Selected quad for the lemma: world_n

Word A	Word B	Word C	Word D	Occurrence	Frequency Band	MI	MI Band	Prominent
world_n	circle_n	equinoctial_a	pole_n	3,004	5	11.8973	5	true

Text snippets containing the quad

ID	Title	Author	Corrected Date of Publication (TCP Date of Publication)	STC	Words	Pages
A89305	Horlogiographia optica. Dialling universall and particular: speculative and practicall. In a threefold præcognita, viz. geometricall, philosophicall, and astronomicall: and a threefold practise, viz. arithmeticall, geometricall, and instrumentall. With diverse propositions of the use and benefit of shadows, serving to prick down the signes, declination, and azimuths, on sun-dials, and diverse other benefits. Illustrated by diverse opticall conceits, taken out of Augilonius, Kercherius, Clavius, and others. Lastly, topothesia, or, a feigned description of the court of art. Full of benefit for the making of dials, use of the globes, difference of meridians, and most propositions of astronomie. Together with many usefull instruments and dials in brasse, made by Walter Hayes, at the Crosse Daggers in More Fields. / Written by Silvanus Morgan.	Morgan, Sylvanus, 1620-1693.; Goddard, John, fl. 1645-1671, engraver.	1652 (1652)	Wing M2741; Thomason E652_16; ESTC R202919	57,946	133

they_o make_v day_n with_o they_o while_o it_o remain_v night_n with_o we_o and_o according_a to_o the_o demonstration_n be_v express_v by_o the_o greot_fw-la circle_n mark_v nsew_n signify_v the_o east_n west_n north_n and_o south_n part_n of_o the_o horizon_n so_o now_o if_o you_o imagine_v a_o circle_n to_o be_v draw_v from_o the_o sun_n leave_v our_o sight_n through_o those_o azimuth_n point_v of_o heaven_n than_o that_o circle_n there_o imagine_v be_v the_o horizon_n and_o be_v accidental_o divide_v as_o a_o man_n change_v his_o place_n and_o divide_v the_o world_n in_o a_o right_a or_o oblique_a sphere_n the_o meridian_n be_v a_o great_a circle_n situate_v at_o right_a angle_n to_o the_o horizon_n equal_o pass_v between_o the_o east_n and_o west_n point_v and_o consequent_o run_v due_a north_n and_o south_n and_o pass_v through_o the_o pole_n of_o the_o world_n be_v steadfast_o fix_v it_o be_v represent_v by_o the_o great_a circle_n mark_v ndsc_n and_o be_v accidental_o divide_v if_o we_o travel_v east_n or_o west_n but_o in_o travail_v north_n or_o south_n alter_v not_o and_o when_o the_o sun_n touch_v this_o circle_n it_o be_v then_o midday_n or_o noon_n now_o if_o you_o imagine_v a_o circle_n to_o pass_v from_o the_o north_n to_o the_o south_n part_n of_o the_o horizon_n through_o your_o zenith_n that_o circle_n so_o imagine_v be_v your_o meridian_n from_o which_o meridian_n we_o account_v the_o distance_n of_o hour_n the_o equinoctial_a likewise_o divide_v the_o world_n in_o two_o equal_a part_n cross_v at_o right_a angle_n between_o the_o two_o pole_n and_o be_v therefore_o distant_a from_o each_o pole_n 90_o degree_n and_o be_v elevate_v from_o the_o horizon_n on_o the_o contrary_a side_n of_o the_o pole_n elevation_n so_o much_o as_o the_o pole_n want_v of_o 90_o deg._n elevation_n demonstrate_v in_o the_o scene_n by_o the_o circle_n pass_v from_o a_o to_o b_o and_o be_v accidental_o elevate_v with_o the_o pole_n as_o we_o change_v our_o horizon_n and_o when_o the_o sun_n touch_v this_o circle_n the_o day_n and_o night_n be_v then_o equal_a and_o to_o those_o that_o live_v under_o this_o citcle_n the_o day_n and_o night_n hang_v in_o equilibra_fw-la continual_o and_o the_o sun_n do_v move_v every_o hour_n 15_o degree_n of_o this_o circle_n make_v the_o hour_n line_n equal_a pass_v 15_o degree_n in_o one_o hour_n 30_o degree_n in_o two_o hour_n 45_o degree_n in_o three_o hour_n 60_o degree_n for_o four_o and_o so_o increase_v 15_o degree_n as_o you_o increase_v in_o hour_n this_o i_o note_v to_o the_o intent_n you_o may_v know_v my_o meaning_n at_o such_o time_n as_o i_o shall_v have_v occasion_n to_o mention_v the_o equinoctial_a distance_n the_o axis_n of_o the_o world_n be_v that_o which_o the_o style_n in_o every_o dial_n represent_v be_v a_o line_n imaginary_a suppose_v to_o pass_v through_o the_o centre_n of_o the_o world_n from_o the_o south_n to_o the_o north_n part_n of_o the_o meridian_n who_o outmost_a end_n be_v the_o pole_n of_o the_o world_n this_o become_v the_o diameter_n about_o which_o the_o world_n be_v imagine_v to_o be_v turn_v in_o a_o right_a sphere_n have_v no_o elevation_n in_o a_o oblique_a to_o be_v elevate_v above_o the_o horizon_n and_o the_o angle_n at_o the_o centre_n number_v on_o the_o arch_n of_o the_o meridian_n between_o the_o apparent_a pole_n and_o the_o horizon_n be_v the_o elevation_n thereof_o represent_v by_o the_o straight_a line_n pass_v from_o e_o to_o f_o the_o arch_n en_fw-fr be_v account_v the_o elevation_n thereof_o which_o according_a to_o our_o demonstration_n be_v the_o latitude_n of_o london_n the_o star_n that_o do_v attend_v the_o arctic_a or_o north_n pole_n be_v the_o great_a and_o lesser_a bear_n the_o last_o star_n in_o the_o lesser_a bear_n tale_n be_v call_v the_o pole_n star_n by_o reason_n of_o its_o nearness_n to_o it_o this_o be_v the_o guide_n of_o mariner_n as_o appear_v by_o ovid_n in_o his_o exile_n thus_o you_o great_a and_o lesser_a bear_n who_o star_n do_v guide_v sydonian_a and_o grecian_a ship_n that_o glide_v even_o you_o who_o pole_n do_v view_v this_o lesser_a ball_n under_o the_o western_a sea_n near_o set_v at_o all_o the_o star_n that_o attend_v the_o southern_a pole_n be_v the_o cross_n as_o be_v see_v in_o the_o globe_n lord_n be_v my_o pole_n make_v i_o thy_o style_n lord_n then_o thy_o name_n shall_v be_v my_o terminus_fw-la ad_fw-la quem_fw-la video_fw-la coelos_fw-la opera_fw-la manuum_fw-la tuarum_fw-la lunam_fw-la et_fw-la stellas_fw-la que_fw-la tu_fw-la fundasti_fw-la chap_n iii_o of_o the_o several_a sort_n of_o plane_n and_o how_o they_o be_v know_v dial_n be_v the_o day_n limiter_n and_o the_o bounder_n of_o time_n whereof_o there_o be_v three_o sort_n horizontal_a erect_a incline_v horizontal_a be_v always_o parallel_a to_o the_o horizon_n erect_v some_o be_v erect_v direct_a other_o erect_v decline_a incline_v also_o be_v direct_a or_o decline_a for_o more_o explanation_n the_o figure_n follow_v shall_v give_v you_o better_a satisfaction_n where_o the_o horizon_n mark_v with_o diverse_a point_n of_o the_o compass_n shall_v explain_v the_o demonstration_n now_o if_o you_o imagine_v circle_n to_o pass_v through_o the_o zenith_n a_o cross_v the_o horizon_n in_o his_o opposite_a point_n as_o from_o sweet_o through_o the_o vertical_a point_n a_o pass_v to_o the_o opposite_a point_n of_o south-west_n to_o north-east_n those_o or_o the_o like_a circle_n be_v call_v azimuth_n parallel_n to_o which_o azimuth_n all_o erect_v sciothericals_n do_v stand_v those_o plane_n that_o lie_v parallel_n to_o the_o horizontal_a circle_n be_v call_v horizontal_a plane_n and_o his_o style_n make_v a_o angle_n with_o the_o pole_n equal_a to_o the_o elevation_n thereof_o then_o the_o elevation_n of_o the_o pole_n be_v the_o elevation_n of_o the_o style_n erect_a vertical_n be_v such_o which_o make_v right_a angle_n with_o the_o horizon_n and_o lie_v parallel_n to_o the_o vertical_a point_n and_o these_o as_o i_o tell_v you_o before_o be_v either_o direct_a or_o decline_a direct_v be_v those_o that_o stand_v in_o a_o direct_a azimuth_n behold_v one_o of_o the_o four_o cardinal_n quarter_n of_o the_o world_n as_o either_o direct_a east_n west_n north_n or_o south_n mark_v with_o these_o letter_n news_n or_o decline_v from_o they_o to_o some_o other_o indirect_a azimuth_n or_o side-lying_a point_n erect_a north_n and_o south_n be_v such_o as_o behold_v those_o quarter_n and_o cut_v the_o meridian_n at_o right_a angle_n so_o that_o the_o plane_n across_v the_o meridian_n due_a east_n and_o west_n and_o the_o pole_n be_v their_o style_n equal_o elevate_v according_a to_o the_o equinoctial_a altitude_n be_v the_o compliment_n of_o the_o pole_n elevation_n for_o in_o all_o north_n face_n plane_n or_o dial_n the_o style_n behold_v the_o north_n pole_n and_o in_o all_o south_n face_n the_o style_n behold_v the_o south_n pole_n therefore_o where_o the_o north_n pole_n be_v elevate_v there_o the_o north_n pole_n must_v be_v point_v out_o by_o the_o style_n and_o where_o the_o south_n pole_n be_v elevate_v vice_fw-la versa_fw-la the_o second_o sort_n of_o vertical_n be_v decline_v which_o eat_v such_o that_o make_v a_o acute_a angle_n with_o the_o quarter_n from_o which_o they_o decline_v for_o a_o acute_a angle_n be_v less_o than_o a_o right_a angle_n and_o a_o right_a angle_n be_v 90_o degree_n these_o decline_a plane_n lie_v in_o some_o accidental_a azimuth_n for_o suppose_v a_o dial_n to_o turn_v from_o the_o south_n or_o north_n towards_o the_o east_n or_o west_n the_o meridian_n line_n of_o the_o south_n decline_v eastward_o happen_v in_o these_o azimuth_n or_o between_o they_o south_n decline_v east_n south_n decline_v west_n s_o by_o e_o 11_o 15_o or_o to_o these_o point_n of_o the_o west_n decliner_n or_o between_o they_o s_o by_o w_n 11_o 15_o s_o s_o e_o 22_o 30_o s_o s_o w_n 22_o 30_o s_o e_o by_o s_o 33_o 45_o s_o w_n by_o s_o 33_o 45_o southeast_n 45_o 00_o south_n west_n 45_o 00_o s._n e_o by_o e_o 56_o 15_o s_o w_n by_o w_n 56_o 15_o e_o s_o e_o 67_o 30_o w_n s_o w_n 67_o 30_o e_o by_o s_o 78_o 45_o w_n by_o s_o 78_o 45_o east_n 90_o 00_o west_n 90_o 00_o again_o north_n decliner_n decline_v towards_o the_o east_n and_o west_n do_v happen_v in_o these_o azimuth_n or_o between_o they_o north_n decline_v east_n north_n decline_v west_n n_o by_o e_o 11_o 15_o or_o to_o these_o point_n of_o the_o west_n decliner_n or_o between_o they_o n_o by_o w_n 11_o 15_o n_o n_o e_o 22_o 30_o n_o n_o w_n 22_o 30_o n_o e_o by_o n_o 33_o 45_o n_n w_n by_o n_n 33_o 45_o north-east_n 45_o 00_o north_n west_n 45_o 00_o n_o e_o by_o e_o 56_o 15_o n_n w_n by_o w_n 56_o 15_o e_o n_o e_o 67_o 30_o w_n

the_o morning_n hour_n and_o 6_o 7_o 8_o the_o evening_n and_o because_o the_o north_n pole_n be_v elevate_v above_o this_o plane_n 38_o deg._n 30_o min._n the_o axis_n must_v be_v from_o the_o centre_n according_a to_o that_o elevation_n point_v upward_o as_o the_o south_n do_v downward_o so_o as_o a_o be_v the_o zenith_n of_o the_o south_n c_o must_v be_v in_o the_o north_n the_o arithmetical_a calculation_n be_v the_o same_o with_o the_o former_a also_o a_o north_n plane_fw-la may_v show_v all_o the_o hour_n of_o the_o south_n by_o consideration_n of_o reflection_n for_o by_o optical_a demonstration_n it_o be_v prove_v that_o the_o angle_n of_o incidence_n be_v all_o one_o to_o that_o of_o reflection_n if_o any_o be_v ignorant_a thereof_o i_o purposely_o remit_v to_o teach_v it_o to_o whet_v the_o ingenious_a reader_n in_o labour_v to_o find_v it_o the_o figure_n of_o a_o direct_a east_n and_o west_n dial_n for_o the_o latitude_n of_o london_n 51_o deg._n 30_o min._n east_n dial_n west_n dial_n chap_n iv._o show_v the_o make_n of_o the_o prime_n vertical_a plane_n that_o be_v a_o direct_a east_n or_o west_n dial_n for_o the_o effect_n of_o this_o dial_n first_o draw_v the_o line_n ad_fw-la on_o one_o end_n thereof_o draw_v the_o circle_n in_o the_o figure_n represent_v the_o equator_n then_o draw_v two_o touch_n line_n to_o the_o equator_n parallel_n to_o the_o line_n ad_fw-la these_o be_v they_o on_o which_o the_o hour_n be_v mark_v divide_v the_o equator_n in_o the_o low_a semicircle_n in_o 12_o equal_a part_n then_o apply_v a_o ruler_n to_o the_o centre_n through_o each_o part_n and_o where_o it_o touch_v the_o line_n of_o contingence_n make_v mark_n from_o each_o touch_n point_n draw_v line_n to_o the_o opposite_a touch_n point_n which_o be_v the_o parallel_n of_o the_o hour_n and_o at_o the_o end_n of_o those_o line_n mark_v the_o easterly_a hour_n from_o 6_o to_o 11_o and_o of_o the_o west_n from_o 1_o to_o 6._o these_o plane_n as_o i_o tell_v you_o want_v the_o meridian_n hour_n because_o it_o be_v parallel_a to_o the_o meridian_n now_o for_o the_o place_n of_o the_o east_n dial_n number_n the_o elevation_n of_o the_o axis_n to_o wit_n the_o arch_n dc_o from_o the_o line_n of_o the_o equator_n to_o wit_n the_o line_n ad_fw-la and_o in_o the_o west_n dial_n number_n the_o elevation_n to_o b_o fasten_v a_o plummet_n and_o three_o in_o the_o centre_n a_o and_o hold_v it_o so_o that_o the_o plummet_n may_v fall_v on_o the_o line_n ac_o for_o the_o east_n dial_n and_o ab_o for_o the_o west_n dial_n and_o then_o the_o line_n ad_fw-la be_v parallel_n to_o the_o equator_n and_o the_o dial_n in_o its_o right_a position_n and_o thus_o the_o west_n as_o well_o as_o east_n for_o according_a to_o the_o say_n contrariorum_fw-la eadem_fw-la est_fw-la doctrina_fw-la contrary_n have_v one_o manner_n of_o doctrine_n here_o you_o may_v perceive_v the_o use_n of_o tangent_fw-la line_n for_o it_o be_v evident_a that_o every_o hour_n distance_n be_v ●●t_v the_o tangent_fw-la of_o the_o equinoctial_a distance_n the_o arithmetical_a calculation_n 1_o have_v draw_v a_o line_n for_o the_o hour_n of_o 6_o whether_o east_n or_o west_n as_o the_o tangent_fw-la of_o the_o hour_n distance_n be_v to_o the_o radius_fw-la so_o be_v the_o distance_n of_o the_o hour_n from_o 6_o to_o the_o height_n of_o the_o style_n 2_o as_o the_o radius_fw-la be_v to_o the_o height_n of_o the_o style_n so_o be_v the_o tangent_fw-la of_o the_o hour_n distance_n from_o 6_o to_o the_o distance_n of_o the_o same_o hour_n from_o the_o substyle_n the_o style_n must_v be_v equal_a in_o height_n to_o the_o semidiameter_n of_o the_o equator_n and_o fix_v on_o the_o line_n of_o 6._o chap_n v._o show_v the_o make_v a_o direct_a parallel_n polar_a plane_n or_o opposite_a equinoctial_a i_o call_v this_o a_o direct_a parallel_n polar_a plane_n for_o this_o cause_n because_o all_o plane_n may_v be_v call_v by_o their_o situation_n of_o their_o pole_n and_o so_o a_o equinoctial_a parallel_a plane_n may_v be_v call_v a_o polar_a plane_n because_o the_o pole_n thereof_o lie_v in_o the_o pole_n of_o the_o world_n the_o gnomon_n must_v be_v a_o quadrangled_a parallelogram_n who_o height_n be_v equal_a to_o the_o semidiameter_n of_o the_o equator_n as_o in_o the_o east_n and_o west_n dial_n so_o likewise_o these_o hour_n be_v tangent_n to_o the_o equator_n arithmetical_a calculation_n draw_v first_o a_o line_n represent_v the_o meridian_n or_o 12_o a_o clock_n line_n and_o another_o parallel_n to_o the_o say_a line_n for_o some_o hour_n which_o may_v have_v place_n on_o the_o line_n say_v as_o the_o tangent_fw-la of_o that_o hour_n be_v to_o the_o radius_fw-la so_o be_v the_o distance_n of_o that_o hour_n from_o the_o meridian_n to_o the_o height_n of_o the_o style_n 2_o as_o the_o radius_fw-la be_v to_o the_o height_n of_o the_o style_n so_o the_o tangent_fw-la of_o any_o hour_n to_o the_o distance_n of_o that_o hour_n from_o the_o meridian_n chap_n vi_o show_v the_o make_n of_o a_o direct_a opposite_a polar_a plane_n or_o parallel_v equinoctial_a dial_n a_o equinoctial_a plane_n lie_v parallel_n to_o the_o equinoctial_a circle_n make_v a_o angle_n at_o the_o horizon_n equal_a to_o the_o elevation_n of_o the_o say_a circle_n the_o pole_n of_o which_o plane_n lie_v in_o the_o pole_n of_o the_o world_n the_o make_n of_o this_o plane_n require_v little_a instruction_n for_o by_o draw_v a_o circle_n and_o divide_v it_o into_o 24_o part_n the_o plane_n be_v prepare_v all_o fix_v a_o style_n in_o the_o centre_n at_o right_a angle_n to_o the_o plane_n as_o the_o radins_n be_v to_o the_o sine_fw-la of_o declination_n so_o be_v the_o cotangent_n of_o the_o pole_n height_n to_o the_o tangent_fw-la of_o the_o distance_n of_o the_o sub-stile_n from_o the_o meridian_n if_o you_o draw_v line_n from_o 7_o to_o 5_o on_o each_o side_n those_o line_n so_o cut_v shall_v be_v the_o place_n of_o the_o hour_n line_n of_o a_o parallel_a polar_a plane_n now_o if_o you_o draw_v to_o each_o opposite_a from_o the_o prick_a line_n those_o line_n shall_v be_v the_o hour_n line_n of_o the_o former_a plane_n chap_n vii_o show_v the_o make_n of_o a_o erect_v vertical_a decline_a dial_n if_o you_o will_v work_v by_o the_o fundamental_a diagram_n you_o shall_v first_o draw_v a_o line_n such_o be_v the_o line_n ab_o represent_v the_o meridian_n then_o shall_v you_o take_v out_o of_o the_o fundamental_a diagram_n the_o secant_n of_o the_o latitude_n viz._n ac_o and_o prick_v it_o down_o from_o a_o to_o b_o and_o at_o b_o you_o shall_v draw_v a_o horizontal_a line_n at_o right_a angle_n such_o be_v the_o line_n cd_o than_o you_o shall_v continue_v the_o line_n ab_o towards_o i_fw-it and_o from_o that_o line_n and_o where_o the_o line_n ab_o cross_v in_o cd_o describe_v a_o arch_a equal_a to_o the_o angle_n of_o declination_n towards_o f_o if_o it_o decline_v eastward_o and_o towards_o g_o if_o the_o plane_n decline_v westward_o then_o shall_v you_o prick_v down_o on_o the_o line_n bf_o if_o it_o bean_n easterly_a decline_a plane_n or_o from_o b_o to_o g_o if_o contrary_n the_o secant_n compliment_n of_o the_o latitude_n viz._n ag_o in_o the_o fundamental_a diagram_n and_o the_o sine_fw-la of_o 51_o degree_n viz._n da_o which_o be_v all_o one_o with_o the_o semidiameter_n of_o the_o equator_n and_o therewithal_o prick_v it_o down_o at_o right_a angle_n to_o the_o line_n of_o declination_n viz._n bf_o from_o b_o to_o h_o and_o g_o and_o from_o f_o towards_o k_o and_o l_o then_o draw_v the_o long_a square_a kikl_o and_o from_o b_o towards_o h_o and_o g_o prick_v down_o the_o several_a tangent_n of_o 15_o 30_o 45_o and_o prick_v the_o same_o distance_n from_o k_o and_o l_n towards_o h_o and_o g_o last_o draw_v line_n through_o each_o of_o those_o point_n from_o f_o to_o the_o horizontal_a line_n cd_o and_o where_o they_o end_v on_o that_o line_n to_o each_o point_n draw_v the_o hour_n line_n from_o the_o point_n a_o which_o plane_n in_o our_o example_n be_v a_o vertical_a decline_v eastward_o 45_o degree_n and_o it_o be_v finish_v but_o because_o the_o contingent_a line_n will_v run_v out_o so_o far_o before_o it_o be_v intersect_v i_o shall_v give_v you_o one_o follow_v geometrical_a example_n to_o prick_v down_o a_o decline_a dial_n in_o a_o right_a angle_a parallelogram_n now_o for_o the_o arithmetical_a calculation_n the_o first_o operation_n shall_v be_v thus_o as_o the_o radius_fw-la to_o the_o cotangent_n of_o the_o elevation_n so_o be_v the_o sine_fw-la of_o the_o declination_n to_o the_o tangent_fw-la of_o the_o substile_n distance_n from_o the_o meridian_n of_o the_o place_n then_o two_o operation_n have_v the_o compliment_n of_o the_o declination_n and_o elevation_n find_v the_o

horologiographia_fw-la optica_fw-la dial_n universal_a and_o particular_a speculative_a and_o practical_a together_o with_o the_o description_n of_o the_o court_n of_o art_n by_o a_o new_a method_n by_o sylvanus_n morgan_n jj._n sculp_v horologiographia_fw-la optica_fw-la dial_n universal_a and_o particular_a speculative_a and_o practical_a in_o a_o threefold_a praecognita_fw-la viz._n geometrical_a philosophical_a and_o astronomical_a and_o a_o threefold_a practice_n viz._n arithmetical_a geometrical_a and_o instrumental_a with_o diverse_a proposition_n of_o the_o use_n and_o benefit_n of_o shadow_n serve_v to_o prick_v down_o the_o sign_n declination_n and_o azimuth_n on_o sun-dial_n and_o diverse_a other_o benefit_n illustrate_v by_o diverse_a optical_a conceit_n take_v out_o of_o augilonius_n kercherius_n clavius_n and_o other_o last_o topothesia_n or_o a_o feign_a description_n of_o the_o court_n of_o art_n full_o of_o benefit_n for_o the_o make_n of_o dial_n use_v of_o the_o globe_n difference_n of_o meridian_n and_o most_o proposition_n of_o astronomy_n together_o with_o many_o useful_a instrument_n and_o dial_n in_o brass_n make_v by_o walter_n hayes_n at_o the_o cross_a dagger_n inmore_n field_n write_v by_o silvanus_n morgan_n london_n print_v by_o r_o and_o w._n leybourn_n for_o andrew_n kemb_n and_o robert_n boydell_n ●_z and_o be_v to_o be_v sell_v at_o st_n margaret_n hill_n in_o southwark_n and_o at_o the_o bulwark_n near_o the_o tower_n 1657._o to_o william_n bateman_n esqrs._n to_o anthony_n bateman_n esqrs._n to_o thomas_n bateman_n esqrs._n son_n to_o the_o late_a honourable_a thomas_n bateman_n esq_n chamberlain_n of_o london_n decease_a gentleman_n your_o late_a father_n be_v a_o patron_n of_o this_o honourable_a city_n do_v not_o a_o little_a invite_v i_o to_o you_o though_o young_a yet_o to_o patronise_v no_o less_o than_o the_o aspire_n of_o coelum_fw-la which_o as_o the_o poet_n feign_v be_v the_o ancient_a of_o the_o god_n and_o where_o you_o may_v see_v sol_fw-la only_o of_o the_o titan_n favour_v jupiter_n sign_n and_o by_o their_o power_n and_o operation_n have_v establish_v art_n or_o learning_n the_o fable_n rather_o according_a to_o that_o establishment_n which_o god_n have_v give_v they_o they_o be_v i_o say_v seek_v out_o of_o those_o that_o take_v their_o pleasure_n therein_o pardon_v my_o boldness_n i_o beseech_v you_o if_o like_o prometheus_n i_o have_v make_v a_o man_n of_o clay_n and_o now_o come_v to_o light_v my_o bundle_n of_o twig_n at_o the_o chariot_n of_o the_o sun_n desire_v that_o you_o will_v infuse_v vigour_n in_o that_o which_o can_v at_o all_o move_v of_o itself_o and_o if_o your_o benevolence_n shall_v but_o shine_v upon_o it_o the_o angle_n of_o incidence_n and_o reflection_n shall_v be_v all_o one_o your_o love_n invite_v i_o to_o be_v so_o bold_a as_o to_o think_v you_o worthy_a of_o my_o labour_n wherein_o if_o fault_n shall_v arise_v in_o the_o cuspis_fw-la of_o the_o ascendent_n they_o shall_v also_o have_v their_o fall_n upon_o my_o self_n and_o if_o any_o shall_v be_v offend_v at_o this_o work_n my_o device_n shall_v be_v a_o dial_n with_o this_o mottoe_n aspicio_fw-la ut_fw-la aspiciar_fw-la only_o to_o all_o favourer_n of_o art_n i_o be_o direct_a erect_v plain_a as_o i_o be_o gentleman_n to_o you_o and_o desire_v to_o be_v you_o in_o the_o best_a of_o my_o service_n s._n m._n to_o the_o reader_n reader_n i_o here_o present_v thou_o with_o some_o celestial_a operation_n draw_v from_o the_o macrocosmall_a world_n if_o i_o shall_v tell_v you_o of_o plurality_n it_o may_v seem_v absurd_a but_o i_o will_v distinguish_v the_o word_n mundus_fw-la the_o world_n be_v sometime_o take_v archtypical_o and_o so_o be_v god_n only_o in_o who_o divine_a mind_n be_v a_o example_n of_o all_o thing_n mundus_fw-la the_o world_n be_v sometime_o take_v angelical_a and_o this_o be_v the_o hierarchical_a government_n of_o angel_n in_o ceruphin_n cherubin_n and_o throne_n mundus_fw-la the_o world_n be_v sometime_o take_v elementary_a and_o this_o be_v the_o philosopher_n common_a place_n the_o salamander_n in_o fire_n the_o bird_n in_o air_n the_o fish_n in_o water_n and_o man_n and_o beast_n on_o earth_n sometime_o macrocosmal_o consider_v the_o whole_a universe_n as_o well_o etherial_a as_o subterene_a yea_o and_o every_o orb_n and_o this_o be_v imaginarily_o set_v down_o in_o the_o praecognita_fw-la astronomical_a sometime_o microcosmal_o as_o in_o the_o little_a world_n man_n and_o this_o be_v describe_v in_o the_o last_o chapter_n of_o the_o praecognita_fw-la philosophical_a sometime_o typical_o and_o that_o either_o geographical_a or_o gnomonicall_a or_o mental_o in_o the_o mind_n of_o the_o workman_n geographical_o in_o map_n or_o globe_n or_o sphere_n in_o plano_fw-la gnomonicall_a in_o this_o present_a art_n of_o dial_n of_o which_o it_o may_v be_v say_v that_o umbra_fw-la horas_fw-la phoebi_fw-la designat_fw-la climate_fw-la nostro_fw-la nodus_fw-la quod_fw-la signum_fw-la sol_fw-la tenet_fw-la arte_fw-la docet_fw-la and_o by_o which_o they_o must_v necessary_o trace_v out_o our_o time_n by_o the_o orbiculation_n of_o the_o rady_n of_o the_o circle_n of_o the_o body_n of_o the_o sun_n again_o the_o world_n be_v mental_o consider_v in_o the_o mind_n of_o a_o artist_n as_o in_o paint_v grave_v carve_v etc._n etc._n but_o have_v thus_o define_v the_o word_n you_o may_v think_v from_o hence_o that_o i_o be_o with_o democrates_n platonissans_fw-la acquaint_v thou_o with_o infinity_n of_o world_n and_o in_o his_o word_n stanza_n 20._o and_o to_o speak_v out_o though_o i_o detest_v the_o sect_n of_o epicurus_n for_o their_o manner_n vile_a yet_o what_o be_v true_a i_o may_v not_o well_o neglect_v of_o truth_n incorruptible_a ne_z can_v the_o stile_n of_o vicious_a pen_n her_o sacred_a worth_n defile_v if_o we_o no_o more_o of_o truth_n shall_v deign_v to_o speak_v then_o what_o unworthy_a mouth_n do_v never_o soil_n no_o truth_n at_o all_o amongst_o man_n will_v find_v a_o place_n but_o make_v they_o speedy_a wing_n and_o back_o to_o heaven_n apace_o howsoever_o thou_o have_v here_o a_o field_n large_a enough_o to_o walk_v in_o which_o if_o thou_o affect_v the_o light_n thou_o may_v trace_v out_o the_o truth_n and_o i_o presume_v i_o have_v do_v that_o for_o thou_o who_o be_v a_o learner_n the_o most_o plain_a way_n that_o be_v ever_o publish_v and_o have_v study_v not_o to_o make_v it_o the_o art_n of_o shadow_n so_o much_o as_o the_o shadow_n of_o that_o art_n who_o gnomon_n may_v be_v say_v to_o touch_v the_o pole_n and_o who_o plane_n may_v be_v several_a planisphere_n a_o scale_n to_o the_o geometrician_n a_o pole_n to_o the_o navigator_n a_o chart_n to_o the_o geographer_n a_o zodiaque_fw-la to_o the_o astronomer_n a_o table_n of_o house_n to_o the_o astrologian_n the_o meridian_n and_o needle_n to_o the_o surveyor_n a_o dial_n to_o we_o all_o to_o put_v we_o in_o mind_n of_o that_o precious_a time_n which_o say_v to_o we_o fugio_fw-la fuge_fw-la and_o which_o time_n shall_v be_v swallow_v up_o of_o eternity_n when_o there_o shall_v be_v but_o one_o day_n without_o tropical_a distinction_n where_o thou_o shall_v not_o need_v help_n from_o any_o other_o nor_o from_o i_o who_o be_o thy_o s._n m._n in_fw-la solarium_fw-la hic_fw-la tibi_fw-la cum_fw-la numero_fw-la spectantur_fw-la nodus_fw-la et_fw-la umbra_fw-la quae_fw-la tria_fw-la quid_fw-la doceant_fw-la commemorare_fw-la libet_fw-la umbra_fw-la notat_fw-la dextrè_fw-la quota_fw-la cursitet_fw-la hora_fw-la dici_fw-la hincque_fw-la monet_fw-la vitam_fw-la sic_fw-la properare_fw-la tuam_fw-la ast_fw-la in_fw-la quo_fw-la signo_fw-la magni_fw-la lux_fw-la publica_fw-la mundi_fw-la versetur_fw-la mira_fw-la nodulus_fw-la arte_fw-la docet_fw-la si_fw-la vis_fw-la scire_fw-la dies_fw-la quot_fw-la quilibet_fw-la occupet_fw-la horas_fw-la id_fw-la numerus_fw-la media_fw-la sede_fw-la locatus_fw-la habet_fw-la on_o my_o friend_n mr._n silvanus_n morgan_n his_o book_n of_o dial_n the_o use_n of_o dial_n all_o man_n understand_v to_o make_v they_o few_o and_o i_o be_o one_o of_o those_o i_o be_o not_o of_o the_o mathematic_a band_n nor_o know_v i_o more_o of_o verse_n than_o verse_n from_o prose_n but_o though_o nor_o diallist_n i_o be_o nor_o poet_n i_o honour_v those_o in_o either_o do_v excel_v our_o author_n be_v skilled_a in_o both_o alike_o i_o know_v it_o shadow_n and_o substance_n here_o run_v parallel_n consider_v then_o the_o pain_n the_o author_n take_v and_o thank_v he_o as_o thou_o benefite_v by_o his_o book_n edward_n barwick_n on_o the_o author_n and_o his_o book_n dare_v zoil_n or_o momus_n for_o to_o carp_v at_o thou_o and_o let_v such_o idiot_n as_o some_o author_n be_v bold_o to_o prosecute_v or_o take_v in_o hand_n such_o noble_a subject_n they_o not_o understand_v only_o for_o ostentation_n pride_n or_o fame_n or_o else_o because_o they_o will_v get_v themselves_o a_o name_n like_o that_o lewd_a fellow_n who_o with_o hateful_a ire_n flinch_v not_o but_o set_v diana_n court_n on_o fire_n his_o

himself_o in_o such_o art_n as_o may_v be_v and_o prove_v to_o be_v profitable_a for_o his_o country_n man_n be_v the_o atlas_n that_o support_v the_o earth_n a_o perfect_a world_n though_o in_o a_o second_o birth_n i_o know_v not_o which_o the_o complete_a world_n to_o call_v the_o senseless_a world_n or_o man_n the_o rational_a one_o claim_v complete_a in_o bigness_n and_o in_o birth_n say_v she_o be_v complete_a for_o man_n be_v last_o bring_v forth_o man_n speak_v again_o and_o stand_v in_o his_o defence_n because_o he_o be_v rational_a have_v complete_a sense_n nature_n now_o see_v they_o to_o disagree_v seek_v for_o a_o mean_n that_o they_o unite_v be_v conclude_v man_n that_o he_o shall_v guide_v the_o sphere_n limit_v their_o motion_n in_o day_n and_o month_n and_o year_n he_o think_v now_o his_o office_n not_o in_o vain_a limit_n the_o sun_n unto_o a_o dial_n plain_a girdle_n the_o world_n in_o circle_n zone_n and_o clime_n to_o show_v his_o art_n unto_o the_o after_o time_n nature_n that_o make_v he_o thus_o complete_a in_o all_o to_o please_v he_o more_o he_o microcosmus_n call_v a_o little_a world_n only_o in_o this_o respect_n of_o quantity_n and_o not_o for_o his_o defect_n pray_v gentle_a reader_n view_v but_o well_o their_o feature_n which_o be_v do_v pray_v tell_v i_o who_o be_v the_o great_a for_o he_o have_v give_v i_o certain_a knowledge_n of_o the_o thing_n that_o be_v namely_o to_o know_v how_o the_o world_n be_v make_v and_o the_o operation_n of_o the_o element_n the_o beginning_n end_v and_o midst_n of_o time_n the_o alteration_n of_o the_o turn_n of_o the_o sun_n and_o the_o change_n of_o season_n the_o circuit_n of_o year_n and_o position_n of_o star_n wisd._n 7._o 17._o the_o end_n of_o the_o praecognita_fw-la philosophical_a the_o argument_n of_o the_o praecognita_fw-la astronomical_a you_o be_v come_v to_o see_v a_o sight_n the_o world_n be_v the_o stage_n perhaps_o you_o will_v sayt'_v but_o a_o stargazing_a age_n what_o come_v you_o out_o to_o see_v one_o use_v a_o instrument_n can_v speculation_n yield_v you_o such_o content_n that_o you_o can_v rest_v in_o learning_n but_o the_o name_n of_o pegasus_n or_o of_o swift_a charles_n wain_n and_o will_v you_o learn_v to_o know_v how_o he_o do_v move_v about_o his_o axis_fw-la set_v at_o work_n by_o jove_n if_o you_o will_v learn_v the_o practice_n read_v and_o then_o i_o need_v not_o thus_o entreat_v you_o by_o my_o pen_n to_o tread_v in_o art_n fair_a step_n or_o to_o attain_v the_o way_n go_v on_o make_v haste_n relinquent_fw-la do_v not_o stay_v or_o will_v you_o scale_v olympic_a hill_n so_o high_a be_v sure_a you_o take_v fast_o hold_v astronomy_n then_o in_o that_o fair_a spread_a canopy_n no_o way_n from_o thou_o be_v hide_v no_o not_o galezia_n they_o that_o descend_v the_o water_n deep_o do_v see_v god_n wonder_n in_o the_o deep_a and_o what_o they_o be_v they_o that_o contemplate_v on_o the_o starry_a sky_n do_v see_v the_o work_n that_o he_o have_v frame_v so_o high_a learn_v first_o division_n of_o the_o world_n and_o how_o it_o be_v seat_v i_o do_v come_v to_o show_v you_o now_o the_o praecognita_fw-la astronomical_a chap_n i_o of_o the_o division_n of_o the_o world_n by_o accidental_a situation_n of_o the_o circle_n cosmus_n the_o world_n be_v divide_v by_o microcosmus_n the_o little_a world_n into_o substantial_a and_o imaginary_a part_n now_o the_o substantial_a be_v those_o material_a part_n or_o substance_n of_o which_o the_o world_n be_v compact_v and_o make_v a_o body_n by_o the_o inter-fold_n of_o one_o sphere_n within_o another_o as_o be_v the_o sphere_n of_o saturn_n jupiter_n mars_n sol_fw-la etc._n etc._n and_o these_o of_o themselves_o have_v a_o gentle_a and_o proper_a motion_n but_o by_o violence_n of_o the_o first_o mover_n have_v a_o rack_a motion_n contrary_a to_o their_o own_o proper_a motion_n whence_o it_o appear_v that_o the_o motion_n of_o the_o heaven_n be_v two_o one_o proper_a to_o the_o sphere_n as_o they_o be_v different_a in_o themselves_o the_o other_o common_a to_o all_o by_o phoebus_n motion_n plain_o do_v appear_v how_o many_o day_n do_v constitute_v one_o year_n will_v you_o know_v how_o many_o day_n do_v constitute_v a_o year_n he_o tell_v you_o who_o say_v ter_n centum_fw-la ter_fw-la viginti_fw-la cum_fw-la quinque_fw-la diebus_fw-la sex_fw-la horas_fw-la neque_fw-la plus_fw-la integer_fw-la annus_fw-la habet_fw-la three_o hundred_o sixty_o five_o day_n as_o appear_v with_o six_o hour_n add_v make_v a_o complete_a year_n the_o just_a period_n of_o the_o sun_n proper_a revolution_n perpetuus_fw-la solis_fw-la distinguit_fw-la tempora_fw-la motus_fw-la the_o imaginary_a part_n trace_v out_o by_o man_n imagination_n be_v circle_n such_o be_v the_o horizon_n the_o equator_n the_o meridian_n these_o circle_n have_v of_o themselves_o no_o proper_a motion_n but_o by_o alteration_n of_o place_n have_v a_o accidental_a division_n divide_v the_o world_n into_o a_o right_a sphere_n cut_v the_o parallel_n of_o the_o sun_n equal_o or_o oblique_a make_v unequal_a day_n and_o night_n whence_o two_o observation_n arise_v first_o where_o the_o parallel_n of_o the_o sun_n be_v cut_v equal_o there_o be_v also_o the_o day_n and_o night_n equal_a second_o where_o they_o be_v cut_v oblique_a there_o also_o the_o day_n and_o night_n be_v unequal_a the_o variety_n of_o the_o heaven_n be_v diverse_o divide_v into_o sphere_n or_o several_a orb_n and_o as_o the_o poet_n have_v find_v out_o a_o galazia_n the_o milky_a way_n of_o juno_n her_o breast_n or_o the_o way_n by_o which_o the_o god_n go_v to_o their_o palace_n so_o they_o will_v assign_v to_o each_o sphere_n his_o several_a god_n goddess_n of_o herald_n calliope_n in_o the_o high_a sphere_n do_v dwell_v astrology_n among_o the_o star_n urania_n do_v excel_v philosophy_n polimnia_n the_o sphere_n of_o saturn_n guide_v gladness_n sterpsicore_n with_o jupiter_n abide_v history_n and_o clio_n reign_v in_o man_n fix_a sphere_n tragedic_n melpomene_n guide_v he_o that_o guide_v the_o year_n solace_n yea_o and_o erata_n do_v fair_a venus_n sway_n loud_a instrument_n mercury_n his_o orb_n euturpe_v do_v obey_v ditty_n and_o horn_a cynthia_n be_v become_v the_o court_n of_o thalia_n to_o sing_v and_o laugh_v at_o sport_n where_o they_o take_v their_o place_n as_o they_o come_v in_o order_n the_o sphere_n be_v say_v to_o be_v right_a where_o the_o pole_n have_v no_o elevation_n but_o lie_v in_o the_o horizon_n so_o that_o to_o they_o the_o equinoctial_a be_v in_o the_o zenith_n that_o be_v the_o point_n just_a over_o their_o head_n the_o sphere_n be_v oblique_a in_o regard_n of_o its_o accidental_a division_n accidental_o divide_v in_o regard_n of_o its_o orbicular_a form_n orbicular_a in_o regard_n of_o its_o accidental_a equal_a variation_n orbicular_a it_o appear_v before_o in_o the_o praecognita_fw-la philosophical_a his_o equal_a variation_n be_v see_v by_o the_o equal_a proportion_n of_o the_o earth_n answer_v to_o a_o celestial_a degree_n for_o circle_n be_v in_o proportion_n one_o to_o another_o and_o parallel_v one_o to_o another_o be_v cut_v equal_o so_o be_v the_o earth_n to_o the_o heaven_n have_v consider_v they_o as_o before_o we_o will_v now_o consider_v another_o sort_n of_o sphere_n which_o be_v call_v parallel_n this_o parallel_a sphere_n be_v so_o that_o the_o parallel_n of_o the_o sun_n be_v parallel_n to_o the_o horizon_n have_v the_o pole_n in_o their_o zenith_n be_v the_o extreme_a intemperate_a cold_a and_o freeze_a zone_n ovid_n in_o his_o banishment_n complain_v thus_o thereof_o hard_o be_v the_o fright_n in_o scythia_n i_o sustain_v over_o my_o head_n heaven_n axis_n do_v remain_v chap_n ii_o of_o the_o circle_n of_o the_o horizon_n the_o equator_n and_o the_o meridian_n the_o great_a circle_n of_o a_o sphere_n be_v that_o which_o divide_v it_o in_o two_o equal_a part_n and_o that_o because_o it_o cross_v diametrical_o and_o the_o diameter_n be_v the_o long_a line_n as_o can_v be_v strike_v in_o a_o circle_n and_o therefore_o the_o great_a which_o great_a circle_n be_v represent_v in_o the_o follow_a figure_n represent_v the_o circle_n of_o a_o sphere_n in_o a_o oblique_a latitude_n according_a to_o the_o latitude_n or_o elevation_n of_o the_o pole_n here_o at_o london_n which_o be_v 51_o deg._n 32_o min._n be_v north_n latitude_n because_o the_o north_n pole_n be_v elevate_v the_o horizon_n be_v a_o great_a circle_n divide_v the_o part_n of_o heaven_n see_v from_o where_o we_o imagine_v a_o antipode_n the_o inhabitant_n be_v to_o we_o a_o antipheristasin_n our_o direct_a opposite_n so_o that_o while_o the_o sun_n continue_v visible_a to_o we_o it_o be_v above_o our_o horizon_n and_o so_o continue_v day_n with_o we_o while_o it_o be_v night_n with_o our_o opposite_n and_o when_o the_o sun_n go_v down_o with_o we_o it_o appear_v to_o

degree_n and_o it_o shall_v leave_v 30_o which_o be_v the_o declination_n of_o the_o wall_n equal_a to_o the_o angle_n efg_o but_o to_o find_v the_o inclination_n or_o reclination_n i_o shall_v show_v when_o i_o come_v to_o the_o use_n of_o the_o universal_a quadrant_n or_o have_v first_o find_v the_o meridian_n line_n you_o may_v prick_v down_o the_o azimuth_n chap_n v._o show_v what_o hourline_n may_v be_v draw_v upon_o any_o plane_n light_n be_v the_o cause_n primary_a of_o shadow_n shadow_n be_v but_o the_o imitation_n of_o the_o secondary_a cause_n that_o be_v substance_n do_v delineate_v unto_o we_o the_o pass_v away_o of_o time_n by_o receive_v light_n on_o the_o substance_n cast_v shadow_n the_o sun_n though_o he_o never_o move_v from_o the_o line_n ecliptic_a wherein_o he_o have_v his_o annual_a or_o yearly_a motion_n yet_o have_v a_o declination_n from_o the_o equinoctial_a north_n or_o south_n make_v his_o diurnal_a or_o daily_a motion_n alter_v the_o day_n and_o night_n according_a to_o all_o the_o diversity_n thereof_o for_o the_o sun_n be_v in_o the_o equinoctial_a have_v no_o declination_n but_o in_o his_o diurnal_a motion_n still_o decline_v from_o the_o equinoctial_a make_v his_o progress_n towards_o the_o north_n or_o south_n describe_v many_o parallel_a circle_n be_v parallel_n to_o the_o equinoctial_a who_o far_a distance_n from_o either_o side_n be_v 23_o deg._n 30_o minute_n so_o that_o so_o many_o degree_n that_o the_o sun_n be_v distant_a from_o the_o equinoctial_a so_o much_o be_v its_o declination_n now_o if_o you_o imagine_v the_o circle_n before_o describe_v to_o represent_v the_o meridian_n circle_n which_o cross_v diametrical_o which_o diameter_n shall_v represent_v the_o equinoctial_a then_o lay_v down_o the_o great_a declination_n on_o either_o side_n of_o it_o draw_v two_o line_n at_o that_o distance_n on_o either_o side_n of_o the_o equinoctial_a parallel_a to_o it_o represent_v the_o tropic_n the_o upper_a represent_v the_o tropic_a of_o cancer_n mark_v with_o ge_z the_o other_o the_o tropic_a of_o capricorn_n mark_v with_o hippolito_o and_o if_o from_o each_o several_a degree_n you_o draw_v parallel_n too_o they_o do_v represent_v the_o parallel_n of_o the_o sun_n which_o shall_v show_v the_o diurnal_a motion_n of_o the_o sun_n now_o if_o you_o cross_v these_o parallel_n with_o a_o line_n from_o e_o to_o h_o that_o then_o represent_v the_o ecliptic_a now_o if_o you_o cross_v the_o equinoctial_a at_o right_a angle_n with_o another_o line_n that_o line_n represent_v the_o axis_n of_o the_o world_n then_o if_o you_o lie_v down_o from_o the_o pole_n the_o elevation_n thereof_o to_o wit_n the_o north_n and_o south_n pole_n according_a to_o the_o elevation_n of_o the_o north_n pole_n downward_o where_o the_o number_n of_o degree_n end_v make_v a_o mark_n then_o account_v the_o same_o elevation_n from_o the_o south_n pole_n upward_o and_o there_o also_o make_v a_o mark_n from_o which_o two_o mark_n draw_v a_o right_a line_n which_o shall_v represent_v your_o horizon_n and_o cut_v the_o parallel_n of_o the_o sun_n according_a to_o the_o time_n of_o his_o abide_n above_o the_o horizon_n first_o a_o east_n and_o west_n dial_n lie_v parallel_n to_o the_o meridian_n therefore_o the_o sun_n in_o the_o meridian_n can_v shine_v on_o they_o nevertheless_o though_o a_o east_n and_o west_n dial_n can_v have_v the_o hour_n of_o 12_o on_o it_o yet_o a_o east_n or_o west_n position_n may_v because_o it_o cross_v the_o horizon_n in_o the_o north_n and_o south_n second_o a_o direct_a north_n dial_n can_v have_v but_o morning_n and_o evening_n hour_n on_o it_o and_o then_o of_o no_o use_n but_o when_o the_o sun_n have_v north_n declination_n for_o then_o his_o amplitude_n or_o distance_n from_o the_o east_n and_o west_n be_v northward_o and_o so_o at_o morning_n or_o night_n shine_v on_o the_o face_n thereof_o three_o a_o north_n recline_a may_v show_v all_o the_o hour_n all_o the_o year_n if_o it_o recline_v from_o the_o north_n southward_o the_o quantity_n of_o the_o compliment_n of_o the_o least_o meridian_n altitude_n but_o if_o but_o the_o compliment_n of_o the_o elevation_n of_o the_o equinoctial_a and_o so_o become_v a_o polar_a plane_n it_o can_v then_o but_o show_v while_o the_o sun_n be_v in_o the_o north_n sign_n for_o the_o dial_n lie_v parallel_n to_o the_o equinoctial_a while_o the_o sun_n be_v in_o south_n declination_n can_v shine_v on_o the_o plane_n because_o it_o lie_v under_o all_o upright_a plane_n decline_v from_o the_o south_n may_v have_v the_o hour_n line_n of_o 12_o so_o also_o may_v all_o north_n decliner_n but_o not_o in_o the_o temperate_a zone_n which_o be_v contain_v between_o the_o degree_n south_n incliner_n also_o may_v have_v the_o line_n of_o 12_o who_o upper_a face_n be_v not_o below_o the_o least_o meridian_n altitude_n as_o also_o if_o great_a than_o the_o great_a meridian_n altitude_n than_o do_v the_o upper_a face_n want_v it_o five_o all_o north_n recliner_n recline_v more_o than_o the_o great_a meridian_n altitude_n compliment_n may_v have_v all_o the_o hour_n but_o will_v show_v but_o one_o part_n of_o the_o year_n six_o all_o south_n declinet_n or_o recliner_n may_v have_v the_o line_n of_o 12_o on_o they_o and_o now_o have_v proceed_v thus_o far_o in_o some_o theorical_a demonstration_n or_o ground_n of_o dial_n for_o the_o geometrical_a projection_n we_o will_v in_o the_o next_o chapter_n lie_v down_o the_o theorical_a demonstration_n for_o the_o arithmetical_a calculation_n and_o so_o proceed_v to_o our_o practical_a way_n of_o operation_n as_o ensue_v chap_n vi_o be_v the_o definition_n of_o the_o several_a line_n of_o sine_n tangent_n and_o secant_n to_o be_v understand_v before_o we_o can_v come_v to_o arithmetical_a calculation_n a_o tangent_fw-la be_v a_o right_a line_n without_o the_o periphery_n to_o the_o extremity_n of_o the_o secant_n to_o the_o radius_fw-la be_v perpendicular_a eraise_v such_o be_v represent_v by_o the_o line_n bc._n a_o secant_n be_v a_o right_a line_n draw_v from_o the_o centre_n through_o the_o circumference_n to_o the_o tangent_fw-la such_o be_v represent_v by_o the_o line_n ab_o the_o semidiameter_n of_o the_o same_o circle_n be_v call_v the_o radius_fw-la you_o may_v furthermore_o for_o very_o convenient_a use_n have_v those_o line_n place_v on_o a_o ruler_n for_o if_o from_o one_o degree_n of_o one_o quadrant_n of_o a_o semicircle_n you_o draw_v line_n to_o the_o same_o degree_n of_o the_o other_o quadrant_n cut_v the_o line_n ga_o that_o line_n so_o cut_v shall_v be_v a_o line_n of_o sine_n and_o if_o from_o the_o centre_n you_o draw_v line_n to_o the_o tangent_fw-la line_n through_o every_o degree_n of_o the_o quadrant_n that_o line_n so_o cut_v be_v a_o tangent_fw-la line_n who_o use_n be_v most_o exquisite_a and_o infinite_a for_o the_o solution_n of_o many_o excellent_a proposition_n chap_n vii_o be_v the_o fundamental_a diagram_n for_o the_o geometrical_a projection_n of_o dial_n the_o style_n be_v the_o representation_n of_o the_o axis_n of_o the_o world_n do_v become_v the_o gnomon_n or_o substance_n cast_v shadow_n on_o all_o plane_n lie_v parallel_n to_o some_o circle_n or_o other_o as_o to_o circle_n of_o azimuth_n in_o all_o vertical_a dial_n so_o that_o the_o figure_n follow_v be_v a_o representation_n of_o divers_a semidiameter_n do_v plain_o show_v the_o theorical_a ground_n of_o the_o practic_a part_n hereof_o where_o the_o line_n in_o the_o demonstration_n note_v the_o semidiameter_n of_o the_o horizon_n signify_v the_o horizon_n for_o so_o suppose_v it_o to_o represent_v a_o horizontal_a dial_n the_o style_n or_o axis_n must_v be_v elevate_v above_o it_o according_a to_o the_o pole_n elevation_n above_o the_o horizon_n and_o then_o the_o semidiameter_n or_o axis_n of_o the_o world_n represent_v the_o style_n or_o axis_n cast_v shadow_n be_v the_o line_n ac_o the_o geometrical_a projection_n of_o dial_n where_o note_n by_o the_o way_n that_o if_o you_o set_v one_o foot_n of_o the_o compass_n in_o b_o and_o with_o the_o semidiameter_n of_o the_o equator_n fix_v the_o other_o foot_n in_o the_o line_n bc_o keep_v that_o last_o foot_n fast_o and_o at_o that_o centre_n draw_v a_o quadrant_n divide_v into_o six_o part_n and_o a_o ruler_n from_o the_o centre_n of_o the_o equator_n through_o each_o division_n shall_v divide_v the_o line_n ab_o as_o a_o contingent_a line_n and_o if_o from_o c_o to_o these_o mark_n on_o the_o line_n ab_o you_o draw_v line_n it_o shall_v be_v the_o hour_n line_n of_o a_o vertical_a dial_n but_o suppose_v a_o dial_n to_o stand_v vertical_a or_o upright_o to_o the_o horizon_n ab_o as_o the_o line_n bc_o then_o that_o be_v represent_v by_o the_o semidiameter_n of_o the_o vertical_a and_o his_o style_n again_o represent_v by_o the_o semidiameter_n or_o axis_n ac_o be_v distant_a from_o the_o

13_o 41_o 42_o 57_o 3_o 73_o 16_o  _fw-fr 64_o 13_o 32_o 27_o 26_o 41_o 57_o 57_o 17_o 73_o 24_o  _fw-fr 65_o 13_o 39_o 27_o 37_o 42_o 11_o 57_o 30_o 73_o 32_o  _fw-fr 66_o 13_o 45_o 27_o 49_o 42_o 25_o 57_o 42_o 73_o 39_o  _fw-fr 67_o 13_o 52_o 27_o 59_o 42_o 38_o 57_o 54_o 73_o 46_o  _fw-fr 68_o 13_o 56_o 28_o 9_o 42_o 50_o 58_o 5_o 73_o 53_o  _fw-fr 69_o 14_o 3_o 28_o 19_o 43_o 2_o 58_o 16_o 73_o 59_o  _fw-fr 70_o 14_o 8_o 28_o 29_o 43_o 13_o 58_o 26_o 74_o 5_o  _fw-fr 71_o 14_o 13_o 28_o 38_o 43_o 24_o 58_o 36_o 74_o 11_o  _fw-fr 72_o 14_o 18_o 28_o 46_o 43_o 34_o 58_o 44_o 74_o 16_o  _fw-fr 73_o 14_o 22_o 28_o 55_o 43_o 43_o 58_o 53_o 74_o 21_o  _fw-fr 74_o 14_o 26_o 29_o 2_o 43_o 52_o 59_o 1_o 74_o 25_o  _fw-fr 75_o 14_o 30_o 29_o 9_o 44_o 0_o 59_o 8_o 74_o 29_o  _fw-fr 76_o 14_o 34_o 29_o 5_o 44_o 8_o 59_o 15_o 74_o 34_o  _fw-fr 77_o 14_o 38_o 29_o 22_o 44_o 15_o 59_o 21_o 74_o 37_o  _fw-fr 78_o 14_o 41_o 29_o 27_o 44_o 22_o 59_o 26_o 74_o 41_o  _fw-fr 79_o 14_o 44_o 29_o 32_o 44_o 28_o 59_o 32_o 74_o 44_o  _fw-fr 80_o 14_o 47_o 29_o 37_o 44_o 34_o 59_o 37_o 74_o 47_o  _fw-fr 81_o 14_o 49_o 29_o 42_o 44_o 39_o 59_o 41_o 74_o 49_o  _fw-fr 82_o 14_o 51_o 29_o 44_o 44_o 43_o 59_o 43_o 74_o 50_o  _fw-fr 83_o 14_o 53_o 29_o 49_o 44_o 47_o 59_o 49_o 74_o 53_o  _fw-fr 84_o 14_o 55_o 29_o 52_o 44_o 51_o 59_o 52_o 74_o 55_o  _fw-fr 85_o 14_o 57_o 29_o 54_o 44_o 53_o 59_o 54_o 74_o 57_o  _fw-fr 86_o 14_o 58_o 29_o 56_o 44_o 56_o 59_o 57_o 74_o 58_o  _fw-fr 87_o 14_o 59_o 29_o 58_o 44_o 58_o 59_o 58_o 74_o 59_o  _fw-fr 88_o 14_o 59_o 29_o 59_o 44_o 59_o 59_o 58_o 74_o 59_o  _fw-fr 89_o 14_o 59_o 30_o  _fw-fr 44_o 59_o 59_o 59_o 75_o  _fw-fr  _fw-fr 90_o 15_o  _fw-fr 30_o  _fw-fr 45_o  _fw-fr 60_o  _fw-fr 75_o  _fw-fr  _fw-fr chap_n viii_o show_v the_o use_n of_o this_o table_n both_o in_o vertical_a and_o horizontal_a plane_n for_o a_o horizontal_a dial_n enter_v the_o table_n with_o the_o elevation_n of_o the_o pole_n on_o the_o left_a hand_n and_o the_o arch_n note_v against_o the_o hour_n and_o the_o elevation_n find_v be_v the_o distance_n of_o the_o hour_n from_o the_o meridian_n for_o a_o vertical_a or_o direct_a south_n or_o north_n enter_v the_o table_n with_o the_o compliment_n of_o the_o elevation_n on_o the_o right_a side_n and_o the_o common_a meeting_n of_o the_o hour_n at_o top_n and_o the_o compliment_n of_o elevation_n be_v the_o distance_n of_o the_o hour_n from_o the_o meridian_n in_o the_o say_a plane_n for_o every_o horizontal_a plane_n be_v a_o direct_a vertical_a in_o that_o place_n who_o latitude_n or_o distance_n of_o their_o zenith_n from_o the_o aequator_fw-la be_v equal_a to_o the_o compliment_n of_o the_o elevation_n of_o the_o horizontal_a plane_n axis_n or_o style_n as_o to_o make_v a_o horizontal_a dial_n for_o the_o latitude_n of_o 51_o degree_n i_o enter_v the_o table_n and_o find_v these_o arch_n for_o 1_o and_o 11_o for_o 2_o and_o 10_o etc._n etc._n now_o the_o same_o distance_n be_v the_o distance_n of_o the_o hour_n line_n of_o a_o direct_a south_n plane_n where_o the_o pole_n be_v elevate_v the_o compliment_n of_o 51_o degree_n that_o be_v 39_o degree_n for_o 51_o and_o 39_o together_o do_v make_v 90._o so_o to_o make_v a_o vertical_a dial_n i_o enter_v the_o table_n with_o 39_o the_o compliment_n of_o the_o elevation_n of_o the_o pole_n and_o find_v the_o arch_n answer_v to_o 1_o and_o 11_o to_o 2_o and_o 10_o etc._n etc._n thus_o much_o in_o general_a of_o the_o use_n of_o the_o table_n now_o follow_v the_o use_n in_o special_a chap_n ix._o show_v the_o use_n of_o the_o table_n in_o make_v any_o decline_a or_o incline_v direct_a dial_n let_v the_o great_a circle_n abcd_o represent_v the_o meridian_n a_o the_o north_n and_o c_o the_o south_n than_o the_o line_n ef_o represent_v a_o south_n recline_v plane_n while_o it_o fall_v back_o from_o the_o south_n northward_o and_o represent_v a_o incline_a plane_n while_o it_o respect_v the_o horizon_n this_o be_v sufficient_o discuss_v before_o so_o much_o as_o the_o plane_n recline_v northward_o beyond_o the_o compliment_n of_o the_o elevation_n of_o the_o pole_n so_o much_o be_v the_o north_n pole_n elevate_v above_o the_o plane_n as_o here_o the_o plane_n be_v represent_v by_o ef_o the_o elevation_n of_o the_o style_n or_o axis_n the_o arch_n eg_o therefore_o in_o this_o case_n subtract_v the_o compliment_n of_o the_o reclination_n of_o the_o plane_n from_o the_o elevation_n of_o the_o elevate_a pole_n and_o the_o remainder_n be_v the_o arch_n of_o the_o pole_n elevation_n above_o the_o plane_n with_o which_o elevation_n enter_v the_o table_n in_o the_o left_a margin_n and_o there_o be_v the_o hour_n arch_n from_o the_o meridian_n if_o the_o reclination_n of_o the_o plane_n be_v less_o than_o the_o compliment_n as_o be_v ik_o subtract_v the_o arch_n of_o reclination_n from_o the_o compliment_n of_o the_o elevation_n there_o be_v leave_v the_o elevation_n of_o the_o south_n pole_n above_o the_o plane_n and_o with_o the_o compliment_n of_o the_o elevation_n of_o the_o pole_n above_o the_o plane_n enter_v the_o table_n on_o the_o right_a margin_n and_o there_o shall_v you_o find_v the_o distance_n of_o the_o hour_n and_o herein_o mr._n faile_n fail_v for_o instead_o of_o subtract_v one_o from_o the_o other_o he_o add_v one_o to_o another_o cause_v a_o great_a error_n the_o distance_n of_o every_o hour_n of_o the_o north_n incliner_n on_o the_o back_n side_n of_o the_o south_n incliner_n as_o much_o be_v equal_a save_v that_o the_o hour_n on_o the_o north_n side_n must_v be_v name_v by_o the_o compliment_n hour_n to_o 12_o and_o as_o the_o north_n pole_n be_v above_o one_o plane_n so_o be_v the_o south_n pole_n above_o the_o other_o you_o may_v also_o conceive_v the_o like_a in_o make_v of_o all_o south_n incliner_n and_o recliner_n by_o frame_v the_o position_n of_o the_o plane_n on_o the_o south_n side_n as_o the_o figure_n be_v on_o the_o north_n and_o in_o north_n recliner_n less_o than_o the_o elevation_n of_o the_o pole_n add_v the_o reclination_n of_o the_o flat_a which_o be_v the_o elevation_n of_o the_o north_n pole_n above_o the_o plane_n herein_o mr._n fail_n fail_v also_o as_o depend_v on_o the_o former_a follow_v the_o doctrine_n of_o contrary_n which_o foremost_a well_o examine_v will_v have_v save_v the_o open_n of_o a_o gap_n to_o this_o second_o error_n with_o the_o say_a elevation_n find_v enter_v the_o table_n for_o the_o horizontal_a arch_n and_o thereby_o make_v a_o horizontal_a plane_n as_o be_v show_v so_o be_v the_o dial_n also_o prepare_v if_o it_o recline_v that_o it_o lie_v between_o the_o horizon_n and_o the_o equator_n then_o to_o the_o elevation_n of_o the_o pole_n add_v the_o compliment_n of_o the_o reclination_n which_o be_v the_o height_n of_o the_o style_n above_o the_o plane_n and_o finish_v it_o as_o a_o horizontal_a plane_n for_o that_o latitude_n and_o not_o as_o a_o vertical_a as_o mr._n faile_n will_v have_v it_o because_o every_o recline_a plane_n be_v a_o horizontal_a plane_n where_o the_o pole_n be_v elevate_v according_a to_o the_o style_n in_o a_o give_a plane_n oblique_a to_o the_o meridian_n and_o to_o the_o horizon_n and_o to_o the_o prime_a vertical_a that_o be_v a_o give_a plane_n incline_v decline_a to_o find_v as_o well_o the_o meridian_n of_o the_o place_n as_o of_o the_o plane_n and_o the_o elevation_n of_o the_o pole_n above_o the_o plane_n prob._n 3_o petici_fw-la liber_fw-la gnomonicorum_fw-la to_o give_v you_o the_o parallel_n of_o pitiscus_n his_o example_n we_o will_v prosecute_v it_o according_a to_o the_o natural_a tangent_n in_o his_o example_n and_o give_v you_o his_o word_n let_v the_o meridian_n of_o the_o place_n be_v abcd_o the_o horizon_n aec_o the_o prime_a vertical_a bed_n the_o oriental_a point_n e_o the_o vertical_a decline_v bkd_o and_o right_o angle_v at_o k_o the_o pole_n of_o the_o world_n g_o and_o i_o the_o pole_n of_o the_o plane_n h_o the_o meridian_n ghi_o the_o angle_n of_o declination_n ebf_o the_o arch_n of_o inclination_n bk_n but_o before_o all_o thing_n the_o arch_a k_o or_o the_o distance_n of_o the_o meridian_n of_o the_o place_n nl_o be_v from_o the_o vertical_a plane_n kl_o shall_v be_v seek_v by_o the_o second_o axiom_n than_o the_o ark_n bn_o by_o the_o three_o or_o four_o axiom_n after_o these_o the_o angle_n bkn_o that_o be_v in_o one_o word_n the_o triangle_n bkn_o be_v find_v by_o which_o discharge_v the_o ark_n bn_o be_v find_v either_o equal_a to_o the_o pole_n