Selected quad for the lemma: hand_n

Word A	Word B	Word C	Word D	Occurrence	Frequency Band	MI	MI Band	Prominent
hand_n	left_a	right_a	stand_v	23,693	5	7.0021	4	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

you_o be_v first_o to_o frame_v a_o table_n of_o angle_n at_o the_o pole_n which_o will_v not_o be_v hard_a to_o perform_v and_o the_o manner_n of_o it_o will_v be_v see_v best_a in_o a_o example_n be_v altogether_o like_o the_o computation_n of_o the_o say_a angle_n at_o the_o pole_n for_o the_o hour_n of_o any_o place_n to_o the_o same_o decline_a plain_n i_o have_v here_o first_o of_o all_o in_o a_o general_a table_n set_v down_o the_o gradual_a distance_n of_o hour_n and_o quarter_n from_o 12_o at_o noon_n or_o midday_n which_o will_v be_v some_o help_n in_o perform_v the_o work_n the_o hour_n that_o be_v on_o the_o left_a side_n of_o the_o degree_n be_v the_o east_n or_o forenoon_n hour_n and_o those_o on_o the_o right_a hand_n be_v the_o west_n or_o afternoon_n hour_n suppose_v as_o before_o prop._n 4._o a_o difference_n of_o longitude_n be_v give_v 39_o gr_n 25_o min._n towards_o the_o east_n and_o it_o be_v require_v to_o know_v what_o angle_v our_o hour_n namely_o those_o 12_o that_o stand_v near_o to_o it_o six_o upon_o one_o side_n and_o six_o upon_o the_o other_o with_o their_o intermediate_v quarter_n do_v make_v with_o this_o longitude_n or_o proper_a meridian_n for_o so_o i_o intend_v to_o call_v it_o i_o first_o take_v the_o give_v longitude_n or_o proper_a meridian_n 39_o gr_n 25_o min_fw-mi and_o enter_v it_o among_o the_o east_n hour_n of_o the_o general_a table_n and_o i_o since_o it_o to_o fall_v in_o at_o a_o that_o be_v between_o a_o quarter_n and_o half_a a_o hour_n past_o 9_o before_o noon_n and_o i_o find_v also_o the_o circumstant_fw-la number_n to_o be_v 37.30_o the_o lesser_a and_o 41.15_o the_o great_a the_o difference_n between_o these_o two_o number_n and_o the_o longitude_n give_v be_v 1_o gr_n 55_o min._n and_o 1_o gr_n 50_o min._n as_o you_o see_v they_o set_v down_o in_o the_o say_v general_a table_n right_a against_o the_o letter_n a._n these_o two_o difference_n be_v to_o be_v first_o place_v in_o this_o second_o table_n of_o angle_n at_o the_o pole_n as_o you_o see_v in_o the_o example_n where_o first_o of_o all_o be_v write_v proper_a meridian_n 00.00_o separate_v from_o the_o rest_n as_o signify_v only_o the_o place_n where_o it_o be_v to_o stand_v and_o above_o it_o be_v place_v the_o difference_n between_o 37.30_o and_o the_o proper_a meridian_n 39.25_o namely_o 1_o gr_n 55_o min._n so_o again_o below_o it_o be_v place_v 1_o gr_n 50_o min._n which_o be_v the_o difference_n of_o 39_o gr_n 25_o min._n the_o proper_a meridian_n from_o the_o next_o great_a number_v 41_o gr_n 15_o min._n now_o to_o these_o two_o radical_a number_n i_o add_v ¼_n ½_o ¾_n and_o one_o whole_a hour_n namely_o a_o b_o c_o and_o thereby_o produce_v e_fw-la f_o g_o on_o both_o side_n the_o proper_a meridian_n then_o to_o r_o e_o f_o g_o i_o add_v 15_o gr_n d_o namely_o the_o number_n of_o one_o hour_n and_o thereby_o do_v further_o produce_v h_o i_o k_o l_o on_o both_o side_n the_o proper_a meridian_n as_o before_o and_o afterward_o for_o more_o ease_n to_o the_o number_n r_o e_o f_o g_o h_o i_o k_o l_o i_o add_v 30_o gr_n or_o two_o hour_n and_o do_v thereby_o produce_v on_o both_o side_n the_o eight_o number_n note_v with_o the_o letter_n m._n and_o so_o still_o add_v 30_o gr_n to_o the_o last_o eight_o number_n note_v with_o m_o or_o else_o add_v 60_o gr_n to_o the_o first_o eight_o number_n note_v with_o r_o e_o f_o g_o h_o i_o k_o l_o i_o shall_v make_v the_o eight_o remain_a number_n note_v with_o the_o letter_n n_o both_z above_z and_o below_o on_o both_o side_n the_o proper_a meridian_n and_o so_o this_o table_n of_o angle_n at_o the_o pole_n be_v complete_v for_o if_o it_o shall_v in_o the_o same_o manner_n be_v further_o continue_v the_o next_o number_n above_z will_v be_v 91_o gr_n 55_o min._n and_o below_z 91_o gr_n 50_o min._n both_o great_a than_o 90_o gr_n beyond_o which_o there_o will_v be_v neither_o need_n nor_o expedience_n to_o go_v this_o way_n of_o form_v the_o angle_n i_o think_v best_a to_o take_v because_o it_o be_v more_o plain_a and_o easy_a than_o any_o other_o which_o else_o may_v have_v be_v in_o this_o work_n use_v you_o be_v afterward_o to_o place_v the_o hour_n in_o this_o last_o table_n about_o the_o proper_a meridian_n just_a as_o you_o see_v their_o order_n to_o be_v about_o the_o letter_n a_o in_o the_o general_a table_n and_o as_o you_o see_v they_o be_v in_o this_o particular_a table_n of_o angle_n at_o the_o pole_n the_o like_a work_n serve_v for_o west_n longitude_n thus_o you_o have_v the_o angle_n for_o 12_o hour_n and_o their_o quarter_n the_o same_o angle_n serve_v for_o the_o other_o 12_o hour_n and_o whatsoever_o be_v hereafter_o compute_v for_o any_o of_o these_o 12_o hour_n must_v be_v understand_v to_o serve_v also_o for_o the_o 12_o opposite_n and_o so_o the_o work_n will_v be_v do_v for_o the_o whole_a circle_n or_o 24_o hour_n of_o the_o natural_a day_n 6._o by_o know_v the_o angle_n at_o the_o pole_n and_o the_o latitude_n of_o the_o place_n or_o horizon_n how_o to_o find_v the_o horizontall_a space_n thereto_o belong_v we_o must_v suppose_v that_o this_o longitude_n or_o meridian_n which_o we_o have_v before_o mention_v be_v proper_a to_o some_o horizon_n or_o other_o above_o which_o also_o the_o elevation_n of_o the_o pole_n must_v be_v imagine_v know_v which_o we_o may_v suppose_v to_o be_v 40_o gr_n as_o before_o prop._n 4._o in_o respect_n of_o this_o plain_a or_o horizon_n it_o be_v that_o the_o space_n now_o mention_v be_v call_v horizontall_a space_n the_o way_n to_o find_v they_o for_o this_o ellipticall_a work_n be_v converse_v to_o that_o which_o be_v usual_a in_o decline_a plain_n namely_o thus_o as_o the_o sine_fw-la of_o the_o pole_n elevation_n above_o this_o horizon_n or_o plain_n be_v to_o the_o radius_fw-la so_o be_v the_o tangent_fw-la of_o each_o of_o these_o angle_n at_o the_o pole_n to_o the_o tangent_fw-la of_o the_o horizontall_a space_n belong_v to_o each_o of_o those_o foresay_a angle_n so_o have_v find_v all_o these_o horizontall_a space_n several_o by_o this_o form_n of_o calculation_n you_o may_v set_v they_o into_o a_o table_n as_o here_o you_o see_v it_o do_v in_o the_o first_o of_o the_o two_o main_a column_n they_o signify_v the_o distance_n of_o every_o of_o the_o hour_n and_o quarter_n from_o the_o proper_a meridian_n and_o be_v to_o be_v account_v as_o number_v in_o the_o degree_n of_o the_o say_v plain_a or_o horizon_n 7._o by_o know_v the_o angle_n at_o the_o pole_n and_o the_o latitude_n of_o the_o plain_a or_o horizon_n how_o to_o find_v the_o equinoctial_a altitude_n or_o depression_n above_o or_o under_o the_o same_o horizon_n due_a to_o the_o say_a angle_n at_o the_o pole_n or_o point_n of_o the_o equinoctial_a the_o proportion_n by_o which_o this_o be_v to_o be_v effect_v be_v this_o as_o the_o radius_fw-la be_v to_o the_o cousin_a of_o the_o pole_n elevation_n above_o the_o plain_a or_o horizon_n so_o be_v the_o cousin_a of_o any_o of_o the_o angle_n specify_v in_o the_o former_a table_n of_o angle_n at_o the_o pole_n to_o the_o sine_fw-la of_o the_o altitude_n require_v and_o due_a to_o that_o angle_n or_o hour_n rather_o in_o the_o equinoctial_a circle_n so_o in_o the_o former_a example_n the_o latitude_n or_o elevation_n of_o the_o pole_n above_o the_o horizon_n be_v 40_o gr_n the_o compliment_n of_o that_o be_v 50_o gr_n which_o be_v the_o meridian_n altitude_n and_o depression_n of_o the_o equinoctial_a circle_n above_o and_o under_o the_o say_a horizon_n or_o plain_n and_o be_v therefore_o to_o be_v set_v for_o the_o altitude_n of_o the_o proper_a meridian_n now_o as_o the_o radius_fw-la be_v to_o the_o altitude_n of_o 50_o gr_n so_o be_v the_o cousin_a of_o every_o angle_n at_o the_o pole_n or_o ark_n of_o the_o equinoctial_a in_o the_o former_a table_n to_o the_o altitude_n due_a thereunto_o hour_n horizon_n space_n altitude_n or_o profu_n hour_n  _fw-fr 88_o 49_o 1_o 24_o  _fw-fr 3_o 86_o 24_o 4_o 16_o 3_o  _fw-fr 83_o 58_o 7_o 08_o  _fw-fr  _fw-fr 81_o 30_o 9_o 59_o  _fw-fr  _fw-fr 79_o 00_o 12_o 49_o  _fw-fr 3_o 76_o 26_o 15_o 37_o 2_o  _fw-fr 73_o 48_o 18_o 24_o  _fw-fr  _fw-fr 71_o 04_o 21_o 08_o  _fw-fr  _fw-fr 68_o 15_o 23_o 50_o  _fw-fr 1_o 65_o 18_o 26_o 28_o 1_o  _fw-fr 62_o 13_o 29_o 03_o  _fw-fr  _fw-fr 59_o 00_o 31_o 33_o  _fw-fr  _fw-fr 55_o 35_o 33_o 58_o  _fw-fr 12_o 51_o 58_o 36_o 17_o 12_o  _fw-fr 48_o 09_o 38_o 29_o  _fw-fr  _fw-fr 44_o 06_o 40_o 33_o  _fw-fr  _fw-fr 39_o 48_o 42_o 29_o  _fw-fr 11_o 35_o 14_o 44_o 14_o 11_o  _fw-fr 30_o 24_o 45_o 47_o  _fw-fr  _fw-fr

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

of_o shall_v be_v to_o take_v away_o that_o inconvenience_n in_o use_n which_o be_v in_o the_o former_a and_o therefore_o suppose_v the._n style_n or_o index_n to_o be_v wried_a from_o the_o proper_a meridian_n of_o the_o plain_a to_o the_o meridian_n of_o the_o place_n or_o to_o the_o point_n of_o 12._o it_o may_v as_o well_o be_v put_v to_o any_o other_o just_a hour_n as_o to_o 12_o but_o be_v it_o so_o in_o this_o example_n and_o let_v the_o point_n be_v l_o select_v from_o all_o the_o rest_n from_o the_o select_a point_n l_o draw_v the_o diameter_n l_o a_o m_o and_o from_o the_o select_a point_n l_o divide_v the_o circle_n into_o 24_o equal_a part_n or_o hour_n then_o from_o each_o two_o hour_n point_v correspondent_o distant_a on_o both_o side_n the_o diameter_n l_o m_o draw_n right_n line_n as_o g_z h_z and_o n_o o_o and_o g_o o_o which_o will_v be_v all_o parallel_n to_o the_o diameter_n l_o m._n draw_v these_o line_n i_o say_v and_o continue_v they_o until_o they_o meet_v with_o the_o horologicall_a line_n r_o a_o s_o sufficient_o prolong_v both_o way_n by_o this_o draught_n thus_o make_v the_o horologicall_a line_n r_o a_o s_o shall_v be_v both_o prolong_v to_o h_z o_o and_o also_o divide_v just_a as_o a_o line_n of_o sines_n so_o the_o part_n of_o it_o be_v in_o the_o same_o proportion_n that_o the_o part_n of_o the_o diameter_n g_o a_o g_o be_v which_o be_v right_a sines_n both_o way_n from_o the_o centre_n or_o verse_v sin_n from_o g_o through_o a_o to_o g._n ¶_o note_v that_o here_o as_o former_o you_o may_v assume_v the_o circle_n of_o what_o extent_n you_o list_v and_o shall_v find_v most_o fit_v your_o purpose_n it_o be_v plain_a then_o by_o this_o example_n first_o that_o the_o radius_fw-la of_o the_o circle_n a_o r_o be_v to_o be_v enlarge_v according_a to_o the_o secant_fw-la of_o the_o equinoctial_a distance_n between_o the_o proper_a meridian_n of_o the_o plain_a and_o that_o just_a hour_n whatever_o it_o be_v inro_fw-la which_o the_o index_n be_v make_v to_o point_n as_o you_o see_v that_o ark_n to_o be_v here_o l_o c_o or_o g_o r_o or_o g_o s_o who_o secant_fw-la be_v a_o h_z or_o a_o o_o in_o respect_n of_o the_o assume_v radius_fw-la a_o r._n and_o second_o that_o h_o o_o thus_o enlarge_v be_v divide_v like_o a_o double_a line_n of_o sines_n as_o it_o ought_v to_o be_v and_o for_o number_v the_o hour_n if_o a_o be_v 12_o and_o the_o index_n look_v towards_o the_o south_n then_o must_v o_o be_v 2_o and_o the_o other_o o_o must_v be_v 6_o and_o the_o first_o o_o 10_o at_o night_n and_o h_o must_v be_v 9_o in_o the_o morning_n the_o other_o h_z 6_o in_o the_o morning_n and_o the_o first_o h_o 3_o in_o the_o morning_n but_o if_o the_o index_n have_v not_o point_v up_o into_o 12_o at_o l_o but_o into_o some_o other_o hour_n as_o p_o then_o must_v a_o diameter_n have_v be_v draw_v at_o first_o from_o p_o to_o the_o centre_n a_o quite_o through_o and_o all_o the_o hour_n parallel_v to_o p_o a_o and_o then_o the_o horologicall_a line_n will_v have_v be_v thus_o number_v with_o 7_o at_o the_o two_o extreme_n and_o 1_o in_o the_o midst_n at_o a._n and_o here_o be_v one_o special_a thing_n to_o be_v note_v as_o former_o pag._n 125_o but_o this_o here_o be_v always_o so_o and_o in_o all_o oblique_a orison_n that_o in_o our_o climate_n where_o the_o day_n be_v in_o summer_n long_o than_o 12_o hour_n the_o shadow_n of_o the_o index_n do_v real_o go_v forward_o and_o backward_o as_o to_o make_v it_o plain_a if_o the_o dial_n be_v describe_v upon_o a_o horizontall_a plain_n for_o instance_n and_o it_o be_v our_o long_a day_n than_o the_o shadow_n of_o the_o index_n will_v begin_v at_o 4_o a_o clock_n figure_v below_o the_o line_n and_o will_v go_v thence_o towards_o the_o left_a hand_n to_o 5_o 6_o and_o 7._o at_z 7_o it_o will_v return_v back_o towards_o the_o right_a hand_n through_o 8_o 9_o 10_o 11_o 12_o 1_o 2_o 3_o 4_o 5_o 6_o until_o 7_o and_o then_o be_v arrive_v at_o 7_o the_o utmost_a point_n on_o the_o right_a hand_n it_o will_v come_v back_o again_o towards_o 8_o and_o 9_o to_o the_o left_a hand_n this_o for_o the_o place_n limit_v and_o divide_v of_o the_o horologicall_a line_n ¶_o three_o concern_v the_o zodiac_n how_o it_o must_v be_v place_v and_o limit_v consider_v of_o these_o thing_n the_o zodiac_n in_o this_o case_n of_o wry_v the_o index_n from_o the_o plain_n proper_a meridian_n must_v be_v augment_v in_o length_n and_o change_v in_o situation_n from_o what_o it_o be_v in_o the_o former_a case_n where_o the_o index_n look_v up_o into_o the_o plain_n proper_a meridian_n yet_o i_o will_v here_o first_o begin_v with_o that_o way_n so_o far_o as_o it_o go_v and_o then_o proceed_v to_o what_o be_v further_a needful_a let_v the_o figure_n pag._n 137_o be_v here_o repeat_v to_o the_o radius_fw-la a_o r_o the_o tangent_fw-la of_o 23_o and_o a_o half_a be_v a_o f_o and_o the_o same_o be_v there_o augment_v thus_o as_o the_o radius_fw-la to_o the_o secant_fw-la of_o the_o pole_n elevation_n above_o the_o plain_a so_o let_v of_o be_v suppose_v to_o be_v to_o ab_fw-la so_o that_o if_o the_o index_n be_v point_v direct_o to_o the_o meridian_n point_n in_o the_o equinoctial_a which_o be_v proper_a to_o the_o plain_a than_o the_o business_n be_v at_o a_o end_n for_o a_o b_o must_v be_v the_o length_n of_o the_o zodiac_n and_o stand_v square_a to_o r_o a_o s._n but_o now_o we_o here_o suppose_v the_o index_n to_o be_v wried_a from_o that_o point_n as_o much_o as_o the_o ark_n c_o l_o come_v too_o which_o turn_v aside_o will_v both_o lengthen_v the_o zodiac_n again_o and_o turn_v it_o out_o of_o its_o perpendicular_a stand_v to_o r_o a_o s._n which_o thing_n be_v thus_o to_o be_v effect_v to_o a_o f_o as_o a_o radius_fw-la find_v the_o tangent_fw-la of_o the_o pole_n elevation_n above_o the_o plain_a suppose_v that_o tangent_fw-la be_v g_z h._n then_o say_v as_o the_o radius_fw-la to_o the_o tangent_fw-la of_o c_o l_o the_o quantity_n of_o wry_v so_o g_z h_z to_o x_o z._n make_v b_o k_o equal_a to_o x_o z_o and_o parallel_n to_o a_o r_o and_o draw_v a_o k_o so_o shall_v a_o k_o be_v the_o length_n and_o shall_v also_o give_v in_o this_o position_n the_o situation_n of_o the_o zodiac_n the_o manner_n how_o to_o divide_v it_o need_v not_o be_v repeat_v because_o it_o have_v be_v often_o set_v down_o heretofore_o you_o must_v only_o remember_v to_o place_v this_o line_n upon_o that_o coast_n of_o a_o b_o which_o be_v contrary_a to_o the_o coast_n of_o the_o index_n deviation_n or_o wry_v from_o the_o proper_a meridian_n point_n of_o the_o plain_a this_o work_n may_v either_o be_v protract_v or_o calculate_v or_o wrought_v instrumental_o as_o shall_v best_o be_v like_v of_o another_o way_n i_o will_v here_o add_v to_o do_v the_o same_o work_n which_o may_v perhaps_o be_v not_o inferior_a to_o the_o former_a let_v all_o thing_n preparatorie_n in_o the_o former_a figure_n be_v here_o again_o repeat_v r_o a_o the_o radius_fw-la and_o a_o f_o the_o tangent_fw-la of_o 23_o degree_n and_o a_o half_a to_o that_o radius_fw-la then_o to_o a_o f_o as_o radius_fw-la find_v the_o sine_fw-la and_o cousin_a of_o the_o pole_n elevation_n above_o the_o plain_a let_v f_o p_o be_v the_o sine_fw-la and_o a_o p_o the_o cousin_a make_v a_o m_o equal_a to_o a_o p_o and_o from_o m_o draw_v the_o line_n m_o n_o make_v the_o angle_n n_o m_o c_o equal_a to_o the_o angle_n b_o a_o c_o pag._n 142_o and_o stand_v on_o the_o contrary_a coast_n which_o be_v the_o angle_n of_o the_o declination_n of_o the_o index_n from_o a_o c_o in_o this_o figure_n the_o proper_a meridian_n of_o the_o plain_a then_o say_v as_o the_o radius_fw-la be_v to_o the_o tangent_fw-la of_o the_o reclination_n of_o the_o index_n which_o be_v the_o compliment_n of_o d_o a_o c_o pag._n 142_o the_o elevation_n of_o the_o index_n above_o the_o plain_a so_o be_v the_o sine_fw-la f_o p_o to_o a_o four_o quantity_n suppose_v the_o same_o to_o be_v d_o g_o make_v m_z n_o equal_a to_o d_o g_o and_o draw_v the_o straight_a line_n a_o ●_o so_o shall_v a_o n_o in_o this_o figure_n be_v equal_a to_o a_o k_o in_o the_o precedent_n and_o the_o angle_n n_o a_o c_o be_v here_o equal_a to_o the_o angle_n k_o a_o b_o in_o the_o former_a so_o that_o a_o n_o must_v be_v the_o length_n of_o the_o half_a zodiac_n and_o will_v lie_v in_o its_o true_a position_n by_o this_o work_n this_o may_v be_v do_v either_o by_o calculation_n protraction_n or_o instrument_n as_o all_o other_o work_n may_v

ellipsis_n first_o find_v the_o tangent_fw-la of_o 23_o degree_n and_o a_o half_a which_o suppose_v to_o be_v r_z ξ_n and_o then_o to_o this_o line_n be_v take_v as_o a_o new_a radius_fw-la find_v the_o cousin_a of_o the_o plain_n latitude_n or_o the_o sine_fw-la of_o the_o equinoctial_o altitude_n which_o suppose_v to_o be_v the_o length_n r_o w_n which_o be_v also_o to_o be_v set_v from_o the_o centre_n r_o upon_o the_o proper_a meridian_n of_o the_o plain_a as_o here_o it_o be_v from_o r_o to_o w._n then_o through_o the_o point_n w_n draw_v a_o line_n as_o w_n z_o parallel_n to_o the_o subindical_a line_n r_o s._n when_o this_o be_v do_v you_o be_v to_o find_v the_o sine_fw-la of_o the_o pole_n elevation_n above_o the_o plain_a to_o the_o same_o radius_fw-la r_o ξ_n which_o sine_fw-la you_o may_v suppose_v to_o be_v the_o length_n of_o the_o line_n φ_n ψ._n then_o say_v again_o as_o the_o radius_fw-la to_o the_o tangent_fw-la of_o the_o index_n reclination_n so_o φ_n ψ_n the_o sine_fw-la of_o the_o pole_n elevation_n above_o the_o plain_a to_o a_o four_o line_n which_o line_n let_v be_v represent_v by_o λ_n ω._n take_v this_o line_n λ_n ω_fw-gr therefore_o and_o set_v it_o upon_o w_n z_o the_o line_n former_o draw_v from_o w_n to_o z._n and_o last_o draw_v the_o line_n r_o z_o and_o make_v r_o y_fw-fr equal_a to_o it_o so_o shall_v z_o y_fw-fr be_v the_o zodiac_n in_o its_o true_a length_n and_o position_n and_o r_o z_o or_o r_o y_fw-fr shall_v give_v the_o half_a of_o it_o which_o half_o be_v to_o be_v estimate_v as_o a_o tangent_fw-la of_o 23_o degree_n and_o a_o half_a and_o so_o the_o zodiac_n to_o be_v set_v on_o as_o have_v former_o be_v often_o show_v you_o be_v here_o to_o take_v care_n that_o all_o thing_n be_v set_v in_o their_o right_a position_n in_o this_o example_n z_o turns_z from_o w_n towards_o the_o left_a hand_n because_o it_o be_v here_o suppose_a that_o the_o north_n pole_n be_v elevate_v upon_o the_o plain_a and_o so_o the_o axis_n rise_v out_o of_o r_o above_o the_o plain_a and_o therefore_o that_o 23½_n tangent_fw-la degree_n upon_o that_o axis_n a●e_v above_o the_o plain_a from_o which_o extreme_a point_n of_o 23½_n above_o the_o plain_a you_o may_v suppose_v a_o line_n to_o issue_v out_o parallel_a to_o the_o index_n which_o incline_v from_o r_o towards_o saint_n and_o therefore_o that_o line_n incline_v so_o too_o must_v project_v that_o extreme_a point_n from_o w_n towards_o z._n all_o the_o reason_n of_o the_o work_n depend_v upon_o that_o which_o have_v be_v former_o say_v namely_o that_o both_o hour_n point_v of_o the_o equinoctial_a and_o declination_n point_v in_o the_o axis_n be_v all_o project_v from_o their_o true_a position_n in_o the_o sphere_n upon_o or_o unto_o a_o plain_a by_o right_a line_n pass_v through_o each_o of_o they_o parallel_n to_o the_o assign_a index_n i_o shall_v need_v to_o say_v no_o more_o because_o i_o think_v enough_o if_o not_o too_o much_o have_v be_v say_v already_o this_o shall_v serve_v for_o the_o effection_n and_o demonstration_n also_o of_o this_o proposition_n or_o problem_n coronidis_fw-la loco_fw-la i_o shall_v here_o further_o add_v how_o upon_o a_o horizontal_n plain_n to_o describe_v a_o ellipticall_a dial_n to_o a_o index_n lie_v aslope_o and_o point_v into_o some_o assign_a longitude_n and_o latitude_n this_o i_o shall_v add_v as_o a_o corollary_n to_o that_o which_o have_v last_o of_o all_o be_v deliver_v in_o general_a for_o all_o plain_n and_o index_n out_o of_o which_o doctrine_n this_o as_o a_o particular_a branch_n be_v deduce_v it_o contain_v not_o any_o new_a thing_n but_o because_o it_o may_v be_v more_o frequent_o make_v use_n of_o in_o practice_n than_o other_o case_n therefore_o i_o add_v it_o that_o it_o may_v also_o be_v the_o more_o plain_a and_o easy_a in_o operation_n it_o be_v for_o more_o ease_n intend_v that_o the_o index_n shall_v point_v up_o into_o some_o just_a hour_n circle_n and_o to_o have_v some_o just_a degree_n of_o reclination_n from_o the_o zenith_n of_o the_o horizon_n i_o purpose_v not_o to_o give_v variety_n of_o way_n for_o they_o be_v show_v in_o the_o last_o precept_n now_o give_v which_o be_v general_a and_o may_v easy_o be_v bring_v and_o apply_v to_o this_o particular_a case_n as_o a_o branch_n of_o that_o general_a before_o suppose_v in_o our_o horizon_n 51_o gr_n 30_o min._n in_o latitude_n and_o to_o two_o index_n set_v upon_o a_o horizontall_a plain_n the_o one_o point_v southeast_n into_o the_o morning_n circle_n of_o 7_o a_o clock_n the_o other_z pointing_z south-west_n into_o the_o evening_n circle_n of_o 5_o a_o clock_n and_o each_o of_o they_o recline_v 45_o gr_n it_o be_v require_v to_o make_v two_o ellipticall_a dial_n how_o must_v they_o be_v do_v it_o must_v be_v note_v that_o the_o make_n of_o one_o will_v make_v the_o other_o because_o they_o be_v to_o be_v set_v upon_o one_o plain_a and_o their_o difference_n of_o the_o index_n longitude_n be_v in_o each_o 5_o hour_n and_o the_o reclination_n of_o the_o index_n in_o each_o 45_o degree_n only_o the_o coast_n in_o respect_n of_o situation_n must_v be_v change_v because_o the_o position_n of_o the_o index_n be_v not_o parallel_v but_o contrary_a one_o to_o the_o other_o and_o so_o will_v the_o ellipse_n be_v as_o you_o may_v see_v in_o the_o next_o page_n the_o first_o thing_n to_o be_v do_v be_v by_o have_v the_o difference_n of_o the_o index_n longitude_n 75_o gr_n and_o the_o reclination_n of_o the_o index_n 45_o gr_n to_o find_v what_o declination_n the_o index_n must_v have_v or_o to_o find_v the_o declination_n of_o the_o subindicall_a line_n from_o our_o meridi●n_n when_o this_o work_n be_v do_v draw_v a_o r_o b_o for_o the_o meridian_n line_n of_o north_n and_o south_n and_o 6_o r_z 6_o for_o the_o line_n of_o east_n and_o west_n cross_v each_o other_o at_o r_o which_o must_v be_v the_o centre_n of_o the_o dial_n and_o draw_v the_o subindicall_a line_n r_o saint_n 60_o gr_n 5_o min._n 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