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the_o cone_n all_o along_o from_o b_o to_o a_o and_o make_v right_a angle_n with_o bc_n the_o diameter_n of_o the_o base_a and_o again_o another_o plain_a fd_a parallel_n to_o eboaz_v cut_v the_o semicone_a bac_n the_o section_n it_o in_o the_o superficies_n of_o the_o cone_n be_v half_a a_o parabola_fw-la the_o other_o half_o underneath_o if_o the_o cone_n be_v suppose_v entire_a and_o be_v not_o to_o be_v project_v in_o plano_fw-la 2_o again_o if_o the_o semicone_a bac_n be_v cut_v by_o another_o plain_a gkz_n parallel_n to_o the_o axis_n axe_n the_o section_n in_o the_o superficies_n of_o the_o semicone_n to_o wit_n gk_v shall_v be_v half_o a_o hyperbola_n and_o the_o like_a for_o the_o other_o half_o underneath_o if_o the_o cone_n be_v suppose_v entire_a and_o further_o whatsoever_o plain_o cut_v the_o semicone_n as_o aforesaid_a be_v produce_v shall_v concur_v with_o the_o plain_a ba_o produce_v towards_o z._n three_o if_o the_o say_v semicone_a be_v cut_v by_o a_o plain_a nph_n neither_o of_o the_o former_a way_n nor_o parallel_n nor_o subcontrary_a to_o the_o base_a the_o line_n in_o the_o superficies_n namely_o nh_o be_v a_o semiellipsis_n subcontrary_a position_n be_v that_o where_o two_o like_a triangle_n be_v join_v at_o a_o equal_a and_o then_o vertical_a angle_n yet_o have_v not_o their_o base_n parallel_v last_o if_o it_o be_v cut_v by_o a_o plain_a lorq_fw-fr parallel_n to_o the_o plain_a of_o the_o base_a the_o section_n or_o be_v a_o semicircle_n definition_n 1._o opposite_a section_n be_v two_o hyperbola_n in_o opposite_a superficies_n cut_v by_o the_o same_o plain_a definition_n 2._o the_o vertex_fw-la of_o a_o section_n be_v a_o point_n in_o the_o great_a curvature_n thereof_o but_o more_o general_o the_o point_n where_o any_o diameter_n cut_v the_o section_n and_o where_o the_o axis_n cut_v be_v call_v the_o high_a vertex_fw-la definition_n 3._o any_o two_o line_n apply_v within_o the_o section_n and_o equidistant_a be_v call_v ordinate_o apply_v in_o respect_n of_o some_o diameter_n which_o divide_v they_o into_o two_o equal_a part_n definition_n 4._o any_o line_n draw_v so_o as_o it_o cut_v the_o section_n and_o divide_v the_o ordinates_n into_o two_o equal_a part_n be_v call_v the_o diameter_n of_o the_o section_n and_o if_o it_o divide_v they_o as_o aforesaid_a and_o at_o right_a angle_n it_o be_v the_o axis_n and_o so_o much_o of_o the_o axis_n or_o diameter_n as_o lie_v betwixt_o the_o vertex_fw-la and_o any_o ordinate_a be_v call_v in_o respect_n of_o that_o ordinate_a the_o intercept_a axis_n or_o intercept_v diameter_n and_o those_o two_o diametet_n which_o mutual_o divide_v line_n apply_v in_o the_o section_n and_o parallel_n to_o the_o diameter_n into_o two_o equal_a part_n be_v call_v conjugate_v diameter_n of_o which_o as_o likewise_o of_o the_o oppsite_a section_n i_o intend_v to_o say_v no_o more_o in_o this_o tract_n definition_n 5._o the_o transverse_a diameter_n of_o a_o hyperbola_n be_v a_o right_a line_n in_o the_o intercept_a diameter_n continue_v without_o the_o section_n and_o be_v equal_a to_o the_o double_a of_o that_o line_n intercept_v betwixt_o the_o vertex_fw-la and_o the_o centre_n and_o connect_v the_o vertices_fw-la of_o opposite_a section_n in_o a_o ellipsis_n or_o circle_n it_o be_v any_o whole_a diameter_n in_o the_o hyperbola_fw-la and_o ellipsis_n if_o it_o be_v the_o continuation_n of_o the_o axis_n or_o the_o axis_n in_o the_o late_a it_o be_v call_v the_o transverse_a axis_n but_o the_o parabola_fw-la who_o diameter_n be_v all_o equidistant_n have_v no_o transverse_a diameter_n nor_o any_o centre_n definition_n 6._o the_o centre_n be_v a_o point_n where_o all_o the_o diameter_n meet_v definition_n 7._o the_o figure_n of_o hyperbola_n and_o ellipse_n and_o circle_n be_v paralleligram_n include_v between_o the_o transverse_a diameter_n and_o the_o contiguous_a parameter_n of_o whicb_a those_o be_v call_v transverse_a side_n and_o these_o coefficient_o by_o some_o definition_n 8._o the_o say_a parameter_n be_v a_o right_a line_n draw_v to_o touch_v the_o section_n at_o the_o end_n of_o the_o intercept_a diameter_n to_o which_o all_o the_o ordinates_n be_v parallel_n and_o according_a to_o which_o they_o be_v compare_v and_o value_v which_o be_v therefore_o call_v juxta_fw-la quam_fw-la possunt_fw-la and_o if_o it_o be_v contiguous_a to_o the_o axis_n it_o be_v call_v the_o right_a parameter_n definition_n 9_o the_o umbilicius_n focus_fw-la or_o burn_a point_n in_o the_o parabola_fw-la be_v a_o point_n in_o the_o axis_n distant_a from_o the_o vertex_fw-la by_o a_o four_o part_n of_o the_o right_a parameter_n but_o in_o the_o other_o two_o section_n the_o burn_a point_n be_v assign_v in_o the_o axis_n of_o either_o section_n distant_a from_o either_o end_n of_o the_o transverse_n axis_fw-la by_o the_o space_n of_o a_o right_a line_n that_o be_v the_o square_a root_n of_o the_o four_o part_n of_o the_o figure_n produce_v by_o the_o say_a transverse_n axis_fw-la and_o the_o right_a parameter_n which_o apply_v to_o the_o transverse_n axis_fw-la be_v in_o the_o hyperbola_fw-la excedent_fw-la in_o the_o ellipsis_n deficient_a the_o same_o point_n in_o any_o ellipsis_n who_o diameter_n or_o diameter_n be_v give_v may_v easy_o be_v find_v by_o the_o mechanic_a way_n of_o describe_v a_o ellipsi_v a_o little_a before_o show_v wherein_o also_o it_o be_v plain_a that_o these_o point_n be_v as_o it_o be_v centre_n proper_a to_o the_o generation_n of_o the_o section_n chap._n xii_o of_o the_o description_n of_o the_o section_n many_o be_v the_o method_n general_n and_o special_a which_o midorgius_n show_v to_o describe_v these_o three_o section_n i_o will_v only_o mention_v one_o or_o two_o 1._o to_o describe_v a_o parabola_fw-la about_o any_o diameter_n give_v with_o one_o of_o the_o ordinate_a line_n let_v the_o diameter_n give_v be_v ab_fw-la and_o let_v bc_n be_v one_o of_o the_o ordinate_a line_n apply_v unto_o it_o by_o which_o the_o angle_n abc_n be_v give_v join_v a_o and_o c_o by_o the_o right_a line_n ac_fw-la and_o let_v ab_fw-la be_v divide_v into_o as_o many_o part_n as_o you_o please_v and_o through_o every_o such_o division_n draw_v right_a line_n parallel_v to_o bc_n and_o produce_v they_o and_o make_v dk_a =_o â_o bc_n in_o dg_n likewise_o el_fw-es =_o â_o bc_n in_o eh_n and_o fm_o =_o â_o bc_n in_o fi_fw-la and_o so_o of_o all_o the_o rest_n and_o the_o point_n c_o k_o l_o m_o a_o etc._n etc._n shall_v be_v all_o in_o the_o same_o section_n so_o that_o a_o line_n draw_v with_o a_o even_a hand_n by_o all_o the_o say_a point_n shall_v be_v by_o the_o first_o prop._n of_o the_o second_o of_o midorgius_n the_o parabola_fw-la require_v and_o bc_n on_o the_o one_o side_n be_v equal_a to_o bc_n on_o the_o other_o side_n because_o by_o supposition_n that_o and_o all_o the_o parallel_n to_o it_o kd_v le_fw-fr mf_n etc._n etc._n eat_v those_o line_n which_o be_v call_v ordinates_n or_o ordinate_o apply_v and_o so_o ab_fw-la in_o respect_n of_o bc_n also_o ae_z in_o respect_n of_o le_fw-fr etc._n etc._n be_v the_o intercept_a diameter_n or_o if_o the_o angle_n abc_n be_v a_o right_a angle_n the_o intercept_a axe_n def._n 4._o and_o if_o you_o make_v adâ²_n dkâ³_n aqâ²â³_n and_o draw_v aq_a parallel_n to_o dk_v than_o aq_n shall_v be_v the_o contiguous_a parameter_n in_o respect_n of_o the_o intercept_a diameter_n add_v and_o so_o may_v the_o parameter_n by_o ab_fw-la or_o any_o other_o diameter_n give_v be_v find_v and_o therefore_o the_o parameter_n aq_fw-fr only_a be_v give_v the_o parabola_fw-la by_o point_n may_v easy_o be_v describe_v 2._o about_o any_o diameter_n and_o one_o ordinate_a line_n to_o describe_v a_o hyperbola_n know_v in_o kind_n in_o a_o plain_a by_o point_n let_v ab_fw-la be_v a_o diameter_n of_o the_o hyperbola_n and_o bc_n a_o ordinate_a to_o it_o comprehend_v the_o angle_n give_v abc_n and_o let_v the_o section_n be_v of_o such_o a_o kind_n as_o that_o the_o transverse_a diameter_n to_o the_o contiguous_a parameter_n may_v be_v as_o r_o to_o s._n make_v abâ²_n bcâ³_n bdâ²â³_n and_o sâ²_n râ³_n bdâ²_n beâ³_n and_o join_v the_o point_n do_v and_o e_o and_o in_o the_o line_n ab_fw-la take_v point_n how_o many_o soever_o and_o by_o they_o points_z f_z g_o t_o etc._n etc._n draw_v line_n parallel_v to_o bc_n as_o fh_v gn_n ti_fw-mi etc._n etc._n the_o more_o the_o better_o and_o make_v the_o triangle_n ded_fw-we complete_a produce_v these_o parallel_n both_o way_n to_o the_o side_n de_fw-fr in_o the_o point_n h_o n_z i_z etc._n etc._n last_o make_v fk_n gd_v tl_n etc._n etc._n the_o square_a root_n of_o the_o rectangle_v afh_a agn_n ati_fw-la etc._n etc._n the_o point_n k_o o_o and_o l_o shall_v be_v in_o the_o hyperbola_fw-la require_v per_fw-la 5._o of_o 2._o midorg_n and_o therefore_o a_o line_n draw_v with_o a_o
require_v shall_v give_v respective_a point_n enough_o in_o each_o hour_n to_o draw_v each_o parallel_n by_o example_n in_o the_o latitude_n 51._o 32â²_n the_o sun_n be_v in_o pisces_fw-la the_o beginning_n thereof_o the_o degree_n of_o the_o sun_n height_n above_o the_o horizon_n at_o every_o hour_n be_v as_o follow_v that_o be_v 25._o 37â²_n at_o one_o of_o clock_n 21._o 49â²_n at_o two_o 15._o 57â²_n at_o three_o 8._o 32â²_n at_o four_o and_o the_o same_o for_o eight_o nine_o ten_o and_o eleven_o respective_o if_o the_o perpendicular_a stile_n be_v radius_fw-la the_o tangent_n of_o the_o compliment_n of_o 25._o 37â²_n 21._o 49â²_n 15._o 57â²_n 8._o 32â²_n be_v apply_v from_o the_o foot_n of_o the_o stile_n to_o the_o respective_a hour_n that_o be_v the_o co-tangent_a of_o 25._o 37â²_n from_o the_o foot_n of_o the_o stile_n to_o the_o hour_n of_o 1._o and_o 11._o and_o so_o the_o other_o they_o shall_v give_v point_n in_o every_o hour-line_n one_o by_o which_o a_o line_n be_v draw_v with_o a_o even_a hand_n shall_v be_v the_o parallel_n at_o the_o begin_n of_o pisces_fw-la and_o the_o like_a of_o all_o the_o rest_n and_o therefore_o general_o in_o vertical_n as_o also_o in_o all_o recliner_n that_o be_v to_o say_v upon_o all_o plane_n whatsoever_o draw_v a_o horizontal_a dial_n proper_a to_o the_o plane_n and_o inscribe_v the_o sign_n or_o parallel_n upon_o it_o by_o set_v off_o from_o the_o foot_n of_o the_o perpendicular_a stile_n the_o tangent_n compliment_n of_o the_o sun_n height_n at_o every_o hour_n in_o the_o begin_n of_o every_o such_o sign_n above_o that_o plane_n take_v as_o a_o horizon_n the_o perpendicular_a stile_n be_v ever_o radius_fw-la and_o at_o the_o end_n of_o these_o tangent_n so_o set_v off_o upon_o every_o respective_a hour-line_n will_v be_v a_o point_n by_o which_o point_n line_n draw_v with_o a_o even_a hand_n shall_v give_v the_o parallel_n desire_v this_o horizontal_a dial_n be_v draw_v in_o obscure_a line_n the_o dial_n for_o the_o plane_n may_v be_v draw_v afterward_o the_o parallel_n serve_v which_o be_v draw_v before_o example_n suppose_v as_o m._n wells_n do_v pag._n 185_o a_o plane_n decline_v 30_o degree_n and_o recline_v 55_o degree_n the_o height_n of_o the_o pole_n above_o the_o plane_n 19_o degree_n 25_o minute_n the_o sun_n height_n at_o the_o begin_n of_o taurus_n to_o be_v at_o the_o hour_n of_o 12h_n 82d_o 5â²_n of_o taurus_n to_o be_v at_o the_o hour_n of_o 1_o 73_o 30_o of_o taurus_n to_o be_v at_o the_o hour_n of_o 2_o 60_o 3_o of_o taurus_n to_o be_v at_o the_o hour_n of_o 3_o 46_o 1_o of_o taurus_n to_o be_v at_o the_o hour_n of_o 4_o 31_o 53_o of_o taurus_n to_o be_v at_o the_o hour_n of_o 5_o 17_o 47_o the_o tangent_n of_o the_o compliment_n of_o 82_o 5â²_n and_o 73_o 30â²_n and_o 60_o 3â²_n etc._n etc._n set_v off_o from_o the_o foot_n of_o the_o perpendicular_a stile_n the_o say_a stile_n be_v the_o radius_fw-la to_o those_o tangent_n to_o the_o obscure_a horizontal_a hour_n of_o 12_o 1_o 2_o etc._n etc._n give_v the_o true_a distance_n between_o the_o foot_n of_o the_o stile_n and_o those_o auxiliary_a hour_n for_o the_o parallel_n of_o taurus_n and_o so_o the_o other_o parallel_n may_v be_v find_v it_o be_v true_a the_o height_n of_o the_o sun_n at_o every_o hour_n of_o the_o day_n at_o the_o begin_n of_o every_o sign_n in_o any_o latitude_n be_v not_o easy_o find_v out_o without_o trigonometrical_a calculation_n by_o logarithm_n of_o the_o sin_n &_o tangent_n or_o by_o trust_v to_o table_n already_o calculate_v if_o any_o happen_v to_o be_v do_v for_o that_o latitude_n already_o the_o way_n of_o make_v a_o table_n shall_v be_v show_v towards_o the_o end_n of_o the_o vertical_a circle_n these_o be_v vulgar_o call_v azimuth_n and_o be_v great_a circle_n who_o pole_n lie_v in_o the_o horizon_n and_o intersect_v one_o another_o in_o the_o zenith_n and_o nadir_n of_o the_o place_n the_o whole_a horizon_n be_v divide_v into_o 32_o part_n equal_a these_o circle_n show_v those_o division_n be_v call_v point_n of_o the_o compass_n and_o mark_v s._n sbe.sse_n etc._n etc._n every_o one_o distant_a from_o other_o by_o 11¼_n degree_n but_o the_o better_a way_n of_o account_v they_o be_v 10_o 20_o 30_o 40_o 50_o 60_o 70_o etc._n etc._n degree_n from_o the_o meridian_n 1_o in_o all_o horizontal_a dial_n the_o perpendicular_a stile_n be_v choose_v make_v the_o foot_n thereof_o the_o centre_n at_o any_o convenient_a distance_n describe_v a_o circle_n and_o account_v from_o the_o meridian_n both_o way_n arch_n equal_a to_o 10_o 20_o 30_o etc._n etc._n degree_n from_o which_o division_n right_a line_n draw_v to_o the-foot_n of_o the_o stile_n aforesaid_a shall_v represent_v those_o azimuth_n upon_o that_o dial_n 2_o upon_o a_o prime_n vertical_a or_o south_n dial_n through_o the_o foot_n of_o the_o perpendicular_a stile_n draw_v a_o right_a line_n parallel_n to_o the_o horizon_n and_o make_v the_o say_a stile_n radius_fw-la upon_o the_o parallel_a line_n set_v off_o both_o way_n from_o the_o meridian_n tangent_n of_o 10_o 20_o 30_o 40_o etc._n etc._n degree_n through_o which_o division_n right_a line_n draw_v all_o at_o right_a angle_n with_o the_o parallel_n line_n shall_v be_v the_o azimuth_n 3_o upon_o any_o decline_a vertical_a the_o same_o be_v do_v shall_v give_v the_o azimuth_n of_o 10_o 20_o 30_o etc._n etc._n from_o the_o meridian_n of_o the_o plane_n or_o from_o the_o meridian_n of_o the_o place_n just_a allowance_n be_v make_v for_o the_o distance_n of_o meridian_n 4_o in_o south_n decline_a reclining_a plane_n the_o perpendicular_a stile_n be_v choose_v and_o make_v the_o radius_fw-la the_o tangent_fw-la compliment_n of_o the_o reclination_n apply_v from_o the_o foot_n of_o the_o say_a stile_n to_o the_o meridian_n of_o the_o place_n shall_v determine_v the_o zenith_n of_o the_o place_n through_o which_o and_o the_o foot_n of_o the_o stile_n that_o be_v the_o zenith_n of_o the_o plane_n a_o right_a line_n draw_v shall_v be_v a_o perpendicular_a to_o the_o horizontal_a line_n which_o shall_v concur_v with_o the_o aequator_fw-la in_o the_o hour_n of_o 6_o and_o the_o therefore_o if_o from_o the_o foot_n of_o the_o stile_n upon_o the_o say_v perpendicular_a towards_o the_o north_n for_o the_o former_a application_n be_v make_v towards_o the_o south_n be_v set_v off_o the_o tangent_fw-la of_o the_o reclination_n a_o line_n draw_v from_o the_o end_n thereof_o at_o right_a angle_n with_o it_o shall_v be_v the_o horizontal_a line_n upon_o which_o the_o tangent_n of_o 10_o 20_o 30_o &c_n &c_n the_o secant_fw-la of_o the_o reclination_n be_v now_o make_v radius_fw-la set_v from_o the_o say_v right_a angle_n line_n draw_v from_o they_o to_o the_o zenith_n of_o the_o place_n shall_v be_v the_o azimuth_n 5_o the_o distance_n betwixt_o the_o meridian_n be_v know_v upon_o the_o horizontal_a line_n the_o azimuth_n which_o be_v account_v from_o the_o meridian_n of_o the_o plane_n may_v be_v fit_v for_o account_n from_o the_o meridian_n of_o the_o place_n with_o easy_a for_o example_n let_v that_o distance_n be_v the_o tangent_fw-la of_o 20_o deg_fw-la than_o that_o azimuth_n which_o be_v 10_o from_o the_o one_o be_v 10_o from_o the_o other_o also_o and_o that_o which_o be_v 30_o on_o the_o same_o side_n of_o the_o substile_a be_v 10_o on_o the_o other_o side_n of_o the_o meridian_n of_o the_o place_n the_o like_a method_n serve_v for_o any_o distance_n note_v 1_o it_o may_v be_v note_v that_o although_o i_o have_v show_v the_o construction_n of_o a_o south_n recline_v plane_n at_o the_o beginning_n hereof_o in_o a_o figure_n proper_a only_o to_o those_o plane_n which_o recline_v not_o further_o than_o the_o pole_n whereas_o in_o those_o that_o do_v and_o although_o there_o be_v some_o variation_n of_o the_o scheme_n as_o you_o may_v see_v by_o compare_v this_o with_o the_o former_a at_o the_o first_o beginning_n of_o this_o subject_n for_o the_o point_n h_o which_o there_o fall_v on_o that_o side_n of_o the_o vertical_a meridian_n zx_n towards_o q_o here_o fall_v on_o the_o other_o side_n towards_o we_o likewise_o the_o hour_n of_o 12_o that_o be_v bc_n do_v there_o fall_v betwixt_o the_o axis_fw-la and_o the_o substile_a but_o fall_v here_o betwixt_o the_o substile_a and_o the_o horizontal_a meridian_n ba_o yet_o this_o notwithstanding_o the_o construction_n be_v the_o very_a same_o in_o both_o note_n 2._o it_o may_v be_v further_a note_a that_o as_o the_o reclination_n may_v increase_v the_o point_n n_o c_o r_o all_o approach_n still_o near_o to_o a_o and_o when_o the_o reclination_n be_v 90_o they_o be_v all_o coincident_a and_o this_o vanish_v into_o a_o horizontal_a dial_n who_o substile_a will_v be_v ba._n also_o if_o the_o declination_n be_v still_o increase_v at_o last_o
43_o  _fw-fr 40_o 51_o  _fw-fr 11_o 45_o 24_o 9_o 37_o 52_o 53_o 24_o 70_o 59_o  _fw-fr 39_o 52_o  _fw-fr 11_o 55_o 24_o 27_o 38_o 15_o 53_o 46_o 71_o 13_o  _fw-fr 38_o 53_o  _fw-fr 12_o 5_o 24_o 43_o 38_o 37_o 54_o 8_o 71_o 28_o  _fw-fr 37_o 54_o  _fw-fr 12_o 13_o 25_o 2_o 38_o 58_o 54_o 29_o 71_o 41_o  _fw-fr 36_o 55_o  _fw-fr 12_o 22_o 25_o 18_o 39_o 19_o 54_o 49_o 71_o 54_o  _fw-fr 35_o these_o table_n need_v no_o explanation_n the_o use_n of_o they_o be_v evident_a but_o if_o they_o prove_v not_o satisfactory_a for_o want_v of_o calculation_n for_o further_a degree_n of_o elevation_n or_o for_o want_v of_o half_n and_o quarter_n of_o degree_n or_o the_o like_a of_o hour_n they_o be_v as_o i_o have_v they_o out_o of_o kercherus_n his_o ars_fw-la magna_fw-la nevertheless_o i_o will_v show_v the_o make_n of_o they_o whereby_o any_o man_n may_v fit_v they_o for_o his_o own_o purpose_n and_o for_o his_o place_n if_o it_o happen_v without_o these_o limit_n by_o his_o own_o calculation_n as_o follow_v first_o for_o the_o table_n a._n radiusâ²_n t._n c._n elevationâ³_n t._n câ²_n declinationâ²_n bâ³_n this_o b_o be_v the_o sine_z compliment_n of_o the_o angle_n at_o the_o pole_n which_o show_v the_o hour_n from_o noon_n in_o winter_n and_o the_o hour_n from_o midnight_n in_o summer_n wherein_o the_o sun_n rise_v have_v declination_n which_o declination_n be_v ready_a in_o table_n the_o make_n of_o which_o shall_v be_v show_v anon_o and_o also_o the_o table_n of_o the_o sun_n declination_n at_o the_o end_n hereof_o shall_v ensue_v the_o angle_n at_o the_o pole_n so_o find_v be_v divide_v by_o 15._o show_n in_o winter_n the_o semidiurnal_a arch_n in_o hour_n which_o be_v have_v by_o the_o first_o work_v in_o degree_n and_o minute_n and_o in_o summer_n the_o seminocturnal_a who_o compliment_n to_o 180_o degree_n or_o to_o 12_o hour_n be_v the_o thing_n require_v here_o all_o the_o time_n from_o the_o vernal_a to_o the_o autumnal_a aequinoctial_a be_v call_v summer_n second_o for_o the_o table_n b._n s._n c._n elevationâ²_n s._n declinationâ³_n radiusâ²_n s._n c._n azimuthâ³_n which_o azimuth_n be_v compare_v with_o 90_o d._n difference_n be_v the_o amplitude_n example_n for_o elevation_n 40._o initio_fw-la â_o to_n radius_fw-la log_n 10000000_o add_v sine_fw-la declination_n 20._o 13â²_n log_n 09538537_o sum_n 19538537_o subtract_v sine_fw-la compliment_n elevation_n remain_v sine_fw-la compliment_n azimuth_n which_o compliment_n here_o be_v the_o amplitude_n 9654283_o the_o arch_n belong_v to_o sine_fw-la 9654283._o being_n seek_v in_o the_o canon_n be_v 26._o 48â²_n which_o be_v the_o amplitude_n require_v where_o the_o elevation_n be_v 40_o degree_n three_o for_o the_o table_n c._n first_o to_o find_v any_o horizontal_a arch_n for_o any_o hour_n as_o for_o example_n 3_o or_o 9_o radiusâ²_n t._n of_o the_o hour_n in_o degree_n that_o be_v here_o t._n 45â³_n sine_fw-la elevationâ²_n t._n of_o the_o arch_a requiredâ³_n or_o else_o t._n c._n 45â²_n râ³_n s._n elevationâ²_n t._n arch_a requiredâ³_n second_o in_o a_o prime_n vertical_a radiusâ²_n t._n hourâ³_n s._n c._n elevationâ²_n t._n of_o the_o archâ³_n it_o be_v at_o first_o in_o the_o symbol_n chap._n 1._o advertise_v that_o the_o letter_n s._n and_o t._n or_o s._n c._n and_o t_o c._n signify_v the_o sine_fw-la and_o tangent_fw-la or_o sine_fw-la compliment_n and_o tangent_fw-la compliment_n of_o a_o arch_n or_o angle_n and_o work_v by_o the_o logarithme_n of_o the_o sin_n and_o tangent_n the_o former_a analogisme_n happen_v not_o but_o in_o their_o stead_n certain_a aequality_n or_o aequation_n as_o follow_v for_o the_o table_n a._n tc_n elevation_n +_o tc_n declination_n =_o rad_n +_o b._n which_o b_o be_v the_o cousin_a of_o the_o thing_n require_v that_o be_v of_o the_o angle_n at_o the_o pole_n which_o divide_v by_o 15_o gives_z the_o time_n for_o the_o table_n b._n rad_n +_o s._n declination_n =_o sc_n elevation_n +_o sc_n azimuth_n for_o the_o table_n c._n s._n elevation_n +_o t._n the_o hour_n =_o radius_fw-la +_o t._n the_o arch_n or_o more_o ready_o thus_o tc_n hourâ²_n râ³_n s._n elevatâ²_n t._n of_o arch_n from_o the_o substileâ³_n it_o must_v still_o be_v remember_v that_o r_o stand_v for_o radius_fw-la the_o elevation_n be_v always_o take_v for_o the_o height_n of_o the_o pole_n above_o the_o horizon_n which_o horizon_n be_v the_o dial_n plane_n in_o other_o plane_n as_o the_o prime_n vertical_a and_o all_o other_o vertical_o the_o height_n of_o the_o pole_n above_o the_o plane_n must_v be_v use_v have_v therefore_o find_v that_o call_v it_o p_o or_o else_o call_v the_o declination_n q_o then_o s._n q_o +_o s._n elevat_fw-la =_o r_o +_o s._n p._n and_o r_o +_o s_o p_o =_o tc_n the_o hour_n +_o t_o the_o arch_n of_o that_o hour_n distance_n from_o the_o substile_a so_o after_o still_o till_o all_o the_o hour_n be_v find_v this_o late_a work_n must_v be_v repeat_v whereas_o we_o use_v tc_n the_o hour_n and_o t._n the_o arch_n by_o the_o hour_n be_v always_o mean_v the_o angle_n at_o the_o pole_n or_o the_o space_n there_o include_v between_o any_o hour_n and_o the_o substile_a as_o 15d_o for_o 1_o 30d_o for_o 2_o etc._n etc._n the_o arch_n be_v the_o distance_n of_o any_o hour_n from_o the_o substile_a measure_v in_o the_o arch_n of_o a_o circle_n who_o centre_n be_v the_o centre_n of_o the_o dial_n when_o it_o be_v project_v upon_o the_o plane_n to_o find_v the_o declination_n of_o a_o place_n the_o declination_n be_v a_o arch_n of_o a_o great_a circle_n pass_v through_o the_o pole_n of_o the_o world_n and_o the_o centre_n of_o the_o place_n who_o declination_n be_v seek_v intercept_v between_o the_o say_a centre_n and_o the_o aequator_fw-la if_o the_o place_n have_v no_o latitude_n that_o be_v if_o it_o be_v in_o the_o ecliptic_a the_o near_a distance_n from_o aries_n or_o libra_n be_v give_v call_v it_o b._n then_o râ²_n s._n 23d_o 32_o mâ³_n s._n bâ²_n s._n eâ³_n and_o e_o be_v the_o declination_n require_v work_v by_o the_o natural_a sin_n second_o if_o the_o place_n have_v latitude_n that_o be_v give_v or_o find_v in_o table_n and_o the_o right_a angle_n which_o the_o circle_n of_o latitude_n make_v with_o the_o ecliptic_a for_o all_o circle_n of_o latitude_n do_v so_o as_o the_o circle_n of_o declination_n do_v with_o the_o aequator_fw-la and_o the_o next_o distance_n to_o aries_n or_o libra_n be_v also_o give_v 1_o then_o if_o the_o place_n lie_v betwixt_o the_o ecliptic_a and_o the_o aequator_fw-la call_v the_o near_a distance_n to_o â_o or_o â_o b_o as_o before_z and_o the_o latitude_n give_v c._n it_o be_v logarichmical_o s._n c_o +_o r_o =_o s_o b_o +_o s_o a_o &_o a_o be_v a_o angle_n which_o be_v take_v out_o of_o 23._o 32â²_n leave_v a_o angle_n which_o angle_n call_v d_o then_z s_z b_o +_o s_o d_o =_o r_o +_o s_o e._n and_o e_o be_v the_o declination_n require_v 2_o if_o the_o place_n lie_v betwixt_o the_o ecliptic_a and_o the_o pole_n the_o angle_n a_o find_v as_o before_o must_v be_v add_v to_o 23._o 32â²_n and_o call_v the_o sum_n f_o then_z s_z b_o +_o s_o f_o =_o r_o +_o s_o e_o etc._n etc._n 3_o last_o let_v the_o place_n lie_v betwixt_o the_o aequator_fw-la and_o the_o other_o pole_n then_z s_z c_o +_o r_o =_o s_o b_o +_o s_o a_o and_o from_o a_o subtract_v 23._o 32â²_n call_v the_o rest_n g._n then_o s_o b_o +_o s_o g_o =_o r_o +_o s_o e_o and_z e_z the_o declination_n to_o find_v the_o right_a ascension_n of_o a_o place_n if_o it_o be_v in_o the_o ecliptic_a as_o the_o sun_n be_v let_v the_o near_a distance_n from_o aries_n be_v call_v still_o b._n and_o work_v by_o logarithm_n it_o be_v r_o +_o sc_fw-la 23._o 32â²_n =_o =_o tc_n b_o +_o t_o a._n and_o a_o be_v the_o right_a ascension_n 2_o if_o the_o place_n have_v latitude_n call_v it_o still_o c_o and_o let_v the_o declination_n find_v with_o latitude_n as_o before_o be_v call_v q._n then_o sc_n b_o +_o r_o =_o sc_fw-la q_o +_o sc_fw-la a_o and_o a_o be_v the_o right_a ascension_n or_o between_o â_o and_o â_o the_o compliment_n of_o it_o to_o find_v the_o ascensional_a difference_n thus_o t._n elevation_n +_o t._n declination_n =_o r_o +_o s.y._n and_o y_o be_v the_o ascensional_a difference_n to_o find_v the_o oblique_a ascension_n in_o the_o southern_a sign_n add_v the_o ascensional_a difference_n to_o the_o right_a ascension_n or_o in_o the_o northern_a sign_n subtract_v the_o same_o from_o the_o right_a ascension_n the_o sum_n in_o winter_n and_o the_o remainder_n in_o summer_n be_v the_o oblique_a ascension_n that_o which_o have_v be_v last_o say_v concern_v the_o declination_n right_a ascension_n ascensional_a diffeence_n and_o oblique_a