Selected quad for the lemma: end_n

Word A Word B Word C Word D Occurrence Frequency Band MI MI Band Prominent
end_n let_v line_n perpendicular_a 1,964 5 14.8700 5 true
View all documents for the selected quad

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

There are 3 snippets containing the selected quad. | View original text

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
which_o will_v cross_v the_o line_n a_o b_o at_o right_a angle_n as_o be_v require_v proposition_n 7._o to_o divide_v a_o line_n give_v into_o two_o equal_a part_n proposition_n the_o seven_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 to_o be_v divide_v into_o two_o equal_a part_n first_o set_v one_o foot_n of_o your_o compass_n at_o the_o one_o end_n of_o the_o line_n at_o a_o and_o open_v the_o other_o to_o any_o distance_n above_o half_a the_o line_n &_o therewith_o draw_v two_o little_a arch_n one_o above_o the_o line_n at_o f_o and_o the_o other_o below_o the_o line_n at_o e_o then_o remove_v your_o compass_n to_o b_o the_o other_o end_n of_o the_o line_n and_o cross_v the_o two_o former_a arch_n at_o f_o and_o e_o then_o lay_v your_o ruler_n to_o these_o two_o cross_n f_o and_o e_o and_o draw_v the_o line_n gc_fw-mi e_z which_o will_v divide_v the_o line_n a_o b_o in_o two_o equal_a part_n in_o the_o point_n c_o so_fw-mi that_o a_o c_o be_v the_o one_o half_a and_o c_o b_o the_o other_o proposition_n 8._o to_o raise_v a_o perpendicular_a at_o the_o end_n of_o a_o line_n another_o way_n proposition_n the_o eight_o proposition_n in_o this_o figure_n let_v the_o line_n give_v be_v a_o b_o and_o it_o be_v require_v to_o raise_v a_o perpendicular_a at_o the_o end_n thereof_o at_o b._n here_o you_o may_v note_v that_o if_o the_o three_o side_n of_o a_o triangle_n be_v make_v of_o these_o three_o number_n 3_o 4_o 5_o or_o any_o other_o number_n that_o be_v proportionable_a thereunto_o as_o 6_o 8_o 10_o 9_o 12_o 15_o 12_o 16_o 20_o 30_o 40_o 50_o it_o will_v have_v one_o right_a angle_n which_o will_v be_v opposite_a to_o the_o great_a side_n as_o in_o the_o triangle_n d_o b_o e_o the_o side_n e_o b_o be_v 3_o the_o side_n b_o d_o be_v 4_o and_o the_o side_n d_o e_z be_v 5_o and_o the_o angle_n at_o b_o be_v a_o right_a angle_n proposition_n 9_o to_o make_v one_o angle_n equal_a or_o like_v to_o another_o proposition_n the_o nine_o proposition_n a_o angle_n be_v the_o join_n or_o cross_v of_o two_o line_n angle_n what_o a_o angle_n be_v with_o the_o general_a kind_n of_o angle_n if_o the_o two_o line_n cross_v one_o another_o or_o join_v one_o to_o another_o perpendicular_o than_o they_o be_v say_v to_o make_v a_o right_a angle_n or_o angle_n if_o two_o line_n meet_v or_o cross_a one_o another_o any_o other_o way_n they_o be_v say_v to_o make_v a_o oblique_a angle_n or_o angle_n thus_o in_o the_o three_o figure_n the_o line_n d_o b_o and_o e_o b_o meeting_n in_o the_o point_n b_o make_v a_o right_a angle_n and_o in_o the_o second_o figure_n the_o line_n a_o b_o and_o g_o e_o cross_v one_o another_o in_o the_o point_n c_o make_v four_o right_a angle_n or_o quadrant_n but_o in_o the_o three_o figure_n the_o line_n e_o d_o and_o b_o d_o meet_v in_o the_o point_n d_o be_v say_v to_o make_v a_o oblique_a angle_n now_o these_o oblique_a angle_n if_o they_o be_v less_o than_o a_o right_a angle_n they_o be_v call_v acute_a or_o sharp_a angle_n if_o they_o be_v more_o than_o a_o right_a angle_n they_o be_v call_v obtuse_a or_o blunt_a angle_n now_o for_o example_n of_o the_o proposition_n let_v the_o angle_n e_o d_o b_o be_v the_o appoint_a angle_n and_o it_o be_v require_v to_o make_v the_o angle_n d_o b_o c_o like_v unto_o it_o in_o this_o example_n because_o the_o line_n d_o b_o be_v limit_v and_o be_v common_a to_o both_o the_o angle_n you_o shall_v need_v only_o to_o set_v one_o foot_n of_o your_o compass_n in_o b_o and_o open_v the_o other_o to_o the_o near_a distance_n of_o the_o line_n d_o e_o which_o you_o may_v do_v by_o draw_v the_o little_a arch_n which_o touch_v the_o line_n between_o 3_o and_o 4_o then_o remove_v your_o compass_n to_o d_o and_o draw_v the_o like_a arch_n at_o c_o then_o lay_v your_o ruler_n to_o the_o point_n b_o and_o the_o very_a edge_n of_o this_o arch_n c_o and_o draw_v the_o line_n b_o c_o so_fw-mi shall_v the_o two_o angle_n be_v of_o one_o quantity_n or_o wideness_n as_o be_v desire_v in_o other_o case_n this_o way_n will_v not_o serve_v but_o this_o be_v sufficient_a for_o the_o present_a purpose_n and_o i_o shall_v show_v you_o other_o way_n to_o perform_v that_o in_o the_o next_o chapter_n proposition_n 10._o to_o divide_v a_o line_n into_o any_o number_n of_o equal_a part_n proposition_n the_o ten_o proposition_n in_o the_o three_o figure_n let_v the_o line_n b_o d_o be_v give_v to_o be_v divide_v into_o four_o equal_a part_n first_o from_o the_o end_n d_o draw_v a_o line_n as_o d_o e_z make_v a_o angle_n with_o the_o line_n d_o b_o at_o pleasure_n then_o from_o the_o other_o end_n of_o the_o line_n b_o make_v the_o angle_n d_o b_o c_o equal_a to_o the_o former_a angle_n as_o be_v show_v in_o the_o last_o proposition_n then_o from_o the_o point_n d_o set_v off_o with_o your_o compass_n such_o a_o number_n of_o any_o equal_a part_n as_o lack_v one_o of_o the_o number_n desire_v which_o in_o this_o example_n therefore_o must_v be_v 3_o set_v off_o therefore_o on_o the_o line_n d_o e_o three_o equal_a part_n 1_o 2_o and_z 3_o than_o you_o must_v with_o the_o same_o distance_n of_o your_o compass_n set_v off_o 1_o 2_o and_z 3_o from_o the_o point_n b_o on_o the_o line_n b_o c_o then_z draw_z cross_a line_n from_o the_o last_o number_n in_o the_o one_o line_n to_o the_o first_o in_o the_o other_o that_o be_v from_o 3_o to_o 1_o from_z 2_o to_z 2_o etc._n etc._n and_o these_o line_n will_v divide_v the_o line_n b_o d_o into_o four_o equal_a part_n as_o be_v desire_v proposition_n 11._o to_o bring_v any_o three_o point_n not_o lie_v in_o a_o straight_a line_n into_o a_o circle_n proposition_n the_o eleven_o proposition_n in_o this_o figure_n let_v a_o b_o c_o be_v the_o three_o point_n give_v and_o it_o be_v require_v to_o draw_v a_o circle_n through_o they_o all_o figure_n the_o four_o figure_n set_v one_o foot_n of_o your_o compass_n in_o the_o middle_a point_n at_o b_o and_o open_v your_o compass_n to_o any_o distance_n you_o please_v so_o it_o be_v above_o half_a the_o distance_n between_o b_o and_o either_o of_o the_o other_o mark_n yea_o it_o be_v no_o matter_n if_o need_v be_v though_o it_o reach_v almost_o to_o or_o quite_o beyond_o the_o near_a of_o the_o other_o mark_n and_o draw_v the_o arch_n d_o e_o f_o g_o 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 g_o f_o which_o cross_v the_o former_a arch_n at_o g_o and_o f_o then_o set_v one_o foot_n of_o your_o compass_n in_o the_o three_o point_n c_o and_o with_o the_o other_o draw_v the_o arch_n e_o d_o which_o cross_v the_o first_o arch_n at_o e_o and_o d_o then_o lay_v your_o ruler_n to_o the_o intersection_n of_o these_o arch_n draw_v the_o line_n g_o f_o h_n and_o d_o e_o h_o which_o will_v cross_v one_o another_o in_o the_o point_n h_n this_o cross_n at_o h_n be_v the_o centre_n of_o the_o circle_n therefore_o set_v one_o foot_n of_o your_o compass_n in_o this_o cross_n at_o h_n open_v the_o other_o to_o any_o of_o the_o three_o point_n a_o b_o or_o c_o and_o draw_v the_o circle_n which_o if_o you_o have_v do_v well_o will_v pass_v through_o all_o the_o three_o point_n a_o b_o c_o as_o be_v require_v chap._n ii_o show_v how_o to_o divide_v a_o circle_n several_a way_n which_o will_v be_v needful_a for_o many_o thing_n the_o first_o usual_a division_n of_o a_o circle_n be_v into_o 24_o equal_a part_n according_a to_o the_o 24_o hour_n of_o a_o natural_a day_n which_o be_v thus_o to_o be_v perform_v second_o another_o usual_a and_o necessary_a division_n of_o a_o circle_n be_v to_o divide_v a_o circle_n into_o 360_o equal_a part_n degree_n to_o divide_v a_o circle_n into_o 360_o degree_n for_o in_o all_o question_n of_o astronomy_n and_o in_o the_o calculation_n of_o all_o triangle_n these_o part_n be_v the_o measure_n of_o the_o angle_n so_o that_o every_o arch_n in_o this_o respect_n be_v suppose_v to_o be_v divide_v into_o 360_o equal_a part_n which_o be_v call_v degree_n and_o each_o degree_n be_v suppose_v to_o be_v divide_v into_o 60_o lesser_a part_n call_v minute_n to_o divide_v a_o circle_n after_o this_o manner_n the_o ready_a way_n be_v thus_o first_o draw_v a_o line_n at_o pleasure_n and_o cross_v it_o at_o right_a angle_n with_o another_o line_n and_o draw_v a_o circle_n as_o before_o then_o keep_v your_o compass_n at_o this_o distance_n divide_v the_o circle_n from_o the_o four_o quarter_n into_o 12_o equal_a
quadrant_n a_o b_o this_o line_n r_o t_n be_v the_o tangent_fw-la line_n which_o you_o must_v divide_v into_o degree_n as_o you_o see_v in_o the_o figure_n by_o draw_v straight_o line_n from_o the_o centre_n a_o to_o the_o limb_n of_o the_o quadrant_n then_o transfer_v this_o line_n to_o the_o side_n of_o the_o quadrant_n a_o b_o and_o a_o d_o and_o then_o set_v one_o foot_n of_o your_o compass_n in_o the_o centre_n a_o open_v the_o other_o to_o the_o several_a degree_n in_o the_o line_n a_o b_o or_o a_o d_o and_o draw_v the_o arch_n now_o you_o must_v know_v that_o these_o arch_n be_v the_o parallel_n of_o latitude_n and_o the_o straight_a line_n draw_v from_o the_o centre_n be_v meridian_n line_n or_o the_o line_n of_o longitude_n the_o arch_n of_o latitude_n you_o must_v number_v as_o in_o the_o figure_n but_o the_o line_n of_o longitude_n you_o may_v number_v as_o your_o occasion_n require_v this_o be_v a_o projection_n of_o a_o part_n of_o the_o globe_n in_o plano_fw-la by_o natural_a tangent_n you_o may_v if_o you_o please_v when_o occasion_n require_v divide_v a_o circle_n into_o four_o quadrant_n and_o draw_v the_o line_n of_o longitude_n from_o the_o centre_n and_o number_v they_o to_o 360_o and_o likewise_o describe_v the_o circle_n of_o latitude_n round_o about_o the_o centre_n and_o you_o may_v make_v this_o projection_n as_o large_a or_o as_o little_a as_o you_o will_v by_o the_o table_n of_o natural_a tangent_n if_o you_o lengthen_v or_o shorten_v your_o radius_fw-la a_o table_n of_o natural_a tangent_n the_o radius_fw-la being_n 1000_o part_n d._n tan_n d._n tangle_n d._n tang._n d._n tangent_fw-la 1_o 017_o 24_o 445_o 46_o 1,036_o 69_o 02,605_o 2_o 035_o 25_o 466_o 47_o 1,072_o 70_o 02,747_o 3_o 052_o 26_o 488_o 48_o 1,112_o 71_o 02_o 904_o 4_o 070_o 27_o 510_o 49_o 1_o 150_o 72_o 03_o 078_o 5_o 087_o 28_o 532_o 50_o 1_o 192_o 73_o 03_o 271_o 6_o 105_o 29_o 554_o 51_o 1,235_o 74_o 03,487_o 7_o 123_o 30_o 577_o 52_o 1_o 280_o 75_o 03,732_o 8_o 141_o 31_o 601_o 53_o 1_o 327_o 76_o 04_o 011_o 9_o 158_o 32_o 624_o 54_o 1,376_o 77_o 04,331_o 10_o 176_o 33_o 649_o 55_o 1,428_o 78_o 04,705_o 11_o 194_o 34_o 675_o 56_o 1,483_o 79_o 05,144_o 12_o 213_o 35_o 700_o 57_o 1_o 540_o 80_o 05_o 671_o 13_o 231_o 36_o 727_o 58_o 1,600_o 81_o 06_o 313_o 14_o 249_o 37_o 754_o 59_o 1,664_o 82_o 07,115_o 15_o 268_o 38_o 781_o 60_o 1_o 732_o 83_o 08_o 144_o 16_o 287_o 39_o 810_o 61_o 1,804_o 84_o 09_o 514_o 17_o 306_o 40_o 839_o 62_o 1_o 881_o 85_o 11,430_o 18_o 325_o 41_o 869_o 63_o 1,963_o 86_o 14,300_o 19_o 344_o 42_o 900_o 64_o 2_o 050_o 87_o 19,081_o 20_o 364_o 43_o 933_o 65_o 2_o 144_o 88_o 28_o 636_o 21_o 384_o 44_o 966_o 66_o 2_o 246_o 89_o 57,290_o 22_o 404_o 45_o 1000_o 67_o 2,356_o 90_o infinite_a 23_o 424_o  _fw-fr rad._n 68_o 2_o 475_o  _fw-fr  _fw-fr let_v your_o radius_fw-la be_v of_o what_o length_n you_o please_v first_o divide_v it_o into_o 10_o equal_a part_n and_o then_o subdivide_v each_o of_o those_o part_n into_o 10_o so_o you_o shall_v have_v 100_o part_n in_o your_o line_n than_o you_o may_v if_o you_o can_v divide_v each_o of_o these_o 100_o part_n into_o 10_o so_o you_o shall_v have_v 1000_o but_o this_o last_o division_n will_v be_v needless_a for_o you_o may_v by_o your_o eye_n guess_v at_o the_o proportion_n ill_a part_n have_v thus_o fit_v your_o scale_n of_o equal_a part_n you_o may_v prick_v down_o the_o line_n of_o tangent_n out_o of_o this_o table_n note_v after_o you_o be_v pass_v 45_o degree_n in_o the_o table_n the_o figure_n before_o the_o comma_n show_v the_o whole_a radius_fw-la or_o how_o many_o time_n the_o whole_a radius_fw-la be_v contain_v therein_o and_o the_o three_o follow_a figure_n the_o part_n to_o be_v reckon_v upon_o the_o scale_n as_o before_o you_o will_v find_v this_o table_n necessary_a either_o when_o you_o will_v make_v a_o large_a tangent_fw-la line_n to_o serve_v for_o place_n only_o near_o the_o pole_n or_o when_o you_o will_v make_v a_o very_a little_a tangent_fw-la line_n that_o so_o you_o may_v bring_v in_o the_o degree_n near_o the_o equinoctial_a into_o your_o quadrant_n easy_a the_o flank_n be_v make_v will_v serve_v for_o many_o example_n so_o that_o the_o work_n will_v be_v very_o easy_a have_v thus_o draw_v this_o blank_a quadrant_n you_o must_v set_v down_o therein_o the_o two_o place_n you_o be_v to_o sail_v between_o according_a to_o their_o latitude_n and_o longitude_n and_o then_o only_o by_o your_o ruler_n draw_v a_o straight_a line_n from_o the_o one_o place_n to_o the_o other_o and_o this_o straight_a line_n will_v represent_v the_o great_a circle_n which_o pass_v between_o the_o two_o place_n and_o will_v exact_o cross_v those_o degree_n of_o longitude_n and_o latitude_n which_o you_o must_v sail_v by_o for_o the_o example_n example_n example_n and_o proof_n hereof_o i_o shall_v take_v mr._n norwoods_n example_n of_o a_o voyage_n from_o the_o summer_n land_n to_o the_o lizard_n the_o latitude_n of_o the_o summer-iland_n be_v 32_o degree_n 25_o minute_n let_v the_o longitude_n thereof_o be_v suppose_v to_o be_v ●00_o degree_n the_o latitude_n of_o the_o lizard_n be_v near_o 50_o degree_n the_o difference_n of_o longitude_n between_v the_o two_o place_n be_v suppose_v to_o be_v 70_o degree_n so_o that_o the_o longitude_n of_o the_o lizard_n will_v be_v 10_o degree_n and_o it_o be_v require_v to_o know_v by_o what_o longitude_n and_o latitude_n the_o arch_n of_o a_o great_a circle_n draw_v between_o these_o two_o place_n do_v pass_v example_n the_o work_n of_o the_o example_n first_o let_v the_o line_n a_o b_o represent_v the_o meridian_n of_o the_o summer_n land_n upon_o which_o you_o must_v mark_v out_o their_o latitude_n 32_o degree_n 25_o minute_n at_o b_o and_o because_o the_o longitude_n thereof_o be_v 300_o set_v down_o 100l_n at_o the_o end_n of_o the_o line_n a_o b_o so_fw-mi the_o summer-iland_n shall_v be_v set_v down_o according_a to_o their_o longitude_n and_o latitude_n then_o count_v still_o forward_o the_o degree_n of_o the_o difference_n of_o longitude_n till_o you_o come_v to_o 70_o degree_n in_o the_o limb_n of_o the_o quadrant_a and_o there_o draw_v the_o line_n a_o c_o 70_o this_o line_n will_v represent_v the_o meridian_n of_o the_o lizard_n and_o upon_o this_o line_n you_o must_v mark_v out_o the_o latitude_n of_o the_o lizard_n which_o be_v 50_o degree_n at_o c_o then_o lay_v your_o ruler_n to_o these_o two_o mark_n at_o b_o and_o c_o and_o draw_v the_o straight_a line_n b_o c._n this_o line_n b_o c_o will_n represent_v the_o arch_n of_o the_o great_a circle_n between_o these_o two_o place_n and_o if_o you_o guide_v your_o eye_n along_o in_o this_o line_n you_o may_v ready_o and_o true_o perceive_v by_o what_o longitude_n and_o latitude_n you_o shall_v sail_v for_o mark_v well_o where_o this_o line_n cross_v the_o arch_n of_o latitude_n and_o the_o line_n of_o longitude_n and_o that_o show_v the_o true_a longitude_n and_o latitude_n of_o the_o arch_n of_o the_o great_a circle_n according_a to_o your_o desire_n proof_n the_o proof_n now_o the_o truth_n hereof_o will_n more_o evident_o appear_v if_o you_o compare_v the_o latitude_n and_o longitude_n which_o this_o line_n intersect_v with_o this_o table_n thereof_o calculate_v by_o mr._n circle_n mr._n in_o the_o ten_o problem_n of_o sail_v by_o the_o arch_n of_o a_o great_a circle_n norwood_n for_o every_o five_o degree_n of_o longitude_n longitude_n latitude_n de._n or_o difference_n of_o longitude_n d._n deg._n m._n 310_o 00_o 32_o 25_o 305_o 05_o 35_o 52_o 300_o 10_o 38_o 51_o 315_o 15_o 41_o 24_o 320_o 20_o 43_o 34_o 325_o 25_o 45_o 24_o 330_o 30_o 46_o 54_o 335_o 35_o 48_o 07_o 340_o 40_o 49_o 04_o 345_o 45_o 49_o 47_o 350_o 50_o 50_o 15_o 355_o 55_o 50_o 31_o 360_o 60_o 50_o 33_o 005_o 65_o 50_o 23_o 010_o 70_o 50_o 00_o now_o you_o may_v hereby_o see_v that_o the_o line_n b_o c_o in_o the_o point_n g_z do_v cross_v the_o 305_o or_o the_o 5_o degree_n of_o longitude_n from_o b_o almost_o at_o the_o arch_n of_o 36_o degree_n of_o latitude_n just_a as_o the_o table_n show_v it_o shall_v at_o 35_o degree_n 52_o minute_n of_o latitude_n again_o the_o line_n b_o c_o do_v cross_a the_o 310_o or_o the_o 10_o degree_n of_o longitude_n from_o b_o in_o the_o point_n h_o almost_o at_o the_o arch_n of_o 39_o degree_n of_o latitude_n agree_v with_o the_o table_n which_o show_v it_o to_o be_v in_o 38_o degree_n 51_o minute_n and_o so_o in_o all_o the_o rest_n it_o so_o near_o agree_v that_o if_o you_o take_v any_o care_n in_o make_v of_o this_o blank_a map_n to_o draw_v the_o arch_n