Selected quad for the lemma: end_n

Word A	Word B	Word C	Word D	Occurrence	Frequency Band	MI	MI Band	Prominent
end_n	north_n	side_n	south_n	2,400	5	9.1749	5	true

Text snippets containing the quad

ID	Title	Author	Corrected Date of Publication (TCP Date of Publication)	STC	Words	Pages
A40031	Elliptical or azimuthal horologiography comprehending severall wayes of describing dials upon all kindes of superficies, either plain or curved, and unto upright stiles in whatsoever position they shall be placed / invented and demonstrated by Samuel Foster ...	Foster, Samuel, d. 1652.; Twysden, John, 1607-1688.; Wingate, Edmund, 1596-1656.	1654 (1654)	Wing F1632; ESTC R7034	96,404	198

another_o slide_a plate_n of_o the_o same_o breadth_n that_o the_o former_a be_v name_o m_n o_o here_o equal_a to_o m_o o_fw-fr in_o the_o former_a and_o m_o n_o must_v in_o both_o be_v just_o equal_a that_o it_o may_v both_o slip_v in_o the_o former_a cavity_n so_o as_o just_a to_o fill_v it_o and_o that_o the_o same_o limb_n centre_n and_o thread_n may_v in_o both_o agree_v a_o lesser_a ellipsis_n i_o say_v must_v be_v describe_v which_o though_o it_o be_v less_o yet_o it_o must_v be_v like_a and_o proportional_a to_o the_o former_a therefore_o assume_v any_o length_n as_o m_n p_o for_o the_o long_a radius_fw-la you_o must_v to_o that_o radius_fw-la make_v m_o r_o and_o m_o s_o equal_o to_o the_o sine_fw-la of_o your_o latitude_n and_o so_o describe_v and_o divide_v it_o as_o former_o be_v order_v then_o again_o to_o this_o new_a ellipsis_n there_o must_v a_o new_a scale_n of_o tangent_n be_v make_v who_o length_n must_v be_v limit_v as_o the_o former_a be_v in_o this_o manner_n to_o m_n p_o as_o radius_fw-la find_v the_o cousin_a of_o your_o latitude_n and_o make_v that_o cousin_a a_o radius_fw-la or_o tangent_fw-la of_o 45_o gr_n and_o according_a thereunto_o continue_v the_o scale_n of_o tangent_n as_o far_o as_o it_o will_v go_v it_o must_v begin_v upon_o the_o same_o line_n that_o the_o other_o scale_n of_o tangent_n begin_v and_o must_v go_v the_o same_o way_n with_o it_o and_o in_o this_o new_a way_n of_o order_v the_o scale_n and_o the_o ellipse_n it_o must_v be_v consider_v what_o the_o other_o part_n of_o the_o instrument_n do_v signify_v the_o end_n of_o the_o low_a plate_n upon_o which_o the_o scale_n begin_v must_v be_v account_v for_o the_o north_n the_o other_o end_n c_o d_o be_v to_o be_v take_v for_o south_n the_o side_n line_n be_v the_o meridian_n the_o degree_n of_o the_o limb_n be_v to_o be_v use_v as_o the_o degree_n of_o the_o equinoctial_a the_o thread_n apply_v to_o those_o degree_n be_v the_o meridian_n come_v from_o the_o centre_n which_o be_v the_o north_n pole_n the_o tangent_n be_v the_o degree_n of_o altitude_n the_o ellipsis_n note_v out_o that_o almicantar_n which_o the_o thread_n index_n stand_v unto_o upon_o the_o tangent_fw-la scale_n and_o further_o it_o be_v to_o be_v here_o note_v that_o if_o the_o meridian_n or_o thread_n come_v from_o the_o centre_n be_v right_o divide_v those_o division_n or_o part_n of_o it_o shall_v signify_v the_o degree_n of_o declination_n from_o the_o equinoctial_a but_o the_o inconvenience_n of_o it_o be_v that_o because_o one_o ellipsis_n be_v to_o represent_v every_o almicantar_n therefore_o the_o radius_fw-la can_v possible_o be_v at_o all_o time_n the_o same_o in_o length_n but_o must_v vary_v according_a to_o the_o remove_n or_o several_a position_n of_o the_o say_a ellipsis_n that_o be_v when_o the_o ellipsis_n signify_v the_o horizon_n or_o stand_v at_o the_o begin_n of_o the_o scale_n without_o any_o altitude_n at_o all_o than_o the_o radius_fw-la m_o o_fw-fr in_o the_o first_o move_v plate_n or_o m_o p_o in_o the_o second_o move_v plate_n be_v the_o scale_n of_o declination_n but_o at_o other_o time_n when_o the_o ellipsis_n signify_v any_o almicantar_n then_o must_v the_o secant_fw-la of_o that_o almicantar_n of_o altitude_n be_v take_v as_o the_o radius_fw-la for_o that_o particular_a work_n but_o always_o the_o radius_fw-la of_o what_o length_n soever_o it_o be_v must_v be_v divide_v as_o a_o whole_a line_n of_o sines_n the_o great_a part_n beginning_n towards_o the_o centre_n the_o least_o part_n end_v at_o the_o remote_a end_n from_o the_o centre_n and_o yet_o then_o again_o the_o numeration_n of_o the_o part_n or_o declination_n of_o it_o must_v begin_v at_o the_o remote_a end_n and_o must_v end_v in_o the_o centre_n at_o the_o pole_n it_o may_v be_v apply_v to_o use_v in_o the_o motion_n of_o the_o star_n but_o that_o will_v be_v troublesome_a therefore_o it_o shall_v suffice_v to_o make_v it_o useful_a only_o for_o the_o sun_n the_o best_a way_n that_o for_o the_o present_a i_o know_v whereby_o to_o divide_v this_o radius_fw-la thus_o of_o several_a length_n be_v this_o divide_v the_o length_n from_o the_o centre_n t_o to_o c_o into_o 90_o sin_n the_o great_a part_n beginning_n at_o the_o centre_n but_o number_v the_o contrary_a way_n this_o line_n may_v be_v draw_v from_o the_o centre_n t_o into_o some_o part_n of_o the_o limb_n where_o it_o may_v have_v room_n to_o receive_v division_n then_o with_o your_o compass_n take_v the_o radius_fw-la t_o v_o equal_a to_o m_n o_o and_o from_o the_o end_n of_o the_o former_a scale_n open_v the_o thread_n to_o the_o least_o distance_n and_o where_o the_o thread_n stay_v there_o make_v a_o mark_n upon_o the_o limb_n v_o d_o for_o there_o be_v a_o new_a scale_n to_o begin_v for_o the_o secant_v that_o be_v mention_v before_o then_o lay_v the_o thread_n from_o t_o to_o 80_o in_o the_o opposite_a limb_n and_o move_v the_o ellipsis_n till_o the_o point_n o_o fall_v just_a under_o the_o thread_n and_o take_v t_o o_fw-fr in_o your_o compass_n and_o put_v in_o that_o distance_n as_o before_o so_o shall_v you_o put_v in_o 10_o gr_n into_o this_o new_a scale_n in_o like_a manner_n lay_v the_o thread_n to_o 70_o 60_o etc._n etc._n and_o bring_v the_o ellipsis_n till_o the_o point_n o_o lie_v under_o it_o so_o shall_v t_n o_o in_o these_o several_a position_n give_v the_o length_n to_o be_v inscribe_v in_o this_o new_a scale_n for_o 20_o gr_n and_o 30_o gr_n etc._n etc._n all_o the_o rest_n must_v be_v do_v in_o like_a manner_n till_o you_o have_v put_v in_o as_o many_o as_o will_v come_v within_o the_o reach_n of_o the_o limb_n which_o will_v be_v upon_o 60_o gr_n or_o thereabouts_o the_o like_a shall_v also_o be_v do_v for_o the_o lesser_a ellipsis_n work_v in_o the_o same_o manner_n by_o the_o thread_n and_o the_o point_n p._n these_o be_v call_v the_o new_a inscribe_v scale_n the_o former_a line_n of_o sines_n serve_v to_o they_o both_o indifferent_o now_o when_o thing_n be_v thus_o fit_v the_o use_n of_o they_o will_v be_v such_o as_o in_o particular_a astrolabe_fw-la be_v vulgar_o know_v some_o of_o the_o uses_n be_v here_o mention_v 1._o have_v the_o sun_n declination_n and_o altitude_n to_o find_v the_o hour_n and_o azimuth_n first_o for_o north_n declination_n set_a the_o ellipsis_n to_o the_o altitude_n count_v in_o the_o tangent_fw-la scale_n then_o count_v the_o same_o altitude_n in_o the_o new_a inscribe_v scale_n of_o secant_v and_o thereto_o lie_v the_o thread_n afterward_o take_v the_o least_o distance_n from_o the_o sun_n declination_n count_v in_o the_o forementioned_a inscribe_v scale_n of_o sines_n to_o the_o thread_n set_a one_o foot_n of_o that_o distance_n in_o the_o centre_n and_o extend_v the_o other_o till_o it_o across_o the_o ellipsis_n and_o where_o it_o cross_v thither_o apply_v the_o thread_n which_o in_o the_o limb_n will_v show_v the_o hour_n and_o scruple_n in_o degree_n require_v the_o same_o point_n of_o the_o compass_n do_v also_o immediate_o show_v upon_o the_o ellipsis_n the_o azimuth_n seek_v for_o if_o the_o compass_n do_v cross_v the_o ellipsis_n twice_o as_o sometime_o it_o will_v take_v that_o cross_v that_o be_v further_a from_o the_o meridian_n second_o for_o south_n declination_n the_o work_n be_v in_o a_o manner_n the_o same_o only_o you_o must_v note_v that_o the_o thread_n will_v cross_v the_o ellipsis_n twice_o and_o you_o be_v in_o this_o case_n to_o take_v that_o cross_v which_o be_v near_a to_o the_o meridian_n by_o suppose_v the_o altitude_n to_o be_v 00_o that_o be_v by_o lay_v the_o ellipsis_n upon_o the_o line_n t_o v_n and_o use_v the_o declination_n as_o before_o you_o may_v find_v both_o the_o amplitude_n and_o ascensionall_a difference_n as_o before_o and_o what_o else_o do_v thereon_o depend_v but_o because_o these_o thing_n be_v do_v near_o the_o horizon_n will_v not_o prove_v good_a especial_o when_o the_o declination_n be_v little_a from_o the_o equinoctial_a and_o because_o the_o work_n at_o the_o best_a be_v but_o troublesome_a i_o shall_v here_o break_v off_o suppose_v that_o i_o have_v already_o write_v too_o much_o a_o demonstration_n of_o the_o ellipticall_a dial_n upon_o a_o horizontall_a plain_n show_v the_o reason_n why_o the_o same_o dial_n by_o a_o upright_a index_n shall_v show_v the_o true_a hour_n the_o reason_n be_v principal_o deduce_v from_o the_o sphere_n itself_o and_o second_o from_o the_o orthographical_a projection_n of_o the_o sphere_n upon_o the_o plain_a of_o the_o horizon_n which_o as_o it_o do_v represent_v the_o sphere_n itself_o so_o it_o do_v perform_v the_o same_o conclusion_n with_o the_o like_a certainty_n that_o the_o sphere_n do_v and_o that_o upon_o this_o general_a ground_n that_o

so_o many_o 4_o sin_n the_o co-sine_n of_o these_o will_v limit_v out_o the_o point_n upon_o the_o hour_n of_o the_o horizontall_a dial_n former_o draw_v through_o which_o the_o ellipsis_n upon_o the_o horizontall_a plain_n make_v for_o a_o upright_a index_n be_v to_o pass_v as_o be_v show_v before_o in_o the_o 28_o 29_o 30_o and_o 31_o page_n which_o point_v in_o the_o figure_n of_o the_o next_o page_n may_v be_v represent_v by_o 8_o 9_o 10_o 11_o 12_o 1_o 2_o 3_o etc._n etc._n 2._o as_o the_o radius_fw-la to_o the_o tangent_fw-la of_o the_o reclination_n of_o the_o index_n so_o be_v the_o 4_o sin_n before_o find_v to_o so_o many_o 7_o term_n 3._o describe_v the_o regular_a horizontall_a ellipsis_n as_o you_o see_v p_o o_fw-fr qui_fw-fr which_o you_o must_v know_v to_o be_v for_o the_o latitude_n of_o 51_o gr_n 30_o min._n and_o that_o p_o q_o be_v the_o point_n of_o the_o two_o six_o and_o o_o k_o the_o point_n of_o the_o two_o twelves_o viz._n at_o noon_n and_o midnight_n and_o also_o that_o all_o the_o hour_n be_v regular_o set_v down_o to_o o_o p_o q_o k_n etc._n etc._n suppose_v here_o a_o index_n to_o  _fw-fr gr_fw-fr m._n recline_v northwards_o 45_o 00_o differ_v in_o longit._n s_o e_o w_o 75_o 00_o consequently_n it_o must_v  _fw-fr decline_v north_n east_n west_n 60_o 05_o have_v north_n latitude_n 50_o 37_o 4._o from_o each_o point_n there_o set_v down_o draw_v line_n parallel_v to_o the_o subindicall_a line_n r_o s_o as_o o_o a_o 8_o c_z 9_o b_o etc._n etc._n the_o angle_n o_o r_o s_o must_v be_v 60_o gr_n 5_o min._n 6._o through_o these_o new_a point_n b_o f_o d_o a_o e_o g_o etc._n etc._n you_o be_v to_o draw_v a_o new_a ellipsis_n which_o will_v be_v distort_v from_o the_o former_a ellipsis_n first_o draw_v thus_o the_o dial_n itself_o for_o the_o hour_n point_n be_v limit_v you_o may_v add_v half_n and_o quarter_n for_o the_o zodiac_n in_o this_o example_n remember_v that_o the_o index_n decline_v north_n east_n west_n 60_o gr_n 5_o min._n recline_v 45_o gr_n differ_v in_o longitude_n south_n east_n west_n 75_o gr_n have_v latitude_n 50_o gr_n 37_o min._n 1._o because_o the_o difference_n of_o longitude_n be_v 75_o gr_n from_o the_o south_n therefore_o our_o two_o hour_n of_o 7_o in_o the_o morning_n and_o 5_o at_o evening_n be_v the_o proper_a meridian_n upon_o which_o the_o index_n must_v slide_v 2._o for_o that_o cause_n you_o must_v consider_v how_o much_o of_o those_o two_o meridian_n be_v intercept_v between_o the_o equinoctial_a and_o our_o horizon_n you_o may_v find_v it_o by_o this_o rule_n as_o the_o radius_fw-la be_v to_o the_o sine_fw-la of_o 15_o gr_n the_o conpl_n of_o 75_o so_o be_v the_o tangent_fw-la of_o 38_o gr_n 30_o min._n to_o the_o tangent_fw-la of_o 11_o gr_n 38_o min._n which_o be_v the_o ark_n require_v 3._o because_o the_o latitude_n of_o the_o index_n be_v 50_o gr_n 37_o min._n north_n the_o compliment_n of_o it_o must_v be_v 39_o gr_n 23_o min._n and_o so_o much_o under_o the_o equinoctial_a point_n of_o 7_o and_o 5_o and_o upon_o the_o hour_n circle_n of_o 7_o and_o 5_o which_o be_v the_o proper_a meridian_n to_o the_o two_o index_n do_v the_o proper_a horizon_n of_o each_o of_o those_o index_n cut_v the_o say_a hour_n of_o 7_o and_o 5_o upon_o the_o southeast_n and_o south-west_n and_o so_o much_o do_v they_o cut_v the_o same_o meridian_n above_o the_o equinoctial_a upon_o the_o south-west_n and_o southeast_n so_o that_o upon_o the_o southerly_a coast_n that_o portion_n of_o these_o meridian_n which_o be_v comprehend_v between_o the_o equinoctial_a and_o our_o horizon_n namely_o 11_o gr_n 38_o min._n must_v be_v take_v from_o 39_o gr_n 23_o min._n and_o the_o remainder_n will_v be_v 27_o gr_n 45_o min._n which_o be_v the_o ark_n comprehend_v between_o the_o proper_a horizon_n of_o the_o index_n and_o our_o own_o horizon_n which_o upon_o the_o south_n part_n in_o this_o particular_a example_n be_v below_o our_o horizon_n on_o the_o north_n part_v above_o 4._o first_o therefore_o the_o limitation_n of_o the_o semi-zodiac_n length_n must_v be_v to_o that_o latitude_n of_o the_o index_n or_o proper_a horizon_n 50_o gr_n 37_o min._n and_o then_o second_o the_o say_a zodiac_n first_o find_v and_o limit_v must_v be_v augment_v in_o this_o example_n in_o proportion_n of_o the_o radius_fw-la to_o the_o secant_fw-la of_o 27_o gr_n 45_o min._n in_o this_o manner_n by_o the_o second_o rule_v give_v at_o the_o begin_n of_o this_o book_n pag._n 11._o to_o the_o radius_fw-la p_o r_o find_v the_o cofine_n of_o the_o latitude_n of_o the_o index_n namely_o the_o sine_fw-la of_o 39_o gr_n 23_o min._n which_o suppose_v to_o be_v n_o t._n to_o this_o length_n n_o t_o as_o a_o radius_fw-la find_v out_o the_o secant_fw-la of_o the_o forementioned_a ark_n 27_o gr_n 45_o min._n which_o suppose_v to_o be_v n_o v._n this_o length_n n_o v_n shall_v give_v the_o radius_fw-la or_o tangent_fw-la of_o 45_o gr_n which_o be_v the_o tangent_fw-la or_o decimall_n scale_n out_o of_o which_o either_o of_o they_o you_o be_v to_o make_v your_o zodiac_n by_o the_o number_n of_o those_o table_n in_o the_o 6_o and_o 7_o page_n to_o this_o radius_fw-la or_o decimall_n scale_n or_o tangent_fw-la of_o 45_o gr_n n_o w_n be_v the_o tangent_fw-la of_o 23_o gr_n and_o a_o half_a wherefore_o the_o semizodiac_n r_o l_o or_o r_o m_o be_v to_o be_v make_v equal_a in_o length_n to_o n_o w._n thus_o the_o zodiac_n length_n be_v limit_v for_o the_o position_n of_o the_o zodiac_n it_o be_v before_o say_v that_o it_o must_v lie_v in_o the_o line_n of_o 7_o in_o the_o morning_n or_o 5_o in_o the_o afternoon_n so_o in_o this_o last_o figure_n you_o see_v it_o point_n to_o z_o which_o be_v 7_o in_o the_o morning_n and_o consequent_o also_o to_o x_o which_o be_v 7_o in_o the_o evening_n in_o the_o distort_a ellipsis_n because_o this_o be_v that_o dial_n who_o index_n look_v north-east_n you_o see_v it_o do_v so_o likewise_o in_o the_o first_o figure_n pag._n 189_o as_o in_o the_o second_o figure_n there_o it_o lie_v to_o 5_o in_o the_o evening_n and_o consequent_o also_o to_o 5_o in_o the_o morning_n observe_v in_o the_o last_o figure_n which_o be_v as_o true_a and_o just_a in_o the_o two_o other_o pag._n 189._o that_o the_o angle_n p_o r_o z_o and_o so_o q_o r_o x_o be_v equal_a to_o the_o angle_n make_v upon_o our_o common_a horizontall_a dial_n between_o 6_o and_o 7_o a_o clock_n namely_o 18_o gr_n 54_o min._n and_o consequent_o that_o 1_o r_z 1_o a_o line_n draw_v from_o 1_o to_o 1_o in_o the_o primary_n ellipsis_n be_v perpendicular_a to_o the_o zodiac_n l_o m_o yet_o p_o r_o c_o be_v not_o equal_a to_o the_o angle_n thereon_o between_o 6_o and_o 8_o a_o clock_n nor_o be_v it_o so_o in_o any_o other_o of_o the_o hour_n observe_v again_o that_o if_o a_o line_n be_v draw_v parallel_n to_o o_o k._n through_o a_o the_o point_n of_o 12_o in_o the_o distort_a ellipsis_n till_o it_o meet_v with_o the_o zodiac_n extend_v at_o y_o observe_v i_o say_v that_o if_o r_o m_o be_v take_v as_o a_o tangent_fw-la of_o 23½_n gr_n as_o it_o be_v take_v in_o this_o work_n then_o will_v r_o y_fw-fr be_v the_o tangent_fw-la of_o the_o compliment_n of_o your_o latitude_n namely_o 38_o gr_n 30_o min._n and_o this_o must_v be_v so_o because_o if_o the_o sun_n shall_v decline_v 38_o gr_n 30_o min._n southward_o than_o the_o sun_n must_v only_o peep_v up_o upon_o the_o horizon_n at_o 12_o and_o consequent_o the_o shadow_n of_o the_o index_n namely_o the_o point_n of_o it_o that_o intersect_v with_o your_o horizon_n for_o the_o sun_n have_v no_o altitude_n at_o that_o place_n and_o time_n must_v run_v full_a from_o south_n to_o north_n to_o show_v the_o point_n of_o 12_o at_o a._n other_o observation_n may_v be_v make_v but_o i_o go_v no_o further_o the_o reason_n of_o the_o precedent_a work_n will_v be_v demonstrate_v out_o of_o the_o former_a thing_n deliver_v in_o this_o book_n especial_o out_o of_o this_o last_o treatise_n which_o begin_v pag._n 171_o and_o end_n pag._n 186._o and_o therefore_o i_o whole_o omit_v to_o add_v any_o thing_n more_o to_o this_o particular_a subject_n they_o that_o understand_v the_o thing_n before_o will_v not_o be_v to_o seek_v in_o the_o necessary_a demonstration_n of_o these_o particular_n a_o note_n concern_v the_o frame_n of_o dial_n to_o find_v the_o azimuth_n as_o the_o axis_n of_o the_o world_n be_v to_o the_o equinoctial_a circle_n so_o be_v the_o zenith_n line_n to_o the_o horizon_n of_o any_o place_n whence_o it_o will_v follow_v that_o whatsoever_o be_v in_o this_o book_n declare_v concern_v the_o projection_n of_o the_o hour_n