mary_n and_o st._n michael_n 2_o isle_n of_o the_o azore_n for_o true_o thus_o it_o suit_v best_o according_a to_o my_o table_n with_o the_o 2_o a_o clock_n circle_n as_o his_o lordship_n will_v have_v it_o do_v a_o advertisement_n because_o there_o be_v several_a who_o either_o want_n time_n or_o patience_n to_o go_v throu_fw-fr '_o the_o whole_a treatise_n i_o here_o present_a the_o reader_n with_o a_o catalogue_n of_o the_o operation_n which_o be_v most_o please_a and_o suitable_a to_o the_o fancy_n and_o humour_n of_o such_o and_o which_o they_o may_v easy_o in_o a_o day_n or_o two_o learn_v especial_o if_o they_o have_v a_o master_n to_o help_v they_o 1._o to_o set_v the_o globe_n level_v pag._n 4._o 2._o to_o compose_v the_o globe_n p._n 8._o 3._o to_o know_v the_o day_n of_o the_o month._n p._n 9_o 4._o to_o take_v the_o sun_n height_n above_o our_o horizon_n when_o he_o shine_v out_o clear_a and_o also_o when_o he_o shine_v dim_o and_o be_v overcloud_v p._n 5._o and_o 6._o 5._o 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find_v where_o it_o be_v day_n and_o where_o it_o be_v night_n all_o the_o world_n over_o compose_v your_o globe_n and_o all_o people_n that_o live_v in_o the_o illuminate_v hemisphere_n enjoy_v day_n at_o that_o moment_n and_o all_o that_o live_v in_o the_o obscure_a one_o night._n operation_n viii_o to_o know_v where_o at_o that_o moment_n of_o time_n the_o inhabitant_n enjoy_v nothing_o but_o day_n and_o where_o nothing_o but_o night_n as_o also_o when_o the_o day_n and_o night_n will_v be_v thus_o perpetual_a in_o any_o place_n subject_n to_o this_o alteration_n describe_v with_o your_o eye_n a_o imaginary_a circle_n about_o the_o day_n illuminate_v pole_n its_o radius_fw-la be_v the_o distance_n from_o the_o say_a pole_n to_o the_o near_a part_n of_o the_o shade_n of_o extuberancy_n and_o all_o place_n within_o that_o circle_n will_v have_v then_o no_o night_n and_o all_o place_n within_o the_o dark_a circle_n of_o the_o like_o radius_fw-la round_o the_o obscure_v place_n or_o 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confine_n or_o extremity_n of_o the_o precede_a and_o follow_v shade_n of_o extuberancy_n you_o may_v conclude_v that_o to_o all_o the_o inhabitant_n under_o the_o first_o the_o sun_n be_v rise_v and_o to_o they_o under_o the_o second_o that_o he_o be_v then_o set_v operation_n x._o to_o find_v where_o the_o sun_n be_v vertical_a at_o any_o time_n i._n e._n what_o people_n have_v he_o just_a over_o their_o head_n the_o sun_n be_v always_o vertical_a to_o those_o that_o lie_v in_o the_o middle_n of_o the_o illuminate_v part_n of_o the_o globe_n i._n e._n to_o those_o that_o dwell_v under_o his_o then_o present_a place_n in_o his_o parallel_n therefore_o as_o i_o show_v you_o in_o the_o 11._o first_o section_n if_o you_o compose_v your_o globe_n and_o hold_v up_o your_o string_n against_o the_o sun_n from_o the_o pole_n till_o its_o shade_n pass_v through_o the_o other_o or_o from_o the_o zenith_n till_o it_o pass_v through_o the_o nadir_n it_o will_v cut_v the_o parallel_n of_o the_o 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she_o shine_v out_o right_a and_o consequent_o cast_v a_o shade_n or_o appear_v only_o faint_a and_o wan_a by_o reason_n of_o thin_a cloud_n or_o by_o the_o excess_n of_o light_n during_o the_o sun_n abode_n above_o the_o horizon_n let_v we_o then_o begin_v with_o her_o almucantar_n and_o azimuth_n as_o be_v the_o basis_n and_o foundation_n of_o all_o operation_n here_o relate_v to_o she_o nor_o can_v there_o be_v the_o least_o difficulty_n in_o any_o of_o they_o unless_o perchance_o in_o the_o seven_o since_o they_o have_v so_o great_a a_o correspondence_n and_o affinity_n with_o those_o already_o handle_v in_o the_o former_a section_n operation_n i._o to_o find_v the_o moon_n be_v almucantar_n or_o height_n this_o be_v to_o be_v perform_v as_o well_o when_o she_o cast_v a_o shade_n as_o when_o she_o cast_v none_o by_o the_o two_o first_o way_n of_o find_v the_o sun_n almucantar_n and_o therefore_o consult_v the_o 5._o second_o operation_n in_o the_o first_o section_n operation_n ii_o 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to_o her_o first_o quarter_n now_o in_o rigour_n we_o shall_v add_v twelve_o hour_n to_o the_o elongation_n we_o find_v when_o she_o be_v go_v from_o her_o full_a towards_o her_o last_o quarter_n but_o see_v she_o be_v in_o the_o plane_n of_o the_o same_o hour-circle_n or_o very_a near_o it_o both_o at_o full_a and_o in_o conjunction_n therefore_o the_o bare_a add_v the_o say_v simple_a elongation_n will_v serve_v as_o well_o in_o one_o case_n as_o in_o the_o other_o for_o if_o the_o full_a moon_n at_o suppose_v 2_o of_o the_o clock_n at_o night_n cast_v real_o her_o shadow_n on_o the_o hour-circle_n of_o 2_o in_o the_o afternoon_n yet_o there_o be_v no_o need_n of_o hint_n the_o thing_n be_v so_o plain_a to_o prevent_v your_o mistake_a day_n for_o night_n the_o like_a also_o be_v to_o be_v say_v of_o the_o last_o quarter_n who_o elongation_n shall_v be_v in_o truth_n eighteen_o hour_n but_o the_o additional_a six_o hour_n as_o we_o allow_v she_o after_o her_o first_o quarter_n be_v 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represent_v the_o illumination_n and_o the_o other_o the_o obscurity_n you_o may_v perform_v this_o operation_n at_o any_o time_n whether_o the_o aforesaid_a luminary_n shine_v or_o no._n how_o easy_a therefore_o be_v it_o to_o conceive_v the_o whole_a mystery_n of_o the_o moon_n four_o principal_a change_n and_o what_o man_n mean_v by_o they_o corollary_n for_o first_o we_o see_v that_o as_o she_o be_v call_v new_a by_o a_o astronomer_n from_o her_o be_v with_o the_o sun_n i._n e._n as_o full_o between_o our_o eye_n and_o the_o sun_n as_o she_o then_o course_n permit_v so_o no_o soon_o have_v he_o find_v by_o their_o several_a motion_n that_o she_o be_v get_v 90_o degree_n or_o six_o hour_n from_o the_o sun_n but_o he_o say_v she_o be_v in_o her_o first_o quarter_n and_o when_o they_o be_v asunder_o 180_o degree_n or_o 12_o hour_n to_o wit_n as_o far_o as_o ever_o they_o can_v be_v that_o she_o be_v full_a and_o last_o as_o soon_o as_o they_o be_v distant_a 270_o degree_n or_o 18_o 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midst_n or_o centre_n of_o it_o for_o the_o sun_n beam_n pass_v throu_fw-fr '_o the_o water_n will_v contract_v in_o a_o point_n and_o ever_o burn_v at_o suppose_v h_n the_o true_a hour-circle_n so_o that_o if_o a_o blindman_n put_v but_o his_o hand_n on_o the_o say_a brazen_a hour_n circle_n he_o will_v soon_o find_v by_o the_o heat_n where_o the_o sun_n mark_n and_o consequent_o tell_v you_o the_o hour_n for_o he_o may_v easy_o feel_v how_o far_o it_o be_v from_o the_o middlemost_a hour_n circle_n i_o mean_v the_o 12_o a_o clock_n circle_n or_o meridian_n as_o for_o the_o reason_n of_o this_o operation_n it_o be_v present_o conceive_v demonstration_n for_o when_o the_o sun_n be_v over_o against_o suppose_v the_o 5_o a_o clock_n hour_n circle_n on_o the_o southside_n of_o the_o dial_n he_o must_v needs_o be_v over_o against_o the_o same_o hour_n on_o the_o north-side_n both_o hour_n make_v but_o one_o circle_n now_o since_o the_o centre_n of_o the_o bowl_n by_o be_v in_o the_o centre_n of_o the_o hemisphere_n be_v in_o the_o plane_n of_o all_o the_o hour_n circle_n and_o since_o according_a to_o the_o nature_n of_o refraction_n all_o parallel_n ray_n of_o the_o sun_n passing_a throu_fw-fr '_o a_o sphere_n of_o water_n be_v where_o they_o meet_v with_o the_o direct_a ray_n that_o pass_v throu_fw-fr '_o the_o say_v centre_n contract_v into_o a_o point_n viz._n on_o the_o opposite_a side_n at_o the_o distance_n of_o half_a its_o diameter_n or_o two_o inch_n according_a to_o our_o present_a example_n i_o say_v see_v this_o it_o must_v needs_o follow_v that_o at_o 5_o of_o the_o clock_n the_o sun_n will_v burn_v on_o the_o correspond_v hour-circle_n and_o if_o so_o than_o a_o blindman_n by_o feel_v the_o heat_n and_o find_v its_o distance_n from_o 12_o must_v needs_o be_v able_a to_o tell_v you_o the_o true_a time_n of_o the_o day_n operation_n xxx_o to_o make_v a_o dial_n to_o show_v the_o hour_n when_o the_o sun_n shine_v not_o prepare_v a_o blue_a glass_n bowl_n as_o in_o scheme_n 36th_o and_o describe_v construction_n on_o it_o with_o their_o respective_a figure_n all_o the_o hour-circle_n of_o the_o globe_n or_o as_o many_o as_o you_o think_v fit_a then_o fix_v it_o where_o you_o intend_v and_o compose_v it_o true_o by_o your_o globe_n if_o you_o place_v yourself_o so_o at_o some_o distance_n that_o a_o little_a hole_n be_v make_v at_o each_o pole_n to_o wit_n at_o p_o p_o you_o may_v see_v quite_o throu_fw-fr '_o the_o bowl_n it_o will_v follow_v that_o the_o hour-circle_n suppose_v a_o which_o the_o sun_n picture_n appear_v on_o will_v be_v the_o true_a time_n of_o the_o day_n i_o call_v this_o to_o know_v what_o a_o clock_n it_o be_v when_o the_o sun_n shine_v not_o because_o now_o the_o least_o faint_a appearance_n of_o he_o serve_v the_o turn_n though_o it_o be_v not_o enough_o to_o cast_v any_o shadow_n nay_o let_v the_o sun_n be_v quite_o cover_v and_o if_o you_o can_v but_o guess_v by_o the_o adjacent_a brightness_n whereabout_o he_o be_v you_o will_v be_v able_a to_o guess_v the_o hour_n without_o any_o sensible_a error_n for_o the_o say_a brightness_n appear_v on_o the_o bowl_n will_v be_v proportionable_o distant_a from_o the_o sun_n be_v true_a place_n there_o as_o it_o be_v from_o the_o sun_n in_o the_o heaven_n it_o be_v clear_a that_o the_o sun_n picture_n must_v fall_v if_o any_o where_o on_o the_o demonstration_n true_a hour-circle_n because_o by_o compose_v the_o bowl_n according_a to_o the_o true_a position_n of_o the_o heaven_n the_o hour-circle_n of_o the_o one_o concur_v with_o the_o other_o and_o fall_v exact_o in_o the_o same_o plane_n therefore_o be_v your_o eye_n in_o the_o centre_n of_o the_o bowl_n its_o true_a
hour_n circle_n i._n e._n that_o which_o correspond_v with_o the_o time_n of_o the_o day_n will_v be_v just_o interpose_v between_o your_o eye_n and_o the_o sun_n but_o since_o the_o whole_a axis_n be_v the_o common_a section_n of_o the_o hour-circle_n let_v your_o eye_n be_v but_o in_o any_o part_n of_o it_o the_o same_o interposition_n must_v happen_v so_o that_o see_v the_o sun_n ray_n by_o reason_n of_o the_o blue_a colour_n penetrate_v not_o the_o glass_n his_o picture_n must_v needs_o be_v on_o the_o outside_n of_o it_o where_o the_o say_a ray_n will_v have_v otherways_o past_a now_o the_o ray_n that_o go_v from_o your_o eye_n throu_fw-fr '_o the_fw-fr two_o holes_n be_v the_o axis_n therefore_o whilst_o your_o eye_n remain_v in_o this_o posture_n it_o will_v follow_v that_o wheresoever_o you_o see_v the_o sun_n picture_n on_o the_o glass_n there_o his_o place_n must_v be_v and_o consequent_o his_o say_a picture_n must_v show_v the_o hour_n operation_n xxxi_o how_o to_o make_v a_o horizontal_n concave_a dial_n by_o the_o globe_n and_o geometrical_o also_o compose_v so_o your_o globe_n in_o the_o concavity_n give_v suppose_v construction_n bac_n in_o scheme_n 37._o that_o a_o the_o centre_n of_o the_o say_a concavity_n shall_v concur_v with_o the_o centre_n of_o the_o say_a globe_n then_o draw_v your_o string_n over_o each_o necessary_a hour_n circle_n on_o the_o globe_n to_o the_o side_n of_o the_o concavity_n mark_v as_o many_o point_n as_o shall_v be_v convenient_a for_o the_o describe_v the_o correspond_v hour_n circle_n and_o the_o pin_n ad_fw-la erect_v in_o the_o nadir_n at_o d_o as_o high_a as_o the_o say_a centre_n a_o i_o mean_v a_o pin_n equal_a to_o the_o semi-diameter_n of_o the_o concavity_n will_v with_o its_o top_n always_o show_v you_o the_o hour_n though_o the_o former_a way_n be_v impracticable_a when_o the_o hole_n be_v less_o way_n than_o the_o globe_n yet_o it_o serve_v to_o illustrate_v and_o make_v easy_a the_o geometrical_a operation_n for_o you_o have_v nothing_o you_o see_v to_o do_v but_o to_o draw_v hour_n circle_n within_o as_o you_o will_v without_o be_v the_o say_a concavity_n a_o whole_a sphere_n and_o then_o the_o top_n of_o its_o semi-diameter_n i._n e._n the_o point_n which_o lie_v in_o the_o centre_n a_o will_v perform_v the_o style_n demonstration_n part_n for_o since_o the_o sun_n be_v every_o hour_n as_o we_o have_v before_o show_v you_o in_o the_o same_o plane_n of_o the_o true_a hour_n circle_n and_o since_o a_o the_o top_n of_o the_o semi-diameter_n be_v in_o the_o centre_n of_o the_o concavity_n be_v part_n of_o the_o axis_n or_o common_a section_n of_o all_o the_o hour-circle_n it_o follow_v that_o its_o shadow_n must_v fall_v on_o the_o true_a hour_n operation_n xxxii_o how_o to_o describe_v geometrical_o a_o ceiling_n dial._n see_v the_o glass_n which_o reflect_v the_o sun_n ray_n to_o show_v we_o the_o hour_n be_v common_o fix_v in_o the_o corner_n and_o by-place_n of_o window_n the_o globe_n can_v seldom_o be_v so_o well_o order_v by_o reason_n of_o its_o bulk_n as_o to_o help_v we_o in_o the_o construction_n of_o this_o dial_n therefore_o i_o shall_v only_o give_v you_o the_o geometrical_a way_n which_o be_v as_o i_o take_v it_o both_o short_a and_o new_a and_o because_o these_o dial_n have_v common_o the_o window_n or_o inlet_n for_o the_o sun_n southerly_a for_o otherwise_o they_o will_v show_v but_o very_o few_o hour_n we_o will_v suppose_v we_o also_o in_o the_o follow_a example_n to_o stand_v thus_o and_o afterward_o you_o shall_v see_v the_o difference_n between_o such_o a_o dial_n and_o those_o who_o window_n have_v another_o aspect_n first_o make_v on_o any_o pasteboard_n trencher_n etc._n etc._n a_o horizontal_n construction_n dial_n as_o in_o scheme_n 38._o and_o fix_v in_o o_o its_o centre_n a_o thread_n of_o a_o good_a length_n to_o wit_n open_v then_o fasten_v the_o say_a dial_n so_o with_o a_o nail_n to_o a_o long_a mason_n ruler_n that_o its_o fiducial_a edge_n kl_n may_v lie_v upon_o the_o meridian_n or_o 12_o a_o clock_n line_n and_o have_v cement_v and_o place_v level_v a_o piece_n of_o look_a glass_n of_o the_o bigness_n of_o a_o three_o penny_n in_o the_o window_n or_o what_o convenient_a place_n else_o you_o please_v of_o your_o chamber_n which_o we_o will_v suppose_v to_o be_v g_z find_v by_o the_o plumet_n ae_n the_o point_v a_o in_o the_o ceiling_n wxyz_n be_v the_o point_n in_o scheme_n 39_o direct_o over_o the_o say_v g_z and_o draw_z throu_fw-fr '_o it_o a_o meridian_n line_n viz._n the_o line_n al._n in_o the_o next_o place_n fix_v one_o end_n of_o a_o piece_n of_o packthread_n on_o g_o the_o centre_n of_o the_o glass_n and_o the_o other_o on_o some_o point_n of_o your_o meridian_n line_n in_o such_o manner_n that_o it_o make_v a_o angle_n with_o it_o of_o 51._o 30′_n i_o e._n the_o angle_n of_o the_o elevation_n which_o may_v be_v easy_o perform_v by_o the_o application_n of_o the_o side_n of_o a_o quadrant_n to_o the_o say_v extend_v packthread_n and_o when_o it_o be_v right_a let_v the_o point_n thus_o find_v in_o your_o meridian_n line_n be_v call_v b._n last_o take_v the_o distance_n between_o the_o aforesaid_a point_n a_o and_o b_o and_o mark_v it_o suppose_v at_o c_o on_o the_o edge_n of_o your_o ruler_n from_o o_o the_o centre_n or_o fasten_v of_o the_o horizontal_n place_v so_o the_o say_a ruler_n fiducial_a edge_n kcl_n along_o the_o meridian_n line_n on_o the_o ceiling_n that_o the_o point_n c_o may_v lie_v just_a on_o a_o and_o all_o be_v do_v for_o than_o if_o you_o draw_v but_o the_o thread_n open_v straight_o over_o each_o hour-line_n of_o the_o horizontal_n it_o show_v you_o where_o you_o be_v to_o draw_v all_o the_o fair_a line_n of_o the_o require_a dial._n sch._n 40._o as_o for_o the_o truth_n of_o this_o demonstration_n dial_n it_o appear_v in_o scheme_n 40._o by_o the_o right_a angle_n triangle_n ogh_n and_o ghf_n where_o hf_n be_v part_n of_o he_o a_o suppose_a meridian_n line_n on_o the_o floor_n under_o that_o in_o the_o ceiling_n g_o the_o station_n of_o the_o glass_n in_o the_o window_n h_n the_o point_n under_o the_o say_a station_n as_o former_o a_o be_v the_o point_n over_o it_o and_o to_o facilitate_v the_o demonstration_n let_v we_o imagine_v gh_o equal_a to_o give_v i._n e._n that_o the_o glass_n lie_v in_o the_o middle_n between_o the_o floor_n and_o ceiling_n this_o be_v so_o suppose_v that_o gh_a instead_o of_o represent_v a_o perpendicular_a line_n in_o the_o wall_n as_o here_o we_o conceive_v it_o have_v be_v a_o perpendicular_a stick_n and_o that_o you_o be_v to_o describe_v a_o horizontal_n dial_n on_o the_o floor_n who_o style_n be_v to_o be_v the_o say_a stick_n i_o say_v suppose_v this_o you_o must_v you_o know_v to_o perform_v the_o operation_n produce_v the_o meridian_n line_n mh_o to_o suppose_v n_o and_o fasten_v a_o string_n on_o g_o find_v in_o it_o the_o point_n v._n g._n o_o for_o the_o centre_n of_o the_o dial_n i_o mean_v a_o point_n to_o which_o a_o string_n be_v extend_v from_o g_o make_v with_o the_o meridian_n oh_o the_o angle_n of_o the_o elevation_n and_o so_o draw_v the_o several_a hour-line_n from_o the_o say_v o_o according_a to_o their_o respective_a angle_n and_o distance_n all_o which_o be_v express_v at_o large_a in_o the_o three_o 73._o scheme_n or_o first_o horizontal_n dial_n for_o there_o you_o see_v gh_n be_v a_o perpendicular_a style_n show_v the_o hour_n with_o its_o top_n and_o that_o o_o be_v the_o centre_n of_o the_o dial_n have_v a_o line_n draw_v to_o it_o from_o g_z make_v the_o angle_n of_o the_o elevation_n with_o the_o meridian_n oh_o now_o since_o o_o in_o our_o present_a case_n be_v a_o point_n without_o the_o chamber_n and_o consequent_o the_o line_n mh_o can_v be_v produce_v to_o it_o you_o must_v draw_v your_o thread_n from_o g_o to_o the_o say_a meridian_n line_n hm_n within_o the_o chamber_n and_o find_v in_o it_o the_o point_n f_o to_o wit_v the_o point_n where_o the_o say_a thread_n gf_n make_v with_o it_o a_o angle_n equal_a to_o that_o of_o the_o elevation_n for_o thereby_o you_o will_v have_v the_o distance_n of_o o_o your_o true_a centre_n from_o h_n as_o be_v the_o distance_n of_o f_o from_o h_n see_v the_o side_n gh_n be_v common_a and_o the_o angle_n in_o both_o triangle_n equal_a this_o be_v so_o if_o you_o put_v out_o of_o the_o chamber_n a_fw-fr horizontal_n dial_n who_o centre_n shall_v lie_v on_o o_o and_o its_o meridian_n line_n concur_v with_o hf_n it_o be_v but_o produce_v all_o its_o hour-line_n on_o the_o floor_n and_o it_o must_v necessary_o follow_v that_o g_o the_o top_n of_o the_o perpendicular_a style_n will_v show_v you_o true_o the_o time_n of_o
the_o day_n but_o by_o construction_n all_o the_o hour-line_n be_v thus_o draw_v on_o the_o ceiling_n and_o consequent_o be_v exact_o over_o the_o suppose_a one_o on_o the_o floor_n ergo_fw-la the_o reflext_a ray_n from_o g_z must_v as_o true_o show_v you_o the_o hour_n above_o as_o the_o direct_a ray_n below_o for_o both_o ray_n be_v ever_o in_o the_o same_o plane_n nor_o be_v there_o to_o be_v any_o real_a difference_n in_o the_o operation_n though_o southward_o the_o chamber-window_n shall_v look_v another_o way_n for_o you_o be_v only_o to_o remember_v that_o whilst_o it_o enjoy_v the_o least_o point_n of_o south_n the_o centre_n of_o your_o dial_n be_v without_o the_o chamber_n when_o it_o look_v full_a east_n or_o west_n it_o be_v in_o the_o side_n or_o edge_n of_o it_o and_o when_o it_o verge_n northward_o it_o be_v altogether_o within_o so_o that_o in_o a_o full_a southern_a aspect_n the_o say_a centre_n will_v be_v most_o abroad_o and_o in_o a_o full_a northern_a one_o the_o contrary_a all_o which_o plain_o appear_v to_o any_o one_o that_o will_v consider_v a_o horizontal_n dial_n true_o place_v have_v a_o perpendicular_a for_o its_o style_n if_o he_o draw_v over_o the_o hour-line_n a_o line_n that_o shall_v represent_v the_o aforesaid_a side_n of_o your_o chamber_n according_a to_o its_o position_n and_o site_n operation_n xxxiii_o to_o make_v a_o compound_n dial_n to_o wit_n one_o contain_v several_a useful_a operation_n innumerable_a be_v the_o ingenious_a dial_n that_n may_v be_v invent_v but_o since_o we_o have_v be_v long_o enough_o on_o this_o subject_a either_o for_o my_o reader_n be_v speculation_n or_o curiosity_n i_o will_v now_o conclude_v and_o that_o with_o a_o recapitulation_n or_o sum_v up_o of_o much_o of_o what_o we_o have_v already_o say_v by_o show_v the_o fabric_n of_o a_o compound_v dial_n that_o be_v to_o say_v one_o that_o contain_v many_o useful_a operation_n beside_o the_o hour_n for_o nothing_o rub_v up_o the_o memory_n more_o efficatious_o or_o make_v we_o more_o master_n of_o our_o rule_n than_o a_o practical_a example_n the_o say_a dial_n show_v as_o follow_v 1._o the_o hour_n with_o we_o at_o all_o time_n 2._o the_o hour_n in_o what_o other_o country_n you_o please_v 3._o the_o sun_n place_n in_o each_o sign_n 4._o the_o day_n of_o the_o month._n 5._o the_o time_n of_o the_o sun_n be_v rise_v and_o set_v 6._o the_o sun_n amplitude_n 7._o the_o sun_n height_n 8._o the_o sun_n azimuth_n 9_o the_o sun_n be_v bear_v according_o to_o the_o point_n of_o the_o compass_n 10._o the_o proportion_n between_o perpendicular_o and_o their_o shadow_n and_o consequent_o the_o height_n of_o any_o tower_n or_o the_o like_a to_o make_v then_o this_o dial_n you_o must_v first_o describe_v a_o horizontal_n home_n as_o in_o sch._n 41._o about_o a_o foot_n in_o diameter_n and_o let_v b_o the_o centre_n of_o the_o plane_n be_v the_o point_n where_o a_o erect_a or_o upright_o style_v according_a to_o our_o direction_n in_o the_o 73._o first_o horizontal_n show_v you_o with_o its_o top_n the_o hour_n now_o because_o the_o shade_n of_o a_o upright_o style_n unless_o it_o be_v very_o short_a will_v present_o fall_v out_o of_o the_o plane_n as_o well_o in_o the_o morning_n as_o towards_o night_n therefore_o it_o will_v be_v convenient_a to_o have_v your_o cock_n or_o style_n make_v so_o that_o ab_fw-la the_o perpendicular_a or_o forepart_n of_o it_o as_o in_o scheme_n 42._o shall_v stand_v at_o b_o the_o say_a centre_n of_o the_o plane_n to_o represent_v this_o upright_a style_n and_o its_o angle_n aob_n at_o o_o the_o centre_n of_o the_o dial_n or_o point_v from_o whence_o all_o the_o hour-line_n be_v draw_v for_o thus_o the_o side_n oa_n make_v with_o the_o meridian_n line_n at_o o_o the_o angle_n of_o the_o elevation_n represent_v the_o axis_n of_o the_o world_n and_o consequent_o cast_v its_o shadow_n on_o the_o hour-line_n as_o the_o usual_a cock_n of_o all_o horizontal_n dial_n do_v place_n 2._o have_v choose_v all_o the_o place_n which_o you_o desire_v from_o time_n to_o time_n to_o know_v what_o a_o clock_n it_o be_v at_o consider_v well_o your_o globe_n and_o find_v under_o what_o hour-circle_n the_o say_v place_n lie_v as_o for_o example_n suppose_v rome_n lie_v under_o the_o 11_o a_o clock_n hour-circle_n constantinople_n under_o that_o of_o 10_o aleppo_n 9_o etc._n etc._n place_v therefore_o the_o say_a town_n towards_o the_o limb_n of_o your_o dial_n under_o the_o correspond_v hour-line_n and_o you_o will_v constant_o know_v the_o time_n of_o the_o day_n in_o the_o say_a place_n for_o call_v it_o always_o noon_n at_o each_o place_n you_o seek_v after_o you_o have_v nothing_o to_o do_v but_o to_o count_v the_o hour_n from_o thence_o to_o the_o shade_n of_o the_o style_n as_o v_o g._n if_o it_o be_v 4_o a_o clock_n with_o you_o in_o the_o afternoon_n and_o you_o will_v know_v the_o hour_n at_o aleppo_n let_v aleppo_n be_v 12_o and_o count_v from_o thence_o 1._o 2._o 3._o etc._n etc._n till_o you_o come_v to_o the_o hour_n of_o the_o day_n i_o mean_v the_o hour_n then_o show_v you_o by_o the_o shade_n you_o will_v find_v it_o to_o be_v 7_o a_o clock_n there_o for_o aleppo_n be_v you_o see_v three_o hour_n eastward_o of_o you_o now_o have_v the_o hour_n with_o you_o be_v 4_o in_o the_o morning_n you_o must_v have_v count_v backward_o as_o 11_o 10_o 9_o 8_o and_o consequent_o you_o will_v have_v find_v it_o there_o 8_o in_o the_o morning_n in_o this_o manner_n than_o you_o must_v operate_v all_o along_o 3_o and_o 4_o find_v by_o your_o globe_n exact_o the_o sun_n height_n every_o month._n hour_n at_o his_o entrance_n into_o each_o sign_n then_o take_v by_o the_o help_n of_o your_o sector_n ab_fw-la the_o erect_a style_n in_o scheme_n 42._o being_n radius_fw-la the_o tangent_fw-la compliment_n of_o the_o height_n and_o put_v one_o foot_n of_o your_o compass_n on_o your_o dial_n at_o b_o make_v prick_n or_o mark_v in_o each_o correspond_v hour-line_n according_o that_o be_v to_o say_v if_o the_o sun_n be_v high_a suppose_v 50_o degree_n at_o 12_o of_o the_o clock_n when_o he_o enter_v ♉_o or_o â™_o then_o take_v the_o tangent_fw-la of_o 40_o and_o prick_v that_o distance_n in_o the_o meridian_n line_n viz._n from_o b_o to_z f_z and_o if_o his_o height_n at_o 1_o and_o 11_o a_o clock_n be_v v._n g._n 48_o degree_n take_v the_o tangent_fw-la of_o 42_o and_o prick_v that_o distance_n in_o the_o 11_o and_o 1_o a_o clock_n line_n viz._n from_o b_o to_z h_z and_o g_o and_o when_o you_o have_v go_v thus_o over_o all_o the_o hour-line_n no_o soon_o will_v the_o sun_n come_v into_o ♉_o or_o â™_o but_o the_o shade_n of_o the_o point_n or_o apex_n of_o the_o style_n ab_fw-la will_v fall_v every_o hour_n on_o the_o aforesaid_a prick_n and_o consequent_o show_v you_o the_o sun_n place_n in_o the_o ecliptic_a in_o like_a manner_n you_o must_v do_v with_o the_o rest_n of_o the_o sign_n and_o then_o with_o the_o 10_o degree_n of_o every_o sign_n place_v still_o the_o character_n of_o each_o sign_n about_o the_o limb_n of_o your_o dial_n near_o the_o last_o mark_n or_o prick_v belong_v to_o it_o this_o be_v do_v see_v by_o your_o globe_n what_o day_n of_o the_o month_n correspond_v with_o each_o sign_n and_o what_o with_o their_o subdivision_n and_o if_o you_o mark_v this_o as_o the_o say_v 41th_o scheme_n show_v you_o on_o both_o side_n of_o the_o meridian_n than_o the_o say_a prick_n will_v by_o the_o help_n of_o the_o shade_n of_o the_o top_n of_o ab_fw-la show_v you_o also_o the_o day_n of_o the_o month_n i_o mention_v here_o prick_v not_o only_o as_o a_o easy_a way_n but_o a_o better_a way_n than_o line_n for_o beside_o the_o great_a difficulty_n of_o draw_v they_o they_o embarras_n and_o confound_v a_o dial_n very_o much_o especial_o if_o there_o be_v many_o of_o they_o whereas_o the_o say_a prick_n be_v never_o out_o of_o a_o hour-line_n and_o consequent_o take_v up_o no_o new_a room_n now_o to_o avoid_v confusion_n and_o mistake_v i_o will_v have_v the_o say_v prick_n of_o 3_o sort_n at_o least_o for_o if_o one_o row_n be_v v._n g._n astericks_n and_o another_o cross_n and_o a_o 3d_o plain_a prick_n you_o will_v then_o know_v at_o first_o sight_n to_o what_o sign_n or_o day_n of_o the_o month_n any_o of_o they_o belong_v 5_o instead_o of_o trouble_v you_o with_o devide_v the_o circle_n sun_n gklt_n the_o upper_a part_n of_o the_o border_n of_o the_o dial_n for_o the_o find_v out_o the_o time_n of_o the_o sun_n rise_v and_o set_v you_o need_v only_o consult_v the_o day_n of_o the_o month_n on_o your_o globe_n first_o when_o he_o rise_v early_a second_o when_o he_o rise_v at_o 4_o a_o
clock_n three_o when_o at_o 4½_n five_o when_o at_o 5_o and_o in_o the_o like_a proportion_n go_v on_o till_o the_o day_n come_v to_o their_o great_a decrease_v and_o put_v the_o say_a day_n of_o the_o month_n in_o order_n as_o they_o be_v in_o the_o scheme_n under_o the_o correspond_v hour_n on_o the_o morning_n side_n of_o your_o dial_n for_o his_o rise_n do_v the_o like_a for_o his_o set_v on_o the_o evening_n side_n of_o it_o and_o you_o may_v perform_v the_o operation_n with_o sufficient_a exactness_n in_o like_a manner_n you_o be_v to_o proceed_v for_o the_o quarter_n half_a quarter_n etc._n etc._n if_o you_o will_v have_v they_o express_v 6_o to_o avoid_v also_o the_o trouble_n of_o devide_v the_o circle_n amplitude_n 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d according_a to_o the_o sun_n diurnal_a increment_n and_o decrement_n in_o amplitude_n you_o need_v only_o find_v by_o your_o globe_n what_o the_o say_a amplitude_n amount_v to_o on_o every_o of_o the_o aforementioned_a day_n which_o be_v mark_v on_o your_o dial_n for_o the_o sun_n rise_v and_o set_v and_o then_o put_v it_o in_o figure_n under_o each_o day_n as_o the_o scheme_n show_v you_o 7_o open_v your_o compass_n at_o the_o tangent_fw-la of_o 28_o degree_n ab_fw-la sun_n be_v the_o radius_fw-la and_o put_v one_o foot_n on_o b_o describe_v the_o circle_n xyz_n afterward_o describe_v another_o according_a to_o the_o tangent_fw-la of_o 35_o degree_n than_o a_o three_o according_a to_o that_o of_o 40_o and_o so_o on_o in_o the_o same_o proportion_n as_o far_o as_o your_o plane_n permit_v now_o if_o you_o mark_v these_o circle_n with_o the_o figure_n of_o the_o compliment_n of_o their_o degree_n that_o be_v to_o say_v the_o circle_n of_o 28_o degree_n with_o the_o figure_n 62_o that_o of_o 35_o with_o 55_o that_o of_o 40_o with_o 50_o etc._n etc._n you_o will_v always_o know_v the_o height_n of_o the_o sun_n for_o what_o circle_n soever_o the_o shade_n of_o ab_fw-la touch_v with_o its_o top_n that_o will_v be_v the_o require_v height_n and_o if_o it_o fall_v between_o 2_o circle_n it_o be_v but_o consider_v which_o of_o they_o it_o come_v near_a to_o and_o then_o you_o may_v guess_v at_o the_o height_n with_o sufficient_a exactness_n 8_o and_o 9_o divide_v one_o of_o these_o circle_n viz._n sew_v into_o bear_v degree_n and_o under_o each_o 11_o degree_n and_o ¼_n place_v the_o several_a point_n of_o the_o pixidis_fw-la nauticae_fw-la or_o mariner_n compass_n in_o the_o order_n as_o they_o be_v express_v in_o our_o say_a scheme_n and_o you_o will_v not_o only_o have_v by_o the_o shade_n of_o ab_fw-la the_o sun_n azimuth_n at_o all_o time_n but_o see_v also_o how_o he_o bear_v from_o you_o according_a to_o the_o point_n of_o the_o compass_n and_o if_o the_o shade_n be_v at_o any_o time_n too_o short_a lay_v on_o it_o but_o a_o ruler_n label_n of_o paper_n or_o the_o like_a and_o that_o will_v true_o lengthen_v the_o say_a shade_n and_o resolve_v your_o question_n 10thly_a divide_v of_o the_o 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the_o construction_n of_o dial_n and_o now_o let_v i_o desire_v all_o those_o that_o be_v please_v to_o follow_v this_o geometrical_a way_n which_o perchance_o be_v as_o expedite_v a_o one_o and_o as_o free_v from_o blind_a line_n as_o can_v be_v not_o to_o rest_v satisfy_v till_o they_o full_o comprehend_v what_o they_o do_v for_o the_o mechanical_a way_n of_o dial_v be_v as_o soon_o lose_v as_o learn_v it_o be_v impossible_a without_o continual_a practice_n not_o to_o forget_v the_o rule_n especial_o if_o one_o can_v make_v many_o dial_n when_o as_o a_o man_n that_o understand_v the_o reason_n of_o the_o operation_n by_o have_v in_o his_o head_n a_o true_a idea_n of_o the_o sphere_n and_o its_o projection_n will_v 20_o year_n after_o without_o memorandum_n or_o note_n be_v able_a reflect_v but_o a_o little_a to_o make_v not_o only_o all_o dial_n he_o former_o know_v but_o new_a one_o also_o at_o first_o fight_n to_o conclude_v i_o here_o present_a my_o reader_n with_o the_o globe_n in_o a_o new_a dress_n for_o be_v paint_v or_o stain_v on_o marble_n according_a to_o sch._n 43._o it_o will_v be_v fit_a for_o any_o garden_n or_o open_a portico_n and_o lest_o it_o may_v appear_v too_o plain_a the_o corner_n of_o its_o base_a or_o pedestal_n may_v be_v adorn_v with_o handsome_a well_o turn_v branch_n which_o not_o only_o embellish_v the_o whole_a machine_n by_o their_o make_n but_o hold_v out_o bowl_n of_o glass_n and_o wyar_n for_o use_v also_o for_o on_o the_o first_o corner_n to_o wit_n that_o mark_v with_o a_o there_o be_v 43._o place_v as_o a_o rarity_n the_o blind_a man_n 111._o dial._n on_o the_o second_o mark_v with_o b._n the_o 112._o dial_n that_o show_v the_o hour_n when_o the_o sun_n shine_v not_o which_o will_v be_v often_o very_o useful_a on_o the_o three_o mark_v with_o c_o the_fw-mi be_v a_o armillary_n wyer_n sphere_n have_v a_o vane_n on_o the_o top_n that_o continual_o show_v on_o the_o brass_n plane_n within_o graduate_v and_o nautical_o character_v from_o what_o quarter_n the_o wind_n exact_o blow_v as_o also_o if_o you_o turn_v the_o say_a vane_n into_o the_o plane_n of_o the_o sun_n his_o azimuth_n and_o bear_v beside_o the_o sphere_n be_v a_o horizontal_n concave_a dial_n show_v the_o hour_n too_o for_o the_o shade_n of_o the_o pin_n top_n in_o the_o centre_n ever_o fall_v on_o the_o true_a hour-circle_n as_o i_o show_v in_o the_o 113._o construction_n of_o such_o a_o dial._n and_o by_o the_o way_n you_o must_v know_v this_o branch_n stand_v not_o in_o its_o true_a place_n in_o the_o scheme_n i_o mean_v on_o the_o three_o corner_n of_o the_o base_a because_o in_o perspective_n it_o will_v fall_v on_o the_o globe_n itself_o and_o consequent_o not_o appear_v well_o to_o the_o eye_n in_o a_o picture_n last_o on_o the_o four_o corner_n mark_v with_o d_o there_o be_v another_o glass_n bowl_n of_o the_o former_a dimension_n contain_v orderly_o all_o the_o constellation_n and_o remarkable_a star_n and_o therefore_o if_o you_o know_v the_o hour_n it_o will_v compose_v the_o say_a bowl_n or_o globe_n and_o so_o represent_v the_o then_o position_n of_o the_o heaven_n but_o though_o you_o be_v ignorant_a of_o the_o hour_n if_o you_o see_v a_o know_a star_n and_o move_v the_o bowl_n on_o its_o axis_n till_o the_o paint_a star_n on_o it_o lie_v just_a between_o your_o eye_n and_o the_o real_a one_o you_o have_v the_o hour_n and_o consequent_o may_v know_v the_o globe_n be_v now_o compose_v any_o star_n or_o constellation_n above_o the_o horizon_n for_o the_o axis_n of_o this_o bowl_n have_v one_o end_n point_v direct_o to_o the_o north_n pole_n and_o the_o other_o fix_v in_o the_o centre_n of_o a_o rundle_n contain_v on_o its_o limb_n the_o day_n of_o each_o month_n fit_v to_o the_o right_a ascension_n of_o the_o star_n and_o move_v also_o on_o a_o plane_n divide_v into_o 24_o equal_a part_n figure_v with_o the_o hour_n of_o a_o natural_a day_n it_o will_v follow_v that_o the_o day_n of_o the_o month_n when_o the_o globe_n be_v compose_v must_v lie_v on_o the_o true_a hour_n as_o the_o true_a hour_n moveed_o to_o the_o day_n of_o the_o month_n must_v compose_v the_o globe_n as_o be_v before_o hint_v these_o short_a direction_n be_v sufficient_a for_o any_o mathematician_n or_o instrument-maker_n and_o as_o for_o the_o branch_n itself_o it_o be_v as_o you_o see_v not_o in_o its_o true_a place_n for_o the_o above_o mention_v reason_n j._n moxon_n to_o the_o reader_n have_v courteous_a reader_n 71._o engage_v to_o show_v you_o the_o problem_n and_o operation_n on_o the_o sector_n which_o the_o noble_a author_n suppose_v every_o one_o that_o study_v the_o geometrical_a way_n of_o dial_v to_o know_v i_o
describe_z the_o projection_n but_o they_o may_v serve_v for_o sch_n 1_o &_o 2_o pag._n 135._o if_o on_o the_o high_a the_o constellation_n be_v suppose_v to_o be_v engraud_v &_o on_o the_o lower_z a_o line_n be_v draw_v from_o the_o centre_n to_o lack_v hour_n in_o the_o limb_n &_o no_o almucantar_n or_o azimuth_n express_v but_o by_o prick_n satisfy_v any_o ordinary_a curiosity_n on_o the_o globe_n itself_o according_a to_o their_o true_a longitude_n and_o latitude_n for_o than_o their_o declension_n parallel_n and_o right_a ascension_n appear_v in_o a_o manner_n at_o first_o view_n which_o must_v needs_o therefore_o facilitate_v the_o other_o operation_n of_o the_o pedestal_n thus_o you_o see_v that_o our_o globe_n though_o it_o be_v a_o terrestrial_a one_o may_v in_o case_n of_o necessity_n be_v serviceable_a in_o relation_n to_o the_o very_a star_n but_o because_o all_o operation_n that_o have_v the_o least_o reflection_n in_o they_o seem_v intricate_a and_o troublesome_a to_o 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rise_v or_o set_v early_o or_o late_a accord_n accord_n op._n 6._o pag._n 11._o 11._o vid._n oper._n 13._o sect._n 2._o preliminary_a consideration_n the_o grand_a division_n of_o the_o earth_n the_o boundary_a between_o europe_n and_o asia_n the_o division_n of_o each_o modern_a country_n from_o the_o other_o the_o ancient_a limit_n of_o several_a nation_n a_o table_n of_o reduce_v degree_n into_o miles_n what_o the_o latitude_n of_o a_o place_n be_v and_o how_o to_o find_v it_o what_o the_o longitude_n be_v of_o the_o grand_a meridian_n of_o the_o most_o note_a place_n where_o author_n be_v have_v place_v the_o grand_a meridian_n where_o we_o fix_v our_o grand_a meridian_n how_o to_o find_v the_o longitude_n of_o any_o place_n a_o memorandum_n a_o preliminary_a discourse_n of_o clime_n what_o a_o clime_n be_v what_o a_o parallel_n be_v of_o the_o antiquity_n and_o number_n of_o clime_n of_o the_o 7_o common_a northern_a clime_n of_o the_o 7_o southern_a clime_n why_o the_o middle_a 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time_n all_o the_o world_n over_o where_o it_o be_v bedtime_n all_o the_o world_n over_o the_o reason_n or_o demonstration_n of_o the_o operation_n operation_n oper._n 10_o sec_fw-la 1._o pag._n 14._o to_o find_v the_o sun_n height_n in_o any_o place_n the_o reason_n of_o the_o operation_n to_o find_v the_o sun_n depression_n to_o find_v all_o the_o place_n that_o have_v the_o sun_n at_o the_o same_o height_n how_o astronomer_n begin_v their_o computation_n of_o time_n how_o the_o italian_n how_o the_o babylonians_n to_o find_v the_o babilonish_a and_o italian_a hour_n when_o the_o sun_n be_v in_o the_o aequator_fw-la aequator_fw-la op._n 10._o sec_fw-la 1._o pag._n 14._o 14._o op._n 10._o sec_fw-la 1._o pag._n 14._o to_o find_v the_o italian_a hour_n when_o the_o sun_n be_v in_o the_o aequator_fw-la to_o find_v the_o hour_n both_o the_o say_a way_n at_o any_o time_n time_n op._n 18._o p._n 19_o a_o most_o ready_a way_n of_o find_v at_o any_o time_n the_o babylonian_a and_o italian_a hour_n all_o the_o world_n over_o of_o the_o judaic_a way_n of_o compute_v time_n a_o most_o ready_a way_n to_o find_v the_o judaic_a hour_n why_o the_o day_n of_o the_o week_n be_v call_v by_o the_o name_n of_o the_o planet_n follow_v not_o each_o other_o after_o the_o order_n of_o the_o planet_n planet_n ♄_o saturn_n ♃_o jupiter_n ♂_o mars_n ☉_o sol_n ♀_o venus_n ☿_o mercury_n ☽_o luna_n the_o advantage_n in_o reckon_v the_o italian_a way_n the_o advantage_n in_o reckon_v the_o babylonian_a way_n of_o the_o parallel_n sphere_n oblique_a sphere_n all_o position_n take_v the_o year_n round_o enjoy_v a_o equal_a share_n of_o the_o sun_n presence_n presence_n vid._n op._n 3._o sec_fw-la 1._o pag._n 8._o the_o demonstration_n how_o the_o earth_n be_v prove_v round_o the_o demonstration_n demonstration_n pag._n 5._o 5._o pag_n 10_o 10_o pag._n 11_o 11_o vid._n pag._n 8._o &_o 15_o a_o memoran_n memoran_n p._n 12._o how_o you_o be_v to_o operate_v a_o memorandum_n a_o example_n two_o memorandum_n the_o reason_n or_o demonstration_n of_o the_o operation_n a_o memorandum_n why_o 6_o hour_n must_v be_v add_v sometime_o to_o the_o table_n table_n p._n 49._o 49._o p._n 16._o 16._o pag._n 49._o 49._o op._n 7._o sec_fw-la 2._o pag._n 33._o 33._o vid._n op._n 1._o &_o 2._o pag._n 49._o a_o corollary_n a_o example_n a_o memorandum_n memorandum_n sect._n 1_o op._n 2._o p._n 5._o 5._o  _fw-fr 1_o 2._o 3._o 4._o 6._o  _fw-fr 12._o 11._o 10._o 9_o 8._o 7._o 6._o 87._o 93._o 110._o 140._o 200._o 300._o 625._o 625._o op._n 2._o sect._n 1._o pag._n 6._o a_o preliminary_a discourse_n discourse_n pag._n 4._o 4._o pag._n 5._o 5._o pag._n 10_o 10_o ☞_o because_o every_o body_n that_o desire_v to_o know_v these_o and_o the_o follow_a problem_n have_v not_o perchance_o at_o hand_n mr._n gunter_n book_n i_o shall_v add_v they_o to_o this_o treatise_n as_o the_o reader_n will_v find_v at_o the_o end_n of_o it_o j._n moxon_n how_o to_o find_v the_o tangent_fw-la and_o secant_fw-la of_o any_o degree_n demonstration_n a_o memorandum_n the_o construction_n a_o example_n how_o to_o draw_v the_o half_a hour_n quarter_n etc._n etc._n the_o construction_n demonstration_n demonstration_n pag._n 71._o the_o demonstration_n demonstration_n pag._n 4._o a_o memorandum_n memorandum_n pag._n 8._o 8._o pag._n 73._o the_o construction_n the_o construction_n construction_n pag._n 79._o how_o to_o draw_v a_o line_n parallel_n to_o the_o horizon_n and_o how_o to_o place_v true_o the_o draught_n on_o its_o plane_n a_o easy_a way_n how_o to_o place_v any_o paper_n draught_n on_o its_o plane_n a_o memorandum_n demonstration_n a_o memorandum_n some_o few_o thing_n to_o be_v premise_v the_o construction_n of_o a_o east_n dial._n of_o a_o west_n dial._n of_o the_o style_n and_o substilar_n the_o demonstration_n the_o construction_n the_o demonstration_n the_o reason_n of_o the_o
unequal_a distance_n of_o these_o hour-line_n what_o a_o decline_a plane_n be_v the_o construction_n construction_n pag._n 80._o to_o describe_v the_o morning_n hour_n of_o a_o decline_a dial._n to_o describe_v the_o afternoon_n hour_n how_o to_o make_v the_o style_n and_o substilar_n of_o a_o decline_a dial._n a_o memorandum_n the_o construction_n the_o demonstration_n of_o these_o 2_o decline_v dial_n a_o memorandum_n memorandum_n pag._n 84._o another_o demonstration_n demonstration_n pag._n 83._o 83._o pag._n 73._o the_o construction_n construction_n pag._n 23._o 23._o pag_n 8._o the_o construction_n a_o ready_a way_n to_o find_v the_o style_n and_o substile_n of_o a_o decline_a dial._n demonstration_n demonstration_n pag._n 92._o the_o demonstration_n of_o the_o style_n and_o substilar_n substilar_n pag._n 82._o 82._o vid._n pag_n 104._o 104._o vid._n pag_n 105._o the_o construction_n and_o demonstration_n how_o to_o make_v a_o horizontal_n plane_n a_o aequinoctial_a one_o the_o demonstration_n the_o geometrical_a construction_n a_o memorandum_n memorandum_n pag._n 8._o the_o construction_n the_o construction_n and_o demonstration_n of_o a_o decline_a direct_a dial_n face_v the_o south_n a_o direct_a north_n recline_v plane_n plane_n pag._n 89._o how_o to_o describe_v the_o plane_n of_o this_o recline_a dial_n on_o the_o globe_n the_o construction_n a_o memorandum_n of_o the_o style_n and_o substilar_n substilar_n pag._n 82._o another_o demonstration_n the_o construction_n construction_n pag._n 2._o first_o way_n way_n pag._n 4._o 4._o pag._n 4._o the_o second_o way_n the_o first_o part_n of_o the_o operation_n operation_n pag._n 89._o the_o second_o part_n of_o the_o operation_n why_o every_o erect_a style_n or_o perpendicular_a show_v not_o always_o the_o true_a hour_n the_o construction_n construction_n pag._n 89._o the_o demonstration_n demonstration_n pag._n 94._o 94._o pag._n 75._o demonstration_n the_o advantage_n or_o use_n of_o this_o dial._n the_o construction_n demonstration_n another_o dial_n of_o the_o same_o nature_n the_o construction_n the_o demonstration_n the_o construction_n demonstration_n the_o construction_n the_o geometrical_a way_n the_o demonstration_n the_o construction_n the_o demonstration_n demonstration_n pag._n 73._o how_o this_o dial_n be_v to_o be_v make_v when_o the_o window_n lie_v not_o southward_o the_o construction_n of_o it_o as_o to_o the_o hour_n at_o home_n home_n pag._n 73._o the_o construction_n of_o it_o as_o to_o the_o hour_n in_o other_o place_n to_o find_v the_o sun_n place_n and_o day_n of_o the_o month._n to_o find_v the_o rise_n and_o set_v of_o the_o sun_n to_o find_v the_o sun_n amplitude_n to_o find_v the_o height_n of_o the_o sun_n to_o find_v the_o sun_n azimuth_n and_o bear_v to_o find_v the_o proportion_n of_o perpendicular_o to_o their_o shade_n the_o description_n of_o the_o branch_n or_o embellishment_n in_o sheme_n 43._o 43._o p._n 111._o 111._o p._n 112._o 112._o vid._n p._n 113._o 113._o p._n 71._o of_o the_o sector_n sector_n op._n 17._o sect._n 1._o pag._n 19_o a_o memorandum_n memorandum_n p._n 6._o 6._o p._n 68_o 68_o op._n 5._o way_n 2._o p._n 10._o a_o memorandum_n of_o the_o first_o plane_n and_o its_o bigness_n of_o the_o circle_n and_o star_n on_o it_o and_o how_o they_o be_v place_v of_o the_o second_o plane_n and_o its_o bigness_n bigness_n p._n 6._o 6._o p._n 68_o 68_o p._n 132._o two_o memorandum_n the_o principle_n on_o which_o this_o projection_n depend_v of_o the_o concentric_a circle_n the_o general_a rule_n for_o project_v the_o great_a oblique_a circle_n of_o project_v the_o ecliptic_a of_o project_v the_o horizon_n of_o project_v the_o primary_n vertical_a of_o project_v the_o rest_n of_o the_o azimuth_n a_o expedite_a way_n of_o find_v the_o say_a centre_n and_o radius_fw-la lemma_n 1._o 1._o eucl._n 27._o 1_o 1_o 6._o 1._o lemma_n 2._o 2._o eucl._n 27._o 1._o 1._o 6._o 1._o the_o ecliptic_a true_o project_v a_o memorandum_n the_o way_n of_o describe_v g._n frisius_n meridian_n the_o way_n of_o describe_v g._n f._n hia_fw-la parallel_n how_o to_o describe_v the_o circle_n of_o altitude_n on_o the_o 2_o plane_n plane_n p._n 138_o and_o 139._o 139._o p._n â—_o first_o kind_n kind_n pag._n 4._o 4._o p_o 8._o &_o 15._o 15._o pag._n 13._o 13._o p._n 31._o 31._o pag._n 36._o 36._o pag._n 39_o 39_o p._n 40._o 40._o p._n 35._o 35._o p._n 5._o 5._o p._n 37._o 37._o p._n 10._o 10._o p._n 11._o 11._o p._n 21._o 21._o p._n 51._o 51._o p._n 65._o 65._o p._n 70._o a_o memorandum_n memorandum_n p._n 8._o 2d_o kind_n kind_n p._n 18._o 18._o p._n 9_o 3_o kind_n kind_n p._n 14._o 14._o p._n 15._o 15._o p._n 35._o 35._o p._n 13._o 13._o p._n 11._o 11._o p._n 10._o &_o 12_o 12_o p._n 16._o 16._o p._n 17._o 17._o p._n 19_o 19_o p._n 17._o 17._o p._n 33._o 33._o p._n 33._o 33._o p._n 34._o 34._o p._n 36._o 36._o p._n 31._o four_o kind_n