Selected quad for the lemma: book_n

Word A	Word B	Word C	Word D	Occurrence	Frequency Band	MI	MI Band	Prominent
book_n	line_n	page_n	read_v	9,933	5	9.6901	5	true

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 first_o therefore_o i_o intend_v to_o relate_v unto_o you_o what_o a_o point_n or_o prick_n be_v and_o afterward_o a_o line_n both_o right_a and_o crooked_a and_o such_o sort_n thereof_o as_o be_v appertinent_a unto_o the_o operation_n and_o use_n of_o this_o scale_n punctum_fw-la or_o a_o point_n be_v the_o begin_n of_o thing_n or_o a_o prick_n suppose_v indivisible_a void_a of_o length_n breadth_n and_o depth_n as_o in_o the_o figure_n follow_v be_v note_v by_o the_o point_n or_o prick_v a._n n1_fw-la or_o a_o line_n be_v a_o suppose_a length_n or_o a_o thing_n extend_v itself_o in_o length_n not_o have_v breadth_n nor_o thickness_n as_o be_v set_v forth_o unto_o you_o by_o the_o line_n bad_a parallela_fw-la or_o a_o parallel_n line_n be_v a_o line_n draw_v by_o the_o side_n of_o another_o line_n in_o such_o sort_n that_o they_o may_v be_v equidistant_a in_o all_o place_n and_o of_o such_o parallel_n two_o only_o belong_v unto_o this_o work_n of_o the_o plain_a scale_n that_o be_v 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unto_o the_o rest_n perpendiculum_fw-la or_o a_o perpendicular_a be_v a_o line_n raise_v from_o or_o let_v fall_v upon_o another_o line_n make_v equal_a angle_n on_o both_o side_n as_o you_o may_v see_v declare_v in_o the_o figure_n where_o in_o the_o line_n ac_fw-la be_v perpendicular_a unto_o the_o line_n bad_a make_v equal_a ●ngles_n in_o the_o point_n a._n diameter_n circuli_fw-la or_o the_o diameter_n of_o a_o circle_n be_v a_o right_a line_n draw_v through_o the_o centre_n of_o any_o circle_n in_o such_o sort_n that_o it_o may_v divide_v the_o circle_n into_o two_o equal_a part_n as_o you_o may_v see_v the_o line_n bad_a be_v the_o diameter_n of_o the_o circle_n bcde_v because_o it_o pass_v through_o the_o centre_n a_o and_o the_o two_o end_n thereof_o do_v divide_v the_o circle_n into_o two_o equal_a part_n in_o the_o two_o extreme_n b_o and_o d_o make_v the_o semicircle_n bcd_v equal_a unto_o the_o semicircle_n deb_n semidiameter_n circuli_fw-la or_o the_o semidiameter_n of_o 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

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 of_o your_o dial_n so_o shall_v the_o triangle_n each_o be_v the_o true_a pattern_n for_o the_o cock_n of_o your_o dial_n the_o substilar_a line_n eglantine_n be_v 〈◊〉_d ●●aw_v the_o line_n xw_o through_o the_o centre_n c_o and_o perpendicular_a to_o eglantine_n this_o do_v take_v the_o distance_n eh_n which_o be_v equal_a to_o the_o style_n height_n and_o set_v that_o distance_n from_o a_o to_o b_o and_o from_o w_o to_o d._n likewise_o take_v the_o distance_n from_o w_o to_z b_o and_o set_v it_o from_o b_o to_o i._o these_o three_o point_n i_o b_o and_o d_o be_v find_v in_o the_o circumference_n of_o the_o circle_n xnsw_n lay_v a_o ruler_n from_o x_o to_o i_o and_o it_o will_v cut_v the_o substilar_a line_n aec_fw-la be_v extend_v in_o the_o point_n g_o which_o be_v the_o centre_n upon_o which_o the_o equinoctial_a circle_n must_v be_v describe_v again_o a_o ruler_n lay_v from_o x_o to_o b_o will_v cut_v the_o substilar_a line_n in_o f_o and_o a_o ruler_n lay_v from_o x_o to_o d_o 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