Selected quad for the lemma: end_n

Word A	Word B	Word C	Word D	Occurrence	Frequency Band	MI	MI Band	Prominent
end_n	line_n	point_n	straight_a	1,843	5	12.8557	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

ponderosity_n or_o a_o centre_n of_o rotundity_n if_o it_o be_v a_o seem_a point_n that_o be_v increase_v or_o diminish_v according_a to_o the_o ocular_a aspect_n as_o be_v sometime_o near_o and_o sometime_o far_o from_o the_o thing_n in_o the_o visual_a line_n the_o thing_n be_v make_v more_o or_o less_o apparent_a a_o centre_n of_o magnitude_n be_v a_o equal_a distribution_n from_o that_o point_n a_o equality_n of_o distribution_n of_o the_o part_n give_v to_o each_o end_n alike_o and_o to_o each_o a_o like_a vicinity_n to_o that_o point_n or_o centre_n a_o centre_n of_o ponderosity_n be_v such_o a_o point_n in_o which_o a_o unequal_a thing_n hang_v in_o equi_fw-la libra_fw-la in_o a_o equal_a distribution_n of_o the_o weight_n though_o one_o end_n be_v long_o or_o big_a than_o the_o other_o of_o the_o quantity_n of_o the_o ponderosity_n a_o centre_n of_o rotundity_n be_v such_o a_o centre_n as_o be_v the_o centre_n of_o a_o globe_n or_o circle_n be_v equal_o distant_a from_o all_o place_n now_o the_o earth_n be_v to_o be_v understand_v to_o be_v such_o a_o centre_n as_o the_o centre_n of_o a_o globe_n or_o sphere_n be_v equal_o distant_a from_o the_o concave_a superficies_n of_o the_o firmament_n neither_o be_v it_o to_o be_v understand_v to_o be_v a_o centre_n as_o a_o point_n indivisible_a but_o either_o comparative_o or_o optical_o comparative_o in_o respect_n of_o the_o superior_a orb_n optical_o by_o reason_n of_o the_o far_a distance_n of_o the_o one_o from_o the_o earth_n as_o that_o the_o fix_a star_n be_v far_o distant_a seem_v by_o the_o weakness_n of_o the_o sense_n to_o be_v conceive_v as_o a_o centre_n indivisible_a when_o by_o the_o force_n and_o vigour_n of_o reason_n and_o demonstration_n they_o be_v find_v to_o exceed_v this_o globe_n of_o earth_n much_o in_o magnitude_n so_o that_o what_o our_o sense_n can_v apprehend_v must_v be_v comprehend_v by_o reason_n as_o in_o the_o circle_n of_o the_o celestial_a orb_n because_o they_o can_v be_v 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equality_n of_o shadow_n for_o example_n let_v the_o great_a circle_n represent_v the_o heaven_n and_o the_o less_o the_o earth_n out_o of_o the_o centre_n of_o the_o great_a now_o the_o sun_n be_v above_o the_o horizon_n ac_o 60_o d._n and_o a_o gnomon_n at_o e_o cast_v his_o shadow_n from_o e_o to_o f_o and_o if_o the_o same_o gnomon_n of_o the_o same_o length_n do_v stand_v till_o the_o sun_n come_v to_o the_o opposite_a side_n of_o the_o horizon_n ac_o and_o the_o sun_n be_v 60_o degree_n above_o that_o horizon_n cast_v the_o shadow_n from_o e_o to_o h_o which_o be_v unequal_a in_o length_n the_o reason_n of_o which_o inequality_n prove_v that_o then_o it_o do_v not_o stand_v in_o the_o centre_n and_o the_o equality_n of_o the_o other_o prove_v that_o it_o be_v in_o the_o centre_n hence_o be_v also_o most_o forcible_o prove_v that_o the_o earth_n be_v complete_o round_a in_o the_o respect_n of_o the_o heaven_n as_o be_v show_v by_o the_o equality_n of_o shadow_n for_o if_o it_o 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n_o w_n 67_o 30_o e_o by_o n_o 78_o 45_o w_n by_o n_n 78_o 45_o east_n 90_o 00_o west_n 90_o 00_o by_o which_o it_o appear_v that_o every_o point_n of_o the_o compass_n be_v distant_a from_o the_o meridian_n 11_o degree_n 15_o minute_n the_o three_o sort_n of_o plane_n be_v incline_v or_o rather_o recline_v who_o upper_a face_n behold_v the_o zenith_n and_o in_o that_o respect_n be_v call_v recline_v but_o if_o a_o dial_n be_v make_v on_o the_o nether_a side_n and_o thereby_o respect_v the_o horizon_n it_o be_v then_o call_v a_o incliner_n so_o that_o the_o one_o be_v the_o opposite_a to_o the_o other_o these_o plane_n be_v likewise_o accidental_o divide_v for_o they_o be_v either_o direct_a recliner_n recline_v from_o the_o direct_a point_n of_o east_n west_n north_n and_o south_n and_o in_o this_o sort_n happen_v the_o direct_a polar_a and_o equinoctial_a plane_n as_o infinite_a more_o according_a to_o the_o inclination_n or_o reclination_n of_o the_o plane_n or_o they_o be_v as_o 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define_v a_o praecognitiall_a part_n of_o magnitude_n as_o useful_a to_o this_o art_n the_o praecognita_fw-la geometrical_a the_o art_n say_v arnobius_n be_v not_o together_o with_o our_o mind_n send_v out_o of_o the_o heavenly_a place_n but_o all_o be_v find_v out_o on_o earth_n and_o be_v in_o process_n of_o time_n soft_a and_o fair_a forge_v by_o a_o continual_a meditation_n our_o poor_a and_o needy_a life_n perceive_v some_o casual_a thing_n to_o happen_v prosperous_o while_o it_o do_v imitate_v attempt_v and_o try_v while_o it_o do_v slip_v reform_v and_o change_v have_v out_o of_o these_o same_o assiduous_a apprehension_n make_v up_o small_a science_n of_o art_n the_o which_o afterwards_o by_o study_n be_v bring_v to_o some_o perfection_n by_o which_o we_o see_v that_o art_n be_v find_v out_o by_o daily_a practice_n yet_o the_o practice_n of_o art_n be_v not_o manifest_a but_o by_o speculative_a illustration_n because_o by_o speculation_n scimus_fw-la ut_fw-la sciamus_fw-la we_o know_v that_o we_o may_v the_o better_o know_v and_o for_o this_o cause_n i_o first_o choose_v a_o speculative_a part_n that_o you_o may_v the_o better_o know_v the_o practice_n and_o therefore_o have_v first_o choose_v this_o speculative_a part_n of_o practical_a geometry_n which_o be_v a_o science_n declare_v the_o nature_n quantity_n and_o quality_n of_o magnitude_n which_o proceed_v from_o the_o least_o imaginable_a thing_n to_o begin_v then_o a_o point_n be_v a_o indivisible_a yet_o be_v the_o first_o of_o all_o dimension_n it_o be_v the_o philosopher_n atom_n such_o a_o nothing_o as_o that_o it_o be_v the_o very_a energy_n of_o all_o thing_n in_o god_n it_o carry_v its_o extreme_n from_o eternity_n to_o eternity_n in_o the_o world_n it_o be_v the_o same_o which_o moses_n call_v the_o beginning_n and_o be_v his_o genesis_n it_o be_v the_o clotho_n that_o give_v clio_n the_o matter_n to_o work_v upon_o and_o spin_v it_o forth_o from_o terminus_fw-la à_fw-la quo_fw-la to_o terminus_fw-la ad_fw-la quem_fw-la in_o the_o alphabet_n it_o be_v the_o alpha_fw-gr and_o be_v in_o the_o cusp_n of_o the_o ascendant_n in_o every_o science_n and_o the_o house_n of_o life_n in_o every_o operation_n again_o a_o point_n be_v either_o centrical_a or_o excentrical_a both_o which_o be_v consider_v geometrical_o or_o optical_o that_o be_v a_o point_n or_o a_o seem_a point_n a_o point_n geometrical_o consider_v be_v indivisible_a and_o be_v central_a be_v of_o magnitude_n without_o consideration_n of_o form_n or_o of_o rotundity_n with_o reference_n to_o figure_n as_o a_o circle_n or_o a_o globe_n etc._n etc._n or_o of_o ponderosity_n with_o reference_n to_o weight_n and_o such_o a_o point_n be_v in_o those_o balance_n which_o hang_v in_o equilibra_fw-la yet_o have_v one_o beam_n long_o than_o the_o other_o if_o it_o be_v a_o seem_a point_n it_o be_v increase_v or_o diminish_v optical_o that_o be_v according_a to_o the_o distance_n of_o the_o object_n and_o subject_n it_o be_v the_o birth_n of_o any_o thing_n and_o indeed_o be_v to_o be_v consider_v as_o our_o principal_a significator_n which_o be_v increase_v do_v produce_v quantity_n which_o be_v the_o require_v to_o magnitude_n for_o magnitude_n be_v no_o other_o than_o a_o continuation_n of_o quantity_n which_o be_v either_o from_o a_o line_n to_o a_o plain_a superficies_fw-la or_o from_o a_o plain_a superficies_n to_o a_o solid_a body_n every_o of_o which_o be_v consider_v according_a to_o the_o quantity_n or_o form_n the_o quantity_n of_o a_o line_n be_v length_n without_o breadth_n or_o thickness_n the_o form_n either_o right_a or_o curve_v the_o quantity_n of_o a_o superficies_n consist_v in_o length_n and_o breadth_n without_o thickness_n the_o form_n be_v divers_a either_o regular_a or_o irregular_a regular_a be_v triangle_n square_n circle_n pentagon_n hexagon_n etc._n etc._n a_o equilateral_a triangle_n consist_v of_o three_o right_a line_n and_o as_o many_o angle_n his_o inscribe_a side_n in_o a_o circle_n contain_v 120_o degree_n a_o square_n of_o four_o equal_a right_a line_n and_o as_o many_o right_a angle_n and_o his_o inscribe_a side_n be_v 90_o degree_n a_o pentagon_n consist_v of_o five_o equal_a line_n and_o angle_n and_o his_o inscribe_a side_n be_v 72_o degree_n of_o a_o circle_n a_o hexagon_n be_v of_o six_o equal_a line_n and_o angle_n and_o his_o side_n within_o a_o circle_n be_v 60_o degree_n which_o be_v equal_a to_o the_o radius_fw-la or_o semidiameter_n a_o angle_n be_v the_o meeting_n of_o two_o line_n not_o in_o a_o straight_o concur_v but_o which_o be_v extend_v will_v cross_v each_o other_o but_o if_o they_o will_v never_o cross_v than_o they_o be_v parallel_n the_o quantity_n of_o a_o angle_n be_v the_o measure_n of_o the_o part_n of_o a_o circle_n

divide_v into_o 360_o degree_n between_o the_o open_a end_n and_o the_o angle_n itself_o be_v the_o centre_n of_o the_o circle_n the_o quantity_n of_o a_o solid_a consist_v of_o length_n breadth_n and_o thickness_n the_o form_n be_v various_a regular_a or_o irregular_a the_o five_o regular_a or_o platonic_a body_n be_v the_o tetrahedron_n hexahedron_n octohedron_n dodecahedron_n icosahedron_n tetrahedron_n be_v a_o solid_a body_n consist_v of_o four_o equal_a equilateral_a triangle_n a_o hexahedron_n be_v a_o solid_a body_n consist_v of_o six_o equal_a square_n and_o be_v right_o angle_v every_o way_n an_fw-mi octahedron_n be_v a_o solid_a body_n consist_v of_o eight_o equal_a equilateral_a triangle_n a_o dodecahedron_n be_v a_o solid_a body_n consist_v of_o 12_o equal_a pentagon_n an_fw-mi icosahedron_n be_v a_o solid_a body_n consist_v of_o 20_o equal_a equilateral_a triangle_n all_o which_o be_v here_o describe_v in_o plano_fw-la by_o which_o they_o be_v make_v in_o pasteboard_n or_o if_o you_o will_v cut_v they_o in_o solid_a it_o be_v perform_v by_o mr._n wells_n in_o his_o art_n of_o shadow_n where_o also_o he_o have_v fit_v plane_n for_o the_o same_o body_n a_o parallel_n line_n be_v a_o line_n equidistant_a in_o all_o place_n from_o another_o line_n which_o two_o line_n can_v never_o meet_v a_o perpendicular_a be_v a_o line_n right_o elevate_v to_o another_o at_o right_a angle_n and_o be_v thus_o erect_v suppose_v ab_o be_v a_o line_n and_o in_o the_o point_n a_o you_o will_v erect_v a_o perpendicular_a set_v one_o foot_n of_o your_o compass_n in_o a_o extend_v the_o other_o upward_o anywhere_o as_o at_o c_o then_o keep_v the_o foot_n fix_v in_o c_o remove_v that_o foot_n as_o be_v in_o a_o towards_o b_o till_o it_o fall_v again_o in_o the_o line_n ab_o then_o if_o you_o lay_v a_o ruler_n by_o the_o foot_n of_o your_o compass_n keep_v the_o foot_n fix_v in_o c_o and_o turn_v the_o other_o foot_n towards_o d_o by_o the_o side_n of_o the_o ruler_n and_o where_o that_o fall_v make_v a_o mark_n from_o whence_o draw_v the_o line_n da_o which_o be_v perpendicular_a to_o ab_o and_o so_o much_o shall_v suffice_v for_o the_o praecognita_fw-la geometrical_a the_o philosophical_a follow_v the_o end_n of_o the_o praecognita_fw-la geometrical_a the_o argument_n of_o the_o praecognita_fw-la philosophical_a not_o to_o maintain_v with_o nice_a philosophy_n what_o unto_o reason_n seem_v to_o be_v obscure_a or_o show_v you_o thing_n hide_v in_o obscurity_n who_o ground_n be_v nothing_o sure_a it_o be_v not_o the_o drift_n of_o this_o my_o book_n the_o world_n in_o two_o to_o part_n nor_o show_v you_o thing_n whereon_o to_o look_v but_o what_o have_v ground_n by_o art_n if_o be_v confirm_v what_o here_o you_o read_v sure_o you_o will_v confirm_v be_v if_o reason_n wont_a demonstrate_v it_o learn_v somewhere_o else_o for_o i_o there_o be_v show_v to_o you_o what_o shadow_n be_v and_o the_o earth_n proper_a place_n how_o it_o the_o middle_n do_v possess_v and_o how_o heaven_n run_v their_o race_n resolve_v many_o a_o proposition_n which_o be_v of_o use_n and_o needful_a to_o be_v know_v the_o praecognita_fw-la philosophical_a chap_n i_o of_o light_n and_o shadow_n he_o that_o seek_v shadow_n in_o its_o predicament_n seek_v a_o reality_n in_o a_o imitation_n he_o be_v right_o answer_v umbram_fw-la per_fw-la se_fw-la in_fw-la nullo_fw-la praedicamento_fw-la esse_fw-la the_o reason_n be_v thus_o render_v as_o have_v be_v it_o be_v not_o a_o reality_n but_o a_o confuse_a imitation_n of_o a_o body_n arise_v from_o the_o object_n of_o light_n so_o than_o there_o can_v be_v no_o other_o definition_n than_o this_o shadow_n be_v but_o the_o imitation_n of_o substance_n not_o incident_a to_o part_n cause_v by_o the_o interposition_n of_o a_o substance_n for_o umbra_fw-la non_fw-la potest_fw-la agere_fw-la sine_fw-la lumine_fw-la and_o and_o it_o be_v twofold_a cause_v by_o a_o twofold_a motion_n of_o light_n that_o be_v either_o from_o a_o direct_a beam_n of_o light_n which_o be_v primary_a or_o from_o a_o secondary_a which_o be_v reflective_a hence_o it_o be_v that_o sun_n dial_n be_v make_v where_o the_o direct_a beam_n can_v never_o fall_v as_o on_o the_o ceiling_n of_o a_o chamber_n or_o the_o like_a but_o in_o vain_a man_n seek_v after_o a_o shadow_n what_o then_o shall_v we_o proceed_v no_o far_o sure_o not_o so_o for_o qui_fw-la semper_fw-la est_fw-la in_fw-la suo_fw-la officio_fw-la be_v semper_fw-la orat_fw-la for_o there_o be_v no_o good_a and_o lawful_a action_n but_o do_v condescend_v to_o the_o glory_n of_o god_n and_o especial_o good_a and_o lawful_a art_n and_o that_o shadow_n may_v appear_v to_o be_v but_o dependent_a on_o light_n it_o be_v thus_o prove_v quod_fw-la est_fw-la et_fw-la existit_fw-la in_fw-la se_fw-la id_fw-la non_fw-la existit_fw-la in_fw-la alio_fw-la that_o which_o be_v and_o subsi_v in_o itself_o that_o subsi_v not_o in_o another_o but_o shadow_n subsi_v not_o in_o itself_o for_o take_v away_o the_o cause_n that_o be_v light_a and_o you_o take_v away_o the_o effect_n that_o be_v shadow_n hence_o we_o also_o observe_v the_o sun_n to_o be_v the_o fountain_n of_o light_n who_o daily_a and_o occurrent_a motion_n do_v cause_v a_o admirable_a lustre_n to_o the_o glory_n of_o god_n see_v that_o by_o he_o we_o measure_v out_o our_o time_n season_n and_o year_n be_v it_o not_o his_o annual_a revolution_n or_o his_o proper_a motion_n that_o limit_n our_o year_n be_v it_o not_o his_o tropical_a distinction_n that_o limit_n our_o season_n be_v it_o not_o his_o diurnal_a motion_n that_o limit_n out_o our_o day_n and_o hour_n and_o man_n true_o that_o arch_a type_n of_o perfection_n have_v limit_v these_o motion_n even_o in_o the_o small_a type_n of_o a_o dial_n plane_fw-la as_o shall_v be_v make_v manifest_a in_o thing_n of_o the_o second_o notion_n that_o be_v demonstration_n by_o which_o all_o thing_n shall_v be_v make_v plain_a chap_n ii_o of_o the_o world_n prove_v that_o the_o earth_n possess_v its_o own_o proper_a place_n we_o have_v now_o with_o the_o philosopher_n find_v out_o that_o common_a place_n or_o place_n of_o be_v that_o be_v the_o world_n will_v you_o know_v his_o reason_n it_o be_v render_v quia_fw-la omnia_fw-la reliqua_fw-la mundi_fw-la corpora_fw-la in_fw-la se_fw-la includit_fw-la i_o will_v tell_v you_o of_o no_o plurality_n not_o of_o planetary_a inhabitant_n such_o as_o the_o lunary_n lest_o you_o grabble_v in_o darkness_n in_o expect_v a_o shadow_n from_o the_o light_n without_o interposition_n for_o can_v the_o light_n real_o without_o a_o substance_n be_v its_o own_o gnomon_n sure_o no_o neither_o can_v we_o imagine_v our_o earth_n to_o be_v a_o change_a cynthia_n or_o a_o moon_n to_o give_v light_n to_o the_o lunary_n inhabitant_n for_o if_o our_o earth_n be_v a_o light_n as_o some_o will_v have_v it_o how_o come_v it_o to_o pass_v that_o it_o be_v a_o gnomon_n also_o to_o cast_v a_o shadow_n on_o the_o body_n of_o the_o moon_n far_o less_o than_o itself_o and_o so_o by_o consequence_n a_o great_a light_n can_v seem_v to_o be_v darken_v on_o a_o lesser_a or_o dull_a light_n and_o if_o not_o darken_v no_o shadow_n can_v appear_v but_o from_o this_o common_a place_n the_o world_n with_o all_o its_o part_n shall_v we_o descend_v to_o a_o second_o grave_n of_o distinction_n and_o come_v now_o to_o another_o which_o be_v a_o proprius_fw-la locus_fw-la and_o divide_v it_o into_o proper_a place_n consider_v it_o as_o it_o be_v divide_v into_o coelum_fw-la solum_fw-la salum_n heaven_n earth_n sea_n we_o need_v not_o so_o far_o a_o distinction_n but_o to_o prove_v that_o the_o earth_n be_v in_o its_o own_o proper_a place_n i_o thus_o reason_n proprius_fw-la locus_fw-la est_fw-la qui_fw-la proxime_fw-la nullo_fw-la alio_fw-la interveniente_fw-la continet_fw-la locatum_fw-la but_o it_o be_v certain_a that_o nothing_o can_v come_v so_o between_o the_o earth_n as_o to_o dispossess_v it_o of_o its_o place_n therefore_o it_o possess_v its_o proper_a place_n furthermore_o ad_fw-la quod_fw-la aliquid_fw-la movetur_fw-la id_fw-la est_fw-la ejus_fw-la locus_fw-la to_o what_o any_o thing_n move_v that_o be_v its_o place_n but_o the_o earth_n move_v not_o to_o any_o other_o place_n as_o be_v stable_n in_o its_o own_o proper_a place_n and_o this_o proper_a place_n be_v the_o terminus_fw-la ad_fw-la quem_fw-la to_o which_o as_o the_o place_n of_o their_o rest_n all_o heavy_a thing_n tend_v in_fw-la quo_fw-la motus_fw-la terminantur_fw-la in_o which_o their_o motion_n be_v end_v chap_n iii_o show_v how_o the_o earth_n be_v to_o be_v understand_v to_o be_v the_o centre_n a_o centre_n be_v either_o to_o be_v understand_v geometrical_o or_o optical_o either_o as_o it_o be_v a_o point_n or_o seem_v a_o point_n if_o it_o be_v a_o point_n it_o be_v conceive_v to_o be_v either_o a_o centre_n of_o magnitude_n or_o a_o centre_n of_o

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 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