Selected quad for the lemma: end_n

Word A	Word B	Word C	Word D	Occurrence	Frequency Band	MI	MI Band	Prominent
end_n	divide_v	equal_a	line_n	1,364	5	9.1106	5	false

Text snippets containing the quad

ID	Title	Author	Corrected Date of Publication (TCP Date of Publication)	STC	Words	Pages
A75737	Speculum nauticum A looking-glasse for sea-men. Wherein they may behold, how by a small instrument, called the plain-scale, all nautical questions, and astronomical propositions, are very easily and demonstratively performed. First set down by John Aspley, student in physick, and practitioner of the mathematicks in London. The sixth edition. Whereunto are added, many new propositions in navigation and astronomy, and also a third book, shewing a new way of dialling. By H.P. and W.L.	Aspley, John.; H. P.; W. L., 17th cent.	1662 (1662)	Wing A4013; ESTC R229501	35,709	72

speculum_fw-la nauticum_fw-la a_o lookingglass_n for_o seaman_n wherein_o they_o may_v behold_v how_o by_o a_o small_a instrument_n call_v the_o plain_a scale_n all_o nautical_a question_n and_o astronomical_a proposition_n be_v very_o easy_o and_o demonstrative_o perform_v first_o set_v forth_o by_o john_n aspley_n student_n in_o physic_n and_o practitioner_n of_o the_o mathematics_n in_o london_n the_o six_o edition_n whereunto_o be_v add_v many_o new_a proposition_n in_o navigation_n and_o astronomy_n and_o also_o a_o three_o book_n show_v a_o new_a way_n of_o dial_v by_o h._n p._n and_o w._n l._n london_n print_v by_o w._n leybourn_n for_o george_n hurlock_n and_o be_v to_o be_v sell_v at_o his_o shop_n at_o magnus_n church-corner_n in_o thamesstreet_n near_o london-bridge_n 1662._o to_o the_o worshipful_a the_o master_n warden_n &_o assistant_n of_o the_o trinity_n house_n john_n aspley_n in_o testimony_n of_o the_o honour_n he_o bear_v to_o the_o governor_n &_o practiser_n of_o the_o art_n of_o navigation_n dedicate_v these_o his_o first_o labour_n the_o printer_n to_o the_o reader_n this_o little_a book_n have_v be_v well_o accept_v of_o among_o seaman_n be_v the_o first_o fruit_n of_o mr._n aspley_n mathematical_a study_n have_v pass_v five_o impression_n without_o any_o alteration_n and_o so_o i_o doubt_v not_o might_n have_v do_v still_o but_o because_o since_o that_o time_n there_o have_v be_v several_a book_n put_v out_o of_o this_o nature_n i_o have_v procure_v this_o to_o be_v revise_v and_o several_a alteration_n and_o addition_n to_o be_v make_v therein_o so_o that_o here_o you_o have_v both_o the_o old_a and_o a_o new_a book_n intermingle_v all_o in_o one_o with_o a_o three_o part_n add_v thereto_o concern_v dialling_n by_o a_o way_n not_o former_o publish_v by_o any_o all_o which_o i_o doubt_v not_o you_o will_v kind_o accept_v of_o and_o receive_v much_o delight_n and_o profit_n thereby_o your_o g._n h._n errata_fw-la page_n 34_o line_n 26_o read_v 360._o page_n 45._o l._n 8._o r._n distance_n i_o m._n page_n 50._o line_n 13._o for_o 14_o etc._n etc._n 〈…〉_z which_o be_v just_a the_o length_n of_o the_o gnomon_n page_n 50_o line_n 28._o for_o increase_n read_v decrease_n page_n 52_o line_n 4._o r._n h_o a_o i._o line_n 18._o r._n point_n o._n page_n 57_o line_n 11_o r._n point_n l._n also_o for_o some_o literal_a fault_n we_o shall_v desire_v your_o pardon_n speculum_fw-la nauticum_fw-la or_o the_o seaman_n glass_n the_o first_o book_n chap._n i._n the_o explanation_n of_o certain_a term_n of_o geometry_n be_v intend_v in_o this_o treatise_n of_o the_o plain_a scale_n to_o declare_v the_o manner_n of_o projection_n of_o the_o sphere_n in_o plano_fw-la i_o have_v think_v fit_v first_o to_o show_v unto_o you_o some_o term_n of_o geometry_n which_o be_v necessary_a for_o the_o unlearned_a to_o know_v for_o who_o sake_n chief_o i_o write_v this_o treatise_n before_o they_o enter_v into_o the_o definition_n of_o the_o sphere_n 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to_o say_v the_o right_n line_v parallel_n and_o the_o circular_a parallel_n right_o line_v parallel_n be_v two_o right_a line_n equidistant_a one_o from_o another_o which_o be_v draw_v forth_o infinite_o will_v never_o touch_v or_o meet_v one_o another_o as_o you_o may_v see_v in_o the_o figure_n where_o the_o line_n h_n i_o be_v parallel_n unto_o the_o line_n ce_fw-fr and_o the_o line_n gf_n be_v parallel_n unto_o they_o both_o a_o circular_a parallel_n be_v a_o circle_n draw_v either_o within_o or_o without_o another_o circle_n upon_o the_o same_o centre_n as_o you_o may_v plain_o see_v by_o the_o two_o circle_n bcde_v and_o xvyw_n these_o circle_n be_v both_o draw_v upon_o the_o centre_n a_o and_o therefore_o be_v parallel_v the_o one_o unto_o the_o other_o there_o be_v another_o kind_n of_o parallel_n also_o which_o be_v call_v a_o serpentine_a parallel_n but_o because_o it_o be_v not_o belong_v unto_o the_o use_n of_o this_o scale_n i_o will_v omit_v it_o and_o so_o proceed_v 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a_o circle_n be_v half_a of_o the_o diameter_n and_o be_v contain_v betwixt_o the_o centre_n and_o the_o one_o side_n of_o the_o circle_n as_o the_o line_n ad_fw-la be_v the_o semidiameter_n of_o the_o circle_n bcde_v this_o semidiameter_n contain_v 60_o degree_n of_o the_o line_n of_o chord_n which_o we_o sometime_o call_v the_o radius_fw-la semicirculus_fw-la or_o a_o semicircle_n be_v the_o one_o half_a of_o a_o circle_n draw_v upon_o his_o diameter_n and_o be_v contain_v upon_o the_o superficies_n or_o surface_n of_o the_o diameter_n as_o the_o semicircle_n bcd_v which_o be_v half_a of_o the_o circle_n bcde_v and_o be_v contain_v above_o the_o diameter_n bad_a quadrant_n circuli_fw-la be_v the_o four_o part_n of_o a_o circle_n and_o be_v contain_v betwixt_o the_o semidiameter_n of_o the_o circle_n and_o a_o line_n draw_v perpendicular_a unto_o the_o diameter_n of_o the_o same_o circle_n from_o the_o centre_n thereof_o divide_v the_o semicircle_n into_o two_o equal_a part_n of_o the_o which_o part_n the_o one_o be_v the_o quadrant_n or_o four_o part_n of_o the_o same_o circle_n as_o for_o example_n the_o diameter_n of_o the_o circle_n bcde_v be_v the_o line_n bad_a divide_v the_o circle_n into_o two_o equal_a part_n then_o from_o the_o centre_n a_o raise_v the_o perpendicular_a ac_fw-la divide_v the_o semicircle_n likewise_o into_o two_o equal_a part_n so_o be_v abc_n or_o acd_v the_o quadrant_n of_o the_o circle_n bcde_v which_o be_v desire_v chap._n ii_o the_o manner_n how_o to_o raise_v a_o perpendicular_a from_o the_o middle_n of_o a_o line_n give_v 〈◊〉_d first_o a_o ground_n line_n whereupon_o you_o will_v have_v a_o perpendicular_a raise_v then_o open_a your_o compass_n unto_o any_o distance_n so_o it_o exceed_v not_o the_o end_n of_o your_o line_n place_v one_o foot_n of_o the_o say_a compass_n in_o the_o point_n from_o whence_o the_o perpendicular_a be_v ●o_o be_v raise_v and_o with_o the_o other_o foot_n make_v a_o mark_n in_o the_o line_n on_o 〈…〉_z remove_n your_o compass_n unto_o any_o other_o distance_n that_o 〈…〉_z set_v one_o foot_n thereof_o in_o one_o of_o the_o mark_n and_o with_o the_o 〈◊〉_d foot_n make_v a_o arch_n over_o the_o middle_a point_n then_o with_o the_o same_o distance_n of_o your_o compass_n set_v one_o foot_n in_o the_o other_o mark_n upon_o the_o line_n and_o with_o the_o other_o foot_n make_v another_o arch_n of_o a_o circle_n over_o the_o middle_a point_n so_o that_o it_o may_v cross_v the_o first_o arch_n and_o from_o the_o meeting_n of_o these_o two_o arch_n draw_v a_o right_a line_n unto_o the_o middle_a point_n from_o which_o the_o perpendicular_a be_v to_o be_v raise_v which_o line_n shall_v be_v the_o perpendicular_a desire_v example_n suppose_v your_o base_a or_o ground_n line_n whereupon_o a_o perpendicular_a be_v to_o be_v raise_v be_v the_o line_n flk_n and_o from_o

l_o the_o perpendicular_a be_v to_o be_v raise_v set_v one_o foot_n of_o your_o compass_n in_o the_o point_n l_o and_o with_o the_o other_o make_v the_o mark_n g_o and_o m_o on_o both_o side_n of_o the_o point_n l_o the●_n open_v your_o compass_n wide_a set_v one_o foot_n in_o the_o point_n m_o and_o with_o the_o other_o draw_v the_o arch_n s_o over_o the_o point_n l_o then_o with_o the_o same_o distance_n of_o your_o compass_n set_v one_o foot_n in_o g_o and_o with_o the_o other_o make_v the_o arch_n r_o cross_v the_o arch_a saint_n in_o the_o point_n t_o then_o from_o t_n draw_v the_o line_n tl_n which_o line_n be_v perpendicular_a unto_o the_o line_n flk_v from_o the_o point_n l_o which_o be_v the_o perpendicular_a desire_v chap._n iii_o to_o let_v a_o perpendicular_a fall_n from_o any_o point_n assign_v unto_o the_o middle_n of_o a_o line_n let_v the_o line_n whereupon_o you_o will_v have_v a_o perpendicular_a let_v fall_n be_v the_o line_n lfk_n and_o the_o point_n assign_v to_o 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let_v the_o line_n flk_v be_v the_o base_a or_o ground_n line_n and_o from_o the_o point_n i_o a_o perpendicular_a be_v to_o be_v let_v fall_n upon_o the_o end_n of_o the_o line_n at_o k_o first_o from_o the_o assign_a point_n i_o draw_v a_o line_n unto_o any_o part_n of_o the_o base_a which_o shall_v be_v the_o line_n ihm_fw-ge then_o find_v the_o middle_n of_o the_o line_n in_o which_o be_v at_o h_n place_n therefore_o one_o foot_n of_o your_o compass_n in_o the_o point_n h_n and_o extend_v the_o other_o unto_o ay_o with_o which_o distance_n draw_v the_o arch_a ink_n upon_o the_o centre_n h_n cut_v the_o base_a or_o ground-line_n in_o the_o point_n k_o then_o draw_v the_o line_n ki_v which_o line_n shall_v be_v the_o perpendicular_a desire_v chap._n vi_o a_o right_a line_n be_v give_v how_o to_o draw_v another_o parallel_n there_o unto_o at_o any_o distance_n require_v let_v the_o line_n give_v be_v ab_fw-la unto_o which_o it_o be_v require_v to_o draw_v another_o right_a line_n cd_o which_o shall_v be_v parallel_n to_o the_o former_a line_n ab_fw-la and_o at_o the_o distance_n ac_fw-la first_o open_v your_o compass_n to_o the_o distance_n ac_fw-la then_o set_v one_o foot_n in_o the_o point_n a_o with_o the_o other_o describe_v the_o arch_n c_o again_o place_n one_o foot_n in_o b_o and_o with_o the_o other_o describe_v the_o arch_n d_o then_o draw_v the_o line_n cd_o so_o that_o it_o may_v only_o touch_v the_o two_o arch_n c_o and_o d_o so_fw-mi shall_v the_o line_n cd_o so_o draw_v be_v parallel_n to_o ab_fw-la and_o at_o the_o distance_n require_v chap._n vii_o a_o right_a line_n be_v give_v how_o to_o draw_v another_o parallel_n thereunto_o which_o shall_v also_o pass_v through_o a_o point_n assign_v let_v ab_fw-la be_v a_o line_n give_v and_o the_o point_n assign_v be_v c_o and_o let_v it_o be_v require_v to_o draw_v another_o line_n parallel_n thereunto_o which_o shall_v pass_v through_o the_o give_v point_n c._n now_o i_o doubt_v not_o but_o you_o understand_v the_o way_n to_o let_v fall_v or_o to_o raise_v any_o manner_n of_o perpendicular_a line_n either_o from_o or_o upon_o any_o part_n of_o a_o line_n as_o also_o to_o draw_v line_n parallel_v one_o to_o another_o at_o any_o distance_n require_v therefore_o now_o i_o intend_v to_o proceed_v unto_o the_o main_a point_n here_o aim_v at_o which_o be_v to_o declare_v and_o make_v know_v unto_o you_o the_o several_a operation_n perform_v by_o the_o plain_a scale_n which_o though_o it_o be_v in_o use_n with_o very_a few_o yet_o it_o be_v most_o necessary_a for_o seaman_n because_o all_o question_n in_o navigation_n be_v thereby_o easy_o and_o plain_o wrought_v and_o also_o all_o question_n in_o astronomy_n belong_v unto_o the_o expert_a and_o industrious_a seaman_n may_v both_o speedy_o and_o easy_o be_v wrought_v by_o the_o same_o scale_n in_o regard_n whereof_o i_o have_v declare_v in_o this_o little_a book_n that_o knowledge_n which_o god_n have_v be_v please_v to_o bestow_v 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that_o radius_fw-la the_o three_o part_n of_o the_o scale_n be_v divide_v into_o eight_o part_n represent_v the_o point_n or_o rumbe_n of_o the_o mariner_n compass_n which_o in_o all_o be_v 32_o point_n but_o upon_o the_o scale_n there_o be_v only_a saint_n reckon_v which_o be_v but_o one_o quadrant_n or_o quarter_n of_o they_o be_v to_o be_v reckon_v from_o the_o meridian_n of_o north_n and_o south_n both_o way_n as_o you_o may_v see_v more_o plain_o by_o this_o figure_n represent_v the_o order_n of_o the_o point_n of_o the_o compass_n it_o be_v usual_a also_o to_o have_v another_o line_n place_v upon_o your_o scale_n to_o she●_n you_o how_o many_o league_n make_v a_o degree_n of_o longitude_n in_o every_o latitude_n concern_v which_o you_o shall_v have_v direction_n in_o the_o 14_o chapter_n follow_v chap._n ix_o know_v the_o course_n any_o ship_n have_v make_v and_o the_o league_n she_o have_v sail_v to_o find_v how_o much_o she_o have_v raise_v or_o depress_v the_o pole_n and_o likewise_o how_o much_o she_o be_v depart_v from_o her_o first_o meridian_n the_o course_n be_v south-west_n and_o by_o south_n the_o league_n sail_v be_v 100_o the_o difference_n of_o the_o latitude_n and_o the_o distance_n of_o the_o meridian_n be_v require_v now_o you_o must_v heedful_o observe_v this_o point_n d_o for_o this_o represent_v the_o place_n where_o your_o ship_n be_v and_o do_v show_v both_o the_o differencefo_o the_o latitude_n of_o the_o place_n you_o be_v in_o and_o also_o your_o distance_n or_o departure_n from_o your_o first_o meridian_n first_o for_o the_o latitude_n you_o see_v the_o line_n df_n be_v parallel_n to_o the_o line_n ab_fw-la cut_v the_o meridian_n line_n

104_o 28_o 17_o 1_o 98_o 48_o  _fw-fr 58_o 10_o 1_o 80_o 88_o  _fw-fr 88_o 0_o 2_o 09_o 105_o 29_o 17_o 1_o 48_o 50_o  _fw-fr 59_o 10_o 0_o 90_o 90_o  _fw-fr 89_o 0_o 1_o 05_o 104_o 30_o 17_o 0_o 96_o 52_o  _fw-fr 60_o 10_o 0_o 0_o 90_o  _fw-fr 90_o 0_o 0_o 0_o 105_o chap._n xv._n the_o difference_n of_o latitude_n and_o the_o rumb_n or_o distance_n sail_v be_v know_v to_o find_v the_o distance_n of_o the_o meridian_n and_o thereby_o to_o find_v the_o degree_n and_o minute_n of_o the_o difference_n of_o longitude_n in_o any_o latitude_n sail_v from_o the_o north_n parallel_n of_o 56_o degree_n and_o 5_o min._n latitude_n 100_o league_n upon_o the_o three_o rumb_n from_o the_o meridian_n viz._n south-west_n and_o by_o south_n until_o i_o find_v the_o pole_n be_v depress_v 4_o deg_n 9_o m._n and_o the_o meridional_a distance_n 56_o league_n the_o longitude_n be_v desire_v thereby_o i●_n the_o first_o figure_n now_o to_o reduce_v this_o 56_o league_n into_o degree_n of_o longitude_n you_o must_v consider_v from_o what_o latitude_n you_o have_v sail_v and_o to_o what_o latitude_n you_o be_v come_v viz._n from_o latitude_n 56_o d._n 5_o m._n to_o 4_o deg_n 9_o min._n less_o which_o be_v 51_o d._n 56_o m._n and_o take_v the_o middle_a latitude_n or_o somewhat_o more_o between_o the_o two_o place_n which_o in_o this_o example_n fall_v out_o to_o be_v 54d_o 01_o m._n then_o by_o the_o table_n in_o the_o former_a chapter_n find_v out_o howmany_a league_n and_o mile_n in_o the_o say_v middle_a latitude_n make_v one_o degree_n of_o longitude_n and_o you_o shall_v find_v in_o that_o table_n that_o in_o the_o latitude_n of_o 54_o d._n there_o be_v but_o 11_o league_n and_o 2_o mile_n and_o 27_o part_n in_o one_o degree_n of_o longitude_n therefore_o open_v your_o compass_n upon_o your_o scale_n of_o league_n to_o this_o 11_o league_n 2_o mile_n 27_o part_n and_o keep_v your_o compass_n at_o that_o distance_n set_v one_o foot_n of_o they_o at_o 56_o league_n in_o your_o scale_n of_o league_n or_o in_o the_o line_n df_n in_o the_o figure_n or_o upon_o the_o like_a line_n in_o your_o chart_n at_o any_o time_n either_o at_o f_o or_o d_o and_o measure_v howmany_a time_n you_o find_v that_o distance_n either_o to_o the_o end_n of_o your_o scale_n come_v backward_o or_o in_o the_o line_n df_n for_o so_o many_o degree_n be_v the_o difference_n o●_n longitude_n and_o if_o any_o odd_a part_n remain_v you_o may_v proportion_v i●_n by_o your_o eye_n judge_v it_o to_o be_v a_o quarter_n a_o three_o a_o half_a or_o any_o part_n more_o or_o less_o of_o a_o degree_n which_o you_o may_v either_o reckon_v by_o part_n or_o 15_o 20_o 30_o etc._n etc._n minute_n thus_o this_o line_n df_n be_v 56_o league_n open_v your_o compass_n to_o 11_o league_n 2_o mile_n 27_o part_n you_o will_v find_v this_o distance_n in_o it_o 4_o time_n and_o 3_o quarter_n so_o that_o the_o difference_n of_o longitude_n be_v 4_o deg_n 45_o min._n or_o you_o may_v reduce_v it_o into_o mile_n and_o work_n by_o the_o rule_n of_o proportion_n so_o you_o shall_v find_v as_o 11_o league_n 2_o mile_n 27_o part_n that_o be_v 35_o mile_n 27_o part_n 35,27_o to_o one_o degree_n of_o longitude_n in_o the_o latitude_n of_o 54_o d._n 01,00_o so_o be_v 56_o league_n or_o 168_o mile_n 168,00_o to_o 4_o degree_n 76_o part_n 04_o 76_o but_o if_o your_o scale_n be_v large_a the_o other_o way_n with_o your_o compass_n will_v give_v you_o the_o degree_n and_o part_n of_o longitude_n as_o exact_o as_o you_o need_v for_o most_o use_n also_o if_o the_o latitude_n fall_v not_o out_o in_o equal_a part_n you_o may_v find_v out_o for_o your_o odd_a minute_n by_o proportion_n for_o which_o purpose_n i_o have_v set_v the_o difference_n between_o each_o degree_n in_o the_o table_n so_o that_o as_o one_o hundred_o part_n or_o 60_o minute_n be_v one_o degree_n to_o the_o difference_n in_o the_o table_n between_o the_o two_o next_o degree_n so_o the_o odd_a hundred_o part_n or_o minute_n of_o latitude_n to_o the_o part_n and_o minute_n proportional_a to_o be_v allow_v chap._n xvi_o sail_v from_o the_o south_n latitude_n of_o 60_o degree_n 51_o min._n and_o from_o longitude_n 25_o degree_n 24_o min._n 99_o league_n upon_o a_o south-west_n course_n the_o latitude_n and_o longitude_n of_o the_o second_o place_n be_v demand_v in_o the_o second_o demonstration_n draw_v the_o quadrant_n abcde_v as_o be_v former_o teach_v then_o in_o regard_n you_o sail_v south-west_n take_v 4_o point_n of_o the_o compass_n from_o your_o scale_n and_o place_v they_o from_o b_o unto_z d_o then_o by_o the_o point_n d_o draw_v the_o line_n adf_n then_o place_v your_o ninety_o nine_o league_n upon_o the_o line_n adf_n from_o a_o unto_o f_o so_o shall_v f_o be_v the_o place_n of_o your_o ship_n then_o from_o f_o draw_v the_o line_n fc_a parallel_n unto_o ae_n cut_v the_o line_n abc_n in_o c_o so_fw-mi shall_v the_o distance_n ca_n be_v the_o league_n you_o have_v run_v south_n which_o be_v seventy_o league_n or_o 3_o deg_n 30_o minute_n which_o be_v add_v to_o the_o latitude_n from_o whence_o you_o dearted_a make_v 64_o deg_n and_o 21_o minute_n for_o the_o latitude_n of_o the_o second_o place_n then_o take_v the_o distance_n cf_n and_o apply_v it_o unto_o the_o line_n of_o equal_a part_n and_o you_o shall_v find_v it_o likewise_o 70_o league_n then_o find_v the_o middle_a latitude_n 62_o degree_n 36_o minute_n in_o the_o table_n chap._n 14._o you_o shall_v find_v that_o 9_o league_n and_o 0_o mile_n and_o 61_o part_n do_v alter_v a_o degree_n of_o longitude_n in_o that_o latitude_n then_o open_v the_o foot_n of_o your_o compass_n to_o 9_o league_n 0_o mile_n 61_o part_n in_o the_o scale_n of_o equal_a league_n and_o keep_v the_o compass_n at_o that_o distance_n see_v howmany_a time_n that_o distance_n be_v in_o the_o line_n cf_n which_o be_v seven_o time_n and_o somewhat_o above_o a_o half_a the_o true_a difference_n of_o longitude_n be_v 7_o deg_n 36_o m._n which_o be_v substract_v from_o the_o longitude_n from_o whence_o you_o depart_v leave_v 17_o degree_n and_o 48_o minute_n for_o the_o longitudeof_o the_o second_o place_n chap._n xvii_o a_o ship_n sail_v from_o the_o north_n parallel_n of_o fifty_o degree_n have_v a_o hundred_o league_n to_o sail_v south-west_n and_o by_o west_n by_o the_o way_n be_v enforce_v by_o contrary_a wind_n to_o sail_v upon_o several_a point_n of_o the_o compass_n first_o sail_v thirty_o league_n upon_o a_o direct_a course_n than_o west_n northwest_n twenty_o league_n than_o south_n sixty_o league_n the_o question_n be_v to_o find_v the_o latitude_n of_o the_o second_o place_n how_o far_o it_o be_v to_o the_o place_n wherewto_fw-mi you_o be_v bind_v the_o distance_n of_o the_o rumb_n that_o be_v betwixt_o they_o the_o distance_n that_o you_o be_v from_o your_o first_o meridian_n and_o thereby_o the_o difference_n of_o longitude_n in_o the_o three_o demonstration_n draw_v the_o line_n ad_fw-la and_o from_o the_o point_n a_o raise_v the_o perpendicular_a ab_fw-la then_o open_a your_o compass_n unto_o the_o radius_fw-la of_o your_o scale_n and_o place_v one_o foot_n thereof_o in_o the_o centre_n a._n and_o with_o the_o other_o draw_v the_o quadrant_n bcd_n then_o take_v three_o point_n of_o the_o compass_n &_o place_v they_o upon_o the_o quadrant_n from_o d._n unto_o c_o then_o from_o the_o centre_n a_o by_o the_o point_n c_o draw_v the_o line_n acl_n 100_o league_n in_o length_n which_o be_v the_o true_a course_n you_o be_v to_o sail_v then_o in_o regard_n you_o sail_v thirty_o league_n direct_v take_v thirty_o league_n from_o your_o scale_n of_o equal_a part_n and_o place_v they_o upon_o the_o line_n aec_fw-la it_o extend_v from_o a_o unto_o e_o then_o in_o regard_n you_o turn_v your_o course_n west_n northwest_o from_o the_o centre_n e_o draw_v the_o line_n eglantine_n parallel_n unto_o a._n d._n and_o again_o from_o the_o centre_n e_o draw_v the_o line_n eh_n perpendicular_a to_o eglantine_n and_o parallel_v to_o ab_fw-la then_o witn_v the_o distance_n of_o the_o radius_fw-la set_v one_o foot_n of_o your_o compass_n in_o the_o centre_n e_o and_o with_o the_o other_o draw_v the_o quadrant_n gmh_o and_o in_o regard_n you_o sail_v west_n northwest_o which_o be_v two_o point_n from_o the_o west_n northward_o take_v from_o your_o scale_n two_o point_n of_o the_o compass_n and_o place_v they_o upon_o the_o quadrant_n gmh_o from_o g_z unto_o m_n then_o from_o the_o centre_n e_o unto_o the_o point_n m_o draw_v the_o line_n efm_n then_o take_v 20_o league_n with_o your_o compass_n from_o the_o scale_n of_o equal_a part_n and_o place_v they_o upon_o the_o line_n efm_n from_o e_z unto_o f_o

descension_n of_o the_o sun_n or_o any_o star_n who_o right_a ascension_n and_o difference_n of_o ascension_n be_v know_v but_o it_o be_v to_o be_v understand_v that_o this_o manner_n of_o operation_n do_v serve_v no_o long_o than_o you_o be_v upon_o the_o north_n side_n of_o the_o equinoctial_a for_o if_o the_o south_n pole_n be_v elevate_v the_o work_n be_v contrary_a for_o so_o long_o as_o the_o sun_n be_v in_o any_o of_o the_o northern_a sign_n the_o difference_n of_o the_o ascension_n be_v to_o be_v add_v unto_o the_o right_a ascension_n to_o find_v the_o oblique_a ascension_n and_o contrariwise_o substract_v to_o find_v the_o oblique_a descension_n likewise_o if_o the_o sun_n or_o star_n be_v in_o the_o southern_a sign_n then_o be_v the_o difference_n of_o ascension_n substract_v from_o the_o right_a ascension_n to_o find_v the_o oblique_a ascension_n and_o add_v to_o find_v the_o oblique_a descension_n the_o end_n of_o the_o second_o book_n the_o seaman_n glass_n the_o three_o book_n show_v how_o by_o the_o plain-scale_n to_o delineate_v houre-line_n upon_o all_o kind_n of_o upright_a plain_n either_o direct_a or_o decline_a in_o any_o latitude_n the_o figure_n of_o the_o plain_a scale_n chap._n ay_o how_o to_o draw_v hour_n line_n upon_o a_o horizontal_n plain_n in_o any_o latitude_n with_o the_o radius_fw-la of_o your_o line_n of_o chord_n upon_o e_o as_o a_o centre_n describe_v the_o circle_n abcd_n and_o cross_v it_o with_o he_o diameter_n ab_fw-la and_o cd_o this_o do_v out_o of_o the_o line_n of_o chord_n take_v the_o compliment_n of_o the_o latitude_n of_o your_o place_n which_o we_o here_o suppose_v to_o be_v london_n who_o latitude_n be_v 51_o deg_n 30_o m._n and_o its_o compliment_n 38._o deg_n 30_o m._n which_o set_v from_o b_o to_z g_z from_o g_z to_z n_o and_o from_o d_o to_o m_n then_o lay_v a_o ruler_n from_o a_o to_o g_o and_o it_o will_v cut_v the_o line_n cd_o in_o h_n and_o from_o a_o to_o n_o it_o will_v cut_v c_o d_o in_o o_o and_o from_o a_o to_o m_o it_o will_v cut_v the_o same_o line_n in_o f._n this_o do_v upon_o o_fw-la as_o a_o centre_n place_v one_o foot_n of_o your_o compass_n and_o extend_v the_o other_o foot_n to_o f_o and_o with_o this_o distance_n describe_v a_o arch_n of_o a_o circle_n which_o if_o the_o rest_n of_o your_o work_n be_v true_a will_v fall_v just_a in_o the_o point_v a_o and_o b_o and_o so_o constitute_v the_o arch_a afb_n represent_v the_o equinoctial_a circle_n and_o so_o we_o shall_v hereafter_o call_v it_o have_v draw_v the_o equinoctial_a afb_n divide_v the_o semicircle_n adb_n into_o 12_o equal_a part_n in_o the_o point_n ***_o etc._n etc._n then_o lay_v a_o ruler_n to_o the_o centre_n e_o and_o every_o one_o of_o these_o mark_n ***_o etc._n etc._n it_o will_v divide_v the_o equinoctial_a circle_n into_o 12_o unequal_a part_n in_o the_o point_n ●●●●_o etc._n etc._n again_o lay_v a_o ruler_n to_o h_n and_o every_o of_o these_o unequal_a part_n ●●●●_o etc._n etc._n it_o will_v cut_v the_o semicircle_n adb_n in_o the_o point_v 7_o 8_o 9_o 10_o 11_o 12_o 1_o 2_o 3_o 4_o 5_o and_o 6._o last_o if_o you_o lay_v a_o ruler_n on_o the_o centre_n e_o and_o from_o thence_o draw_v right_a line_n to_o the_o several_a point_n 7_o 8_o 9_o 10_o etc._n etc._n they_o shall_v be_v 12_o of_o the_o true_a houre-line_n belong_v to_o a_o horizontall_a dial_n for_o the_o latitude_n of_o 51_o degree_n 30_o minute_n but_o for_o the_o hour_n before_o 6_o in_o the_o morning_n and_o after_o 6_o at_o night_n do_v thus_o draw_v the_o hour_n live_v of_o 4_o and_o 5_o in_o the_o evening_n quite_o through_o the_o centre_n e_o and_o they_o shall_v be_v the_o hour_n of_o 4_o and_o 5_o in_o the_o morning_n also_o 7_o and_o 8_o in_o the_o morning_n draw_v through_o the_o centre_n shall_v give_v the_o hour_n of_o 7_o and_o 8_o at_o night_n as_o in_o the_o figure_n chap_n ii_o concern_v direct_a south_n dial_n a_o direct_a south_n dial_n be_v no_o other_o than_o a_o horizontall_a dial_n the_o make_v whereof_o be_v before_o describe_v the_o difference_n consist_v only_o in_o the_o number_n of_o the_o hour_n and_o in_o the_o place_n of_o it_o the_o one_o be_v to_o be_v fix_v on_o a_o post_n or_o the_o like_a and_o the_o other_o to_o be_v fix_v to_o a_o wall_n which_o exact_o behold_v the_o south_n i_o say_v here_o be_v no_o other_o difference_n for_o  _fw-fr degree_n  _fw-fr degree_n an_o horizontall_a dial_n for_o the_o latitude_n of_o 10_o will_v be_v a_o direct_a south_n dial_n in_o the_o latitude_n of_o 80_o 20_o 70_o 30_o 60_o 40_o 50_o 50_o 40_o 60_o 30_o 70_o 20_o 80_o 10_o and_o the_o like_a in_o any_o other_o latitude_n as_o 15_o 16_o 33_o etc._n etc._n chap._n iii_o of_o driect_a north_n diall_n a_o direct_a north_n dial_n be_v the_o same_o with_o a_o direct_a south_n dial_n for_o i●_n you_o take_v a_o south_n dial_n and_o turn_v it_o upside_o down_o cause_v the_o sc●le_n or_o cock_n to_o point_v upward_o as_o the_o cock_n of_o the_o south_n do_v down_o ward_n and_o leave_v out_o the_o hour_n near_o the_o meridian_n in_o these_o northern_a latitude_n as_o the_o hour_n of_o 9_o 10_o 11_o and_o 12_o at_o night_n and_o 1_o 2_o and_o 3_o in_o the_o morning_n all_o which_o time_n the_o sun_n be_v under_o the_o horizon_n i_o say_v a_o south_n dial_n so_o dispose_v and_o fix_v against_o a_o direct_a north_n wall_n shall_v give_v you_o the_o true_a hour_n of_o the_o day_n chap._n iu._n how_o to_o draw_v the_o hour_n line_n on_o a_o direct_a east_n or_o west_n plain_a this_o do_v upon_o the_o point_n g_o with_o the_o radius_fw-la of_o your_o chord_n descirbe_v a_o occult_a arch_n of_o a_o circle_n h_n i_o and_o set_v thereon_o 15_o degree_n fr_n on_fw-we h_n to_o i_o then_o from_o g_z through_z i_o draw_v the_o line_n g_o k_n cut_v n_o min_n k_n on_o k_o as_o a_o centre_n with_o the_o radius_fw-la of_o your_o chord_n describe_v the_o quadrant_a k_o s_o t_o which_o divide_v into_o 6_o equal_a part_n in_o the_o point_n ●●●●_o through_o which_o point_n and_o k_o draw_v the_o line_n k●_n k●_n etc._n etc._n cut_v the_o equinoctial_a ebb_n in_o ****_o etc._n etc._n through_o these_o point_n ***_o etc._n etc._n draw_v right_a line_n quiet_a through_o your_o plain_a perpendicular_a to_o the_o equinoctial_a which_o will_v be_v parallel_n to_o your_o line_n of_o vi_o and_o xi_o and_o will_v be_v the_o true_a hour_n of_o vii_o viii_o ix_o and_o x_o than_o the_o like_a distance_n of_o vii_o and_o viii_o set_v above_o vi_o on_o the_o other_o side_n and_o draw_v parallel_n thereto_o shall_v be_v the_o true_a hour_n of_o four_o and_o v._o and_o thus_o have_v you_o all_o the_o hour_n of_o a_o east_n dial_n true_o draw_v which_o be_v from_o four_o in_o the_o morning_n till_o eleven_o at_o noon_n and_o be_v the_o same_o with_o a_o west_n dial_n only_o name_v the_o hour_n contrary_a for_o in_o the_o east_n dial_n 4_o 5_o 6_o 7_o 8_o 9_o 10_o 11_o in_o the_o morning_n be_v in_o the_o west_n dial_n 8_o 7_o 6_o 5_o 4_o 3_o 2_o 1_o h_o in_o the_o evening_n the_o style_n of_o either_o of_o these_o dial_n be_v a_o t_o in_o plate_n of_o brass_n make_v direct_o of_o the_o breadth_n of_o the_o distance_n between_o the_o hour_n of_o vi_o and_o ix_o and_o must_v be_v place_v direct_o perpendicular_a upon_o the_o line_n of_o vi_o and_o so_o be_v your_o dial_n finish_v chap._n v._n of_o upright_a decline_a plain_n before_o we_o come_v to_o draw_v the_o hour_n line_n upon_o a_o decline_a plain_n two_o thing_n be_v first_o to_o be_v discover_v viz._n first_o the_o height_n of_o the_o pole_n above_o the_o plain_a which_o be_v the_o height_n of_o the_o cock_n or_o style_n second_o the_o deflexion_n or_o distance_n of_o the_o substile_a from_o the_o meridian_n or_o line_n of_o twelve_o a_o clock_n 1._o to_o find_v the_o height_n of_o the_o pole_n above_o a_o decline_a plain_n with_o the_o tadius_fw-la of_o your_o line_n of_o chord_n upon_o a_o as_o a_o centre_n describe_v the_o quadrant_n ab_fw-la c_z than_o your_o latitude_n be_v 51_o deg_n 30_o min._n take_v it_o out_o of_o your_o line_n of_o chord_n and_o set_v it_o from_o b_o to_o f_o and_o draw_v the_o line_n ed_z parallel_n to_o ab_fw-la cut_v the_o line_n ac_fw-la in_o d_o then_o with_o the_o distance_n de_fw-fr on_o the_o centre_n a_o describe_v the_o quadrant_n ghr_n then_o suppose_v your_o plain_n to_o decline_v 30_o deg_n set_v 30_o deg_n from_o b_o to_o f_o in_o the_o quadrant_n bec_n and_o draw_v the_o line_n favorina_n cut_v the_o quadrant_n ghr_n in_o h_n through_o which_o point_n h_n draw_v the_o line_n shn_n parallel_v to_o

ca_n and_o cut_v the_o quadrant_n be_v c_o in_o n_o so_o shall_v the_o arch_n cn_fw-la be_v the_o height_n of_o the_o pole_n above_o the_o plain_a and_o in_o this_o example_n contain_v 32_o deg_n 37_o min._n 2._o to_o find_v the_o deflexion_n or_o the_o distance_n of_o the_o substile_a from_o the_o meridian_n out_o of_o this_o figure_n take_v the_o distance_n his_o and_o set_v it_o in_o the_o line_n de_fw-fr from_o d_o to_o k_o through_o which_o point_n k_o draw_v the_o line_n akl_n cut_v the_o quad_n ant_n bc_n in_o l_o so_o shall_v the_o arch_n cl_n be_v the_o distance_n of_o the_o substile_a from_o the_o meridian_n and_o in_o thls_n example_n will_v be_v find_v to_o be_v 21_o degree_n 42_o minute_n chap._n vi_o how_o to_o draw_v the_o houre-line_n upon_o a_o upright_a plain_n decline_v from_o the_o meridian_n towards_o the_o east_n or_o west_n we_o will_v here_o take_v for_o example_n a_o south_n erect_v plain_a decline_v eastward_o 30_o deg_n have_v by_o the_o five_o chapter_n of_o this_o book_n find_v the_o defl●xion_n of_o such_o a_o plain_a to_o be_v 21_o deg_n 42_o min._n and_o the_o height_n of_o ●he_n ●●ile_n by_o the_o same_o chapter_n to_o be_v 32_o deg_n 37_o min._n we_o may_v proceed_v to_o draw_v the_o dial_n in_o manner_n follow_v with_o the_o radius_fw-la of_o your_o line_n of_o chord_n on_o the_o centre_n c_o describe_v the_o circle_n xnsw_n and_o in_o it_o draw_v sn_a through_o the_o centre_n c_o for_o the_o meridian_n or_o line_n of_o 12._o then_o the_o deflexion_n be_v find_v to_o be_v 21_o deg_n 42_o min._n set_v that_o from_o n_o to_z e_z and_o draw_v the_o line_n ●c_z through_o the_o centre_n to_o g_o this_o line_n represent_v the_o substilar_a line_n of_o your_o dial_n upon_o which_o line_n the_o style_n or_o co●k_n must_v stand_v also_o out_o from_o your_o line_n of_o chord_n take_v 32_o deg_n 37_o min._n the_o height_n of_o the_o s●ile_n and_o set_v that_o distance_n from_o e_o to_o h_n and_o draw_v the_o line_n ch_z for_o the_o style_n 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will_v cut_v the_o substilar_a in_o o._n now_o if_o you_o set_v one_o foot_n of_o your_o compass_n in_o g_o and_o extend_v the_o other_o to_o x_o or_o w_n you_o may_v describe_v the_o equinoctial_a circle_n xow_n which_o if_o you_o have_v not_o err_v in_o your_o former_a work_n will_v pass_v exact_o through_o the_o point_n o_o in_o the_o substilar_a line_n before_o find_v in_o the_o next_o place_n if_o you_o lay_v a_o ruler_n from_o f_o to_o n_o it_o will_v cut_v the_o equinoctial_a circle_n in_o p_o and_o a_o ruler_n lay_v from_o c_o to_o p_o will_v cut_v the_o dial_n circle_n in_o v._n these_o thing_n be_v perform_v the_o next_o thing_n be_v to_o draw_v the_o hour_n line_n which_o will_v be_v easy_o effect_v if_o you_o 〈◊〉_d the_o former_a direction_n first_o from_o the_o point_n five_o last_o find_v begin_v to_o divide_v your_o hour_n circle_n into_o 24_o equal_a part_n or_o only_o one_o half_a of_o it_o into_o 12_o part_n which_o you_o may_v do_v by_o take_v 15_o deg_n out_o of_o your_o line_n of_o chord_n and_o set_v that_o distance_n on_o both_o side_n of_o five_o at_o the_o mark_n ⚹_o ⚹_o ⚹_o etc._n etc._n so_o many_o time_n as_o the_o plain_n be_v capable_a of_o hour_n this_o do_v if_o you_o lay_v a_o ruler_n on_o the_o centre_n c_o and_o every_o of_o these_o point_n ****_o etc._n etc._n you_o shall_v divide_v the_o equinoctial_a circle_n into_o 12_o unequal_a part_n in_o the_o point_n ●●●●_o etc._n etc._n now_o a_o ruler_n lay_v from_o f_o to_o every_o of_o these_o unequal_a point_n ●●●●_o etc._n etc._n will_v divide_v the_o hour_n circle_n into_o 12_o other_o unequal_a part_n mark_v with_o 4._o 5._o 6._o 7._o 8._o 9_o 10._o 11._o 12._o 1._o on_o the_o one_o side_n of_o five_o and_o with_o 2._o 3_o ●n_n the_o other_o side_n of_o v._n last_o a_o ruler_n lay_v from_o c_o to_o the_o several_a point_n 4._o 5._o 6._o 7._o 8._o 9_o 10._o 11._o 12._o 1._o 2._o 3._o and_o line_n draw_v by_o the_o side_n thereof_o they_o shall_v be_v the_o true_a hour_n line_n belong_v to_o such_o a_o decline_a plain_n of_o 30_o deg_n in_o the_o latitude_n of_o 51_o deg_n 30_o min._n but_o if_o you_o desire_v more_o hour_n than_o 12_o the_o equinoctial_a may_v be_v divide_v into_o more_o unequal_a part_n be_v continue_v beyond_o x_o and_o w_n and_o if_o you_o will_v quite_o round_o the_o whole_a circle_n but_o that_o be_v needless_a without_o you_o will_v make_v 4_o diall_n in_o the_o make_v of_o one_o as_o you_o may_v easy_o do_v for_o the_o hour_n that_o be_v on_o the_o west_n side_n of_o the_o meridian_n of_o a_o south_n east_n dial_n be_v draw_v through_o the_o centre_n will_v make_v a_o north_n west_n dial_n of_o the_o same_o declination_n and_o the_o hour_n on_o the_o east_n side_n of_o the_o meridian_n of_o a_o south_n west_n dial_n be_v draw_v through_o the_o centre_n will_v produce_v a_o north_n east_n dial_n of_o the_o same_o declination_n and_o again_o the_o real_a hour_n line_n of_o a_o south_n east_n dial_n be_v draw_v on_o the_o other_o side_n of_o the_o paper_n and_o the_o hour_n name_v by_o their_o compliment_n to_o 12_o that_o be_v 10_o for_o 2_o 9_o for_o 3_o 8_o for_o 4_o etc._n etc._n will_v make_v a_o south_n west_n dial_n of_o the_o same_o declination_n chap._n vii_o how_o to_o place_v any_o upright_a dial_n true_o all_o upright_a diall_n in_o what_o oblique_a latitude_n soever_o have_v the_o meridian_n perpendicular_a to_o the_o horizon_n wherefore_o to_o set_v your_o dial_n exact_a hang_v a_o line_n with_o a_o plummet_n at_o the_o end_n thereof_o and_o with_o a_o nail_n fix_v in_o the_o line_n of_o 12_o towards_o the_o top_n thereof_o to_o hang_v the_o plummet_n upon_o apply_v the_o dial_n to_o the_o place_n where_o it_o be_v to_o be_v fix_v so_o that_o the_o line_n and_o plummet_n may_v hang_v just_a down_o upon_o the_o line_n of_o 12_o neither_o incline_n on_o one_o side_n or_o the_o other_o the_o dial_n thus_o fix_v if_o the_o declination_n be_v true_o take_v and_o the_o dial_n right_o make_v by_o the_o former_a direction_n shall_v at_o all_o time_n the_o sun_n shine_v upon_o it_o give_v you_o the_o true_a hour_n of_o the_o day_n chap._n viii_o how_o to_o insert_v the_o halue_fw-mi and_o quarter_n of_o hour_n in_o all_o diall_n the_o half_n and_o quarter_n of_o hour_n be_v draw_v in_o all_o plain_n by_o the_o same_o rule_n and_o the_o like_a reason_n that_o the_o hour_n be_v insert_v therefore_o take_v notice_n that_o if_o you_o will_v insert_v the_o half_a hour_n into_o any_o dial_n you_o must_v divide_v your_o equinoctial_a circle_n into_o 24_o equal_a part_n instead_o of_o 12_o and_o if_o you_o will_v insert_v the_o quarter_n than_o you_o must_v divide_v it_o into_o 48_o part_n and_o then_o proceed_v in_o all_o respect_n as_o you_o do_v for_o the_o whole_a hour_n chap._n ix_o how_o to_o find_v the_o declinatioon_n of_o any_o upright_a wall_n the_o declination_n of_o a_o plain_a be_v a_o arch_n of_o the_o horizon_n comprehend_v between_o the_o pole_n of_o the_o plain_n horizontall_a line_n and_o the_o meridian_n of_o the_o place_n to_o find_v this_o declination_n two_o observation_n must_v be_v make_v the_o sun_n shine_v and_o both_o at_o one_o instant_a of_o time_n as_o near_o as_o may_v be_v the_o first_o be_v the_o horizontall_a distance_n of_o the_o sun_n from_o the_o pole_n of_o the_o plain_a the_o second_o be_v the_o sun_n altitude_n first_o to_o find_v the_o horizontall_a distance_n apply_v the_o side_n of_o a_o quadrant_n to_o your_o plain_n hold_v it_o as_o near_o as_o may_v be_v horizontall_a that_o be_v to_o say_v level_v then_o hold_v