Selected quad for the lemma: end_n

Word A	Word B	Word C	Word D	Occurrence	Frequency Band	MI	MI Band	Prominent
end_n	draw_v	line_n	perpendicular_a	3,095	5	14.0786	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

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 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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 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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

elevation_n or_o great_a or_o lesser_a if_o the_o ark_n be_v equal_a to_o the_o compliment_n of_o the_o pole_n elevation_n by_o it_o be_v a_o token_n the_o plane_n be_v oblique_a under_o the_o meridian_n to_o be_v incline_v unto_o the_o pole_n in_o that_o case_n the_o meridian_n of_o the_o place_n and_o of_o the_o plane_n and_o also_o the_o axis_n do_v concur_v in_o the_o same_o line_n g_o l_o if_o the_o plane_n be_v suppose_v to_o fall_v in_o the_o same_o great_a circle_n kn_o but_o if_o the_o plane_n be_v not_o suppose_v but_o in_o some_o parallel_n of_o the_o same_o and_o the_o axis_n be_v somewhat_o carry_v away_o as_o necessary_o it_o be_v do_v if_o the_o sciotericall_a be_v absolve_v the_o meridian_n of_o the_o plane_n and_o place_n be_v two_o line_n parallel_a between_o themselves_o and_o be_v mutual_o join_v together_o according_a to_o the_o difference_n of_o longitude_n of_o the_o place_n and_o of_o the_o plane_n which_o difference_n be_v according_a to_o the_o angle_n hgc_o which_o be_v the_o compliment_n of_o the_o angle_n bnk_o late_o find_v because_o the_o angle_n kgh_o be_v right_a by_o 57_o p._n 1._o yea_o forasmuch_o as_o the_o meridian_n of_o the_o plane_n may_v go_v by_o the_o pole_n of_o the_o plane_n but_o concur_v at_o g_o or_o n_o be_v equal_a to_o two_o right_a by_o 20_o p._n 1._o example_n let_v the_o plane_n meridional_a decline_v to_o the_o right_a hand_n 29_o de_fw-fr 59_o m._n incline_v towards_o the_o pole_n arctic_a 23_o de_fw-fr 3_o m._n the_o elevation_n of_o the_o pole_n 49_o de_fw-fr 35_o m._n and_o there_o be_v to_o be_v seek_v in_o the_o same_o the_o meridian_n of_o the_o place_n and_o the_o plane_n and_o the_o elevation_n of_o the_o pole_n or_o axis_n above_o the_o plane_n the_o calculation_n shall_v be_v thus_o to_o 67874_o the_o tangent_fw-la of_o the_o ark_n kn_o the_o distance_n of_o the_o meridian_n of_o the_o place_n from_o the_o vertical_a of_o the_o plane_n 34_o de_fw-fr 10_o m._n per_fw-la axe_n 2_o the_o sine_fw-la of_o the_o ark_n nc_o 49de_fw-la 35_o m._n who_o compliment_n be_v the_o ark_n bn_o 40de_v 25_o m_o per_fw-la axi._n 4._o to_o 60388_o the_o sine_fw-la of_o the_o angle_n bnk_o 37d_o 9m_fw-la who_o compliment_n be_v the_o angle_n hnc_fw-la or_o hgc_o 52_o de_fw-fr 51._o m._n the_o difference_n of_o the_o longitude_n of_o the_o plane_n from_o the_o longitude_n of_o the_o place_n or_o the_o distance_n of_o the_o meridians_fw-la of_o the_o place_n and_o plane_fw-la therefore_o let_v the_o horizon_n of_o the_o place_n be_v lc_o the_o vertical_a of_o the_o plane_n kl_o the_o circle_n of_o the_o plane_n of_o the_o horizon_n knc_o in_o which_o there_o be_v number_v from_o k_o towards_o c_o 34_o de_fw-la 10m_fw-la and_o at_o the_o term_n of_o the_o numeration_n n_o draw_v the_o right_a line_n l_o n_o e_o which_o shall_v be_v the_o meridian_n of_o the_o plane_n and_o place_n if_o the_o centre_n of_o the_o scioteric_a l_o or_o f_o be_v take_v for_o the_o centre_n of_o the_o world_n and_o the_o right_a line_n l_o n_o f_o for_o the_o axis_n but_o because_o in_o the_o perfection_n of_o the_o dial_n ig_o remain_v the_o axis_n with_o e_o the_o centre_n of_o the_o world_n not_o in_o the_o right_a line_n l_o n_o f_o but_o above_o the_o same_o with_o prop_n at_o pleasure_n but_o notwithstanding_o it_o be_v raise_v equal_a in_o height_n with_o ei_o and_o og_o and_o moreover_o the_o plane_n be_v somewhat_o withdraw_v from_o the_o axis_fw-la of_o the_o world_n therefore_o the_o line_n l_o n_o f_o be_v now_o not_o altogether_o the_o meridian_n of_o the_o place_n but_o only_o the_o meridian_n of_o the_o plane_n or_o as_o vulgar_o they_o speak_v the_o substilar_a but_o you_o may_v find_v the_o meridian_n of_o the_o place_n thus_o draw_v ih_o at_o right_a angle_n to_o the_o meridian_n of_o the_o plane_n which_o they_o vulgar_o call_v the_o contingence_n to_o the_o common_a section_n of_o the_o equator_n which_o in_o the_o plane_n let_v e_o the_o centre_n of_o the_o world_n be_v set_v from_o the_o axis_fw-la ig_o in_o the_o meridian_n of_o the_o plane_n l_o n_o f._n then_o to_o the_o centre_n e_o consist_v in_o the_o line_n l_o n_o e_o le_z the_o circle_n of_o the_o equator_n fk_o be_v describe_v and_o in_o the_o same_o towards_o the_o east_n because_o the_o horizon_n of_o the_o plane_n be_v more_o easterly_a than_o the_o horizon_n of_o the_o place_n and_o moreover_o the_o beam_n be_v cast_v soon_o or_o late_a upon_o the_o meridian_n of_o the_o plane_n than_o the_o place_n let_v there_o be_v number_v the_o difference_n of_o longitude_n of_o the_o place_n and_o plane_fw-la 52_o de_fw-la 51_o m._n and_o by_o k_o the_o end_n of_o the_o numeration_n let_v a_o right_a line_n be_v draw_v as_o it_o be_v the_o certain_a beam_n of_o the_o equator_n ekh_o which_o where_o it_o touch_v the_o common_a section_n of_o the_o equator_n with_o the_o plane_n to_o wit_n the_o right_a line_n fh_o by_o that_o point_n let_v c_o the_o meridian_n of_o the_o place_n be_v draw_v perpendicular_a the_o second_o case_n of_o the_o three_o problem_n of_o pitiscus_n his_o liber_fw-la gnomonicorum_fw-la sivero_fw-la arcu_fw-la bn_o repertus_fw-la fuerit_fw-la etc._n etc._n but_o if_o the_o ark_n bn_o shall_v be_v find_v less_o than_o the_o compliment_n of_o the_o pole_n elevation_n it_o be_v a_o sign_n the_o plane_n do_v consist_v on_o this_o side_n the_o pole_n arctic_a and_o moreover_o above_o such_o a_o plane_n not_o the_o pole_n arctic_a but_o the_o pole_n antarctic_a shall_v be_v extol_v to_o such_o a_o angle_n as_o ilm_n be_v who_o measure_n be_v the_o ark_n im_o to_o which_o out_o of_o the_o doctrine_n of_o opposite_n the_o ark_n go_o be_v equal_a which_o you_o may_v certain_o find_v together_o with_o the_o ark_n no_o thus_o as_o mog_o the_o right_a angle_n to_o ng_z the_o difference_n between_o bn_o and_o bg_o so_o ong_o the_o angle_n before_o find_v to_o og_o per_fw-la axi._n 3._o as_o the_o tangent_fw-la ong_o to_o radius_fw-la so_o the_o tangent_fw-la og_o to_o the_o sine_fw-la o_o n_o by_o axi._n 2._o example_n let_v the_o plane_n be_v meridional_a decline_v to_o the_o right_a hand_n 34_o de_fw-fr 30_o m._n incline_v towards_o the_o pole_n arctic_a 16_o de_fw-fr 10_o m._n and_o again_o let_v the_o elevation_n of_o the_o pole_n be_v 49_o de_fw-fr 35_o m._n and_o there_o be_v seek_v the_o meridian_n of_o the_o place_n the_o longitude_n of_o the_o country_n the_o meridian_n of_o the_o plane_n the_o longitude_n of_o the_o plane_n the_o elevation_n of_o the_o pole_n above_o the_o plane_n the_o calculation_n 1._o as_o bf_o radius_fw-la 100000_o to_o fc_fw-la tangent_fw-la compliment_n of_o declination_n 55_o de_fw-fr 30_o m._n 14550_o so_o 27843_o the_o sine_fw-la of_o the_o inclination_n 16_o de_fw-fr 10_o m._n to_o 40511_o the_o tangent_fw-la of_o k_n n_n 22_o de_fw-la 31_o 3_o m._n the_o distance_n of_o the_o meridian_n of_o the_o place_n from_o the_o vertical_a of_o the_o plane_n per_fw-la axi._n 2._o the_o sine_fw-la of_o the_o ark_n n_o c_o 62_o de_fw-la 532_o 3_o m._n who_o compliment_n be_v b_o n_o 27_o de_fw-la 61_o 3_o m._n by_o which_o subtract_v from_o bg_o the_o compliment_n of_o the_o pole_n elevation_n 40_o de_fw-fr 25_o m._n there_o be_v remain_v the_o ark_n n_o g_o 13_o de_fw-la 182_o 3_o m._n by_o axi._n 4._o to_o 61108_o the_o sine_fw-la of_o the_o angle_n b_o n_o k_o or_o o_o n_o g_o 37d_o 40_o m._n per_fw-la axi._n 3._o and_o comp._n 1._o to_o 14069_o the_o sine_fw-la of_o the_o arch_n og_o the_o distance_n of_o the_o axis_fw-la gl_o from_o the_o meridian_n of_o the_o plane_n ol_o 8de_n 51_o 3m_n by_o axe_n 3._o to_o 18410_o the_o sine_fw-la of_o the_o arch_n n_o o_o the_o distance_n of_o the_o meridian_n of_o the_o plane_n ol_o from_o the_o meridian_n of_o the_o place_n n_o l_o 30_o deg._n 36½_n m_o by_o axi._n 2._o the_o calculation_n be_v absolve_v let_v there_o be_v draw_v the_o horizon_n of_o the_o place_n ac_o second_o the_o vertical_a of_o the_o plane_n bq_o three_o the_o horizon_n of_o the_o plane_n abcq_o in_o who_o quadrant_n aq_o to_o wit_n according_a to_o the_o pole_n antartique_fw-la which_o alone_o appear_v above_o such_o a_o plane_n first_o let_v be_v number_v the_o distance_n of_o the_o meridian_n of_o the_o place_n from_o the_o vertical_a of_o the_o plane_n 22_o de_fw-la 3_o m._n and_o by_o the_o end_n of_o the_o numeration_n at_o p_o let_v the_o meridian_n of_o the_o plane_n lp_o be_v draw_v then_o from_o the_o point_n p_o let_v the_o distance_n of_o the_o meridian_n of_o the_o plane_n from_o the_o meridian_n of_o the_o place_n be_v number_v by_o the_o term_n of_o the_o numeration_n m_o let_v the_o meridian_n of_o the_o plane_n lm_o be_v draw_v final_o

0_o 11_o 1_o 59_o 43_o 56_o 34_o 48_o 12_o 36_o 58_o 25_o 40_o 17_o 6_o 13_o 52_o 10_o 2_o 53_o 45_o 50_o 55_o 43_o 12_o 32_o 37_o 21_o 51_o 13_o 38_o 10_o 30_o 9_o 3_o 45_o 42_o 43_o 6_o 36_o 0_o 26_o 7_o 15_o 58_o 8_o 12_o 5_o 15_o 8_o 4_o 36_o 41_o 34_o 13_o 27_o 31_o 18_o 8_o 8_o 33_o 1_o 15_o  _fw-fr  _fw-fr 7_o 5_o 27_o 17_o 24_o 56_o 18_o 18_o 9_o 17_o 0_o 6_o  _fw-fr  _fw-fr  _fw-fr  _fw-fr 6_o 6_o 18_o 11_o 15_o 40_o 9_o 0_o  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr 5_o 7_o 9_o 32_o 6_o 50_o  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr 11_o 37_o 4_o 8_o 1_o 32_o  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr 21_o 40_o this_o table_n be_v in_o mr._n gunter_n book_n page_n 240_o which_o if_o you_o desire_v to_o have_v the_o point_n of_o the_o equinoctial_a for_o a_o horizontal_a plane_n on_o the_o hour_n of_o 12_o enter_v the_o table_n of_o shadow_n with_o 38_o de_fw-fr 30_o m._n and_o you_o shall_v find_v the_o length_n of_o the_o shadow_n to_o be_v 15_o part_n 5_o m._n of_o the_o length_n of_o the_o style_n divide_v into_o 12_o which_o prick_v down_o on_o the_o line_n of_o 12_o for_o the_o equinoctial_a point_n from_o the_o foot_n of_o the_o style_n so_o if_o i_o desire_v the_o point_n of_o the_o tropic_a of_o cancer_n i_o find_v by_o this_o table_n that_o at_o 12_o of_o the_o clock_n the_o sun_n be_v 62_o de_fw-la high_a with_o which_o i_o enter_v the_o table_n of_o shadow_n find_v the_o length_n of_o the_o shadow_n which_o i_o prick_v down_o on_o the_o 12_o a_o clock_n line_n for_o the_o point_n of_o the_o tropic_a of_o cancer_n at_o the_o hour_n of_o 12._o if_o for_o the_o hour_n of_o 1_o i_o desire_v the_o point_n through_o which_o the_o parallel_n must_v pass_v look_v for_o the_o hour_n of_o 1_o and_o 11_o in_o this_o last_o table_n under_o cancer_n and_o i_o find_v the_o sun_n to_o have_v the_o height_n of_o 59_o de_fw-fr 43_o m._n with_o which_o i_o enter_v the_o table_n of_o shadow_n and_o prick_v down_o the_o length_n thereof_o from_o the_o bottom_n of_o the_o style_n reach_v till_o the_o other_o foot_n of_o the_o compass_n fall_v on_o the_o hour_n for_o which_o it_o be_v intend_v do_v so_o in_o all_o the_o other_o hour_n till_o you_o have_v prick_v down_o the_o point_n of_o the_o parallel_n of_o declination_n through_o which_o point_n they_o must_v be_v draw_v hyperbolical_o proceed_v thus_o in_o the_o make_n of_o a_o horizontal_a dial_n but_o if_o it_o be_v a_o direct_a vertical_a dial_n you_o shall_v then_o take_v the_o length_n of_o the_o vertical_a shadow_n out_o of_o the_o say_a table_n or_o work_v it_o as_o a_o horizontal_a plane_n only_o account_v the_o compliment_n of_o the_o elevation_n in_o stead_n of_o the_o whole_a elevation_n for_o a_o decline_a plane_n you_o may_v consider_v it_o as_o a_o vertical_a direct_v in_o some_o other_o place_n and_o have_v find_v out_o the_o equator_n of_o the_o plane_n and_o the_o substyle_n you_o may_v proceed_v in_o the_o same_o manner_n from_o the_o foot_n of_o the_o style_n account_v where_o the_o style_n stand_v to_o be_v no_o other_o way_n than_o the_o meridian_n line_n or_o line_n of_o 12_o in_o a_o horizon_n who_o pole_n be_v elevate_v according_a to_o the_o compliment_n height_n of_o the_o style_n above_o the_o substyle_n and_o so_o prick_v down_o the_o length_n of_o the_o shadow_n from_o the_o foot_n of_o the_o style_n on_o every_o one_o of_o the_o hour_n line_n as_o if_o it_o be_v a_o horizontal_a or_o vertical_a plane_n but_o in_o this_o you_o must_v be_v wary_a remember_v that_o you_o have_v the_o height_n of_o the_o sun_n calculate_v for_o every_o hour_n of_o that_o latitude_n in_o the_o entrance_n of_o the_o 12_o sign_n in_o that_o place_n where_o your_o plane_n be_v a_o horizontal_a plane_n or_o otherways_o by_o consider_v of_o it_o as_o a_o horizontal_a or_o verricallplane_v in_o another_o latitude_n for_o the_o azimuth_n or_o vertical_a circle_n show_v one_o what_o point_n of_o the_o compass_n the_o sun_n be_v in_o every_o hour_n of_o the_o day_n it_o be_v perform_v with_o a_o great_a deal_n of_o facility_n if_o first_o when_o the_o sun_n be_v in_o the_o equator_n we_o do_v know_v by_o the_o last_o table_n of_o the_o height_n of_o the_o sun_n for_o every_o hour_n of_o the_o day_n and_o by_o his_o meridian_n altitude_n with_o the_o help_n of_o the_o table_n of_o shadow_n find_v out_o the_o equinoctial_a line_n whether_o it_o be_v a_o horizontal_a or_o upright_a direct_a plane_n for_o have_v draw_v that_o line_n at_o right_a angle_n with_o the_o meridian_n and_o have_v the_o place_n of_o the_o style_n and_o length_n thereof_o in_o part_n and_o the_o part_n of_o shadow_n to_o all_o altitude_n of_o the_o sun_n be_v prick_v down_o from_o the_o foot_n of_o the_o style_n on_o the_o equinoctial_a line_n through_o each_o of_o those_o point_n draw_v parallel_a line_n to_o the_o meridian_n or_o 12_o a_o clock_n line_n on_o each_o side_n which_o shall_v be_v the_o azimuth_n which_o you_o must_v have_v a_o care_n how_o you_o denominate_v according_a to_o the_o quarter_n of_o heaven_n in_o which_o the_o sun_n be_v in_o for_o if_o the_o sun_n be_v in_o the_o easterly_a point_n the_o azimuth_n must_v be_v on_o the_o western_a side_n of_o the_o plane_n so_o also_o the_o morning_n hour_n must_v be_v on_o the_o opposite_a side_n there_o be_v many_o other_o astronomical_a conclusion_n that_o be_v use_v to_o be_v put_v upon_o plane_n as_o the_o diurnal_a arch_n show_v the_o length_n of_o the_o day_n and_o night_n as_o also_o the_o jewish_a or_o old_a unequal_a hour_n together_o with_o the_o circle_n of_o position_n which_o with_o the_o meridian_n and_o horizon_n distinguish_v the_o upper_a hemisphere_n into_o 6_o part_n common_o call_v the_o house_n of_o heaven_n which_o if_o this_o i_o have_v write_v beget_v any_o desire_n of_o the_o reader_n i_o shall_v endeavour_v to_o enlarge_v myself_o much_o more_o in_o show_v a_o demonstrative_a way_n in_o these_o particular_n i_o have_v last_o insist_v upon_o i_o may_v hear_v also_o show_v you_o the_o exceed_a use_n of_o the_o table_n of_o right_n and_o verse_v shadow_n in_o the_o take_n of_o height_n of_o building_n as_o it_o may_v very_o well_o appear_v in_o the_o several_a use_n of_o the_o quadrant_a in_o diggs_n his_o pantometria_fw-la and_o in_o mr._n gunter_n quadrant_n have_v the_o part_n of_o right_a and_o verse_v shadow_n graduate_v on_o they_o to_o which_o book_n i_o refer_v you_o chap_n xiv_o show_v the_o draw_n of_o the_o ceiling_n dial_n it_o be_v a_o axiom_n pronounce_v long_o since_o by_o those_o who_o have_v write_v of_o optical_a conceit_n of_o light_n and_o shadow_n that_o omnis_fw-la reflectio_fw-la luminis_fw-la est_fw-la secundum_fw-la lineas_fw-la sensibiles_fw-la latitudinem_fw-la habentes_fw-la and_o it_o have_v with_o as_o great_a reason_n be_v pronounce_v by_o geometrician_n that_o the_o angle_n of_o incidence_n and_o reflection_n be_v all_o one_o as_o appear_v to_o we_o by_o euclides_n catoptriques_n and_o on_o this_o foundation_n be_v this_o conceit_n of_o which_o we_o be_v now_o speak_v wherefore_o because_o the_o direct_a beam_n can_v fall_v on_o the_o face_n of_o this_o plane_n we_o must_v by_o help_n of_o a_o piece_n of_o glass_n apt_a to_o receive_v and_o reflect_v the_o light_n place_v somewhere_o horizontal_o in_o a_o window_n proceed_v to_o the_o work_n which_o indeed_o be_v no_o other_o than_o a_o horizontal_a dial_n reverse_v to_o which_o require_v a_o meridian_n line_n which_o you_o must_v endeavour_v to_o draw_v and_o find_v according_a as_o you_o be_v before_o teach_v or_o by_o the_o help_n of_o the_o meridian_n altitude_n of_o the_o sun_n your_o glass_n be_v fix_v mark_v the_o spot_n that_o reflect_v upon_o the_o ceiling_n just_a at_o 12_o a_o clock_n make_v that_o one_o point_n and_o for_o the_o other_o point_n through_o which_o you_o must_v draw_v your_o meridian_n line_n you_o may_v find_v by_o hold_v up_o a_o thread_n and_o plummet_n till_o the_o plummet_n fall_v perpendicular_a on_o the_o glass_n and_o at_o the_o other_o end_n of_o the_o line_n hold_v on_o the_o ceiling_n make_v another_o mark_n through_o both_o which_o draw_v the_o meridian_n line_n now_o for_o so_o much_o as_o the_o centre_n of_o the_o dial_n be_v a_o point_n without_o and_o the_o distance_n between_o the_o glass_n and_o the_o ceiling_n be_v to_o be_v consider_v as_o the_o height_n of_o the_o style_n the_o glass_n itself_o represent_v the_o centre_n of_o the_o world_n or_o the_o very_a apex_n of_o the_o style_n we_o must_v find_v out_o those_o two_o tangent_n at_o right_a angle_n with_o the_o

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 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