Selected quad for the lemma: end_n

Word A	Word B	Word C	Word D	Occurrence	Frequency Band	MI	MI Band	Prominent
end_n	draw_v	equal_a	line_n	2,859	5	9.5591	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

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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 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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 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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

 _fw-fr 44_o 26_o 29_o 36_o  _fw-fr  _fw-fr 48_o 15_o 27_o 54_o  _fw-fr ix_o 51_o 57_o 26_o 7_o iii_o  _fw-fr 55_o 32_o 24_o 14_o  _fw-fr  _fw-fr 59_o 1_o 22_o 16_o  _fw-fr  _fw-fr 62_o 24_o 20_o 14_o  _fw-fr viii_o 65_o 41_o 18_o 8_o iu._n  _fw-fr 68_o 54_o 15_o 59_o  _fw-fr  _fw-fr 72_o 2_o 13_o 47_o  _fw-fr  _fw-fr 75_o 7_o 11_o 33_o  _fw-fr vii_o 78_o 9_o 9_o 17_o v._o  _fw-fr 81_o 9_o 6_o 59_o  _fw-fr  _fw-fr 84_o 7_o 4_o 39_o  _fw-fr  _fw-fr 87_o 4_o 2_o 20_o  _fw-fr vi_o 90_o 0_o 0_o 0_o vi_o for_o this_o purpose_n here_o be_v two_o table_n join_v together_o both_o of_o they_o make_v for_o the_o latitude_n of_o london_n 51_o gr_n 30_o min._n the_o like_a to_o which_o every_o man_n may_v calculate_v for_o his_o own_o place_n the_o first_o of_o they_o be_v a_o table_n of_o such_o angle_n as_o be_v make_v by_o the_o hour_n line_n come_v through_o the_o centre_n of_o the_o ellipsis_n with_o the_o meridian_n line_n or_o line_n of_o 12._o and_o it_o be_v make_v by_o that_o rule_n 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any_o lean_v not_o upright_o plain_v whatsoever_o but_o the_o index_n must_v then_o lie_v in_o the_o zenith_n line_n of_o the_o place_n not_o of_o the_o plain_a and_o the_o ellipsis_n or_o index_n must_v move_v in_o the_o meridian_n of_o the_o place_n not_o of_o the_o plain_a and_o the_o zodiac_n must_v be_v like_a or_o proportional_a to_o the_o zodiac_n of_o the_o horizon_n but_o augment_v for_o the_o most_o part_n in_o this_o proportion_n as_o the_o radius_fw-la to_o the_o secant_fw-la of_o that_o angle_n that_o the_o meridian_n line_n upon_o the_o plain_a make_v with_o the_o horizon_n which_o angle_n must_v be_v get_v by_o a_o clinatorie_n so_o the_o radius_fw-la of_o the_o horizontal_n zodiac_n which_o be_v the_o cousin_a of_o the_o latitude_n to_o the_o radius_fw-la of_o the_o zodiac_n proper_a to_o the_o plain_a which_o zodiac_n must_v be_v set_v according_a to_o the_o line_n of_o 12_o upon_o the_o plain_a 2._o this_o way_n of_o delineation_n may_v likewise_o be_v apply_v to_o 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uses_n first_o if_o the_o index_n stand_v still_o and_o the_o ellipsis_n be_v make_v movable_a you_o may_v upon_o that_o plate_n which_o be_v immovable_a and_o on_o which_o the_o index_n stand_v describe_v a_o circle_n who_o centre_n must_v be_v the_o foot_n of_o the_o index_n and_o draw_v a_o meridian_n line_n upon_o the_o say_v immovable_a plate_n just_a under_o the_o meridian_n of_o the_o ellipsis_n and_o from_o the_o foot_n of_o the_o index_n you_o may_v divide_v that_o circle_n begin_v from_o the_o meridian_n line_n into_o 360_o gr_n or_o so_o many_o of_o they_o as_o shall_v be_v needful_a by_o these_o degree_n you_o shall_v find_v the_o sun_n azimuth_n by_o the_o shadow_n of_o the_o upright_a index_n and_o by_o the_o division_n of_o the_o ellipsis_n you_o may_v know_v the_o hour_n of_o the_o day_n so_o both_o azimuth_n and_o hour_n be_v show_v upon_o the_o two_o plate_n by_o one_o upright_a index_n this_o kind_n of_o dial_n must_v be_v set_v in_o its_o true_a position_n for_o it_o will_v not_o set_v itself_o and_o must_v there_o be_v fix_v if_o it_o be_v upon_o a_o horizontall_a or_o any_o direct_a plain_n you_o may_v draw_v a_o meridian_n line_n thereon_o and_o either_o draw_v the_o azimuth_n true_a upon_o it_o and_o so_o make_v the_o ellipsis_n to_o move_v to_o and_o fro_o according_a to_o that_o meridian_n or_o else_o if_o both_o your_o plate_n be_v to_o be_v fix_v upon_o any_o base_a prepare_v for_o they_o you_o may_v first_o upon_o that_o base_a draw_v a_o true_a meridian_n line_n and_o to_o that_o line_n make_v the_o meridian_n of_o the_o dial_n to_o agree_v the_o like_a must_v

a_o hour_n from_o 12_o in_o the_o ellipsis_n the_o remain_a breadth_n n_o o_o or_o e_o f_o or_o g_o h_n may_v be_v just_o fit_a to_o a_o b_o the_o breadth_n of_o the_o hollow_a area_n in_o which_o this_o lesser_a rectangle_v parallelogram_n e_o f_o g_o h_o may_v be_v move_v to_o and_o fro_o as_o there_o shall_v be_v occasion_n and_o let_v the_o thickness_n or_o depth_n of_o this_o move_a plate_n be_v the_o same_o with_o the_o thickness_n of_o the_o limb_n of_o the_o low_a plate_n the_o division_n of_o the_o ellipsis_n may_v be_v make_v according_a to_o the_o rule_v before_o give_v 3._o in_o the_o midst_n of_o this_o lesser_a plate_n let_v a_o hole_n be_v pierce_v quite_o through_o it_o and_o in_o that_o hole_n let_v a_o thread_n be_v extend_v as_o i_o k_o which_o be_v to_o serve_v for_o a_o index_n by_o which_o the_o say_a semiellipsis_n be_v to_o be_v rectify_v and_o therefore_o it_o be_v best_o that_o the_o thread_n i_o k_n be_v lay_v just_a in_o the_o long_a diameter_n which_o be_v the_o 6_o a_o clock_n line_n 4._o take_v the_o lesser_a parallelogram_n and_o put_v it_o into_o its_o place_n as_o close_o to_o the_o end_n a_o b_o as_o it_o will_v go_v and_o when_o it_o be_v there_o lay_v observe_v where_o the_o thread_n lie_v upon_o the_o low_a area_n and_o draw_v the_o line_n upon_o which_o it_o lie_v which_o must_v be_v the_o line_n 90_o 90_o upon_o which_o the_o scale_n that_o be_v inscribe_v must_v take_v their_o beginning_n and_o likewise_o you_o be_v to_o take_v the_o long_a radius_fw-la o_fw-la m_o and_o as_o the_o plate_n there_o lie_v set_v one_o foot_n of_o that_o radius_fw-la upon_o o_fw-la and_o let_v the_o other_o reach_n as_o far_o as_o it_o will_v which_o must_v be_v upon_o the_o rise_a limb_n beyond_o the_o inner_a edge_n of_o it_o so_o much_o as_o m_n n_o come_v to_o in_o that_o point_n you_o be_v to_o make_v one_o centre_n so_o again_o turn_v your_o lesser_a plate_n about_o you_o must_v lay_v it_o in_o the_o contrary_a way_n close_o to_o a_o b_o as_o you_o do_v before_o and_o from_o the_o point_n o_o you_o may_v find_v the_o second_o centre_n both_o these_o centre_n in_o each_o of_o which_o must_v a_o thread_n be_v fasten_v will_v happen_v to_o fall_v in_o the_o former_a line_n 90_o and_o 90_o near_o the_o point_n t_o and_o v._n be_v thus_o far_o prepare_v you_o may_v take_v away_o the_o lesser_a plate_n and_o divide_v the_o scale_n upon_o the_o great_a plate_n in_o this_o manner_n 5._o first_o for_o the_o two_o limb_n of_o it_o they_o be_v nothing_o else_o but_o the_o degree_n of_o a_o circle_n project_v thereon_o from_o the_o two_o centre_n which_o may_v therefore_o without_o difficulty_n be_v do_v either_o from_o the_o degree_n of_o a_o circle_n or_o else_o by_o tangent_fw-la line_n as_o any_o man_n will_v easy_o perceive_v 6._o second_o for_o the_o other_o scale_n you_o must_v make_v they_o parallel_v to_o the_o edge_n of_o the_o limb_n there_o be_v three_o of_o they_o in_o number_n the_o long_a be_v a_o scale_n of_o tangent_n the_o middlemost_a be_v a_o scale_n of_o hour_n make_v in_o the_o form_n of_o a_o line_n of_o sines_n the_o three_o be_v a_o zodiac_n or_o scale_n of_o the_o year_n the_o tangent_n be_v make_v thus_o take_v m_n o_o as_o radius_fw-la find_v the_o cousin_a of_o your_o latitude_n agreeable_a thereto_o and_o make_v that_o cousin_a as_o a_o radius_fw-la or_o tangent_fw-la of_o 45_o degree_n all_o the_o other_o tangent_n be_v to_o be_v fit_v according_o then_o to_o know_v how_o far_o of_o this_o line_n will_v be_v useful_a put_v the_o lesser_a plate_n again_o into_o its_o place_n as_o close_o to_o the_o end_n c_o d_o as_o it_o will_v go_v so_o shall_v the_o thread_n i_o k_n show_v the_o further_a point_n of_o it_o that_o will_v be_v useful_a the_o middle_a scale_n of_o sines_n be_v make_v thus_o count_n the_o compliment_n of_o your_o latitude_n upon_o the_o new_a make_v tangent_fw-la line_n and_o from_o the_o begin_n of_o the_o scale_n to_o that_o point_n make_v a_o line_n of_o sin_n for_o six_o hour_n and_o their_o quarter_n so_o shall_v this_o scale_n be_v fit_v the_o zodiac_n or_o annual_a scale_n be_v equal_a in_o length_n to_o the_o tangent_fw-la of_o 23_o gr_n 30_o min._n and_o the_o manner_n of_o inscription_n with_o table_n whereby_o to_o do_v it_o be_v set_v down_o before_o and_o need_v not_o be_v here_o repeat_v the_o reason_n why_o this_o instrument_n be_v thus_o contrive_v the_o intent_n of_o the_o contrivance_n be_v that_o it_o shall_v show_v both_o azimuth_n and_o hour_n and_o that_o therefore_o there_o shall_v be_v a_o ci●●●_n and_o a_o ellipsis_n slide_v over_o it_o both_o of_o they_o make_v to_o one_o centre_n so_o that_o the_o centre_n shall_v be_v in_o the_o midst_n and_o the_o circle_n shall_v be_v a_o whole_a entire_a circle_n and_o the_o ellipsis_n also_o whole_a but_o because_o the_o ellipsis_n slide_v upon_o the_o nether_a plain_n do_v sometime_o of_o necessity_n cover_v the_o centre_n so_o as_o that_o there_o can_v be_v no_o thread_n fix_v for_o use_n i_o be_v therefore_o compel_v to_o order_v it_o in_o this_o manner_n that_o be_v before_o express_v that_o the_o motion_n of_o the_o upper_a plate_n and_o the_o centre_n may_v stand_v clear_a without_o hinder_v each_o other_o then_o further_o it_o must_v be_v note_v that_o the_o instrument_n be_v not_o general_a to_o all_o but_o particular_a to_o one_o la●●tude_n the_o use_n of_o it_o do_v here_o follow_v which_o by_o reason_n of_o the_o semiellipsis_n will_v not_o be_v so_o easy_a because_o many_o change_n be_v require_v in_o general_a note_n thus_o much_o 1._o in_o use_v this_o instrument_n you_o must_v always_o suppose_v that_o you_o look_v upon_o the_o north._n 2._o if_o the_o declination_n of_o the_o sun_n or_o star_n be_v north_n hold_v a_o b_o towards_o you_o if_o south_n then_o hold_v c_o d_o towards_o you_o 3._o if_o the_o sun_n or_o star_n be_v eastward_o of_o the_o meridian_n let_v the_o morning_n hour_n be_v towards_o you_o if_o they_o be_v westward_o let_v the_o evening_n hour_n be_v towards_o you_o 4._o always_o use_v that_o thread_n which_o be_v on_o the_o same_o side_n with_o the_o centre_n of_o the_o ellipsis_n and_o that_o side_n lin●_n of_o the_o large_a plate_n be_v ever_o to_o be_v take_v for_o the_o meridian_n and_o consequent_o the_o other_o side_n must_v be_v esteem_v for_o one_o of_o the_o two_o coast_n of_o east_n or_o west_n 5._o because_o north_n be_v further_a from_o you_o therefore_o the_o further_a quarter_n of_o the_o limb_n must_v be_v either_o north-east_n or_o northwest_n the_o near_a southeast_n or_o south-west_n these_o caution_n be_v observe_v the_o conclusion_n that_o be_v to_o be_v wrought_v will_v be_v easy_a 1._o by_o have_v the_o azimuth_n to_o find_v the_o hour_n first_o order_v your_o instrument_n by_o the_o former_a caution_n according_a to_o the_o present_a case_n of_o your_o observation_n and_o rectify_v the_o upper_a ●late_n by_o help_n of_o the_o thread_n index_n either_o to_o the_o declination_n of_o the_o star_n count_v in_o the_o tangent_fw-la line_n or_o to_o the_o sun_n place_n in_o the_o zodiac_n then_o count_v the_o azimuth_n give_v upon_o the_o right_a quarter_n of_o the_o limb_n and_o apply_v the_o thread_n thereto_o so_o shall_v the_o thread_n show_v upon_o the_o ellipsis_n the_o hour_n in_o which_o the_o sun_n or_o star_n be_v if_o the_o work_n be_v for_o the_o sun_n than_o the_o hour_n thus_o show_v be_v the_o sun_n hour_n or_o hour_n of_o the_o day_n if_o the_o work_n be_v for_o a_o star_n it_o than_o show_v the_o star_n hour_n only_o which_o must_v afterward_o be_v reduce_v into_o the_o sun_n hour_n that_o it_o may_v be_v the_o true_a hour_n of_o the_o night_n this_o change_n may_v most_o easy_o be_v do_v by_o a_o common_a nocturnal_a 2._o by_o have_v the_o hour_n in_o which_o the_o sun_n or_o any_o star_n be_v the_o azimuth_n thereof_o may_v be_v find_v the_o instrument_n be_v rectify_v lay_v the_o thread_n upon_o the_o hour_n count_v in_o the_o ellipsis_n the_o same_o thread_n will_v show_v the_o azimuth_n in_o the_o graduation_n upon_o the_o limb_n 3._o to_o find_v the_o ascensionall_a difference_n the_o semidiurnall_a and_o seminocturnall_a arke_n with_o the_o time_n of_o their_o rise_n and_o setting_n in_o general_a note_n this_o if_o the_o sun_n or_o star_n decline_v northward_o than_o the_o semidiurnall_a ark_n be_v great_a than_o six_o hour_n if_o southward_o then_o less_o the_o upper_a plate_n therefore_o be_v rectify_v either_o to_o the_o sun_n place_n or_o to_o the_o star_n declination_n the_o thread_n will_v show_v upon_o the_o middle_a scale_n the_o ascensionall_a difference_n if_o you_o count_v the_o hour_n

or_o 3_o hour_n r_o i_o the_o sine_fw-la of_o 60_o gr_n or_o 4_o hour_n r_o h_o the_o sine_fw-la of_o 5_o hour_n r_o d_o or_o r_z 12_o the_o whole_a sine_fw-la or_o sine_fw-la of_o 90_o gr_n then_o through_o each_o of_o these_o point_n at_o h_z i_o k_o l_o m_o r_o o_o p_o q_o draw_v a_o line_n parallel_n to_o the_o other_o conjugate_v diameter_n namely_o to_o 6_o r_z 6._o this_o do_v make_v r_z 6_o a_o radius_fw-la and_o to_o that_o radius_fw-la make_v m7_n m5_n 07_o 05_o each_v of_o they_o a_o sine_fw-la of_o 5_o hour_n or_o 75_o degree_n make_v l_o 8_o l_o 4_o p_o 4_o p_o 8_o a_o sine_fw-la of_o 4_o hour_n or_o 60_o gr_n make_v k9_n k3_n q3_n q_o 9_o each_o of_o they_o a_o sine_fw-la of_o 3_o hour_n or_o 45_o gr_n so_o i_o 10_o i●_n must_v be_v the_o sine_fw-la of_o 2_o hour_n and_o h_z 11_o h_z 1_o the_o sine_fw-la of_o 1_o hour_n or_o 15_o gr_n by_o this_o work_n you_o shall_v upon_o the_o former_a parallel_n line_n draw_v through_o h_z i_o k_o l_o m_o o_o p_o q_o find_v the_o hour_n point_v of_o 3_o 4_o 5_o 6_o 7_o 8_o 9_o 10_o 11_o 12_o 1_o 2_o 3_o 4_o 5_o 6_o 7_o 8_o 9_o in_o which_o you_o be_v to_o sign_n out_o the_o hour_n point_v and_o through_o which_o you_o be_v to_o draw_v the_o ellipsis_n as_o you_o see_v the_o figure_n for_o a_o pattern_n you_o may_v also_o have_v divide_v each_o of_o the_o radiuss_n note_v with_o r_z 6_o into_o part_n correspondent_a to_o a_o line_n of_o sines_n as_o you_o see_v partly_o do_v at_o the_o letter_n s_o t_o u._fw-mi in_o the_o last_o of_o the_o two_o former_a scheme_n as_o at_o s_o t_o u_o be_v express_v and_o through_o those_o point_n you_o must_v draw_v parallel_n to_o the_o other_o diameter_n d_o r_o g._n then_o to_o the_o radius_fw-la d_o r_o make_v s_o 7_o s_z 5_o the_o sine_fw-la of_o 15_o gr_n or_o 1_o hour_n t_o 8_o t_o 4_o the_o sine_fw-la of_o 30_o gr_n or_o too_o hour_n u._fw-mi 9_o u_z 3_o the_o sine_fw-la of_o 45_o gr_n or_o 3_o hour_n and_o so_o forward_o by_o which_o work_n you_o shall_v find_v the_o same_o hour_n point_v 3_o 4_o 5_o 6_o 7_o 8_o 9_o etc._n etc._n that_o you_o do_v before_o and_o so_o you_o may_v find_v out_o and_o draw_v the_o ellipsis_n by_o they_o the_o same_o manner_n of_o work_n be_v to_o be_v perform_v for_o half_n and_o quarter_n of_o the_o several_a hour_n how_o the_o zodiac_n be_v to_o be_v place_v and_o limit_v it_o be_v the_o same_o work_n with_o that_o which_o go_v before_o pag._n 185._o yet_o i_o will_v here_o insert_v it_o again_o first_o work_v thus_o as_o the_o radius_fw-la be_v to_o the_o tangent_fw-la of_o 23½_n gr_n so_o let_v e_o f_o which_o be_v former_o find_v to_o be_v the_o sine_fw-la of_o the_o equinoctial_o altitude_n above_o the_o horizon_n 38_o gr_n 30_o mn_n in_o respect_n of_o the_o radius_fw-la r_o 6_o and_o must_v now_o again_o be_v here_o use_v be_v to_o a_o four_o quantity_n which_o suppose_v to_o be_v f_o w._n take_v therefore_o that_o length_n f_o w_n and_o set_v it_o from_o r_o to_o x_o on_o the_o north_n side_n in_o this_o example_n and_o through_o x_o draw_v x_o γ_n parallel_v to_o the_o subindicall_a line_n r_o s._n then_o say_v again_o as_o the_o radius_fw-la be_v to_o the_o tangent_fw-la of_o 23_o gr_n and_o a_o half_a so_o let_v r_o c_o which_o be_v before_o find_v to_o be_v the_o sine_fw-la of_o the_o latitude_n of_o the_o place_n 51_o gr_n and_o a_o half_a in_o respect_n of_o the_o radius_fw-la r_o 6_o and_o come_v now_o to_o be_v here_o use_v again_o be_v to_o a_o four_o quantity_n which_o suppose_v to_o be_v f_o z._n take_v therefore_o f_o z_o and_o set_v it_o upon_o the_o line_n former_o draw_v through_o x_o from_o x_o contrary_a to_o the_o go_v of_o the_o subindical_a line_n namely_o southward_o in_o this_o example_n i_o say_v from_o x_o to_o γ_n then_o from_o γ_n through_o r_o draw_v γ_n r_o π_n and_o make_v r_o π_n equal_a to_o r_o γ_n so_o shall_v γ_n π_n be_v the_o zodiac_n both_o place_v right_o and_o just_o limit_v for_o division_n of_o it_o you_o must_v conceive_v that_o r_o γ_n or_o r_o π_n be_v a_o tangent_fw-la of_o 23_o and_o a_o half_a gr_n the_o sun_n great_a declination_n and_o consequent_o you_o may_v by_o it_o set_v on_o either_o 12_o month_n or_o 12_o sign_n as_o you_o will_v the_o manner_n whereof_o have_v be_v often_o show_v in_o this_o book_n and_o especial_o pag._n 10_o 11._o and_o pag._n 14_o 15_o etc._n etc._n so_o that_o now_o all_o this_o work_n be_v come_v to_o a_o end_n the_o index_n must_v slide_v to_o and_o fro_o upon_o the_o line_n γ_n π_n or_o the_o index_n stand_v the_o ellipsis_n must_v move_v after_o the_o same_o rate_n γ_n π_n be_v the_o proper_a meridian_n of_o the_o index_n and_o if_o your_o work_n when_o you_o make_v this_o dial_n according_a to_o this_o case_n here_o before_o put_v be_v exact_o true_a you_o shall_v find_v the_o zodiacall_a line_n π_n γ_n to_o fall_v just_a into_o the_o hour_n line_n of_o 5_o and_o 7_o as_o they_o ought_v to_o do_v because_o the_o difference_n of_o the_o index_n longitude_n be_v assume_v to_o be_v 75_o gr_n from_o the_o south_n meridian_n of_o the_o place_n which_o be_v the_o same_o with_o those_o hour_n the_o sign_n ♋_o must_v be_v place_v at_o γ_n and_o ♈_o at_o π_n in_o this_o dial_n the_o index_n must_v lie_v when_o it_o be_v in_o the_o centre_n r_o just_a over_o the_o line_n r_o s_o and_o must_v always_o move_v in_o a_o parallel_n position_n to_o itself_o and_o it_o must_v in_o this_o example_n recline_v 45_o gr_n or_o rise_v above_o the_o horizon_n or_o above_o r_o saint_n make_v a_o angle_n above_o that_o line_n 45_o gr_n also_o but_o though_o it_o lie_v thus_o yet_o it_o must_v move_v in_o the_o line_n γ_n π_n and_o it_o must_v be_v so_o set_v on_o that_o when_o you_o project_v the_o fiducial_a edge_n of_o it_o into_o a_o point_n as_o workman_n use_v to_o do_v when_o with_o their_o eye_n they_o tr●e_v the_o straightness_n of_o a_o line_n all_o that_o edge_n may_v at_o once_o just_o appear_v to_o run_v into_o the_o line_n γ_n π_n wherever_o the_o index_n be_v set_v in_o the_o zodiac_n this_o be_v to_o be_v do_v careful_o i_o have_v here_o set_v two_o of_o they_o who_o proper_a meridian_n i_o mean_v proper_a to_o the_o index_n which_o be_v the_o line_n of_o their_o zodiac_n viz._n γ_n π_n do_v not_o lie_v in_o one_o and_o the_o same_o right_a line_n or_o parallelism_n which_o be_v the_o sameness_n of_o position_n but_o make_v angle_n one_o to_o the_o other_o this_o be_v do_v because_o they_o shall_v not_o lie_v in_o one_o meridian_n for_o by_o that_o mean_v they_o will_v always_o set_v one_o another_o which_o the_o horizontal_n dial_n with_o the_o single_a ellipsis_n to_o a_o upright_a index_n will_v not_o do_v at_o all_o time_n these_o two_o i_o say_v will_v set_v themselves_o and_o if_o you_o add_v a_o common_a horizontall_a dial_n more_o to_o stand_v between_o they_o as_o you_o see_v do_v there_o they_o will_v be_v the_o more_o specious_a and_o useful_a for_o set_v each_o other_o i_o have_v set_v that_o who_o index_n look_v north-east_n upon_o the_o left_a hand_n you_o may_v set_v it_o on_o the_o right_a hand_n if_o you_o will_v and_o the_o other_o on_o the_o left_a for_o this_o make_v no_o material_a change_n the_o index_n be_v best_a to_o be_v a_o thread_n other_o circumstance_n i_o remember_v none_o but_o what_o the_o workman_n will_v be_v well_o able_a to_o go_v through_o another_o way_n for_o the_o description_n of_o a_o ellipticall_a dial_n upon_o the_o horizontall_a plain_a of_o 51_o gr_n 30_o min._n latitude_n who_o zodiac_n and_o the_o motion_n of_o the_o index_n be_v perform_v upon_o the_o ●oures_n of_o 7_o in_o the_o morning_n and_o of_o 5_o in_o the_o afternoon_n as_o the_o same_o hour_n be_v draw_v upon_o the_o common_a horizontall_a dial_n this_o way_n be_v former_o write_v and_o though_o it_o need_v not_o to_o have_v be_v here_o place_v in_o respect_n the_o way_n last_o give_v be_v the_o best_a yet_o because_o it_o do_v somewhat_o differ_v from_o what_o be_v set_v down_o before_o i_o think_v best_a not_o to_o omit_v it_o because_o it_o be_v delightful_a to_o see_v different_a way_n ●●_o meet_v both_o in_o one_o effect_n 1._o first_o you_o be_v to_o get_v this_o way_n the_o altitude_n of_o each_o hour_n point_n in_o the_o equino●tiall_a above_o the_o horizon_n by_o this_o r●le_n as_o the_o radius_fw-la to_o the_o sine_fw-la of_o 38_o gr_n 30_o min._n so_o ●he_v sines_n of_o 75_o 60_o 45_o 30_o 15_o gr_n to_o