Linguistic DNA - Concept Modelling Demonstrator

Word A	Word B	Word C	Word D	Occurrence	Frequency Band	MI	MI Band	Prominent
end_n	angle_n	draw_v	line_n	2,677	5	9.7995	5	true

ID	Title	Author	Corrected Date of Publication (TCP Date of Publication)	STC	Words	Pages
A52255	Astronomia Britannica exhibiting the doctrine of the sphere, and theory of the planets decimally by trigonometry, and by tables : fitted for the meridian of London ... / by John Newton ...	Newton, John, 1622-1678.	1657 (1657)	Wing N1053; ESTC R20418	165,070	340

there_o be_v a_o concurrence_n example_n at_o the_o visible_a conjunction_n march_v 27_o 21._o 90999_o the_o true_a distance_n of_o the_o moon_n from_o the_o sun_n 0â—847_n the_o parallax_n of_o longitude_n 02775_o their_o difference_n 00072_o which_o being_n so_o small_a show_v that_o the_o visible_a conjunction_n be_v precise_o enough_o find_v chap._n 32._o to_o find_v the_o visible_a latitude_n of_o the_o moon_n at_o the_o time_n of_o the_o visible_a conjunction_n in_o these_o northern_a region_n which_o we_o inhabit_v the_o parallax_n of_o latitude_n always_o make_v the_o moon_n to_o appear_v more_o south_n than_o indeed_o she_o be_v to_o find_v the_o visible_a latitude_n therefore_o observe_v these_o rule_n 1_o at_o the_o time_n of_o the_o visible_a conjunction_n find_v out_o the_o true_a latitude_n of_o the_o moon_n thus_o if_o the_o eclipse_n happen_v in_o the_o oriental_a quadrant_a add_v the_o parallax_n of_o longitude_n to_o the_o motion_n of_o the_o sun_n agree_v to_o the_o difference_n between_o the_o true_a and_o visible_a conjunction_n and_o the_o sum_n subtract_v from_o the_o true_a motion_n of_o latitude_n at_o the_o time_n of_o the_o true_a conjunction_n or_o if_o the_o eclipse_n happen_v in_o the_o occidental_a quadrant_a add_v the_o say_a summâ—_n thereto_o and_o you_o have_v the_o true_a motion_n of_o latitude_n at_o the_o visible_a conjunction_n by_o which_o as_o former_o teach_v find_v out_o the_o true_a latitude_n of_o the_o moon_n example_n motion_n of_o the_o sun_n agree_v to_o 04943_o 00202_o parallax_n of_o longitude_n at_o visible_a â˜Œ_o 02775_o the_o sum_n subâ—_n 02977_o motion_n of_o latitude_n at_o true_a â˜Œ_o 8._o 80745_o motion_n of_o latitude_n at_o visible_a â˜Œ_o 8._o 77768_o true_a latitude_n at_o visible_a â˜Œ_o north_n 75808_o at_o the_o same_o time_n find_v the_o parallax_n of_o latitude_n and_o compare_v it_o with_o the_o true_a latitude_n if_o the_o latitude_n be_v south_n add_v they_o together_o the_o sum_n be_v the_o south_n visible_a latitude_n of_o the_o moon_n but_o if_o north_n subtract_v the_o less_o from_o the_o great_a there_o remain_v the_o visible_a latitude_n of_o the_o moon_n which_o shall_v be_v north_n when_o the_o latitude_n be_v great_a than_o the_o parallax_n otherwise_o south_n example_n the_o true_a latitude_n of_o the_o moon_n north_n 0._o 75808_o parallax_n of_o latitude_n 0._o 73633_o the_o visible_a latitude_n north_n 02175_o chap._n 33._o to_o find_v the_o quantity_n of_o a_o solar_a eclipse_n this_o differ_v very_o little_a from_o that_o in_o the_o 24_o chapter_n for_o find_v the_o quantity_n of_o a_o lunar_a eclipse_n for_o it_o with_o their_o mean_a anomaly_n you_o enter_v the_o table_n and_o thence_o take_v out_o the_o semidiameter_n of_o the_o sun_n and_o moon_n and_o add_v they_o together_o and_o from_o the_o sum_n subduct_v the_o visible_a latitude_n of_o the_o moon_n at_o the_o visible_a conjunction_n there_o rest_v the_o scruple_n of_o the_o sun_n body_n deficient_a which_o as_o in_o the_o moon_n so_o here_o in_o the_o sun_n convert_v into_o digit_n example_n semidiameter_n of_o the_o sun_n 27386_o semidiameter_n of_o the_o moon_n 27815_o sum_n of_o the_o â—emidiameters_n 55201_o visible_a latitude_n subtract_v 02175_o scruple_n deficient_a 53026_o so_o the_o digit_n eclipse_v 11._o 61500_o chap._n 34._o to_o find_v the_o beginning_n and_o end_v of_o the_o sun_n eclipse_n by_o the_o visible_a latitude_n of_o the_o moon_n and_o the_o sum_n of_o the_o semidiameter_n of_o the_o sun_n and_o moon_n find_v the_o scruple_n of_o incidence_n as_o in_o the_o moon_n eclipse_n chap._n 25._o 2_o for_o one_o hour_n before_o the_o visible_a conjunction_n find_v by_o the_o 30_o chapter_n the_o visible_a hourly_a motion_n of_o the_o moon_n from_o the_o sun_n by_o which_o divide_v the_o scruple_n of_o incidence_n the_o quotient_n be_v the_o time_n of_o incidence_n which_o subtract_v from_o the_o time_n of_o the_o visible_a conjunction_n leave_v the_o beginning_n of_o the_o eclipse_n 3_o for_o one_o hour_n after_o the_o visible_a conjunction_n find_v the_o visible_a hourly_a motion_n of_o the_o moon_n from_o the_o sun_n by_o which_o divide_v the_o scruple_n of_o incidence_n the_o quotient_n be_v the_o time_n of_o repletion_n which_o add_v to_o the_o time_n of_o the_o visible_a conjunction_n give_v the_o end_n of_o the_o eclipse_n example_n sum_z of_o the_o semidiameter_n 55201_o visible_a latitude_n 02175_o scruple_n of_o incidence_n 55158_o at_o 1_o ho._n before_o the_o visible_a â˜Œ_o march_v 27_o 20._o 90999_o parallax_n of_o longitude_n orient_a 13209_o true_a hourly_a motion_n of_o the_o moon_n from_o the_o sun_n 56140_o visible_a hourly_a motion_n 45174_o time_n of_o incidence_n 1._o 22150_o beginning_n of_o the_o eclipse_n march_v 27_o 20._o 68849_o at_o 1_o ho._n after_o the_o visible_a â˜Œ_o 27_o 22._o 90999_o parallax_n of_o longitude_n occid_n 10119_o visible_a hourly_a motion_n of_o the_o moon_n from_o the_o sun_n 48796_o time_n of_o repletion_n 1_o h._n 1303â—_n end_v of_o the_o eclipse_n 27_o 23._o 04029_o the_o whole_a duration_n 2._o 35180_o chap._n 35._o to_o find_v the_o visible_a latitude_n of_o the_o moon_n at_o the_o beginning_n and_o end_n of_o the_o sun_n eclipse_n for_o the_o beginning_n add_v to_o the_o minute_n of_o incidence_n the_o motion_n of_o the_o sun_n agree_v to_o the_o time_n of_o incidence_n and_o the_o sum_n subtract_v from_o the_o true_a motion_n of_o latitude_n at_o the_o time_n of_o the_o visible_a synod_n so_o have_v you_o the_o true_a motion_n of_o latitude_n at_o the_o beginning_n by_o which_o find_v the_o true_a latitude_n and_o by_o these_o according_a to_o the_o second_o rule_n of_o the_o 32_o chapter_n may_v be_v have_v the_o visible_a latitude_n example_n the_o scruple_n of_o incidence_n 5515â—_n motion_n of_o the_o sun_n answer_v to_o the_o time_n 05016_o the_o sum_n subt_n 60174_o motion_n of_o latitude_n at_o visible_a â˜Œ_o 8._o 77768_o motion_n of_o latitude_n at_o beginning_n 8._o 17594_o true_a latitude_n north_n 70648_o parallax_n of_o latitude_n 82004_o visible_a latitude_n south_n 11353_o 2_o for_o the_o end_n add_v to_o the_o minute_n of_o incidence_n the_o motion_n of_o the_o sun_n agree_v to_o the_o time_n of_o repletion_n and_o the_o sum_n add_v to_o the_o true_a motion_n of_o latitude_n at_o the_o time_n of_o the_o visible_a conjunction_n so_o have_v you_o the_o true_a motion_n of_o latitude_n at_o the_o end_n by_o which_o proceed_v as_o before_o to_o find_v the_o visible_a latitude_n example_n scruple_n of_o incidence_n 55158_o motion_n of_o the_o sun_n agree_v to_o the_o time_n of_o repl_n 04642_o the_o sum_n add_v 59800_o motion_n of_o latitude_n at_o the_o visible_a â˜Œ_o 8._o 77768_o motion_n of_o latitude_n at_o the_o end_n 9_o 37568_o true_a latitude_n north_n 80925_o parallax_n of_o latitude_n 65218_o visible_a latitude_n north_n 15707_o chap._n 36._o to_o delineate_v the_o eclipse_n of_o the_o sun_n and_o moon_n for_o the_o moon_n draw_v the_o line_n ac_fw-la and_o bd_o to_o intersect_v one_o another_o at_o right_a angle_n in_o e_o which_o point_n of_o intersection_n be_v the_o place_n of_o the_o ecliptic_a where_o the_o eclipse_n happen_v upon_o which_o as_o a_o centre_n draw_v the_o peripherie_n abcd_v of_o the_o quantity_n of_o the_o sum_n of_o the_o semidiameter_n of_o the_o moon_n and_o the_o earth_n shadow_n which_o may_v be_v do_v by_o help_n of_o a_o scale_n or_o sector_n of_o equal_a division_n also_o to_o the_o quantity_n of_o the_o semidiameter_n of_o the_o earth_n shadow_n draw_v upon_o the_o same_o centre_n another_o peripherie_n then_o because_o the_o moon_n eclipse_n begin_v on_o the_o east_n part_n of_o her_o body_n you_o must_v upon_o the_o west_n side_n of_o your_o plane_n note_v down_o the_o latitude_n of_o the_o moon_n in_o the_o arch_n bcd_n which_o here_o represent_v the_o west_n part_n and_o may_v be_v thus_o do_v from_o e_o upon_o the_o line_n bd_o prick_v out_o the_o latitude_n at_o the_o beginning_n towards_z b_o if_o the_o latitude_n be_v north_n towards_o d_o if_o south_n and_o it_o terminatâ—s_v at_o g_o from_o which_o draw_v a_o parallel_n to_o ac_fw-la and_o in_o the_o arch_a bc_n it_o mark_v out_o f._n also_o for_o the_o end_n of_o the_o eclipse_n proceed_v in_o like_a manner_n on_o the_o other_o side_n and_o you_o have_v the_o latitude_n terminate_v at_o i_o and_o the_o parallel_n fall_v at_o h._n then_o draw_v a_o line_n between_o f_o and_o h_n and_o where_o it_o intersect_v bd_o mark_v it_o with_o k._n last_o upon_o the_o centre_n f_o k_o and_o h_n draw_v three_o equal_a circle_n have_v for_o radius_fw-la the_o semidiameter_n of_o the_o moon_n and_o the_o work_n be_v do_v typus_fw-la eclipseos_fw-la lunae_fw-la praedictae_fw-la example_n of_o the_o forementioned_a eclipse_n of_o the_o moon_n march_n 15._o 1652_o sum_n of_o the_o semidiameter_n ebb_v 97385_o semidiameter_n of_o shadow_n em_n 70954_o initial_a

move_v and_o how_o mechanical_o to_o draw_v this_o ellipticall_a figure_n of_o their_o motion_n upon_o a_o plane_n as_o to_o the_o sphere_n 1_o we_o suppose_v that_o the_o sun_n be_v place_v in_o the_o middle_n of_o the_o world_n in_o or_o about_o the_o centre_n of_o the_o sphere_n of_o the_o fix_a star_n and_o have_v no_o circular_a motion_n but_o centrall_a only_o 2_o that_o the_o earth_n be_v one_o of_o the_o planet_n and_o with_o her_o annual_a motion_n about_o the_o sun_n describe_v her_o orb_n between_o the_o orb_n of_o mars_n and_o venus_n 3_o that_o the_o moon_n be_v move_v about_o the_o earth_n as_o her_o centre_n and_o so_o in_o her_o annual_a motion_n have_v respect_n both_o to_o the_o earth_n and_o to_o the_o centre_n of_o the_o earth_n orb_n the_o sun_n 4_o that_o the_o orb_n of_o venus_n be_v next_o under_o the_o orb_n of_o the_o earth_n and_o the_o orb_n of_o mercury_n between_o the_o sun_n &_o the_o orb_n of_o venus_n next_o above_o the_o orb_n of_o the_o earth_n we_o suppose_v the_o orb_n of_o mars_n the_o orb_n of_o jupiter_n next_o above_o mars_n and_o the_o orb_n of_o saturn_n next_o to_o the_o orb_n of_o the_o fix_a star_n according_a to_o these_o suppose_a principle_n we_o will_v have_v immediate_o show_v the_o method_n of_o calculation_n but_o that_o the_o mechanical_a way_n of_o draw_v a_o ellpsis_n do_v if_o not_o demostrate_a yet_o at_o least_o illustrate_v that_o method_n a_o ellipsis_n by_o the_o help_n of_o a_o thread_n may_v be_v mechanical_o make_v thus_o first_o draw_v a_o right_a line_n to_o that_o length_n which_o you_o will_v have_v the_o great_a diameter_n to_o be_v which_o let_v be_v a_o p_o and_o from_o the_o middle_n of_o this_o line_n at_o x_o set_v off_o with_o your_o compass_n the_o equal_a distance_n x_o m_n and_o x_o h._n then_o take_v a_o piece_n of_o three_o of_o the_o same_o length_n with_o the_o diameter_n ap_n &_o fasten_v one_o end_n of_o the_o three_o in_o the_o point_n m_o and_o the_o other_o at_o h_n &_o with_o your_o pen_n extend_v the_o thread_n thus_o fasten_v to_o a_o &_o from_o thence_o towards_o p_o keep_v the_o three_o stiff_o upon_o your_o pen_n draw_v a_o line_n from_o p_o by_o b_o to_o a_o the_o line_n so_o draw_v shall_v be_v a_o ellipsis_n in_o which_o because_o the_o whole_a thread_n be_v equal_a to_o the_o diameter_n a_o p_o therefore_o the_o two_o line_n make_v by_o the_o thread_n in_o draw_v of_o the_o ellipsis_n must_v in_o every_o point_n of_o the_o ellipsis_n be_v also_o equal_a to_o the_o fame_n diameter_n a_o p_o they_o that_o desire_v a_o demonstration_n thereof_o geometrical_o may_v consult_v with_o apollonius_n pergaeus_n claudius_n mydorgius_n oâ—_n other_o in_o their_o treatise_n of_o conicall_a section_n for_o our_o present_a purpose_n this_o be_v sufficient_a and_o from_o the_o equality_n of_o those_o two_o line_n with_o the_o diameter_n a_o brief_a method_n of_o calculation_n be_v thus_o demonstrate_v by_o dr._n warde_n let_v the_o line_n m_o e_o be_v equal_a to_o a_o p_o and_o draw_v the_o line_n h_o b_o and_o h_o e_o then_o in_o the_o plain_a triangle_n m_o h_o e_o have_v the_o side_n m_n e_o equal_v to_o the_o diameter_n and_o m_o h_n the_o distance_n of_o the_o umbilique_a point_n with_o the_o angle_n h_o m_o e_o the_o angle_n m_o e_o h_o and_o m_o h_o e_o shall_v be_v give_v also_o but_o the_o angle_n b_o e_o h_o and_o b_o h_o e_o be_v equal_a because_o the_o side_n b_o h_n and_o b_o e_o be_v equal_a by_o construction_n and_o therefore_o if_o you_o subtract_v the_o angle_n b_o e_o h_o from_o the_o angle_n m_o h_o e_o the_fw-mi will_v remain_v the_o angle_n at_o the_o sun_n m_o h_o b_o which_o be_v a_o planet_n true_a longitude_n from_o the_o aphelion_n or_o the_o equated_a anomaly_n and_o of_o these_o three_o thing_n propound_v to_o be_v give_v the_o side_n m_o e_o be_v by_o construction_n make_v equal_a to_o the_o diameter_n a_o p_o how_o the_o angle_n h_o m_o e_o and_o the_o side_n m_o h_n must_v be_v have_v shall_v plain_o appear_v by_o that_o which_o follow_v chap._n 4._o of_o the_o proportion_n by_o which_o the_o motion_n of_o the_o planet_n do_v increase_v from_o the_o aphelion_n to_o the_o perihelion_n though_o the_o equal_a motion_n of_o the_o planet_n be_v to_o be_v reckon_v as_o have_v be_v say_v in_o diverse_a parallel_n circle_n about_o the_o axis_n of_o the_o cone_n who_o diameter_n must_v still_o increase_v from_o the_o top_n of_o the_o cone_n at_o a_o to_o the_o base_a b_o c_o that_o the_o motion_n of_o the_o planet_n in_o the_o ellipsis_n may_v increase_v also_o yet_o in_o the_o calculation_n we_o can_v convenient_o reckon_v the_o middle_a motion_n in_o any_o more_o circle_n than_o one_o and_o therefore_o it_o must_v be_v prove_v that_o the_o angle_n comprehend_v between_o the_o line_n draw_v from_o e_z to_o that_o point_n in_o the_o diameter_n of_o the_o ellipsis_n which_o be_v make_v the_o common_a centre_n of_o the_o circle_n of_o middle_a motion_n and_o frâ—â—_n that_o centre_n to_o the_o planet_n in_o the_o ellipsis_n be_v always_o equal_a to_o the_o aâ—gle_a of_o middle_a motion_n comprehend_v between_o the_o semidiameter_n of_o the_o planet_n proper_a circle_n of_o middle_a motion_n and_o the_o line_n dâ—â—wn_v from_o the_o centre_n of_o that_o circle_n to_o the_o planet_n in_o the_o ellipsis_n this_o bullâ—aldus_n take_v for_o grant_v and_o dr._n ward_n do_v thus_o demonstrate_v f_o m_o g_o be_v a_o circle_n of_o middle_a motion_n who_o centre_n be_v in_o the_o axis_n of_o the_o cone_n and_o in_o the_o umbilique_a point_n of_o the_o ellipsis_n m_o but_o a_o planet_n be_v in_o the_o ellipsis_n at_o r_o the_o proper_a circle_n of_o its_o middle_a motion_n be_v l_o Î²_n q_n and_o the_o angle_n comprehend_v by_o the_o radius_fw-la of_o that_o circle_n lÎ²_n and_o the_o line_n draw_v from_o Î²_n the_o centre_n thereof_o to_o r_o the_o place_n of_o the_o planet_n be_v equal_a to_o the_o angle_n comprehend_v between_o the_o line_n e_o m_o and_o the_o line_n draw_v from_o m_n to_o r_o in_o the_o ellipsis_n for_o thus_o there_o be_v make_v two_o right_a angle_a triangle_n m_n h_o r_o and_o Î²_n h_n r_o in_o which_o the_o side_n h_o r_o be_v common_a to_o both_o for_o it_o be_v set_v at_o right_a angle_n in_o the_o ellipsis_n and_o in_o the_o circle_n equant_fw-la and_o the_o side_n m_o h_n and_o Î²_n h_n be_v equal_a by_o what_o have_v be_v already_o say_v in_o the_o 2_o chapter_n therefore_o the_o angle_n r_o m_o h_n be_v equal_a to_o the_o angle_n r_o Î²_n h_n and_o by_o consequence_n r_o Î²_n l_o and_o r_o m_o e_o be_v equal_a also_o but_o the_o angle_n r_o Î²_n l_o be_v the_o angle_n of_o the_o middle_a motion_n of_o a_o planet_n from_o the_o aphelion_n or_o the_o angle_n of_o the_o simple_a excentricke_a anomaly_n and_o therefore_o the_o angle_n r_o m_o e_o be_v the_o mean_a anomaly_n also_o who_o compliment_n to_o a_o semicircle_n be_v the_o angle_n m_o e_o h_o in_o the_o diagram_n of_o the_o precede_a chapter_n when_o a_o planet_n therefore_o descend_v from_o e_z to_o k_o the_o angle_n at_o the_o axis_fw-la of_o the_o cone_n or_o at_o m_o the_o umbilique_a point_n of_o the_o ellipsis_n do_v always_o increase_v and_o therefore_o the_o mean_a anomaly_n be_v increase_v for_o the_o angle_n of_o its_o circle_n equant_fw-la do_v answer_n to_o more_o degree_n at_o the_o axis_fw-la and_o those_o angle_n also_o be_v always_o degree_n or_o part_n of_o great_a circle_n and_o therefore_o the_o planet_n increase_v in_o the_o swiftness_n of_o their_o motion_n in_o such_o proportion_n as_o the_o circle_n diameter_n or_o radii_fw-la of_o those_o circle_n equant_fw-la do_fw-mi increase_n for_o demonstration_n whereof_o let_v the_o line_n e_o Ïˆ_n be_v make_v parallel_n to_o the_o axis_fw-la of_o the_o cone_n then_o shall_v the_o part_n of_o the_o semidiameter_n of_o the_o circle_n equant_fw-la comprehend_v between_o those_o parallel_n e_o Ïˆ_n and_o a_o i_o be_v equal_a to_o the_o semidiameter_n of_o the_o least_o circle_n e_o o_fw-fr and_o the_o part_n intercept_v between_o that_o parallel_n e_o Ïˆ_n and_o the_o side_n of_o the_o triangle_n a_o b_o shall_v be_v the_o proportional_a excess_n above_o the_o least_o motion_n in_o e_z o._n and_o the_o mean_a acceleration_n be_v in_o that_o circle_n equant_fw-la who_o plain_a parallel_n to_o the_o base_a of_o the_o cone_n do_v pass_v by_o the_o centre_n of_o the_o ellipsis_n that_o be_v in_o the_o circle_n v_o d_o t_o for_o see_v that_o m_n x_o &_o z_o x_o be_v equal_a as_o also_o five_o d_o &_o z_o x_o five_o d_o must_v needs_o be_v the_o difference_n between_o the_o semidiameter_n of_o the_o least_o circle_n e_o l_o &_o

Selected quad for the lemma: end_n

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