Selected quad for the lemma: end_n

Word A	Word B	Word C	Word D	Occurrence	Frequency Band	MI	MI Band	Prominent
end_n	arch_n	compass_n	line_n	1,389	5	10.2559	5	false

Text snippets containing the quad

ID	Title	Author	Corrected Date of Publication (TCP Date of Publication)	STC	Words	Pages
A74866	The geometrical sea-man: or, the art of navigation performed by geometry. Shewing how all the three kinds of sayling, viz. by the plain chart, by Mercators chart, by a great circle. may be easily and exactly performed by a plain ruler and a pair of compasses, without arithmeticall calculation. / By Henry Phillippes.	Phillippes, Henry, d. 1677?	1652 (1652)	Thomason E652_10; ESTC R205892	65,784	93

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part_n as_o before_o then_o close_v your_o compass_n divide_v each_o of_o these_o 12_o part_n into_o 3_o so_o you_o shall_v have_v in_o all_o 36_o part_n than_o you_o may_v easy_o with_o your_o pen_n divide_v each_o of_o these_o part_n into_o 10_o little_a part_n each_o of_o which_o stand_v for_o a_o degree_n and_o so_o you_o may_v number_v they_o as_o in_o the_o middle_a circle_n of_o the_o figure_n a_o three_o usual_a division_n of_o a_o circle_n be_v into_o 32_o equal_a part_n part_n to_o divide_v a_o circle_n into_o 32_o part_n according_a to_o the_o number_n of_o the_o point_n of_o the_o compass_n which_o may_v be_v thus_o perform_v first_o draw_v the_o line_n of_o east_n and_o west_n and_o cross_v it_o at_o right_a angle_n with_o the_o line_n of_o north_n and_o south_n and_o draw_v the_o circle_n as_o before_o then_o keep_v your_o compass_n at_o that_o distance_n set_v one_o foot_n where_o the_o line_n of_o east_n do_v cross_v the_o circle_n and_o with_o the_o other_o draw_v 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the_o begin_n of_o the_o scale_n again_o open_v the_o other_o to_o 45_o degree_n and_o with_o that_o distance_n set_v one_o foot_n in_o b_o cross_v the_o first_o arch_n at_o c_o and_o then_o draw_v the_o line_n a_o c_o as_o in_o the_o former_a example_n and_o figure_n chap._n iii_o show_v how_o to_o make_v a_o plain_a chart_n and_o many_o proposition_n of_o sail_v by_o it_o the_o draw_v of_o the_o plain_a chart_n and_o the_o way_n of_o sail_v thereby_o be_v the_o most_o plain_a and_o easy_a of_o all_o other_o and_o though_o it_o be_v fit_a to_o be_v use_v only_o in_o place_n near_o the_o equinoctial_a or_o in_o short_a voyage_n yet_o it_o will_v serve_v for_o a_o good_a introduction_n to_o that_o which_o follow_v and_o this_o will_v not_o be_v lose_v labour_n for_o the_o same_o kind_n of_o work_n with_o some_o caution_n must_v be_v observe_v in_o all_o kind_n of_o sail_v the_o description_n and_o make_n of_o the_o plain_a chart._n chart._n the_o description_n of_o the_o plain_a chart._n first_o make_v the_o square_a a_o b_o c_o d_o of_o what_o length_n and_o breadth_n you_o please_v and_o divide_v each_o side_n into_o as_o many_o equal_a part_n as_o your_o occasion_n require_v and_o then_o draw_v straight_a line_n through_o these_o part_n cross_v one_o another_o at_o right_a angle_n and_o so_o make_v many_o little_a geometrical_a square_n each_o of_o which_o you_o may_v suppose_v to_o contain_v one_o degree_n in_o longitude_n and_o latitude_n chapter_n latitude_n according_a to_o account_v 20_o league_n be_v in_o one_o degree_n &_o so_o each_o 10_o part_n will_v be_v 2_o leagus_n but_o it_o be_v somewhat_o more_o as_o you_o may_v see_v in_o the_o three_o proposition_n of_o this_o

table_n hereof_o for_o every_o five_o or_o ten_o degree_n for_o at_o 10_o degree_n of_o longitude_n from_o s_n the_o arch_n pass_v through_o 39_o degree_n of_o latitude_n at_o 20_o through_o 43_o ½_n and_o so_o of_o the_o rest_n position_n the_o angle_n of_o position_n second_o if_o you_o will_v know_v the_o angle_n of_o position_n from_o s_n to_o l_o then_z observe_z in_o what_o point_n the_o arch_n s_o l_o k_n do_v cross_v the_o line_n n_o m_o which_o be_v at_o t_o then_o take_v the_o distance_n n_o t_o and_o measure_v it_o in_o the_o semidiameter_n c_o e_z from_z c_z toward_z e_z and_o it_o will_v reach_v almost_o to_o 49_o degree_n which_o show_v the_o angle_n of_o position_n to_o be_v north-easter_o almost_o 49_o degree_n place_n the_o distance_n of_o the_o place_n three_o if_o you_o will_v know_v the_o distance_n of_o the_o two_o place_n you_o must_v with_o your_o compass_n take_v the_o distance_n of_o the_o two_o place_n s_n and_o l_o and_o measure_v it_o in_o that_o meridian_n which_o agree_v with_o the_o angle_n of_o position_n viz._n 49_o degree_n you_o shall_v find_v it_o will_v reach_v from_o a_o to_o five_o now_o if_o you_o reckon_v the_o degree_n of_o the_o parallel_n of_o latitude_n from_o a_o to_o this_o point_n v_n you_o shall_v have_v the_o distance_n which_o be_v 53_o degree_n and_o a_o half_a likewise_o you_o may_v measure_v any_o part_n of_o this_o arch_n s_o l_o in_o this_o meridian_n a_o v._o if_o you_o always_o set_v one_o foot_n in_o s_o and_o open_v the_o other_o to_o the_o point_n require_v and_o then_o set_v one_o foot_n in_o a_o and_o the_o other_o will_v show_v the_o distance_n of_o that_o place_n thus_o the_o distance_n will_v be_v find_v out_o as_o exact_o as_o by_o any_o other_o geometrical_a way_n but_o in_o regard_n of_o the_o smallness_n of_o the_o projection_n you_o may_v mistake_v some_o few_o mile_n or_o league_n but_o if_o you_o be_v to_o sail_v from_o the_o lizard_n to_o the_o summer-island_n arch_n the_o difference_n in_o sail_v forward_o &_o backward_o by_o the_o arch_n than_o you_o must_v first_o set_v down_o the_o latitude_n of_o the_o lizard_n on_o the_o other_o side_n of_o the_o circle_n as_o i_o note_v before_o &_o so_o the_o work_n will_v fall_v out_o much_o as_o it_o do_v before_o for_o the_o longitude_n and_o latitude_n of_o the_o arch_n will_v be_v the_o same_o only_o account_v they_o backward_o the_o distance_n will_v be_v the_o same_o viz._n 53_o degree_n and_o a_o half_a only_o it_o must_v be_v measure_v in_o another_o meridian_n according_a to_o the_o angle_n of_o position_n from_o the_o lizard_n which_o will_v be_v about_o 81_o degree_n so_o that_o in_o effect_n all_o be_v the_o same_o only_o the_o angle_n of_o position_n which_o be_v of_o little_a use_n but_o to_o find_v out_o the_o scale_n of_o the_o distance_n so_o that_o if_o you_o regard_v it_o well_o one_o labour_n will_v serve_v to_o find_v your_o way_n outward_a and_o homeward_n i_o may_v here_o show_v you_o how_o to_o perform_v the_o parallel_n question_n but_o because_o such_o question_n may_v with_o more_o ease_n and_o certainty_n be_v perform_v by_o the_o former_a way_n i_o shall_v not_o spend_v time_n about_o it_o i_o shall_v only_o instance_n in_o two_o sort_n of_o voyage_n which_o can_v be_v perform_v by_o the_o other_o projection_n and_o in_o such_o case_n as_o these_o there_o will_v be_v some_o need_n of_o this_o way_n and_o not_o else_o first_o when_o one_o of_o the_o place_n be_v under_o the_o equinoctial_a and_o the_o other_o towards_o one_o of_o the_o pole_n the_o other_o be_v when_o the_o one_o place_n have_v north_n latitude_n and_o the_o other_o south_n suppose_v you_o be_v to_o sail_v from_o the_o island_n of_o st._n thomas_n situation_n example_n of_o 2_o place_n in_o another_o manner_n of_o situation_n which_o lie_v under_o the_o equinoctial_a and_o have_v about_o 35_o degree_n of_o longitude_n to_o the_o strait_n of_o magellan_n which_o have_v about_o 53_o degree_n of_o south_n latitude_n and_o differ_v in_o longitude_n from_o the_o former_a place_n 9●_n degree_n to_o the_o westward_o now_o it_o be_v require_v to_o find_v out_o the_o arch_n of_o the_o great_a circle_n between_o these_o two_o place_n and_o the_o longitude_n and_o latitude_n of_o this_o arch_n with_o the_o angle_n of_o position_n and_o the_o distance_n of_o the_o two_o place_n to_o perform_v this_o first_o set_v down_o the_o isle_n of_o st._n thomas_n which_o be_v under_o the_o equinoctial_a at_o the_o one_o end_n of_o the_o equinoctial_a line_n at_o d_o then_o account_v 90_o degree_n of_o longitude_n from_o d_o to_z e_z there_o be_v the_o meridian_n of_o the_o strait_n of_o magellan_n whereupon_o you_o must_v mark_v out_o the_o latitude_n thereof_o which_o be_v 53_o degree_n at_o w_n so_o you_o shall_v have_v these_o three_o point_n d_o w_n c_o by_o which_o you_o may_v find_v the_o centre_n and_o draw_v the_o arch_n d_o w_n c_o now_o this_o part_n of_o the_o circle_n from_o d_o to_z w_o be_v the_o arch_n of_o the_o great_a circle_n which_o lie_v between_o these_o two_o place_n by_o which_o you_o may_v find_v all_o the_o other_o thing_n require_v as_o first_o for_o the_o longitude_n and_o latitude_n of_o this_o arch_n they_o be_v find_v out_o by_o note_v where_o it_o cross_v the_o circle_n of_o longitude_n and_o latitude_n in_o the_o draught_n which_o you_o shall_v find_v for_o every_o ten_o degree_n to_o be_v as_o in_o this_o table_n long_o latitude_n deg_n d._n m._n 10_o 12_o 58_o 20_o 24_o 25_o 30_o 22_o 34_o 40_o 40_o 28_o 50_o 45_o 31_o 60_o 48_o 58_o 70_o 51_o 16_o 80_o 52_o 35_o 90_o 53_o 0_o second_o for_o the_o angle_n of_o rule_n of_o the_o difference_n of_o longitude_n be_v just_a 90_o deg_fw-la the_o angle_n of_o position_n be_v ready_a measure_v in_o the_o semidiameter_n e_o b_o be_v the_o distance_n b_o w_n which_o be_v 37_o degree_n but_o at_o other_o time_n must_v follow_v the_o rule_n position_n between_o the_o two_o place_n this_o be_v show_v by_o the_o arch_n dw_n cross_v the_o semidiameter_n e_o b_o so_fw-mi that_o if_o you_o take_v the_o distance_n b_o w_n and_o measure_v it_o in_o the_o diameter_n c_o d_o it_o will_v reach_v from_o c_o to_o 37_o degree_n which_o be_v the_o angle_n require_v &_o the_o situation_n show_v it_o to_o be_v south_n westerly_a last_o for_o the_o distance_n of_o the_o two_o place_n if_o you_o take_v the_o distance_n d_o w_n and_o measure_n it_o in_o the_o 37_o meridian_n line_n according_a to_o the_o angle_n of_o of_o position_n it_o will_v reach_v from_o a_o to_o the_o equinoctial_a line_n degree_n likewise_o the_o distance_n d_o w_n need_v no_o other_o measure_v but_o must_v needs_o be_v 90_o degree_n which_o show_v the_o distance_n to_o be_v 90_o degree_n the_o last_o example_n shall_v be_v of_o two_o place_n the_o one_o be_v on_o the_o one_o side_n and_o the_o other_o on_o the_o other_o side_n of_o the_o equinoctial_a as_o suppose_v you_o be_v to_o sail_v from_o the_o summer-isle_n to_o the_o cape_n of_o good_a hope_n situation_n example_n of_o place_n in_o another_o situation_n the_o latitude_n of_o the_o summer-isle_n be_v 32_o degree_n 25_o north_n and_o the_o latitude_n of_o the_o cape_n of_o good_a hope_n be_v 35_o degree_n south_n and_o suppose_v the_o difference_n of_o longitude_n between_o these_o two_o place_n to_o be_v 90_o degree_n and_o it_o be_v require_v to_o find_v out_o the_o arch_n of_o the_o great_a circle_n between_o these_o two_o place_n according_a to_o the_o longitude_n and_o latitude_n thereof_o the_o angle_n of_o position_n and_o the_o distance_n of_o the_o two_o place_n to_o perform_v this_o first_o you_o must_v set_v down_o the_o first_o place_n according_a to_o the_o latitude_n thereof_o in_o the_o outmost_a circle_n at_o s_n and_o draw_v the_o diameter_n s_o k_n to_o which_o you_o must_v draw_v the_o line_n n_o m_o squirewise_o at_o right_a angle_n then_o count_v the_o difference_n of_o longitude_n which_o be_v 90_o degree_n from_o c_o the_o meridian_n of_o the_o cape_n of_o good_a hope_n will_v fall_v in_o the_o line_n a_o b_o which_o you_o must_v mark_v out_o according_a to_o its_o latitude_n 35_o degree_n south_n at_o x_o then_o by_o these_o three_o point_n s_n x_o k_o find_v the_o centre_n which_o will_v be_v in_o the_o line_n m_o n_n extend_v and_o so_o draw_v the_o arch_n s_o x_o k._n now_o first_o for_o the_o longitude_n and_o latitude_n of_o this_o arch_n you_o may_v find_v they_o by_o see_v how_o this_o arch_n do_v cross_v the_o circle_n of_o longitude_n and_o latitude_n in_o the_o draught_n which_o for_o every_o ten_o degree_n of_o longitude_n be_v as_o follow_v long._n latitude_n  _fw-fr deg._n deg._n m._n

1,00_o col._n last_o line_n 3._o for_o 0_o 8_o read_z 0_o 58._o the_o geometrical_a seaman_n or_o the_o art_n of_o navigation_n perform_v by_o geometry_n chap._n i._o contain_v some_o geometrical_a proposition_n which_o will_v be_v of_o frequent_a use_n proposition_n 1._o how_o to_o erect_v a_o perpendicular_a line_n at_o the_o end_n of_o a_o line_n proposition_n the_o first_o proposition_n be_v what_o a_o perpendicular_a line_n be_v a_o perpendicular_a line_n be_v a_o line_n that_o stand_v direct_o upright_a from_o another_o line_n as_o in_o the_o figure_n the_o line_n b_o c_o be_v a_o perpendicular_a line_n to_o the_o line_n a_o b._n now_o in_o the_o figure_n there_o be_v two_o way_n of_o raise_v it_o the_o one_o on_o the_o right_a side_n and_o the_o other_o on_o the_o left_a first_o let_v the_o line_n a_o b_o be_v give_v and_o it_o be_v require_v to_o erect_v the_o line_n b_o c_o perpendicular_o to_o it_o at_o the_o end_n of_o the_o line_n in_o the_o point_n b._n way_n another_o way_n the_o second_o way_n to_o perform_v this_o be_v demonstrate_v on_o the_o left_a side_n of_o the_o figure_n let_v the_o line_n a_o b_o be_v give_v as_o before_o and_o it_o be_v require_v to_o erect_v the_o line_n a_o d_o perpendicular_o in_o the_o point_n a._n to_o perform_v this_o first_o set_v one_o foot_n of_o your_o compass_n in_o any_o convenient_a point_n at_o pleasure_n as_o at_o l_o and_o open_v the_o other_o foot_n to_o the_o point_n a_o and_o draw_v the_o arch_n n_o a_o m_o then_o lay_v your_o ruler_n to_o the_o centre_n of_o this_o arch_n l_o and_o the_o place_n where_o it_o cross_v the_o line_n a_o b_o which_o be_v at_o n_n and_o draw_v the_o line_n m_o l_o n_o which_o do_v cross_v the_o arch_n n_o a_o m_o in_o the_o point_n m._n last_o lay_v your_o ruler_n to_o this_o cross_n at_o m_o and_o the_o point_n a_o draw_v the_o line_n d_o m_o a_o so_o you_o shall_v have_v your_o desire_n proposition_n 2._o to_o draw_v one_o line_n parallel_n to_o another_o line_n at_o any_o distance_n require_v proposition_n the_o second_o proposition_n line_n what_o be_v mean_v by_o a_o parallel_n line_n a_o line_n be_v say_v to_o be_v parallel_n to_o another_o line_n when_o it_o be_v equal_o distant_a from_o it_o in_o every_o part_n thereof_o thus_o in_o the_o former_a figure_n the_o line_n p_o s_o be_v parallel_n to_o the_o line_n a_o b._n now_o the_o way_n to_o draw_v a_o parallel_n line_n be_v thus_o let_v the_o line_n a_o b_o be_v the_o first_o line_n give_v and_o it_o be_v require_v to_o draw_v the_o line_n p_o s_o parallel_n to_o it_o according_a to_o the_o distance_n p_o a._n first_o open_v your_o compass_n to_o the_o distance_n you_o have_v occasion_n to_o use_v which_o in_o this_o example_n be_v p_o a_o then_o set_v one_o foot_n in_o a_o with_o the_o other_o draw_v the_o arch_n at_o p_o and_o then_o keep_v your_o compass_n at_o the_o same_o distance_n remove_z one_o foot_n to_o b_o and_o with_o the_o other_o draw_v the_o arch_n at_o s_n last_o lay_v your_o ruler_n on_o the_o very_a edge_n of_o these_o two_o arch_n draw_v the_o line_n p_o s_o which_o will_v be_v parallel_n to_o a_o b_o and_o so_o the_o proposition_n be_v perform_v proposition_n 3._o how_o to_o make_v a_o geometrical_a square_n proposition_n the_o three_o proposition_n a_o geometrical_a square_n be_v a_o square_n who_o four_a side_n be_v all_o of_o one_o and_o the_o same_o length_n now_o in_o the_o first_o figure_n let_v the_o line_n a_o b_o be_v the_o side_n of_o such_o a_o square_a and_o it_o be_v require_v to_o make_v a_o square_a of_o that_o length_n and_o breadth_n first_o square_a how_o to_o make_v a_o square_a you_o must_v draw_v the_o line_n a_o b_o according_o to_z the_o length_n give_v then_o erect_v the_o perpendicular_a line_n a_o d_o at_o one_o end_n thereof_o as_o be_v show_v before_o then_o set_v one_o foot_n of_o your_o compass_n in_o the_o corner_n a_o open_z the_o other_z to_z b_o and_o keep_v one_o foot_n still_o in_o a_o with_o the_o other_o across_o the_o perpendicular_a a_o d_o at_z d_o then_o keep_v your_o compass_n at_o the_o same_o distance_n set_v one_o foot_n in_o b_o and_o with_o the_o other_o draw_v a_o short_a arch_n at_o c_o then_o set_v one_o foot_n at_o the_o cross_n at_o d_o and_o with_o the_o other_o across_o the_o arch_n last_o draw_v in_o the_o point_n c_o now_o if_o you_o draw_v line_n through_o these_o mark_n from_o a_o to_o d_o from_z d_o to_z c_z and_z from_z c_z to_z b_o so_o you_o shall_v make_v the_o geometrical_a square_n a_o b_o c_o d_o as_o be_v require_v if_o you_o will_v try_v your_o work_n whether_o you_o have_v make_v it_o true_a or_o no_o then_o set_v one_o foot_n of_o your_o compass_n in_o a_o square_n how_o to_o try_v a_o square_n and_o open_v the_o other_o to_o the_o corner_n at_o c_o then_o with_o that_o distance_n set_v one_o foot_n in_o b_o and_o turn_v the_o other_o to_o the_o corner_n at_o d_o if_o both_o these_o opposite_a corner_n have_v the_o same_o distance_n the_o square_n be_v true_o make_v otherwise_o not_o square_n a_o long_a square_n if_o you_o will_v make_v a_o long_a square_n as_o the_o square_a a_o p_o s_o b_o first_fw-mi you_o may_v draw_v the_o line_n p_o s_o parallel_n to_o a_o b_o and_o according_a to_o the_o length_n of_o the_o side_n of_o your_o square_n then_o erect_v the_o perpendicular_a either_o at_o a_o or_o b_o and_o draw_v the_o opposite_a side_n parallel_n thereunto_o according_a as_o the_o length_n of_o your_o square_n require_v and_o you_o may_v try_v the_o truth_n of_o this_o square_a also_o by_o the_o opposite_a corner_n as_o before_o proposition_n 4._o to_o raise_v a_o perpendicular_a in_o the_o midst_n of_o a_o line_n proposition_n the_o four_o proposition_n in_o this_o second_o figure_n let_v a_o b_o be_v the_o line_n give_v and_o it_o be_v require_v to_o raise_v a_o perpendicular_a in_o the_o point_n c._n figure_n the_o second_o figure_n first_o set_v one_o foot_n of_o your_o compass_n in_o the_o point_n c_o and_o open_v the_o other_o to_o any_o distance_n at_o pleasure_n and_o mark_v the_o give_v line_n therewith_o on_o both_o side_n from_o c_o at_o the_o point_v a_o and_o b_o then_o set_v one_o foot_n of_o your_o compass_n in_o the_o point_n a_o open_v the_o other_o to_o any_o distance_n you_o please_v beyond_o c_o and_o draw_v a_o little_a arch_n above_o the_o line_n at_o f._n then_o with_o the_o same_o distance_n set_v one_o foot_n in_o b_o and_o with_o the_o other_o cross_n the_o arch_n f_o with_o the_o arch_n d._n last_o lay_v your_o ruler_n to_o this_o cross_n and_o the_o point_n c_o and_o draw_v the_o line_n g_o c_o which_o be_v perpendicular_a to_o the_o line_n a_o b_o in_o the_o point_n c_o as_o be_v require_v proposition_n 5._o from_o a_o point_n aloft_o to_o let_v fall_v a_o perpendicular_a upon_o a_o line_n give_v proposition_n the_o five_o proposition_n let_v g_o be_v the_o point_n aloft_o from_o whence_o it_o be_v require_v to_o let_v fall_v a_o perpendicular_a upon_o the_o line_n a_o b_o in_o the_o second_o figure_n first_o set_v one_o foot_n of_o your_o compass_n in_o the_o point_n give_v which_o be_v g_z and_o open_v your_o compass_n so_o wide_o that_o you_o may_v draw_v the_o arch_n a_o h_n b_o which_o may_v cut_v the_o line_n a_o b_o in_o the_o point_v a_o and_o b_o and_o the_o far_o these_o two_o point_n be_v asunder_o so_o much_o the_o better_a then_o keep_v your_o compass_n at_o this_o distance_n set_v one_o foot_n in_o a_o and_o with_o the_o other_o draw_v the_o arch_n e_o then_z remove_z one_o foot_n to_o b_o and_o cross_v the_o last_o arch_n at_o e_o last_o lay_v your_o ruler_n to_o the_o point_n g_o and_o this_o cross_n at_o e_o draw_v the_o line_n g_o c_o e_o so_fw-mi you_o have_v perform_v the_o proposition_n proposition_n 6._o to_o draw_v a_o line_n squire_n wise_a to_o another_o line_n proposition_n the_o six_o proposition_n in_o the_o second_o figure_n let_v a_o b_o be_v the_o line_n give_v and_o it_o be_v require_v to_o draw_v the_o line_n g_o e_o squire_n wise_a to_o it_o so_o that_o it_o may_v cross_v it_o at_o right_a angle_n first_o open_v your_o compass_n at_o pleasure_n and_o set_v one_o foot_n in_o the_o line_n at_o b_o with_o the_o other_o make_v two_o short_a arch_n one_o above_o the_o line_n at_o d_o and_o the_o other_o below_o the_o line_n at_o e._n then_o with_o the_o same_o distance_n set_v one_o foot_n in_o a_o and_o with_o the_o other_o across_o the_o two_o former_a arch_n at_o d_o and_z e._n last_o lay_v your_o ruler_n by_o these_o two_o crosses_z d_o and_z e_z draw_v the_o line_n g_o e_o

because_o when_o you_o be_v to_o go_v any_o long_a voyage_n it_o will_v be_v needful_a for_o you_o first_o to_o make_v a_o general_a map_n of_o your_o whole_a voyage_n by_o the_o lesser_a line_n whereby_o you_o may_v know_v the_o course_n and_o distance_n thereof_o in_o general_a and_o then_o to_o make_v three_o or_o four_o other_o charts_n by_o the_o great_a line_n upon_o which_o with_o your_o ruler_n and_o compass_n you_o may_v set_v down_o your_o daily_a course_n and_o distance_n more_o exact_o also_o i_o have_v make_v these_o two_o line_n in_o such_o proportion_n that_o the_o one_o be_v the_o ten_o part_n of_o the_o other_o that_o so_o that_o they_o may_v both_o agree_v with_o the_o scale_n upon_o the_o quadrant_n now_o the_o way_n to_o make_v one_o of_o these_o charts_n be_v very_o easy_a line_n to_o make_v a_o sea_n chartley_n by_o these_o meridian_n line_n and_o much_o after_o the_o manner_n of_o the_o plain_a chart_n for_o first_o you_o may_v draw_v the_o line_n of_o east_n and_o west_n a_o b_o of_o what_o length_n you_o please_v and_o divide_v it_o into_o equal_a part_n or_o degree_n than_o you_o may_v erect_v a_o perpendicular_a line_n either_o at_o one_o of_o the_o end_n of_o the_o line_n or_o in_o any_o of_o the_o division_n towards_o the_o midst_n of_o the_o line_n and_o then_o draw_v the_o other_o parallel_n of_o longitude_n parallel_v thereto_o so_o far_o it_o be_v all_o one_o with_o the_o plain_a chart_n but_o when_o you_o come_v to_o draw_v the_o parallel_n of_o latitude_n you_o must_v not_o make_v they_o all_o equal_a though_o they_o must_v be_v all_o parallel_n each_o to_o other_o but_o you_o must_v either_o with_o your_o compass_n take_v they_o out_o of_o the_o quadrant_n or_o which_o be_v more_o easy_a lay_v a_o scroll_n of_o paper_n to_o the_o meridian_n line_n which_o be_v ready_o draw_v to_o your_o hand_n and_o so_o mark_v out_o the_o degree_n of_o latitude_n upon_o the_o scroll_n of_o paper_n and_o then_o lay_v that_o scroll_n to_o the_o side_n of_o your_o chart_n you_o may_v transfer_v the_o degree_n of_o latitude_n into_o the_o side_n of_o your_o chart_n and_o through_o they_o draw_v the_o parallel_n and_o set_v fit_a number_n to_o they_o as_o in_o the_o figure_n the_o figure_n of_o a_o general_a sea-chart_n contain_v almost_o a_o eight_o part_n of_o the_o globe_n north_n now_o though_o this_o be_v not_o a_o general_a chart_n of_o the_o whole_a globe_n yet_o it_o may_v be_v call_v a_o general_a chart_n in_o respect_n of_o other_o which_o will_v serve_v only_o for_o a_o lesser_a portion_n of_o the_o globe_n for_o this_o chart_n contain_v almost_o a_o eight_o part_n of_o the_o globe_n and_o may_v be_v fit_v to_o set_v forth_o any_o part_n thereof_o for_o if_o you_o change_v the_o number_n of_o the_o longitude_n if_o the_o latitude_n be_v northward_o it_o will_v serve_v as_o it_o now_o stand_v but_o if_o the_o latitude_n be_v southward_o you_o must_v turn_v the_o bottom_n upward_o if_o you_o have_v occasion_n in_o one_o chart_n to_o set_v down_o both_o north_n and_o south_n latitude_n than_o you_o must_v draw_v the_o like_a parallel_n of_o latitude_n below_o the_o equinoctial_a as_o these_o be_v above_o it_o now_o i_o will_v show_v you_o how_o the_o several_a proposition_n which_o be_v perform_v by_o the_o plain_a chart_n may_v be_v perform_v by_o this_o and_o wherein_o they_o agree_v and_o wherein_o they_o differ_v proposition_n 1._o know_v the_o longitude_n and_o latitude_n of_o any_o place_n to_o set_v it_o upon_o the_o chart._n chart._n 1._o by_o the_o longitude_n and_o latitede_n to_o find_v the_o point_n of_o any_o place_n in_o the_o chart._n this_o must_v be_v do_v as_o in_o the_o plain_a chart_n for_o first_o lay_v your_o ruler_n by_o the_o longitude_n of_o the_o place_n you_o must_v draw_v a_o little_a occult_a line_n as_o near_o the_o latitude_n of_o the_o place_n as_o you_o can_v guess_v then_o lay_v your_o ruler_n to_o the_o latitude_n of_o the_o place_n across_o that_o line_n you_o draw_v before_o with_o another_o little_a line_n and_o so_o the_o cross_n of_o these_o two_o line_n will_v show_v you_o the_o point_n where_o the_o place_n must_v be_v suppose_v to_o stand_v example_n example_n thus_o suppose_v the_o longitude_n of_o the_o summer_n land_n to_o be_v 300_o degree_n and_o the_o latitude_n thereof_o 32_o degree_n 25_o minute_n you_o will_v find_v that_o it_o must_v be_v set_v at_o s_n upon_o the_o chart_n proposition_n 2._o the_o longitude_n and_o latitude_n of_o two_o place_n be_v know_v to_o find_v the_o rumbe_n which_o you_o must_v sail_v upon_o to_o go_v direct_o from_o the_o one_o place_n to_o the_o other_o example_n 2._o by_o the_o longitude_n and_o latitude_n of_o two_o place_n to_o find_v the_o rumbe_n example_n suppose_v the_o one_o place_n to_o be_v the_o summer_n land_n who_o longitude_n and_o latitude_n we_o will_v suppose_v to_o be_v as_o be_v before_o set_v down_o let_v the_o other_o place_n be_v the_o lizard_n who_o latitude_n be_v about_o 50_o deg_fw-la and_o let_v the_o longitude_n thereof_o be_v suppose_v to_o be_v 10_o degr_n so_o the_o difference_n of_o the_o longitude_n of_o the_o two_o place_n will_v be_v 70_o deg_fw-la as_o mr._n norwood_n both_o in_o his_o book_n of_o the_o doctrine_n of_o triangle_n and_o his_o seaman_n practice_n suppose_v they_o to_o be_v though_o as_o he_o say_v in_o one_o place_n he_o do_v not_o think_v they_o to_o be_v so_o far_o distant_a and_o it_o be_v require_v to_o find_v the_o rumbe_n this_o proposition_n must_v also_o be_v perform_v as_o in_o the_o plain_a chart_n for_o first_o the_o two_o place_n must_v be_v set_v upon_o the_o chart_n according_a to_o their_o longitude_n and_o latitude_n which_o will_v be_v at_o s_n and_o l_o then_o draw_v a_o strait_a line_n from_o s_n to_o l_o this_o represent_v the_o direct_a way_n between_o the_o two_o place_n now_o to_o know_v what_o rumbe_n this_o be_v open_v your_o compass_n to_o the_o radius_fw-la of_o your_o scale_n of_o rumbe_n and_o set_v one_o foot_n of_o your_o compass_n in_o s_n with_o the_o other_o draw_v the_o arch_n r_o m_o then_o set_v one_o foot_n of_o your_o compass_n in_o r_n open_v the_o other_o to_o the_o cross_v of_o the_o line_n and_o the_o arch_n at_o m_n and_o measure_v that_o distance_n on_o your_o scale_n of_o chord_n or_o rumbe_n so_o shall_v you_o find_v it_o to_o be_v 71_o deg_fw-la 21_o min._n or_o the_o sixth_o rumbe_n and_o somewhat_o above_o a_o quarter_n of_o a_o rumbe_n from_o the_o meridian_n proposition_n 3._o know_v the_o longitude_n and_o latitude_n of_o two_o place_n to_o know_v how_o far_o they_o be_v distant_a one_o from_o another_o place_n 3._o to_o measure_v the_o distance_n of_o place_n let_v the_o two_o place_n be_v as_o be_v before_o say_a s_n and_o l_o it_o be_v require_v to_o find_v their_o distance_n in_o the_o work_a this_o proposition_n there_o be_v some_o difference_n from_o the_o plain_a chart_n for_o whereas_o there_o you_o measure_v the_o distance_n of_o place_n by_o one_o and_o the_o same_o scale_n of_o equal_a part_n here_o you_o will_v have_v use_n of_o many_o scale_n according_a to_o the_o latitude_n of_o the_o place_n way_n mr._n gunter_n way_n now_o the_o ordinary_a way_n prescribe_v by_o mr._n gunter_n to_o perform_v this_o be_v thus_o open_v your_o compass_n to_o the_o distance_n of_o the_o two_o place_n and_o then_o set_v your_o compass_n in_o the_o meridian_n line_n so_o that_o the_o one_o point_n of_o the_o compass_n may_v stand_v just_a so_o much_o above_o the_o great_a latitude_n as_o the_o other_o do_v below_o the_o lesser_a latitude_n and_o so_o the_o degree_n between_o they_o be_v the_o distance_n this_o way_n may_v serve_v for_o small_a distance_n as_o master_n gunter_n use_v it_o but_o in_o great_a distance_n it_o will_v not_o always_o hold_v true_a and_o beside_o it_o be_v somewhat_o troublesome_a to_o set_v the_o compass_n just_a as_o much_o above_o the_o one_o latitude_n as_o below_o the_o other_o as_o in_o this_o example_n if_o you_o take_v the_o distance_n s_o l_o in_o your_o compass_n and_o measure_v it_o so_o in_o the_o meridian_n line_n it_o will_v reach_v from_o about_o 16_o degree_n to_o about_o 66_o degree_n and_o a_o half_a that_o be_v 16_o degree_n and_o a_o half_a above_o 50_o degree_n the_o great_a latitude_n and_o 16_o degree_n and_o a_o half_a below_o 32_o degree_n 25_o minute_n the_o lesser_a latitude_n and_o so_o the_o degree_n intercept_v between_o the_o point_n of_o the_o compass_n be_v about_o 50_o degree_n and_o a_o half_a whereas_o the_o distance_n of_o the_o two_o place_n be_v almost_o 55_o degree_n but_o you_o shall_v find_v the_o distance_n more_o exact_o latitude_n the_o way_n to_o measure_v the_o distance_n of_o

place_n but_o it_o be_v only_o their_o distance_n in_o the_o rumbe_n so_o that_o if_o the_o two_o place_n be_v not_o both_o under_o the_o equinoctial_a or_o both_o in_o one_o meridian_n than_o there_o be_v somewhat_o a_o near_a cut_n between_o the_o two_o place_n than_o the_o rumbe_n point_v out_o which_o sometime_o especial_o near_o the_o pole_n be_v very_o considerable_a but_o this_o be_v not_o all_o the_o benefit_n which_o come_v by_o this_o way_n of_o sail_v way_n second_o it_o be_v the_o most_o convenient_a way_n but_o many_o time_n when_o your_o course_n lie_v near_o the_o east_n and_o west_n this_o way_n be_v far_o more_o convenient_a for_o if_o you_o shall_v sail_v full_a east_n or_o west_n you_o must_v altogether_o depend_v upon_o your_o dead_a reckon_n have_v no_o way_n to_o help_v yourself_o by_o the_o observation_n of_o the_o latitude_n but_o now_o if_o you_o sail_v by_o the_o arch_n of_o a_o great_a circle_n between_v two_o such_o place_n you_o not_o only_o go_v the_o near_a way_n but_o also_o may_v alter_v your_o latitude_n many_o degree_n whereby_o your_o account_n may_v be_v often_o rectify_v less_o rectify_v so_o in_o the_o example_n of_o the_o summer_n land_n the_o distance_n by_o the_o rumbe_n be_v 3299_o mile_n the_o distance_n by_o the_o arch_n be_v 3204_o mile_n that_o be_v 95_o mile_n less_o as_o for_o example_n suppose_v you_o be_v to_o sail_v from_o spain_n to_o virginia_n both_o which_o lie_v near_o the_o parallel_n of_o 40_o degree_n and_o suppose_v the_o difference_n of_o longitude_n between_v two_o such_o place_n in_o the_o parallel_n of_o 40_o to_o be_v 70_o degree_n the_o distance_n of_o these_o two_o place_n measure_v in_o the_o parallel_n of_o 40_o which_o be_v the_o rumbe_n that_o lead_v between_v the_o two_o place_n be_v east_n and_o west_n be_v 53_o degree_n 62_o 100_o but_o their_o distance_n in_o the_o arch_n of_o a_o great_a circle_n be_v but_o 52_o degree_n 08_o 100_o that_o be_v 1_o degree_n 54_o 100_o less_o but_o this_o as_o say_v be_v but_o the_o least_o part_n of_o the_o benefit_n that_o come_v by_o this_o way_n of_o sail_v the_o chief_a be_v this_o that_o in_o sail_v between_o two_o such_o place_n by_o the_o arch_n of_o a_o great_a circle_n you_o will_v first_o in_o the_o one_o half_a of_o the_o way_n raise_v the_o pole_n 5_o degree_n 69_o 100_o and_o then_o in_o the_o other_o half_o depress_v the_o pole_n as_o much_o so_o that_o in_o your_o whole_a voyage_n you_o will_v alter_v the_o latitude_n 11_o degree_n 38_o ●0_n &_o so_o by_o the_o observation_n of_o the_o latitude_n you_o may_v rectify_v your_o dead_a reckon_n very_o well_o which_o you_o can_v do_v sail_v in_o the_o parallel_n thus_o you_o see_v this_o way_n of_o sail_v be_v not_o only_o the_o near_a but_o the_o best_a way_n now_o concern_v this_o way_n of_o sail_v there_o have_v be_v but_o little_o write_v by_o any_o subject_n few_o have_v write_v of_o this_o subject_n and_o therefore_o i_o shall_v be_v the_o more_o large_a in_o this_o captain_n saltonstall_n in_o his_o book_n call_v the_o navigator_n have_v say_v somewhat_o how_o to_o direct_v a_o parallel_n course_n but_o for_o any_o other_o course_n he_o have_v say_v nothing_o and_o what_o he_o show_v be_v to_o be_v perform_v by_o arithmetic_n master_n norwood_n in_o his_o book_n of_o trigonometry_n have_v add_v as_o a_o appendix_n many_o problem_n of_o sail_v by_o the_o arch_n of_o a_o great_a circle_n whereby_o those_o who_o both_o can_v and_o will_v take_v the_o pain_n may_v by_o calculation_n find_v out_o all_o thing_n necessary_a in_o this_o way_n of_o sail_v but_o those_o way_n of_o calculation_n as_o they_o be_v very_o difficult_a to_o the_o unlearned_a so_o they_o be_v tedious_a to_o those_o that_o have_v the_o best_a skill_n and_o therefore_o i_o hope_v it_o will_v be_v well_o accept_v if_o i_o here_o show_v you_o how_o the_o same_o may_v be_v perform_v by_o geometry_n both_o plain_o and_o speedy_o and_o yet_o with_o as_o much_o exactness_n as_o need_v be_v require_v know_v the_o chief_a thing_n to_o be_v know_v and_o in_o the_o pursuance_n hereof_o i_o shall_v keep_v as_o close_o to_o master_n norwood_n as_o i_o can_v both_o in_o his_o proposition_n and_o example_n that_o thereby_o you_o may_v see_v how_o near_o my_o plain_a line_n will_v approach_v to_o the_o exactness_n of_o his_o calculation_n now_o if_o you_o observe_v he_o there_o be_v these_o three_o thing_n which_o must_v be_v find_v out_o in_o every_o example_n first_o the_o distance_n of_o the_o two_o place_n in_o the_o arch_n of_o a_o great_a circle_n second_o the_o angle_n of_o position_n from_o the_o one_o place_n to_o the_o other_o three_o to_o find_v out_o what_o longitude_n and_o latitude_n the_o arch_n of_o the_o great_a circle_n do_v pass_v through_o between_o the_o two_o place_n place_n to_o find_v the_o distance_n of_o two_o place_n for_o the_o first_o of_o these_o know_v the_o longitude_n and_o latitude_n of_o two_o place_n to_o find_v their_o distance_n in_o the_o arch_n of_o a_o great_a circle_n which_o be_v always_o the_o near_a distance_n i_o may_v show_v you_o how_o to_o perform_v this_o in_o the_o first_o place_n but_o i_o here_o pass_v it_o by_o for_o these_o reason_n first_o because_o master_n wright_n master_n blundevile_n and_o captain_n saltonstall_n have_v all_o of_o they_o demonstrate_v it_o in_o their_o book_n already_o and_o second_o because_o the_o chief_a benefit_n in_o this_o way_n of_o sail_v do_v not_o so_o much_o consist_v in_o save_v of_o a_o little_a way_n as_o in_o sail_v the_o most_o convenient_a way_n that_o be_v so_o as_o you_o may_v alter_v your_o latitude_n most_o and_o so_o your_o reckon_n may_v be_v the_o more_o certain_a for_o though_o near_o the_o pole_n the_o difference_n of_o the_o distance_n of_o two_o place_n in_o the_o arch_n of_o a_o great_a circle_n and_o in_o their_o rumbe_n may_v be_v considerable_a yet_o in_o most_o voyage_n it_o be_v not_o as_o in_o the_o forename_a example_n of_o two_o place_n 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