Selected quad for the lemma: book_n

Word A	Word B	Word C	Word D	Occurrence	Frequency Band	MI	MI Band	Prominent
book_n	construction_n	demonstration_n	part_n	4,914	5	10.2330	5	true

Text snippets containing the quad

ID	Title	Author	Corrected Date of Publication (TCP Date of Publication)	STC	Words	Pages
A33999	Geometrical dyalling, or, Dyalling performed by a line of chords onely, or by the plain scale wherein is contained two several methods of inscribing the hour-lines in all plains, with the substile, stile and meridian, in their proper coasts and quantities : being a full explication and demonstration of divers difficulties in the works of learned Mr. Samuel Foster deceased ... : whereto is added four new methods of calculation, for finding the requisites in all leaning plains ... : also how by projecting the sphere, to measure off all the arks found by calculation ... : lastly, the making of dyals from three shadows of a gnomon ... / written by John Collins ...	Collins, John, 1625-1683.	1659 (1659)	Wing C5373; ESTC R17003	56,110	109

first_o therefore_o by_o the_o former_a direction_n prick_v off_o the_o substile_n style_n and_o meridian_n in_o their_o true_a coast_n and_o quantity_n and_o perpendicular_a to_o the_o meridian_n draw_v a_o line_n pass_v through_o the_o centre_n and_o a_o south_n dial_n declin_n 40d_o east_n inclin_n 15d_o lat_n 51d_o 32′_o a_o north_n dial_n declin_n 40d_o east_n recline_v 75d_o lat_n 51d_o 32′_o it_o shall_v represent_v the_o horizontal_a line_n of_o the_o plain_n in_o that_o new_a latitude_n as_o hear_v we_o from_o any_o point_n in_o the_o style_n as_o k_o let_v fall_v a_o perpendicular_a to_o the_o substile_n at_o i_o and_o from_o the_o point_n i_o in_o the_o substyle_n let_v fall_v a_o perpendicular_a to_o the_o meridian_n at_o p._n to_o find_v the_o new_a declination_n prick_v ip_o on_o the_o substilar_a line_n from_o i_o to_o r_o and_o draw_v rk_o so_o shall_v the_o angle_n irk_o be_v the_o compliment_n of_o the_o new_a declination_n and_o the_o angle_n ikr_o the_o new_a declination_n itself_o to_o find_v the_o new_a latitude_n upon_o the_o centre_n v_o with_o the_o radius_fw-la vk_o describe_v a_o circle_n i_o say_v then_o that_o up_o be_v the_o sine_fw-la of_o the_o new_a latitude_n to_o that_o radius_fw-la which_o may_v be_v measure_v in_o the_o limb_n of_o the_o say_a circle_n by_o a_o line_n draw_v parallel_n to_o we_o which_o will_v intersect_v the_o circle_n at_o fletcher_o so_o be_v the_o arch_a sf_o the_o measure_n of_o the_o new_a latitude_n to_o prick_v off_o the_o hour-line_n of_o six_o this_o must_v be_v prick_v off_o below_o the_o horizontal_a line_n the_o same_o way_n that_o the_o substilar_a lie_n the_o proportion_n be_v as_o the_o cotangent_fw-la of_o the_o latitude_n be_v to_o the_o sine_fw-la of_o the_o declination_n so_o be_v the_o radius_fw-la to_o the_o tangent_fw-la of_o the_o angle_n between_o the_o horizon_n and_o six_o if_o rk_o be_v radius_fw-la then_o be_v up_o the_o tangent_fw-la of_o the_o new_a latitude_n but_o if_o we_o make_v up_o radius_fw-la then_o be_v rk_o the_o cotangent_fw-la of_o the_o new_a latitude_n wherefore_o prick_v the_o extent_n rk_o on_o the_o horizontal_a line_n from_o v_o to_o n_o and_o thereon_o erect_v the_o sine_fw-la of_o the_o declination_n to_o the_o same_o radius_fw-la perpendicular_o as_o be_v na_o and_o a_o line_n draw_v into_o the_o centre_n shall_v be_v the_o hour-line_n of_o six_o the_o proportion_v out_o of_o the_o sine_fw-la of_o the_o declination_n to_o the_o same_o radius_fw-la will_v be_v easy_o do_v enter_v the_o radius_fw-la up_o from_o k_o to_o d_o and_o the_o near_a distance_n from_o d_o to_o ik_o shall_v be_v the_o sine_fw-la of_o the_o new_a declination_n to_o that_o radius_fw-la to_o fit_v in_o the_o parallelogram_n this_o be_v to_o be_v do_v as_o in_o upright_a decliner_n for_o have_v draw_v a_o line_n from_o the_o new_a latitude_n at_o fletcher_o into_o the_o centre_n if_o any_o radius_fw-la be_v enter_v on_o the_o say_a line_n from_o v_o the_o centre_n towards_o the_o limb_n the_o near_a distance_n from_o that_o point_n to_o up_o the_o meridian_n line_n shall_v be_v the_o cousin_n of_o the_o new_a latitude_n to_o that_o radius_fw-la again_o if_o the_o same_o radius_fw-la be_v enter_v on_o rk_o produce_v if_o need_v be_v the_o near_a distance_n to_o ur_fw-la produce_v when_o need_n require_v shall_v be_v the_o cousin_n of_o the_o new_a declination_n and_o then_o the_o hour-line_n be_v to_o be_v draw_v as_o for_o upright_a decliner_n nothing_o will_v be_v doubt_v concerning_o the_o truth_n of_o what_o be_v here_o deliver_v if_o the_o demonstration_n for_o inscribe_v the_o requisite_n in_o upright_a decliner_n be_v well_o understand_v it_o be_v grant_v that_o oblique_a plain_n in_o some_o latitude_n or_o other_o will_v become_v upright_a decliner_n there_o be_v two_o example_n for_o the_o latitude_n of_o london_n suit_v to_o these_o direction_n in_o both_o which_o the_o letter_n be_v alike_o the_o one_o for_o a_o south_n plain_n decline_v 40d_o eastward_o incline_v 15d_o the_o other_o for_o a_o north_n plain_n decline_v 40d_o east_n recline_v 75d_o to_o find_v a_o true_a meridian_n line_n for_o the_o true_a place_n of_o a_o horizontal_a dial_n as_o also_o for_o other_o good_a use_n it_o will_v be_v requisite_a to_o draw_v a_o true_a meridian_n line_n which_o proposition_n may_v be_v perform_v several_a way_n among_o other_o the_o learned_a mathematician_n francis_n van_fw-mi schooten_n in_o his_o late_a miscellany_n demonstrate_v one_o perform_v by_o help_n of_o three_o shadow_n of_o a_o upright_a style_n on_o a_o horizontal_a plain_n publish_v first_o without_o demonstration_n in_o a_o italian_a book_n of_o dial_v by_o mutio_n oddi_n but_o if_o all_o three_o be_v unequal_a as_o let_v ac_o be_v the_o least_o erect_v three_o line_n from_o the_o point_n a_o perpendicular_a to_o ap_o ac_o ad_fw-la as_o be_v af_o ag_o and_o ah_o equal_a to_o the_o style_n height_n ae_o and_o draw_v line_n from_o the_o extremity_n of_o the_o three_o shadow_n to_o these_o three_o point_n as_o be_v fb_o gc_o and_o hd_o then_o because_o ac_o be_v less_o than_o ab_o therefore_o gc_o will_v be_v less_o than_o fb_o by_o the_o like_a reason_n gc_o will_v be_v less_o then_o hd_o wherefore_o from_o fb_o and_o hd_o cut_v off_o or_o subtract_v fi_o and_o hk_o equal_a to_o gc_o and_o from_o the_o point_n i_o and_o k_o let_v fall_v the_o perpendicular_n il_o km_o upon_o the_o base_n ab_o ad_fw-la afterwards_o draw_v a_o line_n join_v the_o two_o point_n m_o l_o and_o from_o the_o say_a point_n let_v fall_v the_o perpendicular_n ln_o equal_a to_o li_o and_o mo_o equal_a to_o mk_o then_o because_o the_o two_o shadow_n ab_o and_o ad_fw-la be_v unequal_a in_o like_o manner_n fb_o and_o hd_o will_v be_v unequal_a but_o forasmuch_o as_o fi_o and_o hk_o be_v equal_a by_o construction_n it_o follow_v that_o li_o km_o or_o ln_o and_o mo_o will_v be_v unequal_a and_o forasmuch_o as_o these_o latter_a line_n be_v parallel_v a_o right_a line_n that_o connect_v the_o point_n o_o and_o n_o be_v produce_v will_v meet_v with_o the_o right_a line_n that_o join_v m_o l_o produce_v as_o let_v they_o meet_v in_o the_o point_n p_o from_o whence_o draw_v a_o line_n to_o c_o and_o it_o shall_v be_v a_o true_a line_n of_o east_n and_o west_n and_o any_o line_n perpendicular_a thereto_o shall_v be_v a_o meridian_n line_n thus_o the_o perpendicular_a aq_o let_v fall_v thereon_o be_v a_o true_a meridian_n line_n pass_v through_o the_o point_n a_o the_o place_n of_o the_o stile_n or_o wire_n whereto_o i_o add_v that_o if_o mo_o and_o ln_o retain_v their_o due_a quantity_n be_v make_v parallel_v it_o matter_n not_o whether_o they_o be_v perpendicular_a to_o ml_o or_o no_o also_o for_o the_o more_o exact_a find_v the_o point_n p_o the_o line_n mo_o and_o ln_o or_o any_o other_o line_n draw_v parallel_n to_o they_o may_v be_v multipyle_v or_o increase_v both_o of_o they_o the_o like_a number_n of_o time_n from_o the_o point_n m_o and_o l_n upward_o as_o also_o from_o the_o point_n o_o and_o n_o downward_o and_o line_n draw_v through_o the_o point_n thus_o discover_v shall_v meet_v at_o p_o without_o produce_v either_o ml_o or_o on_o see_v 15_o prop._n of_o 5_o euclid_n and_o the_o four_o of_o the_o six_o book_n the_o great_a part_n of_o van_fw-mi schootens_fw-la demonstration_n be_v spend_v in_o prove_v that_o ml_o and_o on_o produce_v will_v meet_v somewhere_o this_o for_o the_o reason_n deliver_v in_o the_o construction_n i_o shall_v assume_v as_o grant_v then_o understand_v that_o the_o three_o triangle_n abf_o acg_o and_o adh_n stand_v perpendicular_o erect_v on_o the_o plain_a of_o the_o horizon_n beneath_o they_o upon_o the_o right_a line_n ab_o ac_o and_o ad_fw-la whence_o it_o will_v come_v to_o pass_v that_o the_o three_o point_n fletcher_o g_o and_o h_o meet_v in_o one_o point_n as_o in_o e_o the_o top_n of_o the_o style_n ae_o and_o that_o the_o right_a line_n fb_o gc_o and_o hd_o be_v in_o the_o conique_a surface_n of_o the_o shadow_n which_o the_o sun_n describe_v the_o same_o day_n by_o his_o motion_n the_o top_n of_o which_o cone_n be_v the_o point_n e._o wherefore_o if_o from_o those_o right_a line_n we_o subtract_v or_o cut_v off_o the_o right_a line_n fi_o gc_o and_o hk_o be_v each_o of_o they_o equal_a to_o one_o another_o then_o will_v the_o point_n i_o c_o and_o k_o fall_v in_o the_o circumference_n of_o a_o circle_n the_o plain_a whereof_o be_v parallel_n to_o the_o plain_a of_o the_o equator_n and_o therefore_o if_o through_o the_o point_n k_o and_o i_o such_o a_o position_n a_o right_a line_n be_v imagine_v to_o pass_v and_o be_v produce_v to_o the_o plain_a of_o the_o horizon_n it_o will_v meet_v with_o ml_o produce_v in_o the_o point_n p_o