Selected quad for the lemma: end_n

Word A	Word B	Word C	Word D	Occurrence	Frequency Band	MI	MI Band	Prominent
end_n	line_n	point_n	require_v	1,303	5	9.1027	5	false

Text snippets containing the quad

ID	Title	Author	Corrected Date of Publication (TCP Date of Publication)	STC	Words	Pages
A48262	Mathematicall recreations. Or, A collection of many problemes, extracted out of the ancient and modern philosophers as secrets and experiments in arithmetick, geometry, cosmographie, horologiographie, astronomie, navigation, musick, opticks, architecture, statick, mechanicks, chemistry, water-works, fire-works, &c. Not vulgarly manifest till now. Written first in Greeke and Latin, lately compi'ld in French, by Henry Van Etten, and now in English, with the examinations and augmentations of divers modern mathematicians whereunto is added the description and use of the generall horologicall ring: and the double horizontall diall. Invented and written by William Oughtred.; Récréation mathématique. English.	Oughtred, William, 1575-1660. aut	1653 (1653)	Wing L1790; ESTC R217635	140,825	339

&_o a_o line_n strike_v perpendicular_a upon_o it_o apply_v the_o straight_a edge_n unto_o the_o wall_n at_o what_o time_n the_o sun_n shine_v upon_o it_o hold_v the_o board_n parallel_n to_o the_o horizon_n set_v the_o dyal_a thereon_o and_o move_v it_o gentle_o every_o way_n until_o the_o same_o hour_n and_o minute_n be_v show_v in_o both_o dial_n and_o so_o let_v it_o stand_v then_o if_o the_o dyal_a have_v one_o of_o the_o side_n parallel_v to_o the_o meridian_n strike_v a_o line_n along_o that_o side_n upon_o the_o board_n cross_v the_o perpendicular_a or_o else_o with_o a_o bodkin_n make_v a_o point_n upon_o the_o board_n at_o each_o end_n of_o the_o meridian_n and_o take_v away_o the_o instrument_n from_o the_o board_n and_o the_o board_n from_o the_o wall_n lay_v a_o ruler_n to_o those_o two_o point_n and_o draw_v a_o line_n cross_v the_o perpendicular_a for_o the_o angle_n which_o that_o line_n make_v with_o the_o perpendicular_a be_v the_o angle_n of_o the_o decli●nation_n of_o the_o wall_n and_o if_o it_o be_v a_o right_a angle_n the_o wall_n be_v exact_o east_n or_o west_n but_o if_o that_o line_n be_v parallel_n to_o the_o perpendicular_a the_o wall_n be_v direct_a north_n or_o south_n without_o any_o declination_n at_o all_o you_o may_v also_o find_v out_o the_o declination_n of_o a_o wall_n if_o the_o dial_n be_v fix_v on_o a_o post_n not_o very_o far_o from_o that_o wall_n in_o this_o manner_n your_o board_n be_v apply_v to_o the_o wall_n as_o be_v show_v hang_v up_o a_o thread_n with_o a_o plummet_n so_o that_o the_o shadow_n of_o the_o thread_n may_v upon_o the_o board_n across_o the_o perpendicular_a line_n make_v two_o prick_n in_o the_o shadow_n and_o run_v instant_o to_o the_o dyal_a and_o look_v the_o horizontal_a distance_n of_o the_o sun_n azumith_n or_o upright_a shadow_n from_o the_o meridian_n then_o through_o the_o two_o prick_n draw_v a_o line_n cross_v the_o perpendicular_a and_o upon_o the_o point_n of_o the_o intersection_n make_v 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teach_v for_o then_o the_o dial_n stand_v in_o its_o true_a situation_n wherefore_o let_v it_o be_v nail_v down_o in_o that_o very_a place_n xiiii_o use_n to_o find_v the_o height_n of_o the_o sun_n at_o high_a noon_n everyday_n seek_v out_o the_o diurnal_a arch_n or_o parallel_n of_o the_o sun_n course_n for_o that_o day_n by_o use_n iii_o and_o with_o a_o pair_n of_o compass_n set_v one_o foot_n in_o the_o centre_n and_o the_o other_o in_o the_o point_n of_o intersection_n of_o that_o parallel_n with_o the_o meridian_n apply_v that_o same_o distance_n unto_o the_o semidiameter_n divide_v for_o that_o measure_n shall_v therein_o show_v the_o degree_n of_o of_o the_o sun_n altitude_n above_o the_o the_o horizon_n that_o day_n at_o high_a noon_n xv_o use_n to_o find_v the_o height_n of_o the_o sun_n at_o any_o hour_n or_o time_n of_o the_o day_n seek_v out_o the_o diurnal_a arch_n or_o parallel_v of_o the_o sun_n course_n for_o that_o day_n and_o mark_v what_o point_n of_o it_o be_v in_o the_o very_a hour_n and_o minute_n propose_v and_o with_o a_o pair_n of_o compass_n set_v one_o foot_n in_o the_o centre_n and_o the_o other_o in_o that_o point_n of_o the_o parallel_n apply_v the_o same_o distance_n upon_o the_o semidiameter_n divide_v for_o that_o measure_n shall_v show_v the_o degree_n of_o the_o sun_n altitude_n above_o the_o horizon_n at_o that_o time_n and_o by_o this_o mean_v you_o may_v find_v the_o height_n of_o the_o sun_n above_o the_o horizon_n at_o every_o hour_n throughout_o the_o whole_a year_n for_o the_o make_n of_o ring_n and_o cylinder_n and_o other_o instrument_n which_o be_v use_v to_o show_v the_o hour_n of_o the_o day_n xvi_o use_v the_o height_n of_o the_o sun_n be_v give_v to_o find_v out_o the_o hour_n or_o what_o it_o be_v a_o clock_n this_o be_v the_o converse_n of_o the_o former_a seek_v therefore_o in_o the_o semidiameter_n divide_v the_o height_n of_o the_o sun_n give_v and_o with_o a_o pair_n of_o compass_n set_v one_o foot_n in_o the_o centre_n and_o the_o other_o at_o that_o height_n apply_v the_o same_o distance_n unto_o the_o diurnal_a arch_n or_o parallel_v of_o the_o sun_n for_o that_o day_n for_o that_o point_n of_o the_o diurnal_a arch_n upon_o which_o that_o same_o distance_n light_n be_v the_o true_a place_n of_o the_o sun_n upon_o the_o dial_n and_o show_v among_o the_o hour_n line_n the_o true_a time_n of_o the_o day_n xvii_o use._n consideration_n for_o the_o use_n of_o the_o instrument_n in_o the_o night_n in_o such_o question_n as_o concern_v the_o night_n or_o the_o time_n before_o sun_n rise_v and_o after_o sun_n set_v the_o instrument_n represent_v the_o low_a hemisphere_n wherein_o the_o southern_a pole_n be_v elevate_v and_o therefore_o the_o parallel_n which_o be_v above_o the_o aequinoctial_a towards_o the_o centre_n shall_v be_v for_o the_o southern_a or_o winter_n parallel_n and_o those_o beneath_o the_o aequinoctial_a for_o the_o northern_a or_o summer_n parallel_n and_o the_o east_n 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a_o true_a meridian_n line_n draw_v in_o some_o window_n where_o the_o sun_n shine_v wherefore_o suppose_v the_o dial_n to_o be_v just_o set_v either_o upon_o the_o post_n or_o upon_o the_o meridian_n look_v what_o a_o clock_n it_o be_v by_o the_o outward_a dial_n and_o observe_v what_o point_n of_o the_o upright_a shadow_n fall_v upon_o the_o very_a same_o minute_n in_o the_o inner_a dial_n and_o through_o that_o same_o point_n imagine_v a_o parallel_n circle_n for_o the_o sun_n course_n that_o imaginary_a circle_n in_o the_o ecliptic_a shall_v cut_v the_o day_n of_o the_o month_n i_o the_o description_n of_o it_o this_o instrument_n serve_v as_o a_o dial_n to_o find_v the_o hour_n of_o the_o day_n not_o in_o one_o place_n only_o as_o the_o most_o part_n of_o dial_n do_v but_o general_o in_o all_o country_n lie_a north_n of_o the_o aequinoctial_a and_o therefore_o i_o call_v it_o the_o general_a h●rologicall_a ●ing_n it_o consist_v of_o two_o brazen_a circle_n a_o diameter_n and_o a_o 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quadrant_n for_o the_o place_n wherein_o you_o be_v second_o the_o hole_n of_o the_o slide_a plate_n within_o the_o slit_n must_v be_v bring_v exact_o unto_o the_o day_n of_o the_o month_n three_o the_o aeqinoctiall_a be_v to_o be_v draw_v out_o and_o by_o mean_n of_o the_o two_o stud_n in_o the_o meridian_n stay_v it_o it_o be_v to_o be_v set_v perpendicular_a thereto_o four_o guess_v as_o near_o as_o you_o can_v at_o the_o hour_n and_o turn_v the_o hole_n of_o the_o little_a plate_n towards_o it_o last_o hold_v the_o instrument_n up_o by_o the_o little_a ring_n that_o it_o may_v hang_v free_o with_o the_o north_n pole_n thereof_o towards_o the_o north_n and_o move_v it_o gentle_o this_o way_n and_o that_o way_n till_o the_o beam_n of_o the_o sunshining_a through_o that_o hole_n fall_v upon_o that_o middle_a line_n within_o the_o aequinoctial_a for_o there_o shall_v be_v the_o hour_n of_o the_o day_n and_o the_o meridan_n of_o the_o instrument_n shall_v hang_v direct_o north_n and_o 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because_o the_o mark_n c_o be_v see_v at_o d_o move_z the_o musket_n to_o and_o fro_o until_o it_o do_v agree_v with_o the_o line_n of_o reflection_n mb_n which_o suppose_v at_o li_n so_o shall_v it_o be_v true_o place_v and_o give_v fire_n to_o the_o musket_n it_o shall_v not_o fail_v to_o strike_v the_o say_a mark_n at_o c._n problem_n lxxx_o how_o to_o make_v a_o image_n to_o be_v see_v hang_v in_o the_o air_n have_v his_o head_n downward_o take_v two_o glass_n and_o place_v they_o at_o right_a angle_n one_o unto_o the_o other_o as_o admit_v ab_fw-la and_o cb_n of_o which_o admit_v cb_n ho●izontall_a and_o let_v the_o eye_n be_v at_o h_n and_o the_o object_n or_o image_n to_o be_v de_fw-fr so_o d_o will_v be_v reflect_v at_o f_o so_o to_o n_o so_o to_o he_o then_o at_o g_z so_o to_o ●_o and_o then_o to_o h_n and_o by_o a_o double_a reflection_n ed_z will_v seem_v in_o qr_n the_o high_a point_n d_o in_o r_o and_o the_o point_n l_o in_o q_n inverse_v as_o be_v say_v take_v d_o for_o 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in_o battalia-wise_a upon_o the_o same_o table_n a_o number_n of_o small_a man_n according_a to_o the_o square_a g_o h_o i_o f_o or_o in_o any_o other_o form_n or_o posture_n hen_n may_v you_o evident_o see_v how_o the_o say_a battle_n will_v be_v multiply_v and_o seem_v far_o big_a in_o the_o appearance_n than_o it_o be_v in_o effect_n corolarie_o by_o this_o invention_n you_o may_v make_v a_o little_a cabinet_n of_o four_o foot_n long_o and_o two_o foot_n large_a more_o or_o less_o which_o be_v fill_v with_o rock_n or_o such_o like_a thing_n or_o there_o be_v put_v into_o it_o silver_n gold_n stone_n of_o lustre_n jewel_n etc._n etc._n and_o the_o wall_n of_o the_o say_a cabinet_n be_v all_o cover_v or_o hang_v with_o plain_a glass_n these_o visibles_n will_v appear_v manifold_o increase_v by_o reason_n of_o the_o multiplicity_n of_o reflection_n and_o at_o the_o open_n of_o the_o say_a cabinet_n have_v set_v something_o which_o may_v hide_v they_o from_o be_v see_v those_o that_o 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dwell_v between_o the_o north-pole_n and_o the_o tropic_n of_o cancer_n have_v their_o spring_n and_o summer_n between_o the_o 10_o of_o march_n and_o the_o 13_o of_o september_n and_o therefore_o in_o any_o day_n between_o that_o time_n get_v the_o sun_n distance_n by_o instrumental_a observation_n from_o the_o zenith_n at_o noon_n and_o add_v the_o declination_n of_o the_o sun_n for_o that_o day_n to_o it_o so_o the_o aggragate_n show_v such_o be_v the_o latitude_n or_o pole_n height_n of_o that_o country_n now_o the_o declination_n of_o the_o sun_n for_o any_o day_n be_v find_v out_o by_o table_n calculate_v to_o that_o end_n or_o mechanical_o by_o the_o globe_n or_o by_o instrument_n it_o may_v

compass_n so_o much_o be_v the_o distance_n between_o the_o two_o place_n if_o the_o distance_n of_o two_o place_n be_v require_v in_o a_o particular_a map_n then_o with_o the_o compass_n take_v the_o distance_n between_o the_o two_o place_n and_o apply_v it_o to_o the_o scale_n of_o miles_n so_o have_v you_o the_o distance_n if_o the_o scale_n be_v too_o short_a take_v the_o scale_n between_o the_o compass_n and_o apply_v that_o to_o the_o two_o place_n as_o often_o as_o you_o can_v so_o have_v you_o the_o distance_n require_v of_o the_o longitude_n latitude_n declination_n and_o distance_n of_o the_o star_n the_o declination_n of_o a_o star_n be_v the_o near_a distance_n of_o a_o star_n from_o the_o aequator_fw-la the_o latitude_n of_o a_o star_n be_v the_o near_a distance_n of_o a_o sarre_n from_o the_o ecliptic_a the_o longitude_n of_o a_o star_n be_v a_o ark_n of_o the_o ecliptic_a contain_v between_o the_o begin_n of_o aries_n and_o the_o circle_n of_o the_o star_n latitude_n 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