_n and_o the_o difference_n of_o latitude_n in_o a_o rightlined_n triangle_n in_o the_o practical_a part_n of_o the_o sea_n the_o rumb_n be_v always_o give_v as_o in_o the_o first_o question_n in_o the_o common_a chart_n 71_o d._n 10_o m._n so_o that_o the_o brief_a rule_n of_o mercator_n do_v alter_v the_o rumb_n 11_o m._n which_o alter_v the_o difference_n of_o longitude_n 33_o m._n and_o the_o distance_n 30_o m._n otherwise_o this_o latter_a rightlined_n triangle_n will_v agree_v with_o the_o former_a i_o shall_v pass_v by_o these_o small_a error_n and_o proceed_v to_o the_o great_a in_o mercators_n plani-sphere_n and_o upon_o the_o globe_n the_o difference_n of_o longitude_n between_o the_o meridian_n and_o parallel_n of_o bermudus_n and_o the_o meridian_n of_o the_o lizard_n be_v prove_v to_o be_v 3545_o m._n
b_o h_n or_o 59_o d._n 05_o m._n and_o the_o difference_n of_o longitude_n be_v prove_v to_o be_v 3126_o m._n b_o a_o according_a to_o the_o common_a chart_n so_o that_o the_o difference_n of_o longitude_n in_o mercator_n plani-sphere_n and_o upon_o the_o globe_n be_v more_o than_o the_o difference_n of_o longitude_n in_o the_o common_a chart_n by_o 419_o m._n a_o h_n therefore_o if_o i_o be_v to_o sail_v from_o b_o to_o h_n i_o must_v outrun_v the_o meridian_n of_o the_o lizard_n in_o the_o common_a chart_n 419_o m._n before_o i_o can_v expect_v to_o arrive_v in_o the_o meridian_n of_o mercator_n or_o the_o meridian_n of_o the_o globe_n then_o if_o i_o be_v to_o sail_v from_o l_o to_o h_n by_o the_o magnetic_a compass_n i_o must_v sail_v in_o a_o angle_n of_o 21_o d._n 40_o m_o south-eastward_a by_o the_o magnetic_a compass_n to_o arrive_v in_o the_o meridian_n of_o the_o globe_n or_o mercator_n so_o that_o i_o have_v show_v you_o how_o great_a the_o disproportion_n be_v between_o the_o meridian_n of_o the_o common_a chart_n and_o the_o meridian_n of_o mercator_n or_o the_o meridian_n of_o the_o globe_n therefore_o the_o meridian_n of_o the_o magnetic_a compass_n be_v never_o right_o understand_v likewise_o in_o mercators_n plani-sphere_n and_o upon_o the_o globe_n the_o difference_n of_o longitude_n between_o the_o meridian_n and_o parallel_n of_o the_o lizard_n and_o the_o meridian_n of_o bermudus_n be_v prove_v to_o be_v 2711_o m._n l_o q_n or_o 45_o d._n and_o the_o difference_n of_o longitude_n be_v prove_v to_o be_v 3126_o l_o t_o according_a to_o the_o common_a chart_n so_o that_o the_o difference_n of_o longitude_n be_v mercator_n plani-sphere_n and_o upon_o the_o globe_n be_v less_o than_o the_o difference_n of_o longitude_n in_o the_o common_a chart_n by_o 426_o m._n q_o t_o so_o that_o if_o i_o be_v to_o sail_v from_o l_o to_o t_o i_o must_v run_v 426_o m._n before_o i_o can_v arrive_v in_o the_o meridian_n of_o bermudus_n in_o the_o common_a chart_n then_o if_o i_o be_v to_o sail_v from_o b_o to_o q_o by_o the_o magnetic_a compass_n i_o must_v sail_v in_o a_o angle_n of_o 21_o d._n 59_o m._n northeastward_a before_o i_o can_v arrive_v in_o the_o meridian_n of_o the_o globe_n or_o mercator_n so_o that_o i_o have_v show_v you_o how_o great_a the_o disproportion_n be_v between_o the_o meridian_n of_o the_o common_a chart_n and_o the_o meridian_n of_o mercator_n or_o the_o meridian_n of_o the_o globe_n therefore_o the_o meridian_n of_o the_o magnetic_a compass_n be_v never_o right_o understand_v in_o regard_n there_o be_v such_o various_a opinion_n in_o navigation_n and_o the_o disproportion_n between_o one_o position_n and_o the_o other_o be_v so_o great_a insomuch_o that_o the_o question_n may_v be_v ask_v what_o be_v truth_n in_o navigation_n i_o have_v prove_v by_o demonstration_n and_o observation_n that_o the_o magnetic_a compass_n as_o it_o be_v horizontal_n do_v point_n to_o the_o pole_n of_o east_n and_o west_n in_o the_o celestial_a sphere_n in_o all_o meridian_n and_o parallel_n of_o the_o earth_n and_o sea_n without_o give_v any_o difference_n of_o observation_n for_o the_o semi-diameter_n of_o the_o earth_n but_o by_o observation_n from_o the_o meridian_n altitude_n of_o the_o sun_n and_o star_n the_o magnetic_a compass_n do_v run_v parallel_n to_o the_o pole_n of_o north_n and_o south_n in_o the_o terrestrial_a sphere_n the_o circulation_n of_o the_o earth_n therefore_o it_o have_v be_v impossible_a to_o prove_v the_o magnetic_a compass_n shall_v run_v parallel_n to_o the_o pole_n of_o north_n and_o south_n in_o the_o terrestrial_a sphere_n if_o the_o magnetic_a compass_n do_v not_o run_v parallel_n to_o the_o latitude_n of_o place_n by_o observation_n likewise_o i_o have_v prove_v by_o observation_n and_o demonstration_n that_o the_o magnetic_a compass_n as_o it_o be_v horizontal_n do_v point_n to_o the_o pole_n of_o north_n and_o south_n in_o the_o terrestrial_a sphere_n in_o all_o meridian_n and_o parallel_n of_o the_o earth_n and_o sea_n which_o meridian_n do_v cross_v the_o east_n and_o west_n pole_n of_o the_o magnetic_a compass_n as_o it_o be_v horizontal_n to_o the_o celestial_a sphere_n at_o right-angle_n in_o all_o meridian_n and_o parallel_n in_o the_o world_n therefore_o the_o meridian_n of_o the_o magnetic_a compass_n be_v horizontal_n must_v run_v parallel_n to_o the_o pole_n of_o east_n and_o west_n in_o the_o terrestrial_a sphere_n as_o the_o magnetic_a compass_n be_v horizontal_n do_v run_v parallel_n to_o the_o pole_n of_o north_n and_o south_n in_o the_o terrestrial_a sphere_n last_o of_o all_o the_o magnetic_a compass_n be_v of_o right-line_n do_v measure_v the_o superficies_n of_o the_o globe_n by_o right-line_n as_o if_o the_o superficies_n of_o the_o globe_n be_v always_o a_o plain_a to_o the_o horizon_n â—_o so_o that_o whatever_o projection_n disagreeâ—_n with_o the_o rumb_n and_o the_o difference_n oâ—_n latitude_n and_o the_o difference_n of_o longitude_n and_o the_o distance_n of_o place_n as_o it_o be_v in_o proportion_n in_o a_o rightlined_n triangle_n must_v be_v a_o false_a position_n in_o navigation_n therefore_o there_o be_v but_o one_o truth_n in_o navigation_n and_o that_o be_v the_o common_a chart_n that_o have_v be_v so_o much_o reject_v by_o all_o writer_n for_o the_o meridian_n and_o parallel_n of_o place_n can_v be_v know_v upon_o the_o globe_n or_o mercators_n projection_n but_o as_o it_o be_v transfer_v from_o the_o common_a chart_n which_o be_v in_o proportion_n to_o a_o rightlined_n triangle_n i_o shall_v proceed_v to_o the_o arch_n of_o a_o great_a circle_n which_o be_v the_o three_o position_n or_o principal_a kind_n of_o sail_v so_o call_v wherein_o i_o shall_v show_v you_o that_o the_o question_n can_v be_v give_v from_o the_o practical_a part_n of_o the_o sea_n but_o must_v alter_v the_o meridian_n and_o parallel_n of_o all_o place_n upon_o the_o globe_n sail_v by_o the_o arch_n of_o a_o great_a circle_n the_o true_a distance_n between_o two_o place_n in_o the_o arch_n of_o a_o great_a circle_n as_o in_o the_o follow_a rule_n 1._o if_o both_o place_n have_v no_o latitude_n as_o be_v under_o the_o aequinoctial_a and_o one_o of_o they_o no_o longitude_n than_o the_o longitude_n of_o the_o other_o place_n be_v the_o distance_n if_o it_o be_v not_o above_o 180_o d._n but_o if_o it_o be_v above_o 180_o d._n then_o subtract_v it_o out_o of_o 360_o d._n the_o remainder_n be_v the_o distance_n 2._o if_o both_o place_n have_v longitude_n under_o the_o aequinoctial_a the_o difference_n of_o longitude_n be_v the_o distance_n so_o it_o be_v under_o 180_o d._n but_o if_o it_o be_v above_o 180_o d._n then_o subtract_v it_o out_o of_o 360_o d._n and_o the_o remainder_n be_v the_o difference_n of_o longitude_n 3._o if_o both_o place_n have_v one_o and_o the_o same_o meridian_n and_o one_o of_o they_o have_v latitude_n than_o the_o latitude_n be_v the_o distance_n 4._o if_o both_o place_n have_v latitude_n as_o both_o northerly_a or_o both_o southerly_a be_v under_o the_o same_o meridian_n the_o difference_n be_v the_o distance_n 5._o if_o one_o place_n have_v north_n latitude_n and_o the_o other_o south_n latitude_n be_v under_o the_o same_o meridian_n the_o sum_n of_o both_o be_v the_o distance_n the_o arch_n of_o a_o great_a circle_n in_o the_o terrestrial_a globe_n do_v give_v a_o near_a distance_n of_o place_n than_o the_o common_a chart_n so_o that_o the_o arch_n of_o a_o great_a circle_n do_v not_o run_v in_o the_o parallel_n of_o the_o globe_n without_o it_o be_v in_o the_o aequinoctial_a likewise_o the_o angle_n of_o position_n in_o the_o arch_n of_o a_o great_a circle_n do_v differ_v from_o the_o angle_n of_o position_n by_o the_o magnetic_a compass_n insomuch_o that_o the_o question_n can_v be_v give_v from_o the_o rumb_n by_o the_o magnetic_a compass_n in_o the_o practical_a part_n of_o the_o sea_n but_o you_o must_v alter_v the_o meridian_n and_o parallel_n of_o all_o place_n in_o the_o globe_n example_n there_o be_v two_o place_n in_o the_o parallel_n of_o 50_o d._n that_o differ_v in_o longitude_n 70_o d._n in_o the_o aequinoctial_a i_o demand_v the_o angle_n of_o position_n and_o the_o distance_n the_o demonstration_n follow_v e_o f_o d_o the_o aequinoctial_a l_o c_o b_o the_o parallel_n of_o latitude_n 50_o d._n l_o q_o b_o the_o near_a distance_n l_o q_o half_a the_o near_a distance_n e_o l_o the_o latitude_n 50_o d._n l_o p_o the_o compliment_n of_o the_o latitude_n 40_o d._n e_o p_o d_o the_o angle_n at_o the_o pole_n or_o the_o difference_n of_o longitude_n in_o the_o aequinoctial_a 70_o d._n e_o p_o f_o the_o angle_n of_o half_a the_o difference_n of_o longitude_n 35_o d._n to_o find_v the_o distance_n pag_n 72._o from_o hence_o you_o may_v observe_v that_o the_o arch_n of_o a_o great_a
in_o the_o middle_a parallel_n of_o place_n differ_v in_o longitude_n and_o latitude_n it_o be_v prove_v mercator_n divide_v his_o plani-sphere_n in_o proportion_n to_o the_o difference_n of_o meridian_n upon_o the_o globe_n therefore_o the_o meridian_n of_o mercator_n do_v not_o run_v in_o the_o meridian_n of_o the_o magnetic_a compass_n or_o the_o meridian_n of_o the_o common_a chart_n in_o regard_n the_o difference_n of_o meridian_n upon_o mercator_n plani-sphere_n do_v increase_v from_o the_o pole_n to_o the_o aequinoctial_a and_o the_o difference_n of_o meridian_n in_o the_o common_a chart_n which_o be_v in_o proportion_n to_o the_o rumb_n and_o the_o right-line_n of_o the_o magnetic_a compass_n be_v of_o equal_a distance_n which_o lead_v i_o to_o this_o consideration_n all_o point_n of_o the_o magnetic_a compass_n as_o they_o be_v draw_v be_v of_o right-line_n therefore_o the_o north_n and_o south_n point_n of_o the_o magnetic_a compass_n do_v cross_v the_o east_n and_o west_n point_n of_o the_o magnetic_a compass_n at_o right-angle_n so_o that_o it_o be_v prove_v by_o observation_n that_o the_o east_n and_o west_n point_n of_o the_o magnetic_a compass_n will_v direct_v you_o the_o circulation_n of_o the_o earth_n and_o sea_n in_o all_o parallel_n of_o latitude_n then_o observe_v the_o north_n and_o south_n point_n of_o the_o magnetic_a compass_n as_o it_o be_v draw_v do_v cross_v the_o east_n and_o west_n point_n of_o the_o magnetic_a compass_n at_o right-angle_n in_o all_o meridian_n and_o parallel_n of_o the_o earth_n and_o sea_n therefore_o the_o difference_n of_o meridian_n by_o the_o magnetic_a compass_n must_v run_v parallel_n in_o all_o meridian_n and_o parallel_n of_o the_o earth_n and_o sea_n in_o proportion_n to_o the_o difference_n of_o the_o parallel_n of_o latitude_n otherwise_o you_o may_v as_o well_o say_v the_o north_n and_o south_n point_n of_o the_o magnetic_a compass_n as_o it_o be_v draw_v do_v not_o cross_v the_o east_n and_o west_n point_n of_o the_o magnetic_a compass_n at_o right-angle_n i_o have_v prove_v by_o observation_n that_o the_o meridian_n of_o the_o magnetic_a compass_n do_v cross_v the_o east_n and_o west_n point_v of_o the_o magnetic_a compass_n at_o right-angle_n in_o all_o meridian_n and_o parallel_n of_o the_o earth_n and_o sea_n therefore_o the_o meridian_n of_o the_o magnetic_a compass_n must_v run_v parallel_n to_o the_o pole_n of_o east_n and_o west_n as_o the_o parallel_n of_o the_o magnetic_a compass_n run_v parallel_n to_o the_o pole_n of_o north_n and_o south_n so_o that_o the_o common_a chart_n be_v the_o only_a truth_n in_o navigation_n in_o regard_n it_o be_v in_o proportion_n to_o the_o rumb_n and_o the_o right-line_n of_o the_o magnetic_a compass_n therefore_o the_o magnetic_a compass_n do_v measure_v the_o superficies_n of_o the_o globe_n by_o right-line_n as_o if_o the_o superficies_n of_o the_o globe_n be_v a_o plain_a to_o the_o horizon_n finis_fw-la advertisement_n there_o will_v be_v publish_v the_o practical_a part_n of_o the_o sea_n with_o some_o question_n in_o astronomy_n useful_a in_o navigation_n by_o the_o same_o author_n appendix_n the_o forego_v treatise_n be_v only_o upon_o a_o single_a question_n in_o the_o three_o principal_a kind_n of_o sail_v so_o call_v prove_v that_o the_o work_n of_o navigation_n can_v be_v perform_v by_o the_o arch_n of_o a_o great_a circle_n or_o by_o mercator_n position_n and_o that_o the_o common_a chart_n that_o have_v be_v so_o much_o reject_v be_v the_o only_a truth_n in_o navigation_n in_o regard_n it_o be_v in_o proportion_n to_o the_o rumb_n and_o the_o right_a line_n of_o the_o magnetic_a compass_n therefore_o i_o shall_v illustrate_v this_o position_n of_o the_o common_a chart_n by_o a_o double_a question_n in_o the_o practical_a part_n of_o the_o sea_n compare_v it_o with_o the_o same_o question_n by_o mercator_n position_n wherein_o the_o defect_n of_o mercator_n position_n will_v more_o plain_o appear_v than_o in_o a_o single_a question_n before_o i_o proceed_v to_o give_v this_o question_n i_o shall_v show_v you_o by_o what_o practical_a question_n at_o sea_n the_o work_n of_o navigation_n be_v perform_v by_o the_o common_a chart_n and_o by_o mercator_n first_o by_o the_o common_a chart_n if_o you_o have_v daily_a observation_n than_o you_o have_v the_o difference_n of_o latitude_n and_o the_o rumb_n rectify_v to_o all_o impediment_n to_o find_v the_o distance_n and_o the_o difference_n of_o longitude_n in_o a_o rightlined_n triangle_n by_o mercator_n if_o you_o have_v daily_a observation_n than_o you_o have_v the_o difference_n of_o latitude_n in_o meridional_a part_n and_o the_o rumb_n rectify_v to_o all_o impediment_n to_o find_v the_o difference_n of_o longitude_n in_o the_o equinoctial_a the_o second_o question_n in_o the_o practical_a part_n of_o the_o sea_n by_o the_o common_a chart_n if_o you_o have_v no_o observation_n for_o many_o day_n and_o that_o you_o have_v run_v several_a traverse_n than_o you_o have_v your_o daily_a distance_n run_v by_o your_o log_n and_o the_o rumb_n rectify_v to_o all_o impediment_n upon_o each_o traverse_n to_o find_v the_o difference_n of_o latitude_n and_o the_o difference_n of_o longitude_n this_o traverse_n be_v call_v a_o dead_a reckon_n but_o as_o soon_o as_o you_o have_v observation_n have_v as_o before_o allow_v for_o all_o impediment_n of_o the_o rumb_n in_o your_o daily_a traverse_n and_o that_o you_o find_v the_o ship_n before_o your_o observation_n or_o astern_a of_o your_o observation_n than_o you_o must_v add_v or_o subtract_v by_o a_o due_a proportion_n to_o each_o distance_n run_v by_o your_o log_n so_o as_o to_o fall_v into_o your_o latitude_n by_o observation_n the_o several_a traverse_n be_v thus_o resolve_v you_o must_v find_v the_o difference_n of_o longitude_n and_o the_o distance_n and_o the_o rumb_n upon_o which_o you_o have_v make_v your_o way_n from_o your_o last_o observation_n in_o a_o rightlined_n triangle_n which_o be_v in_o proportion_n to_o the_o rumb_n and_o the_o right_a line_n of_o the_o magnetic_a compass_n the_o second_o question_n in_o the_o practical_a part_n of_o the_o sea_n by_o mercator_n if_o you_o have_v no_o observation_n for_o many_o day_n and_o that_o you_o have_v run_v several_a traverse_n than_o you_o have_v your_o daily_a distance_n run_v by_o your_o log_n and_o the_o rumb_n rectify_v to_o all_o impediment_n upon_o each_o traverse_n to_o find_v the_o difference_n of_o longitude_n in_o the_o equinoctial_a this_o traverse_n be_v call_v a_o dead_a reckon_n here_o you_o may_v observe_v mercator_n brief_a rule_n be_v not_o in_o proportion_n to_o the_o rumb_n and_o distance_n in_o a_o rightlined_n triangle_n therefore_o mercator_n must_v take_v the_o latitude_n of_o place_n as_o they_o be_v find_v in_o each_o traverse_n in_o a_o rightlined_n triangle_n than_o mercator_n have_v the_o meridional_a part_n contain_v in_o the_o difference_n of_o latitude_n and_o the_o rumb_n in_o each_o rightlined_n triangle_n to_o find_v the_o difference_n of_o longitude_n in_o the_o equinoctial_a which_o must_v be_v add_v or_o subtract_v as_o you_o increase_v or_o lessen_v the_o degree_n of_o longitude_n in_o the_o equinoctial_a until_o you_o come_v to_o shape_v a_o direct_a course_n to_o your_o port_n according_a to_o mercator_n position_n by_o a_o rightlined_n triangle_n in_o the_o last_o place_n have_v make_v several_a traverse_n in_o the_o sea_n if_o you_o desire_v to_o know_v a_o direct_a course_n from_o your_o ship_n to_o your_o port_n in_o the_o common_a chart_n you_o have_v the_o difference_n of_o latitude_n between_o the_o ship_n in_o the_o sea_n and_o your_o port_n and_o the_o difference_n of_o longitude_n between_o your_o ship_n in_o the_o sea_n and_o the_o port_n you_o be_v to_o sail_v to_o to_o find_v the_o rumb_n and_o distance_n upon_o a_o direct_a course_n to_o your_o port_n by_o a_o rightlined_n triangle_n by_o mercator_n have_v make_v several_a traverse_n in_o the_o sea_n if_o you_o desire_v to_o know_v a_o direct_a course_n to_o your_o port_n you_o have_v the_o difference_n of_o latitude_n in_o meridional_a part_n between_o your_o ship_n in_o the_o sea_n and_o your_o port_n and_o the_o difference_n of_o longitude_n in_o the_o equinoctial_a between_o your_o ship_n in_o the_o sea_n and_o the_o port_n you_o be_v to_o sail_v to_o to_o find_v the_o rumb_n and_o distance_n upon_o a_o direct_a course_n to_o your_o port_n by_o a_o rightlined_n triangle_n have_v give_v you_o this_o general_a account_n of_o the_o practical_a part_n of_o the_o sea_n by_o the_o plain_a chart_n and_o by_o mercator_n projection_n i_o shall_v proceed_v to_o the_o question_n two_o ship_n sail_v from_o the_o lizard_n in_o the_o latitude_n of_o 50_o d._n the_o first_o ship_n sail_n in_o a_o angle_n of_o 71_o d._n 10_o m._n southwestward_n 3268_o mile_n the_o second_o ship_n sail_n west_n northwest_n 2400_o mile_n i_o demand_v the_o rumb_n or_o
the_o world_n do_v point_n to_o the_o east_n and_o west_n part_n of_o the_o celestial_a sphere_n as_o it_o point_v to_o the_o north_n and_o south_n part_n of_o the_o celestial_a sphere_n therefore_o as_o the_o magnetic_a compass_n make_v the_o same_o position_n to_o the_o east_n and_o west_n part_n of_o the_o celestial_a sphere_n as_o it_o do_v to_o the_o north_n and_o south_n part_n of_o the_o celestial_a sphere_n in_o all_o meridian_n and_o parallel_n of_o the_o world_n therefore_o it_o must_v be_v grant_v that_o the_o magnetic_a compass_n run_v in_o parallel_n meridian_n as_o it_o run_v in_o parallel_n of_o latitude_n upon_o on_o the_o terrestrial_a sphere_n to_o which_o the_o observation_n of_o eclipse_n in_o the_o equinoctial_a and_o the_o observation_n from_o the_o pole_n of_o the_o north_n and_o south_n do_v agree_v 4._o in_o the_o last_o place_n if_o the_o sun_n or_o moon_n be_v not_o eclipse_v in_o the_o equinoctial_a than_o the_o altitude_n of_o the_o sun_n or_o moon_n be_v observe_v in_o several_a meridian_n and_o parallel_n at_o the_o beginning_n or_o end_n of_o the_o eclipse_n the_o difference_n of_o such_o observation_n be_v compare_v can_v give_v the_o difference_n of_o meridian_n or_o the_o difference_n of_o longitude_n in_o proportion_n with_o the_o parallel_n of_o latitude_n in_o regard_n the_o sun_n or_o moon_n so_o eclipse_v out_o of_o the_o equinoctial_a such_o observation_n can_v cross_v the_o parallel_n of_o latitude_n at_o right_a angle_n for_o such_o observation_n be_v as_o much_o out_o of_o proportion_n with_o the_o parallel_n of_o latitude_n as_o the_o parallel_n meridian_n of_o the_o pole_n ecliptic_a will_v be_v out_o of_o proportion_n with_o the_o parallel_n meridian_n of_o the_o north_n and_o south_n pole_n upon_o the_o terrestrial_a sphere_n so_o that_o the_o difference_n of_o longitude_n or_o the_o difference_n of_o meridian_n upon_o the_o terrestrial_a sphere_n can_v be_v find_v by_o observation_n from_o the_o star_n or_o from_o the_o planet_n without_o it_o be_v when_o the_o sun_n and_o moon_n be_v eclipse_v in_o the_o equinoctial_a to_o prove_v the_o earth_n the_o centre_n of_o the_o starry-heaven_n and_o not_o to_o have_v any_o inclination_n towards_o the_o pole_n as_o copernicus_n will_v have_v it_o the_o earth_n by_o observation_n keep_v its_o parallel_n with_o the_o starry-heaven_n all_o the_o year_n without_o alteration_n for_o by_o observation_n that_o star_n that_o be_v in_o the_o equinoctial_a part_n of_o heaven_n be_v always_o in_o the_o equinoctial_a part_n of_o the_o earth_n so_o likewise_o take_v all_o the_o star_n in_o their_o several_a parallel_n to_o the_o pole_n from_o the_o equinoctial_a and_o you_o will_v find_v they_o keep_v their_o parallel_n with_o the_o earth_n for_o ever_o we_o need_v not_o go_v to_o the_o equinoctial_a part_n of_o the_o earth_n to_o prove_v the_o earth_n to_o keep_v her_o parallel_n with_o the_o equinoctial_a part_n of_o the_o starry_a heaven_n for_o observe_v in_o this_o parallel_n or_o latitude_n of_o london_n 51_o d._n 30_o m._n the_o amplitude_n of_o any_o star_n in_o the_o equinoctial_a either_o upon_o his_o rise_n or_o set_v and_o you_o shall_v find_v amplitude_n to_o be_v east_n or_o west_n of_o you_o for_o ever_o in_o this_o parallel_n or_o any_o other_o likewise_o observe_v the_o meridian_n altitude_n of_o any_o star_n in_o the_o equinoctial_a in_o this_o parallel_n or_o in_o any_o other_o parallel_n or_o latitude_n and_o you_o shall_v find_v his_o meridian_n altitude_n to_o be_v the_o elevation_n of_o the_o equinoctial_a for_o ever_o in_o this_o parallel_n or_o latitude_n or_o in_o any_o other_o parallel_n or_o latitude_n and_o by_o daily_a observation_n we_o find_v the_o sun_n to_o alter_v his_o amplitude_n and_o meridian_n altitude_n and_o parallel_n with_o the_o starry_a heaven_n and_o the_o earth_n and_o we_o find_v the_o starry_a heaven_n to_o keep_v its_o parallel_n with_o the_o earth_n always_o in_o regard_n the_o star_n keep_v their_o meridian_n altitude_n and_o amplitude_n with_o the_o earth_n without_o alteration_n but_o if_o we_o shall_v admit_v the_o sun_n the_o centre_n of_o the_o starry_a heaven_n and_o the_o earth_n shall_v have_v her_o declination_n towards_o her_o pole_n then_o the_o sun_n must_v be_v always_o in_o the_o equinoctial_a part_n of_o the_o starry_a heaven_n and_o the_o sun_n must_v have_v the_o same_o amplitude_n and_o meridian_n altitude_n with_o the_o star_n in_o the_o equinoctial_a in_o all_o parallel_n and_o then_o the_o sun_n and_o all_o the_o star_n in_o heaven_n shall_v have_v a_o daily_a calculation_n of_o the_o declination_n of_o the_o earth_n as_o the_o earth_n shall_v alter_v her_o parallel_n by_o incline_v or_o decline_a towards_o her_o pole_n but_o it_o be_v prove_v by_o observation_n that_o the_o sun_n can_v be_v the_o centre_n of_o the_o starry-heaven_n in_o regard_n the_o sun_n be_v not_o always_o in_o the_o equinoctial_a part_n of_o that_o heaven_n and_o the_o sun_n have_v not_o the_o same_o meridian_n altitude_n and_o amplitude_n and_o parallel_n with_o the_o starry-heaven_n in_o the_o equinoctial_a but_o twice_o in_o the_o year_n and_o that_o be_v as_o the_o sun_n incline_v and_o decline_v from_o one_o tropic_a to_o another_o and_o it_o be_v prove_v by_o observation_n that_o the_o equinoctial_a part_n of_o the_o starry-heaven_n be_v always_o in_o the_o equinoctial_a part_n of_o the_o earth_n for_o the_o meridian_n altitude_n of_o the_o star_n in_o equinoctial_a be_v the_o elevation_n of_o the_o equinoctial_a in_o all_o parallel_n now_o there_o be_v a_o necessity_n that_o the_o declination_n of_o the_o sun_n shall_v be_v calculate_v for_o every_o day_n in_o the_o year_n in_o regard_n of_o his_o declination_n towards_o his_o pole_n 23_o d._n 30_o m._n which_o be_v the_o cause_n the_o sun_n alter_v his_o parallel_n and_o amplitude_n and_o meridian_n altitude_n every_o day_n but_o for_o star_n in_o the_o starry-heaven_n their_o declination_n or_o distance_n from_o the_o equinoctial_a be_v the_o same_o for_o ever_o and_o keep_v its_o parallel_n with_o the_o earth_n by_o observation_n another_o example_n from_o the_o sun_n to_o prove_v the_o earth_n the_o centre_n of_o the_o starry-heaven_n most_o mathematician_n hold_v that_o when_o the_o sun_n be_v depress_v below_o the_o horizon_n 15_o d._n that_o twilight_n appear_v upon_o the_o horizon_n the_o proof_n of_o which_o be_v very_o suitable_a in_o this_o parallel_n or_o latitude_n example_n london_n latitude_n 51_o d._n 30._o north_n the_o sun_n declination_n 23_o d._n 30_o m._n north_n the_o sun_n depression_n 15_o d._n 00_o m._n i_o demand_v the_o time_n of_o twylight_n by_o the_o work_n you_o will_v find_v the_o sun_n be_v depress_v 15_o d._n at_o midnight_n the_o 11_o day_n of_o june_n in_o the_o latitude_n of_o 51_o d._n 30._o you_o will_v have_v twilight_n appear_v in_o the_o north_n all_o night_n at_o which_o time_n we_o find_v by_o observation_n in_o the_o equinoctial_a and_o in_o this_o parallel_n and_o in_o all_o other_o parallel_n the_o sun_n to_o be_v distant_a from_o the_o north_n poles_n 66_o d._n 30_o m._n now_o if_o the_o sun_n be_v the_o centre_n of_o the_o starry-heaven_n the_o sun_n will_v be_v always_o distant_a from_o the_o pole_n 90_o d._n as_o the_o star_n in_o the_o equinoctial_a be_v and_o as_o the_o sun_n be_v the_o 10_o day_n of_o march_n or_o the_o 10_o day_n of_o september_n when_o he_o be_v in_o the_o equinoctial_a i_o shall_v add_v one_o observation_n more_o from_o the_o magnetic_a compass_n as_o it_o be_v horizontal_n to_o prove_v the_o earth_n the_o centre_n of_o the_o starry-heaven_n it_o be_v grant_v by_o all_o astronomer_n that_o star_n of_o the_o least_o magnitude_n be_v big_a than_o the_o earth_n so_o that_o the_o least_o star_n appear_v as_o a_o centre_n to_o we_o upon_o the_o earth_n in_o like_a manner_n i_o shall_v prove_v the_o earth_n by_o observation_n by_o the_o magnetic_a compass_n appear_v but_o as_o a_o centre_n to_o the_o star_n and_o that_o the_o earth_n be_v the_o centre_n of_o the_o starry-heaven_n example_n the_o magnetic_a compass_n as_o it_o be_v horizontal_n in_o all_o meridian_n and_o parallel_n of_o the_o world_n rectify_v to_o its_o true_a pole_n where_o there_o be_v occasion_n do_v point_n to_o the_o star_n in_o the_o equinoctial_a and_o to_o the_o east_n and_o west_n and_o to_o the_o north_n and_o south_n part_n of_o the_o celestial_a sphere_n cross_v the_o celestial_a sphere_n at_o right_a angle_n without_o give_v any_o difference_n of_o observation_n for_o the_o diameter_n of_o the_o earth_n so_o that_o the_o earth_n appear_v as_o a_o centre_n to_o the_o star_n and_o be_v the_o centre_n of_o the_o starry_a heaven_n by_o the_o horizontal_n observation_n of_o the_o magnetic_a compass_n in_o regard_v you_o have_v no_o difference_n of_o observation_n for_o the_o whole_a diameter_n of_o the_o earth_n but_o if_o the_o earth_n shall_v incline_v or_o decline_v towards_o its_o pole_n as_o copernicus_n suppose_v it_o do_v 23_o d._n 30_o m._n then_o the_o horizontal_n observation_n of_o the_o magnetic_a compass_n can_v point_v to_o the_o star_n in_o the_o equinoctial_a or_o to_o the_o east_n and_o west_n part_n of_o the_o celestial_a sphere_n for_o if_o the_o earth_n as_o a_o centre_n shall_v move_v upon_o its_o axis_n 23_o d._n 30_o m._n to_o each_o tropic_a than_o the_o earth_n must_v alter_v the_o equinoctial_a part_n of_o the_o starry_a heaven_n as_o the_o sun_n and_o the_o rest_n of_o the_o planet_n do_v therefore_o copernicus_n be_v under_o a_o very_a great_a mistake_n to_o suppose_v the_o sun_n the_o centre_n of_o the_o starry_a heaven_n in_o the_o next_o place_n i_o shall_v prove_v the_o forego_n position_n by_o observation_n and_o by_o demonstration_n the_o outward_a sphere_n represent_v the_o starry-heaven_n the_o lesser_a sphere_n the_o earth_n 1._o to_o demonstrate_v the_o earth_n to_o be_v the_o centre_n of_o the_o starry_a heaven_n if_o the_o earth_n shall_v move_v upon_o its_o axis_n 23_o d._n 30_o m._n towards_o the_o north_n or_o south_n pole_n than_o there_o be_v a_o necessity_n the_o earth_n must_v alter_v its_o parallel_n with_o the_o sun_n and_o the_o star_n in_o the_o equinoctial_a part_n of_o heaven_n 23_o d._n 30_o m._n but_o on_o the_o contrary_a it_o be_v prove_v by_o observation_n in_o all_o meridian_n and_o parallel_n of_o the_o world_n that_o a_o be_v always_o in_o the_o equinoctial_a part_n of_o the_o starry-heaven_n and_o that_o b_o be_v always_o in_o the_o tropic_a of_o cancer_n and_o that_o c_z be_v always_o in_o the_o tropic_a of_o capricorn_n so_o that_o the_o earth_n always_o keep_v its_o parallel_n with_o the_o starry-heaven_n without_o alteration_n therefore_o the_o earth_n be_v the_o centre_n of_o the_o starry-heaven_n 2._o if_o the_o sun_n shall_v be_v the_o centre_n of_o the_o starry-heaven_n according_a to_o copernicus_n supposition_n then_o the_o sun_n by_o observation_n shall_v be_v always_o in_o the_o equinoctial_a part_n of_o the_o starry-heaven_n as_o it_o be_v the_o ten_o day_n of_o march_n and_o the_o ten_o day_n of_o september_n at_o which_o time_n the_o sun_n be_v by_o observation_n distant_a from_o the_o pole_n 90_o m._n but_o on_o the_o contrary_a the_o sun_n be_v by_o observation_n when_o he_o be_v in_o the_o tropic_n 66_o d._n 30_o m._n distant_a from_o the_o pole_n therefore_o the_o sun_n do_v alter_v its_o place_n in_o the_o ecliptic_a with_o the_o constellation_n of_o the_o starry-heaven_n by_o incline_v from_o the_o tropic_a of_o capricorn_n to_o the_o tropic_a of_o cancer_n 47_o d._n so_o that_o the_o sun_n can_v be_v the_o centre_n of_o the_o starry-heaven_n but_o by_o supposition_n between_o pag._n 156_o and_o 157._o what_o i_o have_v offer_v to_o the_o world_n in_o this_o small_a treatise_n i_o have_v prove_v by_o observation_n and_o demonstration_n therefore_o whatever_o man_n may_v pretend_v to_o if_o they_o do_v not_o accord_v with_o the_o like_a rule_n it_o be_v but_o fancy_n or_o imagination_n finis_fw-la
parallel_n of_o the_o common_a chart_n to_o the_o globe_n otherwise_o you_o will_v alter_v the_o meridian_n and_o parallel_n of_o place_n upon_o the_o globe_n as_o they_o be_v transfer_v from_o only_o one_o meridian_n and_o parallel_n of_o the_o common_a chart_n in_o regard_v the_o meridional_a part_n contain_v in_o the_o difference_n of_o latitude_n and_o the_o rumb_n according_a to_o mercator_n be_v only_o in_o proportion_n to_o the_o difference_n of_o longitude_n in_o the_o equinoctial_a in_o a_o single_a traverse_n but_o not_o in_o the_o practical_a part_n of_o navigation_n by_o which_o the_o meridian_n and_o parallel_n of_o all_o the_o know_a part_n of_o the_o world_n be_v find_v example_n the_o second_o ship_n in_o her_o second_o traverse_n sail_n from_o c_o in_o the_o latitude_n of_o 65_o d._n 18_o m._n in_o a_o angle_n of_o 23_o d._n 56_o m._n 2159_o mile_n or_o 35_o d._n 59_o m._n into_o the_o latitude_n of_o 32_o d._n 25_o m._n then_o take_v with_o your_o compass_n 35_o d._n 59_o m._n the_o distance_n sail_v from_o the_o equinoctial_a part_n of_o the_o globe_n place_v one_o foot_n in_o the_o meridian_n and_o parallel_n of_o the_o second_o ship_n in_o her_o first_o traverse_n as_o it_o be_v transfer_v from_o the_o common_a chart_n the_o globe_n then_o turn_v the_o globe_n eastward_o in_o regard_n your_o ship_n be_v go_v to_o the_o westward_o until_o the_o other_o point_n do_v cut_v under_o the_o brass_n meridian_n of_o the_o globe_n in_o the_o latitude_n of_o 32_o d._n 25_o m._n there_o make_v a_o mark_n upon_o the_o globe_n and_o you_o shall_v have_v 23_o d._n 25_o m._n the_o difference_n of_o longitude_n in_o the_o equinoctial_a as_o it_o be_v find_v by_o mercator_n brief_a rule_n in_o that_o single_a traverse_n which_o be_v add_v to_o the_o difference_n of_o longitude_n in_o the_o equinoctial_a that_o the_o second_o ship_n make_v in_o her_o first_o traverse_v from_o the_o lizard_n 70_o d._n 20_o m._n you_o have_v 93_o d._n 45_o m._n the_o difference_n of_o longitude_n in_o the_o equinoctial_a west_n of_o the_o meridian_n of_o the_o lizard_n then_o subtract_v 69_o d._n 15_o m._n the_o difference_n of_o longitude_n in_o the_o equinoctial_a the_o second_o ship_n make_v in_o proportion_n to_o the_o difference_n of_o longitude_n in_o each_o single_a traverse_n in_o a_o right_n line_v triangle_n from_o the_o lizard_n according_a to_o the_o practical_a rule_n of_o mercator_n in_o each_o traverse_n and_o you_o have_v 24_o d._n 30_o m._n that_o you_o must_v alter_v the_o meridian_n and_o parallel_n of_o the_o second_o ship_n in_o the_o equinoctial_a part_n of_o the_o globe_n which_o prove_v mercator_n practical_a rule_n in_o navigation_n to_o be_v notorious_o false_a in_o regard_n mercator_n rule_n do_v disagree_v in_o the_o practical_a part_n with_o the_o rumb_n and_o the_o right_a line_n of_o the_o magnetic_a compass_n therefore_o as_o the_o meridian_n and_o parallel_n of_o place_n can_v be_v find_v by_o the_o practical_a part_n of_o navigation_n by_o the_o arch_n of_o a_o great_a circle_n or_o by_o the_o brief_a rule_n of_o mercator_n so_o likewise_o you_o can_v transfer_v the_o meridian_n and_o parallel_n of_o place_n from_o the_o common_a chart_n to_o the_o globe_n but_o only_o from_o one_o meridian_n and_o parallel_n of_o the_o common_a chart_n by_o such_o demonstration_n you_o shall_v have_v the_o same_o latitude_n and_o distance_n of_o place_n to_o all_o the_o know_a part_n of_o the_o world_n upon_o the_o globe_n as_o it_o be_v transfer_v from_o any_o one_o meridian_n and_o parallel_n of_o the_o common_a chart_n otherwise_o the_o meridian_n and_o parallel_n of_o place_n can_v be_v know_v upon_o the_o globe_n as_o they_o be_v find_v by_o the_o practical_a part_n of_o navigation_n therefore_o the_o common_a chart_n be_v the_o only_a true_a chart_n in_o navigation_n in_o the_o last_o place_n there_o have_v be_v some_o that_o pretend_v to_o find_v the_o difference_n of_o longitude_n or_o the_o difference_n of_o meridian_n by_o observation_n from_o the_o celestial_a body_n first_o i_o shall_v prove_v it_o be_v not_o to_o be_v find_v by_o observation_n from_o the_o star_n second_o i_o shall_v prove_v it_o be_v not_o to_o be_v find_v by_o observation_n from_o the_o planet_n upon_o their_o great_a inclination_n or_o declination_n into_o the_o equinoctial_a without_o it_o be_v when_o the_o sun_n or_o moon_n be_v eclipse_v in_o the_o equinoctial_a 1._o in_o the_o first_o place_n i_o shall_v prove_v the_o difference_n of_o meridian_n or_o the_o difference_n of_o longitude_n can_v be_v find_v by_o observation_n from_o the_o star_n example_n suppose_v yourself_o to_o be_v in_o any_o meridian_n and_o parallel_n of_o the_o terrestrial_a sphere_n there_o you_o take_v the_o meridian_n altitude_n of_o one_o or_o more_o star_n in_o the_o equinoctial_a or_o out_o of_o the_o equinoctial_a the_o meridian_n altitude_n of_o those_o star_n or_o the_o altitude_n of_o the_o guard_n upon_o their_o angle_n of_o position_n with_o the_o north_n star_n be_v the_o same_o the_o whole_a circulation_n of_o the_o earth_n in_o that_o parallel_n you_o make_v your_o observation_n in_o so_o that_o you_o have_v no_o difference_n of_o observation_n to_o give_v the_o difference_n of_o longitude_n or_o the_o difference_n of_o meridian_n therefore_o the_o difference_n of_o longitude_n or_o the_o difference_n of_o meridian_n can_v be_v find_v by_o observation_n from_o any_o of_o the_o star_n without_o you_o have_v difference_n of_o observation_n to_o give_v the_o difference_n of_o meridian_n 2._o in_o the_o next_o place_n i_o shall_v prove_v the_o difference_n of_o longitude_n or_o the_o difference_n of_o meridian_n can_v be_v find_v by_o observation_n from_o any_o of_o the_o planet_n upon_o their_o great_a inclination_n or_o declination_n into_o the_o equinoctial_a or_o day_n after_o day_n example_n if_o you_o observe_v in_o any_o meridian_n and_o parallel_n of_o the_o world_n the_o meridian_n altitude_n of_o any_o of_o the_o planet_n upon_o their_o great_a inclination_n or_o declination_n into_o the_o equinoctial_a or_o day_n after_o day_n you_o will_v find_v the_o difference_n in_o your_o observation_n in_o any_o one_o meridian_n and_o parallel_v you_o observe_v in_o not_o to_o have_v a_o proportion_n to_o the_o difference_n of_o longitude_n or_o the_o difference_n of_o meridian_n with_o the_o circulation_n of_o the_o earth_n therefore_o the_o difference_n of_o longitude_n or_o the_o difference_n of_o meridian_n can_v be_v find_v by_o observation_n from_o the_o meridian_n altitude_n of_o any_o of_o the_o planet_n without_o you_o have_v difference_n of_o observation_n in_o proportion_n to_o the_o difference_n of_o longitude_n or_o the_o difference_n of_o meridian_n the_o circulation_n of_o the_o earth_n 3._o in_o the_o last_o place_n i_o shall_v show_v you_o how_o the_o difference_n of_o longitude_n or_o the_o difference_n of_o meridian_n may_v be_v find_v by_o observation_n when_o eclipse_n shall_v happen_v to_o be_v in_o the_o equinoctial_a and_o not_o otherwise_o example_n if_o the_o sun_n or_o moon_n be_v eclipse_v in_o the_o equinoctial_a and_o that_o several_a person_n in_o several_a meridian_n and_o parallel_n of_o the_o world_n do_v observe_v the_o altitude_n of_o the_o sun_n or_o moon_n at_o the_o beginning_n or_o end_n of_o the_o eclipse_n these_o observation_n be_v compare_v the_o difference_n of_o observation_n between_o such_o place_n shall_v give_v the_o difference_n longitude_n or_o the_o difference_n of_o meridian_n between_o those_o place_n such_o observation_n be_v make_v in_o in_o regard_n the_o sun_n or_o moon_n be_v eclipse_v in_o the_o equinoctial_a do_v appear_v at_o that_o instant_n of_o time_n those_o observation_n be_v take_v at_o the_o beginning_n or_o end_n of_o the_o eclipse_n as_o a_o pole_n in_o the_o east_n or_o west_n so_o that_o the_o difference_n of_o longitude_n or_o the_o difference_n of_o meridian_n must_v have_v the_o like_a proportion_n by_o observation_n from_o such_o eclipse_n to_o prove_v the_o meridian_n do_v run_v parallel_n to_o the_o east_n and_o west_n part_n of_o the_o terrestrial_a sphere_n as_o the_o parallel_n of_o latitude_n be_v prove_v to_o run_v parallel_n by_o observation_n to_o the_o the_o equinoctial_a and_o to_o the_o north_n and_o south_n pole_n of_o the_o terrestrial_a sphere_n therefore_o it_o be_v a_o very_a strange_a opinion_n in_o any_o man_n to_o grant_v the_o magnetic_a compass_n rectify_v to_o his_o true_a pole_n to_o run_v east_n or_o west_n in_o all_o parallel_n of_o latitude_n to_o the_o equinoctial_a and_o to_o the_o pole_n of_o north_n and_o south_n and_o not_o to_o grant_v the_o meridian_n of_o the_o magnetic_a compass_n to_o run_v parallel_n to_o the_o east_n and_o west_n part_n of_o the_o terrestrial_a sphere_n in_o the_o forego_n treatise_n i_o have_v prove_v by_o observation_n that_o the_o magnetic_a compass_n in_o all_o meridian_n and_o parallel_n of_o