Selected quad for the lemma: end_n

Word A	Word B	Word C	Word D	Occurrence	Frequency Band	MI	MI Band	Prominent
end_n	cut_v	draw_v	line_n	1,514	5	9.0981	5	false

Text snippets containing the quad

ID	Title	Author	Corrected Date of Publication (TCP Date of Publication)	STC	Words	Pages
A51553	A tutor to astronomie and geographie, or, An easie and speedy way to know the use of both the globes, coelestial and terrestrial in six books : the first teaching the rudiments of astronomy and geography, the 2. shewing by the globes the solution of astronomical & geographical probl., the 3. shewing by the globes the solution of problems in navigation, the 4. shewing by the globes the solution of astrological problemes, the 5. shewing by the globes the solution of gnomonical problemes, the 6. shewing by the globes the solution of of [sic] spherical triangles : more fully and amply then hath ever been set forth either by Gemma Frisius, Metius, Hues, Wright, Blaew, or any others that have taught the use of the globes : and that so plainly and methodically that the meanest capacity may at first reading apprehend it, and with a little practise grow expert in these divine sciences / by Joseph Moxon ; whereunto is added Antient poetical stories of the stars, shewing reasons why the several shapes and forms are pictured on the coelestial globe, collected from Dr. Hood ; as also a Discourse of the antiquity, progress and augmentation of astronomie.	Moxon, Joseph, 1627-1691.; Hood, Thomas, fl. 1582-1598.	1659 (1659)	Wing M3021; ESTC R23159	189,557	267

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thus_o the_o 1_o a_o clock_n hour-line_n 11.40_o who_o compliment_n 90._o be_v 78.20_o 2_o 24.15_o 65.45_o 3_o 38.4_o 51.56_o 4_o 53.36_o 36.24_o i_o measure_v in_o a_o quadrant_n of_o the_o same_o radius_fw-la with_o those_o arch_n already_o draw_v from_o the_o equinoctial_a line_n for_o the_o 1_o a_o clock_n hour_n 78.20_o 2_o 65.45_o 3_o 51.56_o 4_o 36.24_o and_o transfer_v these_o distance_n to_o the_o arch_n draw_v on_o the_o ceiling_n for_o then_o straight_a line_n draw_v through_o the_o mark_n in_o the_o arch_n and_o through_o the_o mark_n in_o the_o equator_fw-la and_o prolong_v both_o way_n to_o a_o convenient_a length_n shall_v be_v the_o several_a hour-line_n a_o foresay_a and_o when_o the_o sun_n shine_v upon_o the_o glass_n at_o nodus_fw-la its_o beam_n shall_v reflect_v upon_o the_o hour_n of_o the_o day_n prob._n xvi_o to_o make_v a_o dyal_n upon_o a_o solid_a ball_n or_o globe_n that_o shall_v show_v the_o hour_n of_o the_o day_n without_o a_o gnomon_n the_o 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this_o be_v a_o universal_a dyal_n and_o serve_v in_o all_o latitude_n therefore_o when_o you_o place_v it_o you_o must_v set_v one_o of_o the_o xii_o be_v downward_o and_o the_o axis_n parallel_n to_o the_o axis_n of_o the_o world_n but_o note_n both_o face_n of_o this_o dyal_n ought_v to_o be_v divide_v and_o the_o gnomon_n must_v appear_v on_o both_o side_n like_o the_o stick_n in_o a_o whirligig_n which_o childeren_n use_v or_o else_o you_o must_v turn_v it_o upside_o down_o so_o oft_o as_o the_o sun_n pass_v the_o equinoctial_a prob._n iii_o to_o make_v a_o horizontal_n dyal_n describe_v a_o circle_n on_o your_o plane_n as_o c_o b_o d_o e_o and_o through_o the_o centre_n a_o of_o that_o circle_n draw_v a_o meridian_n line_n as_o b_o e_z across_o that_o line_n at_o right_a angle_n with_o another_o line_n as_o c_o d_o so_o shall_v your_o circle_n be_v divide_v into_o four_o equal_a part_n divide_v each_o of_o these_o four_o part_n into_o 90._o degree_n so_o shall_v the_o whole_a 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through_o 40_o 50_o yea_o 60._o degree_n of_o the_o horizon_n in_o one_o hour_n time_n viz_o while_o 15._o degree_n of_o the_o equator_fw-la pass_v through_o the_o meridian_n but_o in_o a_o other_o hour_n time_n you_o will_v scarce_o have_v 4_o or_o 5_o degree_n pass_v through_o the_o horizon_n while_o 15_o degree_n of_o the_o equator_fw-la pass_v through_o the_o meridian_n but_o that_o you_o may_v know_v the_o motion_n of_o the_o sun_n represent_v by_o this_o meridian_n line_n through_o the_o horizon_n in_o all_o latitude_n elevate_v the_o pole_n to_o the_o elevation_n of_o your_o place_n and_o choose_v instead_o of_o a_o meridian_n line_v draw_v through_o the_o place_n of_o the_o sun_n the_o vernal_a colour_n to_o be_v your_o meridian_n line_n both_o because_o it_o be_v most_o visible_a and_o because_o from_o thence_o the_o degree_n of_o the_o equator_fw-la be_v begin_v to_o

on_o the_o meridian_n till_o the_o graduated_a edge_n cut_v the_o degree_n of_o the_o ecliptic_a the_o sun_n be_v in_o then_o i_o examine_v on_o the_o meridian_n what_o degree_n the_o upper_a end_n of_o the_o quadrant_n of_o altitude_n touch_v which_o in_o this_o example_n i_o find_v be_v 38½_n degree_n therefore_o i_o subtract_v 38½_n from_o 51½_n london_n latitude_n and_o there_o remain_v 13._o then_o count_v on_o the_o meridian_n 13._o degree_n backward_o from_o the_o place_n where_o the_o quadrant_n of_o altitude_n touch_v the_o meridian_n i_o come_v to_o 25½_n on_o the_o meridian_n northwards_o therefore_o i_o say_v in_o the_o north_n latitude_n of_o 25½_n degree_n and_o in_o the_o longitude_n of_o london_n which_o be_v in_o africa_n in_o the_o kingdom_n of_o numidia_n the_o sun_n may_v 10._o at_o 53._o minute_n past_o 8._o a_o clock_n in_o the_o morning_n have_v the_o same_o altitude_n above_o the_o horizon_n it_o have_v here_o at_o london_n the_o quadrant_n of_o altitude_n thus_o apply_v to_o the_o east_n point_n of_o the_o horizon_n make_v right_a angle_n with_o all_o point_n on_o the_o meridian_n even_o as_o all_o the_o meridian_n proceed_v from_o the_o pole_n do_v with_o the_o equator_fw-la therefore_o the_o quadrant_n be_v apply_v both_o to_o the_o east_n point_n and_o the_o sun_n place_n project_n a_o line_n to_o intersect_v the_o meridian_n perpendicular_o in_o equal_a degree_n from_o which_o intersection_n the_o sun_n have_v at_o the_o same_o time_n equal_a height_n be_v the_o degree_n few_o or_o many_o for_o those_o 5._o degree_n to_o the_o northwards_o of_o this_o intersection_n have_v the_o sun_n in_o the_o same_o height_n that_o they_o 5_o degree_n to_o the_o southwards_o have_v it_o and_o those_o 10_o 20_o 30._o degree_n more_o or_o less_o to_o the_o northwards_o have_v the_o sun_n in_o the_o same_o height_n that_o they_o have_v that_o be_v 10_o 20._o 30._o degree_n more_o or_o less_o to_o the_o southwards_o so_o that_o this_o prob._n may_v be_v perform_v another_o way_n more_o easy_o with_o your_o compass_n thus_o have_v first_o rectify_v the_o globe_n and_o hour_n index_n turn_v about_o the_o globe_n till_o the_o hour_n index_n point_n to_o the_o hour_n of_o the_o day_n then_o pitch_v one_o foot_n of_o your_o compass_n in_o the_o sun_n place_n and_o extend_v the_o other_o to_o the_o degree_n of_o latitude_n on_o the_o meridian_n which_o in_o this_o example_n be_v 51½_n degree_n north_n then_o keep_v the_o first_o foot_n of_o your_o compass_n on_o the_o degree_n of_o the_o sun_n turn_v about_o the_o other_o foot_n to_o the_o meridian_n and_o it_o will_v fall_v upon_o 25½_n as_o before_o blaew_n comment_v upon_o this_o problem_n take_v notice_n how_o gross_o they_o ere_o that_o think_v they_o can_v find_v the_o height_n of_o the_o pole_n at_o any_o hour_n of_o the_o day_n by_o the_o sun_n height_n because_o they_o do_v not_o consider_v that_o it_o be_v impossible_a to_o find_v the_o hour_n of_o the_o day_n unless_o they_o first_o know_v the_o height_n of_o the_o pole_n prob._n xlviii_o to_o find_v the_o length_n of_o the_o long_a and_o short_a artificial_a day_n or_o night_n the_o artificial_a day_n be_v that_o space_n of_o time_n which_o the_o sun_n be_v above_o the_o horizon_n of_o any_o place_n and_o the_o artificial_a night_n be_v that_o space_n of_o time_n which_o the_o sun_n be_v under_o the_o horizon_n of_o any_o place_n they_o be_v measure_v in_o the_o hour_n circle_n by_o hour_n and_o minute_n there_o be_v a_o constant_a unequallity_n of_o proportion_n in_o the_o length_n of_o these_o day_n and_o night_n which_o be_v cause_v both_o by_o the_o alteration_n of_o the_o sun_n declination_n and_o the_o difference_n of_o the_o pole_n elevation_n those_o that_o inhabit_v on_o the_o north_n side_n the_o equator_fw-la have_v their_o long_a day_n when_o the_o sun_n enter_v ♋_o and_o those_o that_o inhabit_v on_o the_o south_n side_n the_o equator_fw-la have_v their_o long_a day_n when_o the_o sun_n enter_v ♑_o but_o to_o know_v how_o long_o the_o long_a day_n be_v in_o any_o north_n or_o south_n elevation_n raise_v the_o north_n or_o south_n pole_n according_a to_o the_o elevation_n of_o the_o place_n and_o bring_v ♋_o for_o north_n elevation_n or_o ♑_o for_o south_n elevation_n to_o the_o meridian_n and_o the_o index_n of_o the_o hour_n circle_n to_o 12._o then_o turn_v the_o globe_n about_o till_o ♋_o for_o north_n elevation_n or_o ♑_o for_o south_n elevation_n come_v to_o the_o west_n side_n the_o horizon_n and_o the_o number_n of_o hour_n and_o minute_n point_v at_o on_o the_o hour_n circle_n double_v be_v the_o number_n of_o hour_n and_o minute_n of_o the_o long_a day_n the_o length_n of_o the_o night_n to_o that_o day_n be_v find_v by_o substract_v the_o length_n of_o the_o day_n from_o 24._o for_o the_o remainder_n be_v the_o length_n of_o the_o night_n the_o short_a day_n in_o that_o latitude_n be_v the_o length_n of_o the_o short_a night_n find_v as_o before_o and_o the_o long_a night_n be_v of_o the_o same_o length_n with_o the_o long_a day_n example_n i_o will_v know_v the_o length_n of_o the_o long_a day_n at_o london_n therefore_o i_o elevate_v the_o north_n pole_n 51½_n degree_n and_o bring_v ♋_o to_o the_o meridian_n and_o the_o index_n of_o the_o hour_n circle_n to_o 12._o then_o i_o turn_v ♋_o to_o the_o western_a side_n the_o horizon_n and_o find_v the_o index_n point_n at_o 8._o hour_n 18._o minute_n which_o be_v double_v make_v 16._o hour_n 36._o minute_n for_o the_o length_n of_o the_o long_a day_n here_o at_o london_n prob._n xlix_o to_o find_v how_o much_o the_o pole_n be_v raise_v or_o depress_v where_o the_o long_a day_n be_v a_o hour_n long_o or_o short_a than_o it_o be_v in_o your_o habitation_n rectify_v the_o globe_n to_o the_o latitude_n of_o your_o place_n and_o make_v a_o prick_n at_o that_o point_n of_o the_o tropic_a which_o be_v at_o the_o meridian_n i_o mean_v at_o the_o tropic_a of_n ♋_o if_o your_o habitation_n be_v on_o the_o north_n side_n the_o equator_fw-la or_o ♑_o if_o your_o habitation_n be_v on_o the_o south_n side_n the_o equator_fw-la and_o if_o you_o will_v know_v where_o the_o long_a day_n be_v just_a a_o hour_n long_o than_o it_o be_v at_o your_o habitation_n turn_v the_o globe_n to_o the_o westward_n till_o 7½_n degree_n of_o the_o equato●_fw-la pass_v through_o the_o meridian_n and_o make_v there_o another_o prick_n on_o the_o tropic_a then_o turn_v about_o the_o globe_n till_o the_o first_o prick_v come_v to_o the_o horizon_n and_o move_v the_o meridian_n through_o the_o notch_n of_o the_o horizon_n till_o the_o second_o prick_n on_o the_o tropic_a come_v to_o the_o horizon_n so_o shall_v the_o arch_n of_o the_o meridian_n contain_v between_o the_o elevation_n of_o your_o place_n and_o the_o degree_n of_o the_o meridian_n at_o the_o horizon_n be_v the_o number_n of_o degree_n that_o the_o pole_n be_v elevate_v high_a than_o it_o be_v in_o your_o latitude_n example_n i_o will_v know_v in_o what_o latitude_n the_o long_a day_n be_v a_o hour_n long_o than_o it_o be_v at_o london_n therefore_o i_o rectify_v the_o globe_n to_o 51½_n deg_n and_o where_o the_o meridian_n cut_v the_o tropic_a of_n ♋_o i_o make_v a_o prick_n then_o i_o note_v what_o degree_n of_o the_o equator_fw-la be_v at_o the_o meridian_n and_o from_o that_o degree_n on_o the_o equator_fw-la count_v 7½_n degree_n to_o the_o eastward_n and_o bring_v those_o 7½_n degree_n to_o the_o meridian_n also_o and_o again_o where_o the_o meridian_n cut_v the_o tropic_a of_n ♋_o i_o make_v another_o prick_n so_o shall_v 7½_n degree_n of_o the_o tropic_n be_v contain_v between_o those_o 〈◊〉_d prick_v then_o i_o turn_v the_o globe_n about_o till_o the_o first_o prick_n come_v to_o the_o horizon_n and_o with_o a_o quill_n thrust_v between_o the_o meridian_n and_o the_o ball_n i_o fasten_v the_o globe_n in_o this_o position_n afterward_o i_o move_v the_o meridian_n through_o the_o 〈◊〉_d of_o the_o horizon_n 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order_n or_o late_a author_n give_v the_o plain_n their_o name_n upon_o the_o same_o ground_n you_o may_v also_o learn_v to_o know_v they_o i_o confess_v both_o way_n admit_v of_o some_o just_a exception_n against_o for_o in_o the_o old_a rule_n a_o plain_a about_o the_o pole_n be_v call_v a_o equinoctial_a plain_n when_o as_o to_o a_o sudden_a apprehension_n it_o will_v sound_v more_o significant_a to_o call_v it_o a_o polar_a plain_n as_o late_a author_n do_v again_o late_a author_n call_v a_o horizontall_a plain_n a_o vertical_a plain_n when_o as_o it_o sound_v more_o significant_a to_o call_v it_o a_o horizontal_n plain_n as_o old_a author_n do_v because_o it_o lie_v flat_a upon_o the_o horizon_n but_o i_o shall_v give_v you_o the_o name_n according_a to_o both_o rule_n and_o leave_v you_o to_o your_o liberty_n to_o accept_v of_o which_o you_o please_v first_o therefore_o you_o have_v a_o equinoctial_a plain_n otherwise_o call_v a_o polar_a plain_n this_o plain_n have_v two_o 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contingence_n elevate_v to_o the_o height_n of_o the_o equinoctial_a draw_v line_n from_o the_o centre_n through_o every_o 15_o degree_n of_o the_o circle_n of_o position_n and_o by_o continue_v they_o intersect_v the_o line_n of_o contingence_n in_o the_o point_n from_o whence_o the_o hour_n line_n of_o a_o east_n or_o west_n dyal_n be_v to_o be_v draw_v example_n but_o because_o in_o our_o latitude_n the_o sun_n rise_v before_o 4._o in_o the_o morning_n therefore_o two_o hour-line_n be_v yet_o want_v viz._n 5_o and_o 4_o which_o i_o may_v find_v either_o by_o apply_v the_o thread_n first_o to_o 15_o and_o next_o to_o 30_o degree_n from_o 0_o towards_o g_o in_o the_o semicircle_n and_o so_o mark_v where_o it_o cut_v the_o contingent_a line_n as_o before_o or_o else_o by_o transfer_v the_o distance_n of_o the_o same_o number_n of_o hour_n line_n from_o the_o 6_o a_o clock_n line_n already_o draw_v on_o the_o side_n e_o 〈◊〉_d to_o the_o side_n e_o g_o as_o in_o prob._n 2._o of_o this_o 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be_v 9_o in_o the_o west_n must_v be_v 3._o etc._n etc._n prob._n viii_o to_o make_v a_o polar_a dyal_n polar_a dial_n be_v horizontal_n dial_n under_o the_o equinoctial_a they_o be_v of_o the_o same_o kind_n with_o east_n and_o west_n dial_n only_o whereas_o east_n and_o west_n dial_n have_v but_o the_o hour_n line_n of_o half_a the_o long_a day_n describe_v on_o they_o these_o have_v all_o the_o hour_n line_n of_o the_o whole_a day_n and_o be_v mark_v on_o both_o side_n the_o noon_n line_n as_o in_o the_o follow_a figure_n the_o style_n of_o this_o dyal_n must_v stand_v over_o the_o noon_n line_n parallel_n to_o the_o plane_n for_o than_o it_o will_v also_o be_v parallel_n to_o the_o axis_n of_o the_o world_n and_o its_o height_n above_o the_o plane_n must_v be_v the_o distance_n between_o the_o centre_n i_o of_o the_o semicircle_n and_o the_o point_n in_o the_o contingent_a line_n cut_v by_o the_o noon-line_n but_o i_o have_v insert_v the_o figure_n which_o alone_o be_v sufficient_a instruction_n prob._n ix_o to_o make_v erect_a south_n dial_n decline_a eastward_n or_o westward_n draw_v on_o your_o plane_n a_o horizontal_n line_n and_o on_o it_o describe_v a_o semicircle_n as_o you_o be_v teach_v in_o prob_n 4._o then_o rectify_v the_o globe_n quadrant_n of_o altitude_n colour_n and_o hour_n index_n as_o by_o the_o same_o problem_n and_o bring_v the_o low_a end_n of_o the_o quadrant_n of_o altitude_n to_o the_o degree_n of_o declination_n from_o the_o east_n or_o west_n point_n according_a be_v your_o declination_n be_v eastward_n or_o westward_n for_o then_o the_o quadrant_n of_o altitude_n shall_v represent_v a_o plane_n decline_v from_o the_o south_n eastward_n or_o westward_n according_o then_o tu●n_v the_o globe_n eastward_n till_o the_o index_n of_o the_o hour-circle_n point_v to_o all_o the_o hour_n before_o noon_n and_o examine_v in_o what_o number_n of_o degree_n from_o the_o zenith_n the_o colour_n cut_v the_o quadrant_n of_o altitude_n when_o the_o index_n point_v to_o each_o hour_n for_o a_o line_n draw_v from_o the_o centre_n a_o through_o the_o same_o number_n of_o degree_n reckon_v from_o the_o perpendicular_a a_o b_o which_o be_v the_o 12_o a_o clock_n line_n towards_o con_n the_o plane_n shall_v be_v the_o same_o hour-line_n the_o index_n point_v at_o example_n i_o will_v make_v a_o erect_a dyal_n decline_v from_o the_o south_n towards_o the_o east_n 27._o degree_n the_o globe_n quadrant_n of_o altitude_n vernal_a colour_n and_o hour_n index_n rectify_v as_o before_o i_o bring_v the_o low_a end_n of_o the_o quadrant_n of_o altitude_n to_o 27._o degree_n count_v from_o the_o east_n point_n of_o the_o horizon_n towards_o the_o north_n then_o i_o turn_v the_o globe_n east-ward_n till_o the_o index_n point_v to_o 11_o a_o clock_n or_o till_o 15._o deg_n of_o the_o equator_fw-la pass_v through_o the_o meridian_n and_o find_v the_o colour_n cut_v the_o quadrant_n of_o altitude_n in_o 9.43_o count_v from_o the_o zenith_n 10_o 19.0_o 9_o 25.57_o 8_o 35.10_o 7_o 45.56_o 6_o 60.15_o 5_o 79.45_o and_o these_o be_v the_o distance_n of_o the_o forenoon_n hour-line_n which_o i_o seek_v in_o the_o west_n side_n of_o the_o plane_n viz._n from_o b_o towards_z c_z and_o through_o these_o distance_n i_o draw_v line_n from_o the_o centre_n and_o these_o line_n shall_v be_v the_o forenoon_n hour-line_n now_o herein_o be_v a_o difference_n between_o decline_a dial_n and_o direct_v dial_n for_o have_v find_v the_o distance_n of_o the_o hour_n line_n for_o one_o half_a of_o the_o day_n be_v it_o either_o for_o before_o noon_n or_o after_o noon_n in_o a_o direct_a dyal_n you_o have_v also_o find_v the_o distance_n for_o the_o other_o half_a day_n because_o as_o be_v say_v prob._n 3._o equal_a number_n of_o hour_n have_v equal_a distance_n from_o the_o noon_n line_n but_o in_o decline_a dial_n it_n be_v not_o so_o because_o the_o sun_n remain_v long_o upon_o that_o side_n of_o the_o plane_n which_o it_o decline_v to_o than_o it_o do_v upon_o the_o contrary_a side_n there_o will_v be_v a_o great_a number_n of_o hour_n line_n upon_o it_o and_o by_o consequence_n the_o distance_n of_o the_o hour_n line_n less_o than_o on_o the_o contrary_a side_n of_o the_o plane_n therefore_o for_o find_v the_o after_o noon_n hour_n line_n i_o turn_v about_o the_o quadrant_n of_o altitude_n upon_o the_o zenith_n point_n till_o the_o low_a end_n of_o it_o come_v to_o the_o degree_n of_o the_o horizon_n opposite_a to_o that_o degree_n of_o declination_n that_o the_o quadrant_n of_o altitude_n be_v place_v at_o when_o i_o seek_v the_o before_o noon_n hour_n line_n viz_o to_o 27._o degree_n count_v ●om_n the_o west_n towards_o the_o south_n and_o bring_v the_o ver●al_a colour_n again_o to_o the_o meridian_n and_o the_o index_n as_o before_o to_o 12._o then_o turn_v the_o globe_n westward_n till_o the_o index_n point_v to_o 1_o a_o clock_n or_o till_o 15_o degr_n of_o the_o equator_fw-la pass_v through_o the_o meridian_n i_o find_v the_o colour_n cut_v the_o quadrant_n of_o altitude_n in_o 11.20_o count_v from_o the_o zenith_n 2_o 26.47_o 3_o 49.20_o 4_o 75.52_o and_o these_o be_v the_o distance_n of_o the_o after_o noon_n hour_n line_n which_o dista●●●●_n i_o seek_v in_o the_o east_n side_n of_o the_o plane_n viz._n from_o b_o towards_z d_o as_o before_o and_o so_o draw_v line_n from_o the_o centre_n a_o through_o these_o distance_n i_o have_v all_o the_o afternoon_n hour_n line_n also_o draw_v on_o my_o plane_n you_o may_v note_v that_o this_o plane_n be_v capable_a to_o receive_v no_o more_o hour_n line_n after_o noon_n then_o 4._o for_o when_o the_o colour_n go_v off_o the_o quadrant_n of_o altitude_n the_o sun_n go_v

westward_n have_v thus_o find_v out_o where_o this_o plane_n become_v horizontal_n make_v your_o dyal_n to_o this_o plane_n as_o by_o the_o second_o rule_n in_o this_o problem_n find_v also_o the_o style_n as_o be_v there_o direct_v 5._o if_o your_o plane_n be_v a_o decline_a incliner_n the_o globe_n and_o quadrant_n of_o altitude_n rectify_v bring_v the_o colour_n to_o the_o meridian_n and_o the_o quadrant_n of_o altitude_n to_o the_o degree_n of_o the_o horizon_n opposite_a to_o the_o degree_n of_o the_o plane_n declination_n and_o count_v upward_o on_o the_o quadrant_n of_o altitude_n the_o degree_n of_o inclination_n and_o make_v a_o 〈◊〉_d there_o for_o in_o the_o 〈◊〉_d of_o that_o prick_n find_v as_o by_o 〈◊〉_d 〈◊〉_d of_o the_o second_o book_n that_o decline_a in_o 〈◊〉_d shall_v become_v a_o horizontal_n plane_n then_o find_v the_o latitude_n and_o difference_n of_o longitude_n of_o this_o 〈◊〉_d by_o the_o 〈◊〉_d 〈◊〉_d and_o make_v a_o ●yal_a to_o that_o 〈◊〉_d by_o the_o second_o 〈◊〉_d in_o this_o problem_n find_v also_o the_o style_n as_o therein_o be_v direct_v prob._n xv._n to_o make_v a_o dyal_n on_o the_o ceiling_n of_o a_o room_n where_o the_o direct_a beam_n of_o the_o sun_n never_o come_v find_v some_o convenient_a place_n in_o the_o transum_fw-la of_o a_o window_n to_o place_v a_o small_a round_a piece_n of_o looking-glass_n about_o the_o bigness_n of_o a_o groat_n or_o less_o so_o as_o it_o may_v lie_v exact_o horizontal_n the_o point_n in_o the_o middle_n of_o this_o glass_n we_o will_v mark_v a_o and_o for_o distinction_n sake_n with_o mr_n palmer_n call_v it_o nodus_fw-la through_o this_o nodus_fw-la you_o must_v draw_v a_o meridian_n line_n on_o the_o floor_n thus_o hang_v a_o plumb_n line_n in_o the_o window_n exact_o over_o nodus_fw-la and_o the_o shadow_n that_o that_o plumb_n line_n cast_v on_o the_o floor_n just_a at_o noon_n will_v be_v a_o meridian_n line_n or_o you_o may_v find_v a_o meridian_n line_n otherwise_o as_o by_o the_o preface_n 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line_n black_v with_o small_a cole_n or_o any_o other_o culler_n as_o carpenter_n do_v and_o that_o line_n b_o c_o on_o the_o ceiling_n shall_v be_v a_o meridian_n line_n as_o well_o as_o that_o on_o the_o floor_n then_o examine_v the_o altitude_n of_o the_o equinoctial_a as_o by_o prob._n 6._o of_o the_o second_o book_n you_o do_v the_o meridian_n altitude_n of_o the_o sun_n and_o fasten_v a_o string_n just_a on_o the_o nodus_fw-la and_o remove_v that_o string_n in_o the_o meridian_n line_n on_o the_o ceiling_n till_o it_o have_v the_o same_o elevation_n in_o a_o quadrant_n that_o the_o equinoctial_a have_v in_o your_o habitation_n and_o through_o the_o point_n where_o the_o string_n touch_v the_o meridian_n line_n in_o the_o ceiling_n shall_v a_o line_n be_v draw_v at_o right_a angle_n with_o the_o meridian_n to_o represent_v the_o equinoctial_a line_n thus_o in_o our_o latitude_n the_o elevation_n of_o the_o equator_fw-la be_v 38½_n degree_n i_o remove_v the_o string_n fasten_v to_o the_o nodus_fw-la forward_o or_o backward_o in_o the_o meridian_n line_n of_o the_o ceiling_n till_o the_o plumb_n line_n of_o a_o quadrant_n when_o one_o of_o the_o side_n be_v apply_v to_o the_o string_n fall_v upon_o 38½_n degree_n and_o then_o i_o find_v it_o touch_v the_o meridian_n line_n at_o d_o in_o the_o ceiling_n therefore_o at_o d_o i_o make_v a_o mark_n and_o through_o this_o mark_n strike_v the_o line_n d_o e_o as_o before_o i_o do_v the_o meridian_n line_n to_o cut_v the_o meridian_n line_n at_o right_a angle_n this_o line_n shall_v be_v the_o equinoctial_a line_n then_o i_o place_v the_o centre_n of_o the_o semicircle_n of_o position_n upon_o nodus_fw-la and_o underprop_v it_o so_o that_o the_o flat_a side_n of_o it_o may_v lie_v parallel_n to_o the_o string_n when_o it_o be_v strain_v between_o the_o nodus_fw-la and_o the_o equinoctial_a and_o also_o so_o as_o the_o string_n may_v lie_v on_o the_o division_n of_o the_o semicircle_n mark_v o_o when_o it_o be_v help_v up_o to_o the_o meridian_n line_n in_o the_o ceiling_n then_o remove_v the_o string_n the_o space_n of_o 15._o degree_n in_o the_o circle_n of_o position_n to_o the_o eastward_n and_o extend_v it_o to_o the_o equator_fw-la on_o the_o ceiling_n where_o the_o string_n touch_v the_o equator_fw-la there_o shall_v be_v a_o point_n through_o which_o the_o 1_o a_o clock_n hour-line_n shall_v be_v draw_v and_o remove_v the_o string_n yet_o 15._o degree_n further_o to_o the_o eastward_n in_o the_o semicircle_n of_o position_n and_o extend_v it_o also_o to_o the_o equator_fw-la where_o it_o touch_v the_o equator_fw-la there_o shall_v be_v a_o point_n through_o which_o the_o 2_o a_o clock_n hour-line_n shall_v be_v draw_v remove_v the_o string_n yet_o 15._o degree_n further_o to_o the_o eastward_n in_o the_o semicircle_n of_o position_n and_o extend_v it_o to_o the_o equator_fw-la there_o shall_v be_v a_o point_n through_o which_o the_o 3_o a_o clock_n hour-line_n shall_v be_v draw_v the_o like_a 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distance_n of_o any_o hour_n line_n from_o the_o meridian_n line_n even_o so_o a_o line_n draw_v through_o every_o 15._o degree_n of_o the_o semicircle_n of_o position_n posit_v as_o aforesaid_a point_v out_o in_o the_o equinoctial_a line_n on_o the_o ceiling_n the_o distance_n of_o each_o respective_a hour_n line_n from_o the_o meridian_n line_n have_v thus_o find_v out_o the_o point_n in_o the_o equator_fw-la through_o which_o the_o afternoon_n hour-line_n be_v to_o be_v draw_v i_o may_v find_v the_o forenoon_n hour_n distance_n also_o the_o same_o way_n viz._n by_o bring_v the_o string_n to_o the_o several_a 15._o degree_n on_o the_o west_n side_n the_o semicircle_n of_o position_n or_o else_o i_o need_v only_o measure_v the_o distance_n of_o each_o hour_n distance_n find_v in_o the_o equator_fw-la from_o the_o meridian_n line_n on_o the_o ceiling_n for_o the_o same_o number_n of_o hour_n from_o 12_o have_v the_o same_o distance_n in_o the_o equinoctial_a line_n on_o the_o other_o 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