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upon_o the_o plain_a of_o
the_o instrument_n be_v a_o part_n of_o the_o horizon_n the_o parallel_n meridian_n &_o vertical_a circle_n that_o be_v contain_v or_o may_v be_v describe_v in_o our_o latitude_n sufficient_o necessary_a induce_v any_o one_o in_o the_o understanding_n of_o the_o use_n of_o it_o that_o be_v but_o indifferent_o verse_v in_o the_o linament_n and_o principle_n of_o the_o globe_n what_o to_o speak_v and_o what_o to_o answer_v in_o a_o proposition_n without_o far_a direction_n and_o have_v have_v this_o horizontall_a quadrant_n for_o many_o year_n past_a as_o a_o pocket_n instrument_n diverse_a about_o this_o kingdom_n be_v importunate_a with_o i_o for_o to_o have_v it_o or_o to_o publish_v the_o use_n of_o it_o see_v its_o great_a facility_n and_o expedition_n in_o comparison_n of_o such_o pocket_n instrument_n as_o be_v now_o use_v here_o or_o in_o foreign_a part_n i_o be_v willing_a at_o last_o after_o i_o have_v give_v order_n for_o the_o make_n of_o four_o of_o these_o instrument_n in_o silver_n for_o several_a noble_a personage_n to_o disburden_v myself_o of_o transcribe_v the_o use_n of_o the_o instrument_n and_o table_n for_o the_o make_n of_o it_o to_o satisfy_v those_o which_o be_v importunate_a and_o to_o let_v other_o that_o be_v studious_a in_o mathematical_a practice_n also_o participate_v of_o it_o now_o what_o i_o have_v deliver_v upon_o the_o accommodate_v of_o the_o instrument_n thus_o the_o make_v thereof_o with_o the_o use_n that_o i_o have_v deliver_v in_o this_o tractat_fw-la upon_o it_o follow_v i_o acknowledge_v due_a to_o none_o inferior_a assistant_n but_o to_o my_o own_o industry_n search_n and_o labour_n and_o that_o 64._o 65._o and_o 66._o page_n of_o the_o book_n of_o the_o sector_n before_o specify_v in_o which_o be_v only_o show_v the_o 2._o 3._o 19_o 22._o 25._o and_o 30._o proposition_n of_o the_o index_n or_o table_n follow_v as_o use_n of_o the_o say_a projection_n but_o i_o have_v extend_v they_o to_o many_o more_o and_o abundant_o and_o plentiful_o supply_v the_o obscurity_n of_o that_o scheme_n or_o diagramme_n there_o draw_v as_o for_o a_o general_a good_a in_o the_o use_n of_o this_o horizantal_n quadrant_n i_o deliver_v therefore_o first_o the_o make_n of_o it_o first_o by_o the_o sector_n somewhat_o different_a from_o that_o of_o master_n gunter'_v second_o by_o geometry_n and_o last_o i_o show_v a_o three_o way_n how_o it_o may_v be_v project_v and_o make_v by_o my_o mathematical_a ring_n and_o by_o number_n which_o i_o have_v calculate_v and_o accommodate_v to_o that_o end_n in_o table_n for_o more_o exactness_n part_v of_o the_o general_a scope_n and_o use_v of_o which_o instrument_n i_o deliver_v in_o the_o index_n or_o table_n follow_v a_o index_n or_o table_n of_o the_o use_n of_o the_o horizontall_a quadrant_n viz_o of_o the_o horizon_n line_n of_o shadow_n calendar_n parallel_n aequator_fw-la ecliptic_a houreline_n index_n 1_o by_o the_o horizon_n to_o show_v 1._o the_o sun_n or_o star_n altitude_n at_o any_o time_n pag._n 53._o 2._o at_o any_o day_n of_o the_o year_n how_o far_o the_o sun_n rise_v or_o set_v from_o the_o true_a east_n or_o west_n pag._n 28._o 3._o the_o sun_n azimuth_n and_o altitude_n at_o any_o hour_n for_o any_o day_n pag._n 62._o 4._o the_o meridian_n line_n upon_o any_o appearance_n of_o the_o sun_n pag._n 55._o 5._o the_o uncertainty_n of_o time_n by_o note_v the_o shadow_n of_o thing_n pag._n 63._o 6._o the_o site_n of_o a_o building_n or_o cost_v of_o a_o place_n pag._n 57_o 7._o the_o variation_n of_o the_o needle_n pag._n 59_o 8._o the_o declination_n of_o a_o wall_n or_o plain_a the_o sun_n shine_v thereon_o pag._n 71._o 9_o the_o inclination_n of_o a_o plain_a and_o to_o place_v a_o plain_a horizontall_a pag._n 89._o 2._o by_o the_o line_n of_o shadow_n be_v have_v 10._o at_o what_o hour_n in_o any_o day_n of_o the_o year_n the_o shadow_n of_o a_o altitude_n be_v equal_a double_a triple_a etc._n etc._n unto_o it_o pag._n 35._o 11._o instant_o the_o hour_n of_o the_o day_n the_o azimuth_n and_o altitude_n of_o the_o sun_n with_o the_o meridian_n line_n without_o observation_n or_o sight_n of_o the_o sun_n by_o know_v the_o proportion_n between_o the_o length_n of_o a_o shadow_n upon_o a_o horizontall_a plain_a &_o that_o which_o cast_v the_o shadow_n pag._n 67._o 12._o at_o any_o hour_n a_o altitude_n of_o the_o sun_n or_o azimuth_n what_o proportion_n shadow_n have_v to_o their_o body_n pag._n 37._o 13._o whether_o and_o altitude_n be_v above_o or_o below_o the_o jewel_n of_o the_o eye_n &_o how_o much_o 14._o the_o height_n of_o a_o altitude_n accessible_a or_o in_o accessible_a pag._n 100_o 101._o 15._o the_o measure_n of_o any_o part_n of_o altitude_n not_o approchable_a pag._n 102._o 3._o by_o the_o calendar_n be_v know_v 16._o the_o inequality_n of_o time_n in_o equal_a month_n or_o equal_a number_n of_o day_n pag._n 44._o 17._o what_o number_n of_o day_n will_v make_v the_o day_n and_o hour_n long_o or_o short_a at_o any_o time_n pag._n 43._o 18._o the_o hour_n of_o the_o sun_n rise_v set_v with_o the_o length_n of_o the_o day_n at_o any_o time_n pag._n 23._o 19_o what_o day_n be_v alike_o in_o length_n &_o what_o day_n the_o sun_n rise_v in_o the_o one_o shall_v be_v the_o sun_n set_v in_o the_o other_o pag._n 24._o 20._o the_o inequality_n of_o time_n between_o day_n break_v and_o sun_n rise_v pag._n 41._o 4._o by_o the_o parallel_n to_o search_v out_o 21._o at_o any_o day_n the_o sun_n declination_n pag._n 24_o 22._o the_o latitude_n of_o a_o place_n or_o hight_v of_o the_o pole_n above_o the_o horizon_n pag._n 60._o 23._o at_o what_o hour_n in_o any_o day_n the_o sun_n azimuth_n and_o altitude_n will_v be_v equal_a and_o how_o much_o the_o altitude_n &_o azimuth_n will_v be_v pag._n 42._o 5._o by_o the_o aequator_fw-la be_v see_v 24._o the_o sun_n equal_a motion_n right_a ascention_n and_o oblique_a ascension_n pag._n 26._o 6._o by_o the_o ecliptic_a to_o give_v 25._o the_o sun_n place_n at_o any_o time_n of_o the_o year_n pag._n 25._o 26._o the_o degree_n of_o the_o aequator_fw-la in_o the_o horizon_n by_o suppose_v the_o degree_n of_o the_o ecliptic_a in_o the_o horizon_n pag_n 46._o 27._o the_o degree_n of_o the_o ecliptic_a in_o the_o horizon_n by_o suppose_v the_o degree_n of_o the_o aequator_fw-la in_o the_o horizon_n pag._n 47._o 28._o the_o degree_n of_o medium_fw-la coeli_fw-la or_o the_o degree_n of_o the_o ecliptic_a in_o the_o meridian_n by_o suppose_v the_o degree_n of_o the_o ecliptic_a in_o the_o horizon_n well_fw-mi contra_fw-la pag._n 47._o 29._o the_o horoscope_n or_o the_o degree_n ascendant_n '_o or_o descendant_n and_o the_o nonagessima_fw-la degree_n at_o any_o hour_n pag._n 49._o 30._o what_o angle_n the_o ecliptic_a make_v with_o the_o horizon_n or_o the_o altitude_n of_o the_o nonagessima_fw-la degree_n and_o what_o azimuth_n it_o be_v in_o at_o any_o hour_n pag._n 50._o 7._o by_o the_o hour_n line_n to_o find_v 31._o the_o hour_n of_o the_o day_n and_o azimuth_n of_o the_o sun_n pag._n 54._o 32._o the_o hour_n of_o the_o day_n agreeable_a to_o any_o altitude_n or_o azimuth_n pag._n 39_o 33._o the_o sun_n difference_n of_o ascension_n for_o any_o day_n pag._n 23._o 34._o the_o quarter_n of_o the_o year_n and_o day_n of_o the_o month_n hour_n of_o the_o day_n meridian-line_n and_o azimuth_n of_o the_o sun_n if_o it_o be_v forget_v pag._n 64._o 8._o by_o the_o index_n adjoin_v with_o other_o line_n you_o have_v 35._o at_o what_o hour_n &_o altitude_n the_o sun_n will_v be_v due_a east_n at_o any_o day_n of_o the_o year_n pag._n 27._o 36._o the_o sun_n azimuth_n &_o hour_n without_o observation_n pag._n 58._o 37._o the_o time_n of_o daybreak_a or_o end_n of_o twilight_n for_o any_o day_n in_o the_o year_n pag._n 30._o 38._o the_o height_n or_o depression_n of_o the_o sun_n in_o the_o meridian_n for_o any_o day_n in_o the_o year_n here_o or_o for_o any_o latitude_n pag._n 29._o 39_o the_o sun_n depression_n &_o azimuth_n at_o any_o hour_n of_o the_o night_n assign_v pag._n 40._o 40._o the_o hour_n of_o the_o day_n to_o our_o antipode_n by_o suppose_v the_o sun_n depression_n under_o the_o horizon_n pag._n 42._o 41._o what_o hour_n &_o altitude_n the_o sun_n come_v upon_o a_o decline_a wall_n any_o day_n in_o the_o year_n &_o how_o long_o the_o sun_n shine_v thereon_o pag._n 32._o 42._o at_o what_o hour_n and_o altitude_n the_o sun_n must_v have_v to_o be_v opposite_a or_o perpendicular_a to_o a_o declination_n plain_a pag._n 33._o 43_o the_o declination_n of_o a_o wall_n by_o see_v the_o sun_n beginning_n to_o shine_v thereon_o or_o go_v from_o it_o pag._n 69._o 44._o the_o hour_n &_o altitude_n of_o a_o star_n come_v to_o the_o meridian_n at_o
the_o column_n m._n 5294._o which_o i_o take_v from_o the_o scale_n b._n and_o protract_v it_o from_o t._n to_o 30._o in_o the_o line_n 2._o 10._o now_o place_v one_o foot_n of_o the_o compass_n in_o 30._o next_o 10._o and_o extend_v the_o other_o foot_n to_o p._n the_o ecliptic_a may_v be_v intersect_v in_o the_o point_n of_o â_o and_o â_o and_o place_v in_o 30._o towards_o 2._o the_o same_o extent_n will_v intersect_v the_o ecliptic_a in_fw-la â_o and_o â_o in_o like_a manner_n may_v the_o centre_n of_o the_o rest_n of_o the_o degree_n of_o the_o ecliptic_a be_v protract_v in_o the_o line_n 2._o 10._o from_o t._n out_o of_o the_o colume_n m._n and_o p._n and_o so_o all_o the_o ecliptic_a divide_v from_o degree_n to_o degree_n but_o this_o may_v be_v otherwise_o do_v beside_o that_o which_o be_v deliver_v touch_v the_o draw_n of_o the_o parallel_n ecliptic_a and_o hour_n line_n there_o remain_v yet_o how_o to_o put_v on_o the_o calendar_n to_o graduate_v the_o index_n and_o to_o draw_v and_o divide_v the_o line_n of_o shadow_n this_o may_v be_v easy_o do_v from_o the_o table_n r._n calculate_v and_o accommodate_v to_o that_o purpose_n for_o the_o year_n 1640_o and_o may_v sufficient_o serve_v for_o many_o year_n after_o without_o any_o sensible_a error_n have_v divide_v the_o quadrant_n constru_n â£_o ction_n e.s._n and_o e.n._n as_o before_o into_o the_o usual_a degree_n of_o a_o quadrant_n lay_v a_o ruler_n upon_o the_o centre_n z._n and_o account_v the_o degree_n from_o the_o point_n e._n in_o the_o quadrant_n towards_o n._n and_o s._n out_o of_o the_o table_n r._n according_a to_o the_o several_a colume_n of_o the_o table_n r._n and_o intersect_v the_o quadrant_n calendar_n how_o to_o inscribe_v the_o calendar_n with_o small_a short_a line_n so_o shall_v the_o ark_n of_o the_o horizon_n of_o the_o instrument_n from_o e._n be_v divide_v into_o the_o usual_a day_n of_o the_o month_n which_o be_v the_o calendar_n and_o the_o beginning_n of_o these_o division_n may_v be_v at_o the_o 10._o of_o march_n and_o so_o go_v on_o to_o the_o 11._o of_o june_n and_o then_o again_o to_o begin_v from_o the_o 10._o of_o march_n and_o go_v on_o unto_o the_o 10._o of_o december_n and_o these_o day_n may_v be_v note_v upon_o the_o inside_n of_o the_o horizontall_a ark_n with_o short_a line_n from_o e._n as_o before_o and_o at_o every_o month_n may_v be_v place_v a_o representative_a letter_n for_o that_o month_n and_o every_o 10._o and_o 5._o day_n of_o every_o month_n may_v be_v note_v with_o a_o small_a stroke_n somewhat_o long_o than_o the_o rest_n to_o help_v the_o memory_n the_o ready_a to_o number_v in_o like_a manner_n may_v the_o rest_n of_o the_o day_n of_o the_o calendar_n be_v intersect_v in_o the_o out_o side_n of_o the_o horizontall_a ark_n towards_o the_o limb_n begin_v at_o the_o 13._o of_o september_n and_o so_o go_v on_o to_o the_o 11._o of_o june_n than_o again_o from_o the_o 13._o of_o september_n and_o go_v on_o unto_o the_o 10._o of_o december_n and_o these_o month_n may_v be_v also_o note_v with_o significant_a letter_n appropriate_a to_o each_o month_n and_o each_o 10._o and_o 15._o day_n of_o the_o month_n may_v be_v also_o denote_v as_o before_o with_o a_o stroke_n somewhat_o long_o than_o the_o rest_n according_a to_o the_o scheme_n against_o page_n the_o 1._o how_o to_o graduate_v the_o index_n for_o the_o instrument_n let_v the_o index_n be_v equal_a to_o the_o semidiameter_n z._n e._n and_o then_o may_v it_o be_v divide_v out_o of_o the_o table_n q._n by_o the_o help_n of_o the_o scale_n a._n beginning_n at_o the_o centre_n the_o index_n be_v divide_v and_o place_v on_o the_o centre_n of_o the_o instrument_n at_o z._n it_o shall_v help_v to_o put_v on_o and_o divide_v the_o line_n of_o shadow_n as_o follow_v lay_v the_o edge_n of_o the_o index_n to_o a._n in_o the_o limb_n which_o be_v near_o the_o 10._o of_o december_n and_o move_v it_o to_o any_o degree_n in_o the_o table_n s._n and_o account_v the_o like_a degree_n in_o the_o index_n and_o then_o make_v a_o mark_n upon_o the_o plain_a of_o the_o instrument_n where_o that_o degree_n touch_v and_o so_o go_v on_o from_o point_n to_o point_n until_o the_o whole_a line_n be_v describe_v and_o divide_v according_a to_o the_o table_n s._n this_o line_n may_v be_v place_v between_o the_o calendar_n and_o the_o limb_n or_o in_o a_o quadrant_n etc._n etc._n but_o i_o have_v cause_v it_o to_o be_v describe_v as_o be_v see_v upon_o the_o scheme_n against_o page_n the_o 1._o for_o expedition_n and_o conveniency_n â_o let_v a._n b._n c._n d._n be_v a_o plain_a divide_v the_o length_n a._n b._n within_o half_a a_o inch_n of_o the_o high_a end_n and_o a_o inch_n of_o the_o low_a end_n in_o to_o 3._o equal_a part_n which_o suppose_v the_o line_n m.n._n then_o divide_v each_o part_n into_o half_n so_o the_o line_n m._n n._n shall_v be_v divide_v into_o 6._o equal_a part_n the_o middle_a of_o which_o will_v be_v at_o z._n then_o take_v 4._o of_o these_o part_n for_o radius_fw-la and_o on_o z._n describe_v the_o obscure_a ark_n a._n e._n b._n and_o upon_o z._n erect_v a_o perpendicular_a to_o the_o line_n m._n n._n to_o cut_v the_o ark_n a._n b._n in_o e._n now_o from_o e._n to_o a._n protract_v 40._o gr_n and_o from_o e._n to_o b._n protract_v 50._o gr_n so_o the_o angle_n e._n z._n m._n shall_v be_v 90._o and_o also_o a.z.b._n shall_v be_v 90._o now_o have_v make_v a_o scale_n of_o z.e._n like_v to_o the_o scale_n a._n according_a to_o the_o former_a direction_n then_o out_o of_o the_o column_n c._n and_o by_o help_n of_o the_o say_a scale_n a._n from_o z._n you_o may_v protract_v z._n â_o 2493._o z.q._n 4823._o and_o z._n â_o 7673._o and_o from_o the_o column_n f._n y_fw-fr u._fw-mi may_v protract_v the_o distance_n of_o the_o centre_n of_o those_o intersection_n from_o z._n viz._n z._n 1.5269_o z._n 2.7949_o and_o z._n 3.16217_o and_o so_o place_v the_o compass_n in_o these_o centre_n you_o may_v describe_v the_o equator_fw-la and_o both_o tropic_n but_o if_o z._n m_o and_o z._n n._n be_v divide_v according_a to_o the_o scale_n a._n then_o from_o z._n you_o may_v account_v the_o intersection_n of_o the_o parallel_n and_o distance_n of_o the_o centre_n and_o so_o describe_v the_o parallel_n with_o great_a expedition_n and_o so_o shall_v you_o have_v the_o scheme_n or_o trapeziall_a form_n of_o the_o instrument_n b._n a._n â_o â_o and_o may_v be_v finish_v according_a to_o that_o against_o page_n the_o 1._o by_o the_o table_n and_o direction_n here_o calculate_v and_o deliver_v to_o that_o end_n now_o to_o augment_v the_o instrument_n to_o any_o proportion_n assign_v as_o if_o between_o the_o tropicke_n be_v suppose_v to_o be_v 10._o inch_n the_o radius_fw-la may_v be_v find_v out_o or_o if_o the_o radius_fw-la be_v 4._o foot_n which_o be_v according_a to_o my_o own_o instrument_n what_o distance_n may_v there_o be_v between_o the_o tropicke_n the_o proportion_n will_v be_v as_o 516._o to_o 1000_o so_o the_o breadth_n to_o the_o scale_n or_o as_o 1000_o to_o 516._o so_o the_o scale_n to_o the_o breadth_n therefore_o by_o the_o ring_n bring_v 516._o in_o the_o movable_a to_o 1000_o in_o the_o fix_a so_o right_a against_o any_o radius_fw-la in_o the_o fix_a be_v the_o distance_n between_o the_o tropicke_n in_o the_o movable_a or_o against_o the_o distance_n assign_v for_o the_o tropicke_n in_o the_o movable_a be_v the_o measure_n of_o the_o radius_fw-la or_o scale_n in_o the_o fix_a so_o if_o â_o â_o be_v allot_v to_o be_v 10._o inch_n for_o the_o distance_n between_o the_o tropicke_n the_o scale_n or_o radius_fw-la of_o the_o instrument_n shall_v be_v 19_o 4_o 10._o fere_n but_o if_o the_o scale_n or_o radius_fw-la be_v 4._o foot_n or_o 48._o inch_n than_o the_o distance_n between_o the_o tropicke_n of_o â_o and_o â_o will_v be_v near_o 24_o 77_o 100_o inches_n thus_o for_o the_o make_n of_o the_o instrument_n the_o description_n of_o which_o follow_v the_o description_n of_o the_o horizontall_a quadrant_n the_o form_n of_o this_o instrument_n be_v like_o a_o mix_a trapezia_n as_o appear_v against_o page_n 1._o where_o of_o two_o side_n be_v right_a and_o the_o other_o two_o side_n be_v circular_a which_o fall_v out_o to_o be_v so_o from_o the_o nature_n of_o the_o projection_n and_o that_o part_n which_o i_o have_v think_v most_o convenient_a for_o use_v and_o be_v full_o sufficient_a for_o that_o which_o i_o have_v deliver_v upon_o it_o and_o may_v be_v make_v of_o any_o plain_a material_a but_o fit_a in_o brass_n or_o silver_n the_o several_a part_n of_o which_o instrument_n be_v five_o viz._n the_o back_n the_o face_n the_o
the_o south_n pole_n under_o the_o horizon_n which_o be_v always_o equal_a to_o the_o elevation_n of_o the_o north_n pole_n above_o the_o horizon_n so_o if_o upon_o the_o ten_o of_o april_n exam._n the_o meridian_n altitude_n shall_v be_v find_v to_o be_v 50._o gr_n the_o declination_n belong_v to_o that_o day_n by_o the_o 3._o pro._n be_v 11._o gr_n and_o a_o half_a north_n which_o be_v subtract_v according_a to_o the_o former_a direction_n leave_v 38._o gr_n 30._o m_o the_o height_n of_o the_o aequinoctial_a above_o the_o horizon_n &_o that_o take_v from_o 90._o leaf_n 51._o gr_n 30._o m_o the_o depression_n of_o the_o south_n pole_n under_o the_o horizon_n or_o the_o elevation_n of_o the_o north_n pole_n above_o the_o horizon_n for_o the_o height_n of_o the_o aequinoctial_a know_v the_o compliment_n thereof_o be_v always_o the_o latitude_n of_o the_o place_n or_o height_n of_o the_o pole_n and_o here_o note_v general_o that_o the_o height_n of_o the_o pole_n and_o aequinoctial_a together_o do_v always_o make_v a_o quadrant_n or_o 90._o gr_n therefore_o the_o height_n of_o one_o of_o they_o be_v know_v the_o height_n of_o the_o other_o be_v also_o know_v and_o further_a here_o note_v that_o if_o the_o sun_n have_v north_n declination_n the_o sun_n be_v so_o much_o high_a than_o the_o aequinoctial_a at_o none_o that_o day_n by_o so_o much_o as_o his_o declination_n come_v to_o but_o if_o the_o sun_n have_v south_n declination_n than_o the_o sun_n be_v low_a than_o the_o aequinoctial_a that_o day_n at_o noon_n by_o so_o much_o as_o his_o declination_n come_v to_o by_o which_o you_o may_v easy_o gether_o when_o to_o add_v or_o subtract_v the_o sun_n declination_n to_o or_o from_o the_o sun_n meridianall_a altitude_n to_o get_v the_o height_n of_o aequator_fw-la which_o know_v the_o pole_n height_n can_v be_v unknown_a pro._n 34_o eight_o to_o find_v the_o sun_n azimuth_n and_o altitude_n for_o any_o hour_n constru_n ¦_o ctio_fw-la 44_o mark_n where_o the_o parallel_n for_o the_o day_n of_o the_o month_n meet_v with_o the_o give_v hour_n and_o bring_v the_o edge_n of_o the_o index_n thereto_o so_o the_o degree_n that_o the_o edge_n of_o the_o index_n cut_v in_o the_o limb_n of_o the_o instrument_n that_o shall_v be_v the_o sun_n azimuth_n and_o the_o degree_n that_o the_o hour_n cut_v in_o the_o index_n that_o shall_v be_v the_o sun_n altitude_n require_v so_o if_o upon_o the_o ten_o of_o december_n at_o nine_o of_o the_o clock_n in_o the_o morning_n exam._n the_o sun_n azimuth_n and_o altitude_n be_v require_v mark_v first_o where_o the_o tropic_a of_o capricorn_n which_o be_v the_o parallel_n for_o that_o day_n give_v meet_v with_o the_o give_v hour_n of_o nine_o and_o bring_v the_o index_n thereto_o so_o the_o edge_n of_o it_o in_o the_o limb_n point_v out_o near_o 40._o gr_n and_o a_o half_a &_o so_o much_o be_v the_o sun_n azimuth_n from_o the_o south_n at_o nine_o of_o the_o clock_n in_o the_o forenoon_n the_o say_v ten_o of_o december_n and_o the_o hour_n line_n meet_v with_o the_o index_n show_v near_o 5._o gr_n 25._o m._n so_o much_o be_v the_o sun_n altitude_n at_o that_o time_n now_o if_o you_o move_v the_o index_n soft_o along_o as_o the_o edge_n of_o it_o pass_v by_o any_o hour_n for_o any_o day_n of_o the_o year_n so_o the_o edge_n of_o the_o index_n in_o the_o limb_n of_o the_o instrument_n show_v the_o sun_n azimuth_n and_o the_o intersection_n of_o the_o parallel_n with_o the_o index_n shall_v show_v the_o sun_n altitude_n belong_v to_o that_o hour_n nine_o to_o show_v the_o uncertainty_n pro._n 35_o of_o time_n by_o note_v the_o shadow_n of_o thing_n it_o be_v usual_o note_v by_o some_o that_o when_o the_o shadow_n of_o the_o edge_n of_o a_o window_n door_n wall_n or_o such_o like_a shall_v touch_v such_o or_o such_o mark_n that_o it_o shall_v be_v then_o such_o or_o such_o a_o hour_n of_o the_o day_n and_o so_o constant_o to_o hold_v for_o all_o the_o year_n this_o observation_n be_v far_o from_o truth_n and_o the_o principal_n of_o astronomy_n and_o may_v be_v easy_o contradict_v by_o such_o which_o have_v but_o indifferent_a judgement_n in_o the_o nature_n of_o shadow_n and_o the_o sun_n passage_n by_o the_o meridian_n and_o vertical_a circle_n of_o the_o heaven_n for_o by_o how_o much_o great_a the_o propinquity_n of_o the_o sun_n approachment_n be_v unto_o the_o zenith_n or_o vertical_a point_n by_o so_o much_o the_o more_o shall_v the_o hour_n or_o time_n be_v various_a in_o one_o and_o the_o same_o azimuth_n so_o in_o the_o last_o pro._n the_o azimuth_n of_o the_o sun_n the_o ten_o of_o december_n at_o nine_o of_o the_o clock_n in_o the_o forenoon_n be_v find_v to_o be_v 40._o gr_n and_o a_o half_a exam_n and_o the_o sun_n distance_n from_o the_o zenith_n at_o that_o time_n be_v near_o 84._o gr_n 35._o m_o now_o admit_v the_o sun_n distance_n from_o the_o zenith_n the_o ten_o of_o june_n be_v but_o 32._o gr_n 35._o m_o the_o sun_n be_v in_o the_o same_o azimuth_n the_o hour_n will_v be_v half_a a_o hour_n past_o 10._o for_o the_o index_n be_v lay_v to_o the_o hour_n of_o 9_o in_o the_o tropic_n of_o â_o which_o be_v the_o sun_n parallel_n for_o the_o say_v ten_o of_o december_n and_o it_o cut_v the_o constru_n ¦_o ctio_fw-la 45_o parallel_n of_o the_o sun_n motion_n in_o the_o inequality_n of_o time_n and_o so_o the_o compliment_n of_o the_o former_a 32._o gr_n 35._o m_o in_o the_o index_n meet_v with_o the_o tropic_n of_o â_o which_o be_v the_o sun_n parallel_n for_o the_o ten_o of_o june_n in_o half_a a_o hour_n past_o 10._o so_o that_o it_o evident_o appear_v that_o the_o shadow_n of_o a_o perpendicular_a thing_n on_o the_o ten_o of_o december_n denote_v the_o hour_n of_o the_o day_n to_o be_v 9_o of_o the_o clock_n the_o same_o shadow_n the_o ten_o of_o june_n shall_v represent_v half_o a_o hour_n past_o 10._o so_o the_o error_n shall_v be_v a_o hour_n and_o a_o half_a but_o if_o you_o move_v the_o index_n unto_o the_o hour_n of_o 9_o belong_v to_o the_o ten_o of_o june_n the_o index_n shall_v point_v you_o out_o in_o the_o limb_n near_o 68_o gr_n of_o azimuth_n for_o that_o hour_n which_o at_o 9_o of_o the_o clock_n the_o ten_o of_o december_n be_v but_o 40._o gr_n &_o a_o half_a so_o the_o difference_n of_o azimuth_n in_o one_o and_o the_o same_o hour_n shall_v be_v 27._o gr_n and_o a_o half_a &_o the_o time_n as_o before_o a_o hour_n and_o a_o half_a which_o difference_n be_v sufficient_a to_o confirm_v the_o point_n ten_o to_o find_v the_o quarter_n of_o pro._n 36_o the_o year_n and_o day_n of_o the_o month_n if_o it_o be_v forget_v constru_n ¦_o ctio_fw-la 46_o at_o any_o appearance_n of_o the_o sun_n by_o the_o 27._o pro._n take_v the_o sun_n altitude_n then_o place_v the_o north_n and_o south_n edge_n of_o the_o instrument_n unto_o the_o meridian_n line_n former_o draw_v if_o in_o the_o forenoon_n otherwise_o place_v the_o east_n and_o west_n edge_n of_o instrument_n to_o the_o meridian-line_n and_o erect_v the_o prependicular_a at_o the_o end_n of_o the_o index_n then_o move_v the_o index_n to_o and_o fro_o until_o the_o shadow_n of_o the_o prependicular_a fall_n by_o the_o side_n of_o the_o index_n so_o the_o parallel_n that_o meet_v with_o the_o degree_n of_o the_o sun_n observe_v altitude_n in_o the_o edge_n of_o the_o index_n parallel_n in_o the_o calendar_n that_o shall_v show_v the_o day_n of_o the_o month_n require_v so_o if_o exam._n upon_o a_o certain_a day_n in_o the_o year_n the_o sun_n altitude_n be_v observe_v and_o find_v to_o be_v 36._o gr_n have_v place_v the_o edge_n of_o the_o instrument_n to_o the_o meridian_n line_n and_o rectify_v the_o index_n then_o move_v the_o index_n until_o the_o shadow_n of_o the_o prependicular_a fall_n by_o the_o edge_n of_o the_o instrument_n let_v the_o instrument_n rest_n at_o this_o position_n and_o account_v the_o former_a 36._o gr_n upon_o the_o index_n which_o degree_n meet_v with_o the_o hour_n in_o the_o aequator_fw-la and_o also_o that_o intersect_v the_o calendar_n in_o the_o ten_o of_o march_n &_o the_o thirteen_o of_o september_n but_o which_o of_o these_o day_n be_v the_o day_n of_o the_o month_n the_o next_o day_n observation_n of_o the_o sun_n upon_o the_o same_o hour_n will_v help_v you_o for_o if_o the_o sun_n altitude_n besound_v to_o be_v great_a than_o the_o day_n of_o the_o month_n inquire_v after_o it_o be_v the_o ten_o of_o march_z because_o the_o sun_n from_o the_o ten_o of_o december_n unto_o the_o eleven_o of_o june_n do_v every_o day_n at_o one_o &_o the_o same_o hour_n ascend_v but_o if_o the_o sun_n altitude_n be_v find_v to_o be_v