shall_v here_o begin_v i._o upon_o a_o line_n give_v ab_fw-la to_o erect_v cd_o a_o perpendicular_a if_o there_o be_v a_o point_n as_o c_z give_v in_o ab_fw-la the_o line_n on_o which_o the_o perpendicular_a be_v to_o fall_v mark_v on_o both_o side_n of_o the_o say_a point_n with_o your_o compass_n the_o equidistant_a point_n m_o and_o n_o then_o open_v they_o at_o pleasure_n put_v one_o foot_n on_o m_n and_o describe_v the_o blind_a arch_n of_o and_o put_v the_o other_o foot_n in_o n_o describe_v the_o blind_a arch_n gh_o and_o the_o fair_a line_n from_o d_o their_z intersection_n to_o the_o point_n c_o will_v be_v the_o perpendicular_a require_v now_o if_o you_o have_v no_o point_n assign_v in_o the_o say_a line_n ab_fw-la to_o terminate_v your_o perpendicular_a by_o take_v two_o point_n there_o at_o pleasure_n as_o suppose_v m_n and_o n_o and_o open_v how_o you_o will_v your_o compass_n describe_v the_o blind_a arch_n of_o and_o gh_v above_o your_o line_n and_o open_v and_o qr_n below_o it_o and_o the_o intersection_n of_o these_o arch_n to_o wit_n d_o and_o saint_n will_v be_v two_o point_n to_o draw_v your_o perpendicular_a by_o ii_o upon_o c_o the_o end_n of_o ac_fw-la a_o give_v line_n to_o draw_v dc_o a_o perpendicular_a open_v your_o compass_n at_o a_o convenient_a width_n and_o put_v one_o foot_n on_o c_o let_v the_o other_o within_o reach_n of_o ac_fw-la mark_v any_o where_o as_o at_o f_o then_o touch_v or_o cut_v from_o thence_o the_o say_v ac_fw-la with_o the_o move_a foot_n of_o your_o compass_n at_o suppose_v e_o and_o describe_v on_o the_o other_o side_n of_o f_o the_o blind_a arch_n gh_o lay_v your_o ruler_n on_o fe_o and_o it_o will_v cut_v the_o say_a arch_n at_o suppose_v d_o so_o that_o dc_o will_v be_v the_o require_v perpendicular_a iii_o a_o line_n ab_fw-la be_v give_v how_o to_o draw_v dg_n a_o parallel_n to_o it_o have_v take_v two_o point_n in_o the_o say_a line_n as_o suppose_v a_o and_o b_o open_v your_o compass_n at_o what_o width_n you_o please_v and_o put_v one_o foot_n on_o a_o describe_v the_o blind_a arch_n cde_v and_o put_v one_o foot_n on_o b_o describe_v the_o blind_a arch_n fgh_o then_o if_o you_o lay_v your_o ruler_n on_o the_o high_a part_n or_o great_a extuberancy_n of_o the_o say_a arch_n to_o wit_n on_o the_o point_n d_o and_o g_o the_o line_n so_o draw_v will_v be_v the_o require_v parallel_n iv._o to_o describe_v a_o true_a square_n ab_fw-la be_v a_o line_n as_o long_o as_o the_o side_n of_o the_o square_a you_o design_v erect_v on_o the_o end_n a_o the_o perpendicular_a da_fw-la of_o the_o former_a length_n then_o take_v between_o your_o compass_n the_o say_v ab_fw-la put_v one_o foot_n on_o d_o and_o describe_v the_o blind_a arch_n of_o and_o again_o put_v one_o foot_n on_o b_o describe_z the_o blind_a arch_n gh_o to_o cut_v of_o and_o if_o from_o their_o intersection_n c_o you_o draw_v the_o fair_a line_n cb_n and_o cd_o you_o have_v a_o true_a square_n v._o to_o draw_v a_o oblong_a or_o as_o they_o commonby_o call_v it_o a_o long_a square_n ab_fw-la be_v the_o long_a side_n of_o this_o square_a erect_v on_o the_o end_n a_o the_o perpedicular_a da_fw-la of_o the_o length_n of_o the_o short_a then_o take_v between_o your_o compass_n the_o line_n ab_fw-la put_v one_o foot_n on_o d_o and_o describe_v the_o blind_a arch_n of_o and_o take_v between_o your_o compass_n the_o line_n ad_fw-la describe_v the_o blind_a arch_n gh_o to_o cut_v the_o say_v of_o and_o if_o from_o their_o intersection_n c_o you_o draw_v the_o fair_a line_n cb_n and_o cd_o you_o have_v the_o square_a you_o design_n vi_o to_o describe_v a_o equilateral_a triangle_n or_o a_o isosceles_a open_v your_o compass_n at_o ab_fw-la be_v the_o side_n of_o the_o triangle_n you_o design_n and_o put_v one_o foot_n on_o a_o describe_v the_o blind_a arch_n of_o and_o again_o put_v one_o foot_n on_o b_o describe_z the_o blind_a arch_n gh_o to_o cut_v the_o say_v of_o and_o if_o from_o their_o intersection_n c_o you_o draw_v the_o fair_a line_n ca_n and_o cb_n you_o have_v a_o true_a equilateral_a triangle_n nor_o be_v there_o any_o difference_n in_o the_o description_n of_o the_o isosceles_a asb_n for_o the_o only_a difference_n between_o they_o be_v that_o the_o side_n as_o and_o b_n of_o the_o isosceles_a be_v long_o or_o if_o you_o please_v they_o may_v be_v short_a than_o the_o base_a ab_fw-la whenas_o all_o three_o side_n be_v equal_a in_o the_o equilateral_a triangle_n vii_o to_o make_v a_o triangle_n of_o three_o give_v line_n suppose_v the_o first_o line_n give_fw-mi be_fw-mi ab_fw-la the_o second_o ac_fw-la the_o three_o bc_n and_o that_o you_o be_v to_o make_v a_o triangle_n of_o they_o let_v ab_fw-la be_v the_o base_a and_o take_v the_o give_v line_n ac_fw-la between_o your_o compass_n put_v one_o foot_n on_o the_o base_a at_o a_o and_o describe_v the_o blind_a arch_n of_o then_o take_v the_o give_v line_n bc_n between_o your_o compass_n put_v one_o foot_n on_o the_o base_a at_o b_o and_o describe_v the_o blind_a arch_n gh_o to_o cut_v the_o say_a arch_n of_o and_o if_o you_o draw_v line_n from_o their_o intersection_n at_o c_o to_o a_o and_o b_o on_o the_o aforesaid_a base_a you_o have_v your_o intent_n viii_o to_o describe_v a_o oval_a cross_a rp_n at_o right_a angle_n with_o in_o and_o take_v with_o your_o compass_n on_o the_o say_a line_n from_o the_o intersection_n o_o equal_a distance_n to_o wit_n oa_n ob_fw-la oc_fw-la and_o odd_a and_o draw_v through_o the_o point_n c_o the_o line_n ak_v and_o bh_n each_o equal_a to_o twice_o ac_fw-la as_o also_o throu_fw-fr '_o d_o the_o line_n a_o and_o bl_n each_o equal_a to_o twice_o bc_n than_o a_o and_o b_o being_n centre_n describe_v the_o arch_n kpm_v and_o hlr_n in_o like_a manner_n c_o and_o d_o being_z centre_n describe_v the_o arch_n hik_fw-mi and_o lmn_n and_o the_o figure_n thus_o draw_v will_v be_v a_o perfect_a oval_n sector_n so_o much_o for_o the_o geometrical_a problem_n necessary_a for_o dial_v and_o as_o for_o the_o instrumental_a one_o i._n e._n those_o perform_v by_o the_o sector_n they_o be_v as_o i_o may_v say_v of_o two_o sort_n some_o belong_v to_o one_o side_n of_o it_o and_o some_o to_o the_o other_o for_o the_o side_n mark_v with_o l_o be_v divide_v into_o 100_o equal_a part_n and_o call_v the_o line_n of_o line_n and_o the_o side_n mark_v with_o saint_n the_o line_n of_o sines_n first_o then_o of_o the_o line_n of_o line_n which_o by_o the_o way_n though_o it_o be_v divide_v as_o i_o say_v but_o into_o 100_o part_n may_v yet_o stand_v for_o 1000_o if_o you_o fancy_v every_o 10_o division_n a_o line_n of_o 100_o part_n and_o in_o like_a manner_n it_o will_v stand_v for_o 10000_o part_n if_o every_o division_n be_v deem_v 100_o therefore_o a_o line_n v._n g._n of_o 75_o equal_a part_n may_v be_v express_v by_o 75_o of_o those_o division_n or_o by_o 7½_n or_o by_o ¾_n the_o use_n of_o the_o line_n of_o line_n mark_v with_o l._n i._o to_o divide_v a_o line_n into_o any_o number_n of_o equal_a part_n suppose_v your_o line_n be_v to_o be_v divide_v in_o 23_o equal_a part_n take_v it_o between_o your_o compass_n and_o open_v your_o sector_n place_n one_o foot_n of_o your_o say_a compass_n on_o the_o 23_o division_n of_o the_o sector_n and_o the_o other_o foot_n on_o the_o 23_o over_o against_o it_o and_o the_o distance_n between_o the_o figure_n 1_o and_o 1_o on_o the_o say_a sector_n will_v give_v you_o one_o equal_a division_n of_o your_o line_n and_o the_o distance_n between_o 2_o and_o 2_o will_v give_v you_o two_o equal_a division_n of_o it_o and_o in_o this_o manner_n proceed_v till_o you_o quite_o run_v over_o it_o as_o you_o design_n ii_o to_o find_v the_o proportion_n between_o any_o two_o line_n set_a over_o the_o great_a line_n at_o 100_o and_o 100_o on_o the_o sector_n then_o take_v the_o lesser_a between_o your_o compass_n find_v where_o it_o will_v be_v just_o set_v over_o also_o or_o lie_v parallel_n to_o the_o former_a which_o happen_v suppose_n at_o 50_o and_o 50_o you_o may_v conclude_v that_o the_o proportion_n require_v be_v as_o 100_o to_o 50._o iii_o to_o divide_v a_o line_n as_o any_o other_o line_n propose_v be_v divide_v that_o be_v to_o say_v according_a to_o any_o proportion_n suppose_v you_o see_v a_o line_n contain_v 65_o equal_a part_n of_o the_o sector_n divide_v into_o three_o piece_n the_o first_o contain_v five_o equal_a part_n of_o the_o sector_n the_o other_o fifteen_o so_o that_o the_o last_o must_v be_v 45_o then_o suppose_v you_o will_v divide_v after_o this_o proportion_n another_o line_n contain_v but_o thirteen_o equal_a
as_o this_o small_a bulk_n can_v afford_v but_o free_v also_o from_o the_o usual_a crowd_n of_o town_n and_o place_n very_o often_o neither_o of_o note_n nor_o use_n unless_o for_o distraction_n for_o the_o business_n of_o a_o terrestrial_a globe_n be_v to_o represent_v the_o situation_n of_o famous_a region_n and_o province_n and_o how_o they_o be_v distant_a each_o from_o the_o other_o to_o show_v we_o also_o where_o the_o late_a discovery_n be_v where_o more_o may_v chance_v to_o be_v make_v what_o proportion_n any_o place_n bear_v to_o the_o know_a part_n or_o they_o to_o the_o whole_a terraqueous_a mass_n these_o i_o say_v and_o the_o like_a be_v what_o a_o globe_n be_v proper_o to_o represent_v for_o small_a and_o inconsiderable_a place_n ought_v not_o to_o be_v there_o as_o be_v the_o chief_a object_n of_o chorographical_a and_o topographical_n chart_n to_o which_o the_o curious_a be_v to_o recur_v upon_o occasion_n as_o for_o the_o first_o or_o grand_a division_n of_o this_o globe_n to_o wit_n the_o four_o earth_n quarter_n their_o name_n be_v in_o the_o midst_n of_o they_o in_o remarkable_a capital_a letter_n nor_o be_v there_o any_o trouble_n about_o their_o bound_n after_o that_o that_o join_v europe_n and_o asia_n be_v consider_v for_o bate_v the_o little_a isthmus_n make_v by_o the_o mediterranean_a and_o marerubrum_fw-la which_o contain_v the_o limit_n of_o asia_n and_o africa_n there_o be_v no_o part_n of_o the_o say_a quarter_n which_o be_v not_o surround_v by_o the_o sea_n for_o the_o separation_n then_o or_o boundary_a between_o europe_n and_o asia_n it_o be_v a_o fine_a black_a line_n that_o beginning_n at_o asia_n the_o mouth_n of_o the_o tanais_n run_v up_o the_o stream_n to_o tuia_n situate_v on_o its_o most_o easterly_a flexure_n and_o thence_o go_v to_o the_o near_a bank_n of_o the_o river_n oby_n accompany_v it_o till_o it_o fall_v into_o the_o northern_a ocean_n this_o i_o say_v be_v the_o separation_n draw_v by_o i_o and_o not_o from_o tuia_n to_o the_o mouth_n of_o duina_n at_o archangel_n for_o since_o there_o be_v as_o to_o the_o question_n in_o hand_n different_a and_o various_a opinion_n among_o geographer_n i_o follow_v the_o rather_o this_o division_n than_o any_o other_o since_o it_o contain_v almost_o all_o the_o vast_a dominion_n of_o the_o russian_a emperor_n and_o so_o make_v he_o as_o it_o be_v a_o entire_a european_a monarc_n the_o division_n of_o each_o modern_a country_n from_o the_o other_o which_o other_o have_v all_o their_o name_n on_o they_o in_o small_a capital_a letter_n be_v also_o a_o black_a price_v line_n and_o that_o you_o may_v have_v a_o glimpse_n also_o of_o ancient_a geography_n i_o have_v express_v some_o of_o the_o most_o considerable_a old_a nation_n and_o empire_n by_o prick_n line_n of_o nation_n several_a colour_n as_o the_o direction_n on_o the_o globe_n itself_o show_v you_o to_o amplify_v or_o contract_v their_o bound_n when_o they_o agree_v not_o with_o the_o present_a limit_n but_o as_o for_o city_n and_o town_n there_o be_v as_o i_o say_v but_o very_o few_o of_o any_o sort_n set_v down_o for_o in_o all_o the_o island_n of_o great_a britain_n we_o mention_v but_o london_n and_o edinburgh_n beside_o a_o port_n or_o two_o in_o which_o proportion_n we_o proceed_v all_o along_o thus_o have_v acquaint_v you_o with_o these_o few_o preliminary_n we_o will_v now_o after_o you_o have_v a_o little_a consider_v the_o name_n of_o each_o country_n and_o how_o they_o all_o lie_n from_o your_o zenith_n where_o you_o be_v ever_o to_o suppose_v the_o country_n or_o place_n to_o be_v which_o the_o globe_n be_v make_v for_o i_o say_v we_o will_v now_o after_o you_o have_v a_o little_a consider_v these_o thing_n fall_v upon_o the_o operation_n a_o employment_n common_o much_o more_o divert_v and_o pleasant_a than_o speculation_n operation_n i._n how_o to_o find_v the_o distance_n between_o any_o two_o place_n if_o the_o question_n be_v for_o example_n between_o constantinople_n and_o the_o place_v you_o dwell_v at_o which_o we_o shall_v for_o the_o future_a suppose_v still_o to_o be_v at_o london_n draw_v your_o string_n from_o the_o zenith_n straight_o over_o constantinople_n and_o have_v mount_v your_o bead_n thither_o bring_v it_o to_o the_o meridian_n or_o quadrant_n of_o altitude_n and_o it_o will_v lie_v count_v from_o the_o zenith_n to_o it_o on_o the_o 24_o degree_n or_o thereabouts_o which_o multiply_v by_o 60_o the_o number_n of_o miles_n contain_v according_a to_o the_o common_a account_n in_o each_o degree_n show_v you_o that_o the_o distance_n require_v be_v some_o 1440_o mile_n but_o if_o it_o be_v demand_v how_o far_o it_o be_v from_o constantinople_n to_o tangier_n i._n e._n from_o any_o other_o two_o place_n when_o neither_o lie_n under_o your_o zenith_n then_o take_v a_o pair_n of_o compass_n and_o place_v one_o foot_n on_o the_o first_o town_n and_o the_o other_o foot_n on_o the_o second_o find_v in_o the_o meridian_n aequator_fw-la horizon_n or_o any_o other_o divide_v great_a circle_n the_o number_n of_o degree_n between_o the_o foot_n which_o make_v about_o 31._o amount_n to_o near_o 1860_o mile_n or_o if_o you_o have_v no_o compass_n fix_v the_o loose_a or_o plummet_n end_n of_o your_o string_n with_o your_o finger_n on_o tangier_n and_o draw_v the_o rest_n of_o it_o straight_o over_o constantinople_n place_n there_o the_o bead_n and_o if_o you_o measure_v that_o distance_n in_o any_o of_o the_o say_v divide_v circle_n it_o will_v give_v you_o the_o above_o mention_v degree_n and_o mile_n and_o here_o be_v please_v to_o remember_v that_o to_o free_v you_o from_o multiplication_n miles_n in_o relation_n to_o miles_n i_o have_v order_v a_o little_a table_n to_o be_v place_v in_o the_o vacant_a part_n of_o the_o globe_n towards_o the_o southern_a ocean_n where_o you_o may_v find_v from_o 1._o degree_n to_o 20._o how_o many_o mile_n any_o number_n of_o degree_n give_v but_o if_o your_o question_n contain_v more_o degree_n than_o be_v set_v down_o as_o for_o example_n 31._o you_o be_v only_o to_o add_v 660._o which_o you_o will_v see_v in_o the_o table_n be_v the_o value_n of_o 11._o degree_n to_o 1200_o the_o value_n of_o 20._o and_o the_o sum_n total_a make_v 1860._o mile_n for_o the_o require_a distance_n in_o this_o manner_n you_o must_v operate_v in_o other_o case_n the_o table_n of_o reduction_n be_v to_o be_v in_o the_o follow_a manner_n 1_o 60_o 11_o 660_o 2_o 120_o 12_o 720_o 3_o 180_o 13_o 780_o 4_o 240_o 14_o 840_o 5_o 300_o 15_o 900_o 6_o 360_o 16_o 960_o 7_o 420_o 17_o 1020_o 8_o 480_o 18_o 1080_o 9_o 540_o 19_o 1140_o 10_o 600_o 20_o 1200_o operation_n ii_o how_o to_o find_v the_o latitude_n and_o longitude_n of_o any_o place_n the_o latitude_n of_o a_o place_n be_v its_o near_a distance_n from_o the_o aequator_fw-la it_o if_o therefore_o you_o will_v know_v the_o latitude_n of_o suppose_v constantinople_n draw_v the_o string_n from_o the_o pole_n over_o the_o say_a city_n and_o place_v thereon_o the_o bead_n bring_v it_o to_o the_o gradual_a division_n of_o the_o colurus_n aequinoctiorum_fw-la or_o 6_o a_o clock_n hour_n circle_n and_o it_o will_v lie_v on_o the_o 43_o degree_n and_o about_o 5_o minute_n more_o for_o the_o latitude_n require_v the_o longitude_n of_o a_o place_n be_v the_o number_n of_o degree_n reckon_v be_v eastward_o in_o the_o aequator_fw-la from_o the_o grand_a meridian_n to_o the_o hour_n circle_n or_o particular_a meridian_n that_o pass_v through_o the_o place_n require_v as_o for_o the_o say_v grand_a or_o general_a meridian_n it_o be_v that_o from_o meridian_n whence_o we_o begin_v our_o reckon_a and_o since_o it_o matter_n not_o as_o you_o will_v plain_o see_v in_o the_o memorandum_n of_o the_o three_o or_o follow_a operation_n where_o we_o commence_v to_o wit_n whether_o from_o the_o meridian_n that_o run_v through_o london_n or_o that_o through_o paris_n rome_n or_o any_o other_o place_n if_o people_n be_v acquaint_v with_o it_o before_o hand_n i_o say_v since_o this_o be_v so_o what_o wonder_n be_v it_o there_o be_v by_o reason_n of_o some_o accidental_a propriety_n and_o cause_n infinite_a fit_a place_n if_o geographer_n and_o other_o learned_a man_n quarrel_n in_o the_o affair_n and_o earnest_o strive_v to_o have_v the_o prerogative_n grant_v that_o country_n which_o they_o be_v please_v to_o propose_v of_o all_o place_n the_o hesperides_n azore_n and_o canary_n by_o reason_n meridian_n of_o their_o westerly_a site_n or_o the_o pretend_a non-variation_n of_o the_o needle_n in_o some_o of_o they_o have_v have_v the_o most_o vogue_n but_o since_o each_o of_o the_o say_a place_n make_v not_o one_o but_o many_o isle_n they_o afford_v new_a occasion_n of_o dispute_n for_o among_o the_o hesperides_n or_o isle_n of_o cape_n verd_fw-mi some_o will_v have_v fuego_n to_o
find_v where_o it_o be_v day_n and_o where_o it_o be_v night_n all_o the_o world_n over_o compose_v your_o globe_n and_o all_o people_n that_o live_v in_o the_o illuminate_v hemisphere_n enjoy_v day_n at_o that_o moment_n and_o all_o that_o live_v in_o the_o obscure_a one_o night._n operation_n viii_o to_o know_v where_o at_o that_o moment_n of_o time_n the_o inhabitant_n enjoy_v nothing_o but_o day_n and_o where_o nothing_o but_o night_n as_o also_o when_o the_o day_n and_o night_n will_v be_v thus_o perpetual_a in_o any_o place_n subject_n to_o this_o alteration_n describe_v with_o your_o eye_n a_o imaginary_a circle_n about_o the_o day_n illuminate_v pole_n its_o radius_fw-la be_v the_o distance_n from_o the_o say_a pole_n to_o the_o near_a part_n of_o the_o shade_n of_o extuberancy_n and_o all_o place_n within_o that_o circle_n will_v have_v then_o no_o night_n and_o all_o place_n within_o the_o dark_a circle_n of_o the_o like_o radius_fw-la round_o the_o obscure_v place_n or_o obumbrate_v pole_n will_v have_v then_o no_o day_n now_o if_o you_o desire_v to_o know_v when_o it_o will_v be_v in_o this_o manner_n perpetual_a day_n or_o night_n at_o any_o place_n between_o the_o pole_n and_o the_o polar_a circle_n for_o you_o know_v it_o be_v never_o perpetual_a day_n and_o night_n any_o where_o else_o you_o have_v nothing_o to_o do_v but_o to_o measure_v with_o your_o string_n or_o compass_n the_o distance_n between_o the_o place_n require_v and_o the_o next_o pole_n which_o now_o for_o example_n sake_n we_o will_v suppose_v the_o northern_a pole_n i_o say_v you_o have_v nothing_o to_o do_v but_o to_o measure_v this_o distance_n for_o place_v one_o end_n of_o your_o string_n or_o one_o foot_n of_o your_o compass_n on_o the_o interfection_n of_o the_o meridian_n and_o the_o aequator_fw-la if_o you_o observe_v what_o northern_a parallel_n the_o other_o end_n of_o your_o string_n or_o foot_n of_o the_o compass_n extend_v at_o the_o aforesaid_a distance_n touch_v it_o will_v show_v you_o by_o touch_v v._n g._n the_o parallel_n mark_v with_o the_o 10_o of_o april_n and_o 12_o of_o july_n that_o it_o begin_v to_o be_v on_o the_o say_v 10_o of_o april_n perpetual_a day_n there_o and_o so_o continue_v until_o the_o 12_o of_o july_n now_o if_o you_o measure_v from_o the_o before_o mention_a intersection_n towards_o the_o southern_a pole_n and_o find_v the_o end_n of_o your_o string_n or_o foot_n of_o the_o compass_n to_o touch_v the_o 13_o of_o october_n and_o 9th_o of_o january_n it_o be_v certain_a that_o from_o the_o say_a day_n in_o october_n to_o that_o of_o january_n it_o will_v be_v perpetual_a night_n there_o and_o consequent_o from_o the_o 12_o of_o july_n to_o the_o 13_o of_o october_n the_o day_n and_o night_n succeed_v each_o other_o after_o the_o ordinary_a manner_n operation_n ix_o to_o find_v where_o the_o sun_n be_v rise_v and_o where_o he_o be_v set_v all_o the_o world_n over_o compose_v your_o globe_n and_o have_v consider_v the_o confine_n or_o extremity_n of_o the_o precede_a and_o follow_v shade_n of_o extuberancy_n you_o may_v conclude_v that_o to_o all_o the_o inhabitant_n under_o the_o first_o the_o sun_n be_v rise_v and_o to_o they_o under_o the_o second_o that_o he_o be_v then_o set_v operation_n x._o to_o find_v where_o the_o sun_n be_v vertical_a at_o any_o time_n i._n e._n what_o people_n have_v he_o just_a over_o their_o head_n the_o sun_n be_v always_o vertical_a to_o those_o that_o lie_v in_o the_o middle_n of_o the_o illuminate_v part_n of_o the_o globe_n i._n e._n to_o those_o that_o dwell_v under_o his_o then_o present_a place_n in_o his_o parallel_n therefore_o as_o i_o show_v you_o in_o the_o 11._o first_o section_n if_o you_o compose_v your_o globe_n and_o hold_v up_o your_o string_n against_o the_o sun_n from_o the_o pole_n till_o its_o shade_n pass_v through_o the_o other_o or_o from_o the_o zenith_n till_o it_o pass_v through_o the_o nadir_n it_o will_v cut_v the_o parallel_n of_o the_o day_n at_o the_o sun_n true_a place_n and_o consequent_o show_v you_o who_o they_o be_v that_o have_v he_o then_o just_a over_o their_o head_n which_o happen_v for_o example_n sake_n on_o the_o 10_o of_o april_n about_o our_o 6_o in_o the_o morning_n to_o they_o that_o dwell_v about_o the_o middle_n of_o the_o coast_n of_o malabar_n operation_n xi_o to_o know_v where_o they_o be_v rise_v where_o they_o be_v at_o dinner_n where_o at_o supper_n and_o where_o go_v to_o bed_n all_o over_o the_o world_n this_o operation_n depend_v on_o this_o maxim_n that_o it_o be_v the_o same_o hour_n with_o all_o people_n that_o have_v the_o same_o longitude_n that_o be_v to_o say_v that_o live_v under_o the_o same_o semi-hour_n circle_n or_o semi-meridian_n therefore_o as_o the_o draw_n of_o your_o string_n from_o the_o over_o pole_n over_o half_a the_o illuminate_v part_n of_o the_o globe_n i._n e._n over_o the_o sun_n be_v present_a place_n show_v you_o that_o it_o be_v noon_n or_o dinnertime_n with_o all_o that_o inhabit_v under_o the_o say_a string_n so_o the_o draw_v it_o over_o any_o place_n distant_a 6_o hour_n westward_o i._n e._n over_o so_o many_o over_o hour_n towards_o the_o left_a hand_n from_o the_o vertical_a point_n show_v where_o it_o be_v then_o all_o the_o world_n over_o 6_o in_o the_o morning_n or_o tunc_fw-la to_o rise_v whereas_o have_v you_o draw_v it_o six_o hour_n eastward_o i._n e._n towards_o over_o your_o right-hand_n it_o will_v have_v show_v you_o where_o it_o be_v six_o in_o the_o evening_n or_o suppertime_n and_o four_o hour_n further_o i._n e._n two_o hour_n short_a of_o midnight_n or_o the_o point_n opposite_a to_o noon_n over_o where_o it_o be_v 10_o of_o clock_n or_o bedtime_n operation_n xii_o how_o much_o any_o people_n if_o it_o be_v day_n with_o they_o be_v past_a morning_n or_o want_v of_o evening_n and_o if_o it_o be_v night_n with_o they_o how_o much_o they_o be_v past_a evening_n or_o want_n of_o morning_n if_o the_o place_v you_o propose_v have_v a_o diurnal_a parallel_n that_o run_v over_o it_o then_o see_v what_o point_n of_o the_o say_v parallel_v the_o precede_a shade_n of_o extuberancy_n cut_v and_o if_o you_o count_v the_o hour_n circle_n or_o distance_n in_o time_n between_o the_o say_a point_n and_o the_o propose_a place_n it_o will_v give_v you_o if_o it_o be_v there_o night_n how_o much_o it_o lack_n be_v of_o morning_n and_o the_o distance_n in_o time_n between_o the_o say_a place_n and_o the_o point_v make_v by_o the_o follow_v shade_n of_o extuberancy_n give_v you_o how_o much_o it_o be_v since_o evening_n on_o the_o other_o side_n if_o it_o be_v day_n there_o the_o distance_n between_o the_o say_a place_n and_o point_v make_v by_o the_o precede_a shade_n tell_v you_o how_o long_o it_o be_v since_o morning_n and_o the_o follow_v shade_n how_o long_o it_o be_v since_o evening_n now_o if_o there_o be_v no_o parallel_n that_o run_v over_o or_o near_o your_o say_v propose_v place_n mount_v your_o bead_n to_o it_o and_o move_v your_o say_a bead_n on_o the_o noose_n from_o the_o pole_n it_o will_v describe_v a_o parallel_n and_o then_o you_o may_v operate_v as_o before_o the_o reason_n of_o the_o operation_n be_v this_o the_o shade_n of_o extuberancy_n operation_n get_v every_o hour_n in_o the_o aequator_fw-la as_o you_o see_v 14._o before_o fifteen_o degree_n it_o will_v proceed_v in_o the_o same_o proportion_n on_o all_o parallel_n over_o which_o it_o pass_v therefore_o if_o the_o distance_n between_o any_o point_n in_o the_o aequator_fw-la and_o the_o follow_v shade_n be_v the_o distance_n in_o time_n of_o the_o say_a point_n from_o evening_n or_o sunset_n and_o if_o the_o distance_n there_o between_o any_o point_n and_o the_o precede_a shade_n be_v the_o distance_n of_o the_o say_a point_n from_o morning_n or_o sunrising_n it_o follow_v that_o the_o distance_n between_o any_o point_n in_o a_o aequinoctial_a parallel_n and_o these_o two_o shade_n of_o extuberancy_n that_o cut_v it_o must_v be_v also_o it_o be_v true_a measure_n or_o distance_n in_o time_n both_o from_o morning_n and_o evening_n operation_n xiii_o to_o find_v the_o sun_n height_n in_o any_o place_n where_o the_o globe_n show_v it_o be_v day_n or_o his_o depression_n where_o it_o show_v it_o be_v night_n as_o also_o what_o people_n throughout_o the_o world_n see_v the_o sun_n at_o the_o same_o height_n suppose_v on_o the_o 10_o of_o april_n have_v compose_v your_o globe_n and_o place_n find_v it_o about_o 6_o in_o the_o morning_n with_o you_o you_o shall_v desire_v to_o know_v how_o high_a the_o sun_n be_v at_o rome_n as_o also_o all_o the_o people_n that_o then_o see_v he_o at_o that_o or_o any_o other_o determine_v height_n measure_v by_o your_o string_n or_o compass_n the_o near_a
must_v know_v ourselves_o and_o so_o be_v all_o other_o people_n and_o place_n of_o the_o world_n that_o be_v in_o neither_o of_o the_o two_o former_a one_o for_o take_v any_o point_n not_o under_o the_o pole_n or_o the_o aequator_fw-la for_o your_o zenith_n and_o it_o will_v be_v impossible_a to_o describe_v a_o horizon_n or_o circle_n 90_o degree_n from_o it_o which_o cut_v not_o the_o aequator_fw-la and_o all_o its_o parallel_n oblique_o it_o be_v this_o obliquity_n then_o that_o give_v name_n to_o the_o position_n and_o it_o be_v this_o that_o make_v the_o great_a inequality_n in_o day_n and_o night_n for_o if_o the_o horizon_n have_v a_o great_a portion_n of_o one_o diurnal_a parallel_n above_o it_o than_o of_o another_o as_o it_o must_v needs_o have_v by_o its_o slant_v it_o will_v follow_v when_o the_o sun_n be_v in_o such_o a_o parallel_n that_o the_o day_n will_v be_v long_o than_o when_o the_o portion_n be_v less_o and_o consequent_o since_o more_o of_o one_o parallel_n be_v under_o the_o horizon_n than_o of_o another_o that_o one_o night_n be_v short_a than_o another_o and_o see_v the_o near_a the_o pole_n be_v to_o the_o horizon_n the_o more_o equal_o it_o cut_v the_o say_v parallel_n and_o the_o further_a it_o be_v from_o it_o the_o great_a the_o inequality_n happen_v to_o be_v it_o be_v no_o wonder_n that_o by_o how_o much_o the_o great_a the_o elevation_n be_v by_o so_o much_o the_o long_o the_o day_n be_v and_o when_o the_o whole_a horizon_n fall_v below_o some_o of_o the_o parallel_n that_o then_o during_o the_o sun_n abode_n there_o the_o inhabitant_n have_v no_o night_n at_o all_o therefore_o it_o follow_v that_o if_o a_o star_n be_v near_o the_o pole_n than_o be_v the_o latitude_n of_o a_o place_n it_o can_v never_o set_v in_o that_o place_n presence_n yet_o notwithstanding_o this_o strange_a inequality_n and_o disproportion_n of_o day_n and_o night_n all_o people_n in_o all_o position_n by_o that_o time_n the_o sun_n finish_v his_o annual_a course_n make_v they_o even_o and_o thereby_o enjoy_v a_o equal_a share_n of_o both_o for_o if_o under_o the_o pole_n the_o sun_n be_v six_o month_n above_o the_o horizon_n he_o be_v as_o long_o under_o it_o and_o if_o we_o and_o the_o rest_n that_o live_v in_o the_o oblique_a sphere_n have_v summer_n day_n of_o a_o mighty_a length_n our_o winter_n night_n be_v of_o the_o same_o dimension_n therefore_o it_o follow_v that_o at_o the_o long_o run_v the_o inhabitant_n under_o the_o aequator_fw-la or_o in_o the_o right_a sphere_n who_o have_v always_o 12_o hour_n of_o day_n and_o as_o much_o of_o night_n can_v boast_v of_o have_v more_o of_o the_o sun_n company_n than_o they_o that_o live_v in_o the_o two_o other_o and_o consequent_o that_o the_o assertion_n be_v true_a it_o be_v in_o the_o oblique_a sphere_n then_o that_o the_o abovementioned_a brazen_a horizon_n be_v chief_o intend_v but_o as_o i_o say_v in_o the_o beginning_n it_o be_v forty_o to_o one_o so_o many_o universal_a operation_n be_v perform_v by_o the_o globe_n in_o its_o set_a posture_n that_o in_o 7_o year_n a_o man_n light_n on_o a_o question_n that_o can_v invite_v he_o to_o change_v it_o be_v it_o movable_a as_o other_o globe_n be_v so_o that_o have_v show_v you_o that_o in_o case_n of_o necessity_n it_o may_v be_v in_o effect_n alter_v even_o without_o stir_v it_o from_o its_o pedestal_n i_o shall_v proceed_v operation_n xvi_o how_o to_o take_v the_o elevation_n of_o the_o pole_n in_o any_o place_n whatsoever_o suppose_v you_o be_v in_o a_o strange_a place_n and_o that_o your_o globe_n be_v one_o that_o have_v be_v fit_v for_o london_n you_o desire_v to_o know_v the_o present_a elevation_n expose_v your_o globe_n to_o the_o sun_n on_o a_o meridian_n line_n with_o the_o pin_n or_o needle_n in_o the_o 8._o hole_n on_o the_o parallel_n of_o the_o 10_o of_o april_n or_o true_a day_n of_o the_o month_n and_o observe_v at_o 12_o a_o clock_n when_o the_o sun_n come_v into_o the_o plain_a of_o the_o globe_n meridian_n that_o the_o shade_n of_o the_o say_a needle_n or_o pin_n lose_v not_o itself_o as_o it_o will_v do_v be_v the_o sun_n direct_o opposite_a to_o it_o for_o so_o it_o have_v happen_v at_o london_n or_o in_o any_o place_n in_o the_o latitude_n of_o 51_o e_o 30′_n i_o say_v have_v thus_o expose_v your_o globe_n and_o observe_v this_o move_v your_o pin_n or_o needle_n from_o hole_n to_o hole_n or_o from_o one_o degree_n of_o the_o meridian_n to_o the_o other_o till_o its_o shade_n be_v whole_o lose_v and_o find_v the_o say_a needle_n or_o pin_n on_o the_o parallel_n suppose_v of_o june_n 11_o which_o be_v about_o 11._o 30′_n high_o than_o it_o be_v proper_a place_n to_o wit_n the_o parallel_n of_o the_o 10_o of_o april_n you_o may_v conclude_v that_o your_o present_a elevation_n be_v 63_o degree_n i._n e._n 11._o 30′_n high_o than_o the_o globe_n whereas_o have_v you_o be_v oblige_v to_o move_v your_o needle_n or_o pin_n so_o many_o degree_n low_a than_o the_o 10_o of_o april_n your_o elevation_n have_v be_v but_o 40._o the_o demonstration_n be_v obvious_a for_o since_o the_o earth_n be_v round_o demonstration_n as_o nothing_o perchance_o prove_v it_o better_o than_o the_o experience_n we_o have_v that_o as_o so_o many_o mile_n suppose_n 60_o elevate_v or_o depress_n the_o pole_n one_o degree_n so_o just_a 60_o mile_n more_o elevate_v or_o depress_n it_o another_o i_o say_v since_o the_o world_n be_v round_o and_o that_o the_o degree_n round_o of_o the_o globe_n answer_v to_o its_o degree_n it_o must_v follow_v that_o the_o difference_n between_o the_o pin_n situation_n now_o on_o the_o globe_n and_o where_o it_o will_v have_v stand_v on_o it_o at_o london_n be_v the_o true_a difference_n of_o the_o two_o elevation_n operation_n xvii_o how_o to_o know_v in_o what_o elevation_n the_o sun_n rise_v or_o set_v a_o hour_n or_o any_o other_o space_n of_o time_n early_o or_o late_a than_o he_o do_v in_o the_o globe_n elevation_n if_o the_o sun_n rise_v at_o london_n on_o the_o 10_o of_o april_n about_o 5_o and_o set_v about_o 7_o you_o will_v know_v in_o what_o elevation_n or_o latitude_n he_o then_o rise_v for_o example_n sake_n at_o 4_o and_o set_v at_o 8_o take_v the_o distance_n of_o 90_o degree_n with_o your_o string_n or_o compass_n in_o any_o great_a circle_n and_o place_v one_o end_n of_o your_o string_n or_o one_o foot_n of_o your_o compass_n where_o the_o parallel_n of_o the_o day_n intersect_v with_o the_o hour-circle_n of_o either_o 4_o in_o the_o morning_n or_o 8_o at_o night_n observe_v where_o or_o at_o what_o point_n the_o other_o end_n of_o your_o say_a string_n or_o other_o foot_n of_o your_o say_a compass_n touch_v in_o the_o meridian_n or_o 12_o a_o clock_n circle_n of_o the_o globe_n and_o you_o will_v find_v it_o to_o be_v at_o or_o about_o 8_o degree_n and_o 30_o minute_n beyond_o the_o zenith_n towards_o the_o north_n pole_n so_o that_o the_o elevation_n require_v be_v great_a than_o your_o own_o by_o those_o 8_o degree_n and_o 30_o minute_n that_o be_v to_o say_v the_o elevation_n be_v that_o of_o 60_o or_o thereabouts_o whereas_o have_v your_o string_n or_o compass_n touch_v 8._o °_o 30_o ′_o on_o the_o other_o side_n of_o your_o zenith_n the_o require_a elevation_n will_v have_v be_v less_o than_o your_o own_o so_o many_o degree_n i._n e._n it_o will_v have_v be_v that_o of_o 43_o degree_n or_o thereabouts_o this_o appear_v true_a by_o place_v your_o brazen_a horizon_n or_o by_o demonstration_n describe_v a_o imaginary_a one_o over_o the_o two_o point_n make_v by_o the_o intersection_n of_o the_o parallel_n of_o the_o day_n and_o hour-circle_n of_o 4_o in_o the_o morning_n and_o 8_o in_o the_o evening_n for_o in_o the_o elevation_n belong_v to_o such_o a_o horizon_n it_o be_v evident_a that_o the_o sun_n rise_v at_o 4_o and_o set_v at_o 8._o now_o the_o pole_n of_o every_o circle_n be_v 90_o degree_n from_o it_o and_o the_o point_n in_o the_o meridian_n be_v 90_o degree_n from_o the_o aforementioned_a intersection_n it_o follow_v that_o the_o say_a point_n in_o the_o meridian_n be_v the_o zenith_n or_o pole_n of_o this_o new_a horizon_n and_o consequent_o by_o be_v distant_a from_o the_o aequator_fw-la 60_o degree_n that_o so_o many_o degree_n be_v the_o latitude_n or_o elevation_n require_v the_o end_n of_o the_o second_o section_n sect_n iii_o of_o the_o moon_n have_v now_o finish_v with_o the_o sun_n we_o will_v make_v a_o step_n if_o you_o please_v to_o the_o moon_n and_o show_v you_o how_o to_o resolve_v all_o the_o useful_a ordinary_a question_n concern_v she_o whether_o we_o see_v she_o by_o night_n or_o by_o day_n for_o it_o be_v equal_a to_o we_o whether_o
she_o shine_v out_o right_a and_o consequent_o cast_v a_o shade_n or_o appear_v only_o faint_a and_o wan_a by_o reason_n of_o thin_a cloud_n or_o by_o the_o excess_n of_o light_n during_o the_o sun_n abode_n above_o the_o horizon_n let_v we_o then_o begin_v with_o her_o almucantar_n and_o azimuth_n as_o be_v the_o basis_n and_o foundation_n of_o all_o operation_n here_o relate_v to_o she_o nor_o can_v there_o be_v the_o least_o difficulty_n in_o any_o of_o they_o unless_o perchance_o in_o the_o seven_o since_o they_o have_v so_o great_a a_o correspondence_n and_o affinity_n with_o those_o already_o handle_v in_o the_o former_a section_n operation_n i._o to_o find_v the_o moon_n be_v almucantar_n or_o height_n this_o be_v to_o be_v perform_v as_o well_o when_o she_o cast_v a_o shade_n as_o when_o she_o cast_v none_o by_o the_o two_o first_o way_n of_o find_v the_o sun_n almucantar_n and_o therefore_o consult_v the_o 5._o second_o operation_n in_o the_o first_o section_n operation_n ii_o to_o find_v the_o moon_n be_v azimuth_n this_o be_v also_o to_o be_v find_v by_o the_o two_o first_o way_n of_o find_v the_o sun_n azimuth_n treat_v of_o in_o the_o 10_o 5_o operation_n of_o the_o first_o section_n operation_n iii_o to_o find_v her_o true_a place_n on_o the_o globe_n if_o she_o cast_v no_o shade_n her_o place_n be_v to_o be_v find_v by_o she_o almucantar_n and_o azimuth_n as_o we_o hint_v in_o the_o 11_o 6_o operation_n of_o the_o first_o section_n since_o she_o must_v ever_o be_v where_o these_o two_o circle_n intersect_v but_o if_o she_o shine_v out_o clear_a you_o have_v nothing_o to_o do_v have_v place_v your_o globe_n on_o a_o meridian_n line_n but_o to_o see_v what_o hour_n the_o shade_n of_o the_o enlighten_v pole_n or_o that_o of_o your_o string_n pass_v over_o both_o pole_n mark_n be_v for_o this_o give_v you_o her_o hour-circle_n which_o we_o will_v call_v the_o lunar_a hour_n hereafter_o her_o height_n or_o almucantar_n must_v needs_o tell_v you_o in_o what_o part_n of_o the_o say_a circle_n she_o reside_v this_o operation_n be_v to_o be_v well_o understand_v and_o ready_o perform_v see_v most_o that_o follow_v be_v as_o it_o be_v corollary_n from_o it_o and_o for_o the_o better_a illustrate_v and_o explain_v they_o we_o will_v imagine_v the_o moon_n be_v place_v to_o be_v in_o the_o hour_n circle_n of_o 2_o in_o the_o afternoon_n about_o 43_o degree_n above_o the_o horizon_n operation_n iv._o to_o know_v the_o moon_n be_v declension_n from_o the_o aequator_fw-la this_o be_v only_o the_o near_a distance_n of_o her_o true_a place_n from_o the_o aequator_fw-la which_o your_o bead_n or_o compass_n will_v show_v you_o to_o be_v about_o 12_o degree_n northward_o if_o according_a to_o the_o forego_n example_n she_o be_v 43_o degree_n high_a in_o the_o hour_n circle_n of_o 2_o in_o the_o afternoon_n operation_n v._o to_o find_v the_o moon_n be_v diurnal_a parallel_n and_o consequent_o how_o to_o compose_v the_o globe_n by_o the_o moon_n by_o the_o moon_n diurnal_a parallel_n i_o mean_v a_o real_a or_o imaginary_a circle_n parallel_n to_o the_o aequator_fw-la and_o answerable_a to_o her_o present_a declension_n which_o by_o the_o former_a operation_n we_o suppose_v to_o be_v about_o 12_o degree_n have_v therefore_o this_o parallel_n you_o may_v compose_v the_o globe_n by_o the_o moon_n as_o you_o do_v by_o the_o memoran_n sun_n and_o here_o you_o must_v remember_v that_o though_o the_o find_n of_o the_o parallel_n imply_v at_o first_o a_o meridian_n line_n yet_o the_o know_v how_o to_o compose_v thus_o your_o globe_n will_v not_o be_v useless_a for_o now_o you_o be_v no_o long_o confine_v to_o one_o place_n or_o line_n but_o may_v compose_v it_o where_o you_o please_v by_o the_o help_n of_o the_o say_a parallel_n operation_n vi_o to_o find_v the_o moon_n be_v bear_v according_a to_o the_o point_n of_o the_o compass_n this_o be_v to_o be_v perform_v after_o the_o way_n of_o find_v the_o sun_n bear_v in_o the_o 12._o seven_o operation_n of_o the_o first_o section_n for_o if_o you_o draw_v your_o string_n from_o the_o zenith_n over_o the_o moon_n present_a place_n the_o say_a string_n cut_v by_o our_o example_n the_o horizon_n at_o s._n w._n and_o some_o few_o degree_n towards_o the_o south_n for_o she_o then_o bear_v operation_n vii_o to_o know_v what_o a_o clock_n it_o be_v by_o the_o moon_n there_o be_v no_o operation_n treat_v of_o so_o intricate_a as_o this_o and_o therefore_o if_o the_o reader_n who_o will_v have_v his_o curiosity_n satisfy_v have_v not_o patience_n enough_o to_o descend_v to_o a_o little_a niceness_n he_o have_v better_o fall_v upon_o another_o subject_n but_o though_o we_o may_v be_v somewhat_o long_o at_o first_o in_o lay_v down_o and_o explicate_v all_o particular_n yet_o at_o the_o end_n we_o will_v contract_v the_o whole_a into_o half_n a_o dozen_o line_n and_o thereby_o make_v the_o operation_n very_o expedit_fw-la and_o easy_a i_o say_v there_o be_v no_o operation_n so_o intricate_a as_o this_o for_o the_o moon_n by_o reason_n of_o her_o different_a place_n in_o her_o epicicle_n be_v so_o inconstant_a in_o her_o daily_a elongation_n from_o the_o sun_n that_o sometime_o she_o spend_v from_o v_o g._n her_o conjunction_n to_o her_o first_o quarter_n above_o 8_o day_n though_o at_o another_o time_n a_o great_a deal_n less_o than_o 7_o will_v serve_v the_o turn_n and_o to_o this_o variety_n and_o skittishness_n be_v the_o space_n also_o between_o any_o of_o she_o other_o change_n liable_a if_o then_o her_o distance_n from_o the_o sun_n be_v so_o uncertain_a and_o yet_o be_v the_o thing_n that_o must_v be_v know_v before_o her_o place_n or_o shade_n on_o the_o globe_n can_v give_v we_o the_o hour_n seek_v how_o strange_o fallible_a be_v the_o usual_a way_n as_o well_o in_o some_o author_n of_o note_n as_o in_o ordinary_a almanac_n of_o find_v it_o to_o wit_n the_o add_v of_o as_o many_o 48_o minute_n to_o the_o hour_n she_o show_v on_o a_o dial_n as_o she_o be_v day_n old_a for_o the_o table_n make_v in_o pursuance_n of_o this_o rule_n suppose_v she_o always_o on_o the_o 15_o of_o her_o age_n to_o be_v at_o full_a which_o may_v happen_v as_o i_o now_o mention_v not_o only_o much_o soon_o but_o also_o much_o late_a so_o that_o most_o common_o her_o true_a age_n and_o the_o say_a table_n be_v at_o variance_n nay_o when_o they_o agree_v there_o can_v be_v no_o reliance_n on_o they_o see_v that_o if_o v._n g._n at_o 6_o they_o show_v tolerable_o what_o a_o clock_n it_o be_v yet_o by_o 12_o there_o may_v happen_v a_o error_n of_o near_a a_o quarter_n by_o reason_n that_o she_o be_v every_o moment_n at_o a_o new_a distance_n from_o the_o sun_n and_o at_o one_o also_o which_o present_o become_v very_o sensible_a thus_o therefore_o we_o see_v that_o there_o must_v be_v exception_n and_o restriction_n in_o any_o one_o rule_n that_o appertain_v to_o this_o business_n nor_o be_v it_o to_o be_v perform_v by_o a_o instrument_n in_o a_o trice_n as_o the_o operation_n common_o be_v belong_v to_o the_o star_n that_o have_v a_o regular_a motion_n or_o to_o the_o sun_n who_o extravagance_n be_v not_o soon_o perceptible_a i_o say_v thus_o we_o see_v that_o there_o must_v be_v here_o exception_n and_o restriction_n and_o in_o truth_n nothing_o but_o a_o down_o right_o astronomical_a calculation_n can_v real_o perform_v it_o yet_o since_o such_o a_o critical_a exactness_n in_o the_o hour_n be_v never_o necessary_a in_o our_o ordinary_a affair_n i_o shall_v propose_v this_o method_n which_o will_v at_o least_o come_v always_o very_a near_o the_o mark._n when_o you_o desire_v to_o know_v what_o a_o clock_n it_o be_v by_o the_o moon_n operate_v take_v a_o almanac_n for_o if_o you_o will_v only_o have_v her_o true_a age_n you_o must_v recur_v to_o one_o or_o to_o something_o analogical_a and_o reckon_v therein_o how_o many_o day_n there_o be_v in_o the_o present_a quarter_n from_o one_o change_n to_o the_o other_o i_o e._n from_o new_a moon_n to_o her_o first_o quarter_n or_o from_o her_o first_o quarter_n to_o her_o full_a and_o so_o on_o for_o i_o call_v any_o of_o these_o four_o aspect_n a_o cardinal_n point_n or_o change_v and_o the_o whole_a time_n between_o one_o change_n and_o the_o other_o a_o quarter_n i_o say_v reckon_v how_o many_o day_n there_o be_v in_o the_o then_o quarter_n and_o you_o will_v find_v either_o 6½_n or_o 7_o or_o 7½_n or_o 8_o so_o that_o if_o the_o number_n be_v 6½_n her_o elongation_n from_o the_o sun_n be_v 55_o minute_n and_o ½_o per_fw-la diem_fw-la if_o 7_o day_n 51′½_n if_o 7_o day_n and_o half_a 48′_n and_o last_o if_o 8_o day_n 48′_n i_o mean_v not_o nevertheless_o that_o from_o change_n to_o change_v there_o maynot_v sometime_o
mention_v seven_o scheme_n show_v you_o so_o that_o by_o the_o help_n of_o your_o sector_n or_o of_o any_o line_n of_o chord_n or_o quadrant_n you_o may_v mark_v they_o successive_o in_o your_o blind_a circle_n on_o both_o side_n of_o the_o diameter_n and_o then_o if_o you_o draw_v from_o the_o centre_n lines_n throu_fw-fr '_o those_o mark_n your_o dial_n be_v finish_v for_o as_o to_o the_o style_n and_o substilar_n you_o need_v no_o other_o instruction_n than_o what_o you_o have_v in_o the_o last_o operation_n which_o also_o direct_v you_o to_o the_o demonstration_n since_o the_o same_o serve_v both_o operation_n vii_o how_o to_o draw_v a_o line_n parallel_n to_o the_o horizon_n together_o with_o two_o way_n how_o to_o place_v true_o all_o paper_n draught_n on_o their_o respective_a plane_n have_v late_o advise_v you_o to_o delineate_v all_o dial_n on_o 79._o paper_n before_o you_o draw_v they_o on_o your_o design_a plane_n and_o have_v show_v you_o how_o to_o describe_v this_o dial_n it_o be_v now_o time_n to_o teach_v plane_n you_o how_o to_o draw_v a_o horizontal_n line_n on_o this_o plane_n that_o you_o may_v thereby_o true_o place_v your_o draught_n slip_v therefore_o out_o your_o two_o ruler_n which_o be_v under_o the_o the_o pedestal_n as_o i_o already_o mention_v and_o place_v the_o end_n of_o one_o on_o a_o convenient_a centre_n choose_v by_o you_o in_o your_o plane_n you_o will_v have_v by_o the_o end_n of_o the_o other_o when_o the_o plummet_n fall_v on_o the_o asterisk_n or_o little_a star_n a_o con_v point_n and_o consequent_o mark_v to_o draw_v the_o require_a line_n by_o so_o that_o if_o you_o then_o place_v the_o centre_n of_o your_o say_a draught_n on_o the_o centre_n of_o the_o plane_n and_o its_o 6_o a_o clock_n hour_n line_n on_o your_o horizontal_n line_n all_o the_o other_o line_n will_v fall_v on_o their_o true_a place_n and_o thereby_o show_v you_o where_o with_o a_o coal_n or_o the_o like_a to_o mark_v out_o point_v for_o the_o perfect_a and_o final_a draw_v of_o they_o the_o cock_n also_o of_o the_o paper_n dial_n will_v direct_v you_o in_o the_o place_n of_o the_o other_o for_o they_o be_v both_o to_o be_v of_o the_o same_o height_n above_o their_o respective_a plane_n with_o their_o top_n point_v the_o same_o way_n viz._n downward_o to_o the_o horizon_n in_o all_o these_o south_n dial_n but_o if_o you_o will_v have_v yet_o a_o more_o easy_a way_n of_o place_v a_o paper_n plane_n draught_n not_o only_o on_o this_o but_o on_o any_o plane_n for_o which_o it_o be_v make_v look_v what_o a_o clock_n it_o be_v by_o your_o globe_n and_o move_v your_o say_a draught_n on_o its_o plane_n till_o it_o show_v exact_o the_o true_a hour_n do_v but_o fix_v it_o there_o and_o you_o may_v mark_v out_o the_o point_n for_o your_o fair_a line_n with_o all_o the_o ease_n imaginable_a operation_n viii_o how_o to_o make_v a_o vertical_a or_o erect_a direct_a north_n dial_n for_o the_o elevation_n of_o london_n there_o be_v no_o difference_n between_o the_o fabric_n of_o this_o dial_n and_o the_o former_a unless_o it_o be_v in_o figure_v it_o for_o a_o south_n dial_n reverse_v be_v a_o north_n dial_n the_o afternoon_n hour_n line_n be_v mark_v with_o the_o morning_n figure_n and_o the_o morning_n one_o with_o those_o of_o the_o afternoon_n so_o that_o the_o top_n of_o the_o style_n point_v now_o upward_o as_o may_v be_v see_v by_o scheme_n 9th_o and_o by_o the_o upper_a part_n of_o scheme_n 10_o to_o wit_n by_o the_o semi_a circle_n ptc_n therefore_o when_o you_o choose_v a_o centre_n in_o your_o design_v or_o real_a plane_n for_o this_o dial_n let_v it_o be_v in_o the_o low_a part_n of_o it_o to_o have_v room_n for_o the_o hour_n line_n to_o run_v upward_o and_o by_o the_o way_n you_o must_v here_o remember_v that_o though_o i_o bid_v memorandum_n you_o in_o the_o make_n of_o this_o your_o vretical_a south_n dial_n to_o take_v the_o distance_n between_o the_o zenith_n and_o the_o intersection_n of_o the_o string_n with_o the_o next_o hour_n circle_n for_o the_o 1_o and_o 11_o a_o clock_n hour_n line_n &c_n &c_n yet_o that_o section_n of_o your_o globe_n by_o your_o string_n from_o the_o zenith_n as_o aforesaid_a give_v in_o truth_n a_o north_n dial_n and_o therefore_o in_o strictness_n you_o ought_v to_o have_v take_v the_o distance_n between_o the_o nadir_n and_o the_o several_a intersection_n of_o the_o plane_n with_o the_o hour-circle_n but_o since_o both_o dial_n be_v as_o i_o tell_v you_o alike_o it_o be_v best_o always_o to_o operate_v thus_o from_o the_o zenith_n as_o be_v more_o at_o hand_n than_o the_o nadir_n and_o consequent_o more_o convenient_a the_o demonstration_n or_o reason_n why_o these_o dial_n show_n the_o demonstration_n hour_n differ_v even_o at_o first_o conception_n but_o little_a and_o at_o the_o second_o not_o at_o all_o from_o that_o already_o give_v for_o the_o horizontal_n dial._n by_o the_o first_o conception_n i_o mean_v our_o consider_v these_o plane_n as_o vertical_a and_o erect_a for_o since_o the_o hour-line_n of_o all_o dial_n be_v as_o i_o show_v you_o in_o the_o former_a demonstration_n the_o intersection_n only_o of_o the_o respective_a hour-circle_n with_o the_o plane_n and_o since_o the_o hourly_a indicating_z shade_n be_v the_o shade_n of_o the_o axis_n or_o of_o the_o hour-circle_n which_o then_o lie_v in_o the_o plane_n of_o the_o sun_n it_o must_v follow_v that_o the_o mark_v make_v for_o example_n sake_n by_o the_o 4_o a_o clock_n morning_n hour_n circle_n on_o the_o string_n and_o the_o centre_n of_o the_o say_a plane_n which_o be_v the_o common_a passage_n of_o all_o the_o hour-circle_n will_v be_v two_o true_a mark_n or_o point_n for_o you_o to_o draw_v that_o hour-line_n by_o and_o consequent_o that_o the_o shade_n of_o the_o axis_n will_v still_o fall_v on_o the_o say_a hour-line_n as_o often_o as_o the_o sun_n come_v into_o the_o plane_n of_o that_o hour-circle_n now_o your_o blind_a circle_n be_v by_o construction_n equal_a to_o the_o circle_n make_v by_o the_o string_n on_o the_o globe_n and_o the_o mark_n on_o its_o limb_n be_v equal_a to_o the_o mark_n on_o the_o say_a string_n therefore_o the_o dial_n must_v be_v true_o draw_v and_o the_o style_v place_v on_o the_o 12_o a_o clock_n line_n to_o wit_n on_o the_o intersection_n of_o that_o hour-circle_n which_o fall_v on_o the_o plane_n at_o right_a angle_n must_v true_o cast_v its_o shade_n from_o time_n to_o time_n see_v by_o its_o site_n and_o angle_n it_o correspond_v with_o the_o axis_n of_o the_o world_n as_o for_o our_o second_o conception_n in_o reference_n to_o these_o dial_n we_o shall_v find_v by_o it_o that_o their_o plane_n be_v real_a horizontal_n one_o to_o some_o people_n or_o other_o for_o this_o section_n of_o the_o globe_n be_v a_o great_a circle_n will_v be_v the_o horizon_n to_o those_o that_o live_v in_o the_o pole_n of_o it_o viz._n to_o those_o under_o our_o meridian_n 90_o degree_n from_o our_o zenith_n which_o be_v a_o point_n in_o our_o horizon_n make_v their_o horizontal_n dial_n always_o our_o direct_a vertical_a one_o and_o their_o direct_a vertical_a dial_n our_o horizontal_n one_o it_o be_v plain_a then_o that_o the_o present_a dial_n be_v exact_o describe_v if_o our_o former_a direction_n and_o proof_n of_o a_o horizontal_n one_o be_v true_a for_o all_o the_o hour_n line_n be_v here_o draw_v from_o the_o centre_n to_o the_o several_a intersection_n of_o the_o hour-circle_n and_o horizon_n which_o as_o we_o be_v to_o suppose_v the_o string_n represent_v nor_o do_v the_o cock_n of_o these_o dial_n differ_v from_o the_o former_a rule_n for_o have_v the_o meridian_n or_o 12_o a_o clock_n line_n for_o substilar_n for_o the_o former_a reason_n and_o be_v 38_o degree_n and_o a_o half_a above_o it_o it_o make_v a_o angle_n equal_a to_o the_o elevation_n of_o the_o people_n who_o have_v the_o say_a plane_n for_o horizon_n operation_n ix_o to_o make_v the_o aforesaid_a north_n and_o south_n dial_n geometrical_o for_o the_o elevation_n of_o london_n there_o be_v no_o need_n of_o a_o scheme_n for_o this_o operation_n since_o it_o be_v a_o corollary_n from_o what_o we_o have_v now_o say_v for_o make_v but_o a_o horizontal_n dial_n geometrical_o as_o we_o former_o show_v you_o in_o scheme_n the_o 6_o according_a to_o the_o compliment_n of_o the_o elevation_n of_o your_o place_n and_o that_o will_v serve_v the_o figure_v only_o consider_v for_o either_o dial._n here_o than_o you_o may_v see_v that_o os_fw-mi or_o on_o the_o basis_n or_o foot_n memorandum_n of_o the_o style_n of_o these_o dial_n that_o be_v to_o say_v the_o distance_n between_o its_o centre_n and_o its_o horizontal_n edge_n or_o side_n be_v ever_o the_o tangent_fw-la of_o the_o elevation_n for_o it_o
be_v the_o tangent_fw-la compliment_n of_o f_n or_o nr_n the_o stiles_n height_n above_o the_o plane_n and_o here_o also_o you_o see_v that_o the_o very_a same_o dial_n the_o figure_n only_o transpose_v will_v serve_v both_o for_o a_o horizontal_n and_o this_o direct_v vertical_a one_o to_o those_o that_o live_v in_o the_o latitude_n of_o 45_o degree_n since_o the_o elevation_n of_o the_o pole_n and_o compliment_n of_o it_o be_v there_o the_o same_o operation_n x._o to_o describe_v by_o the_o globe_n meridian_n dial_n or_o as_o other_o call_v they_o east_n or_o west_n dial_n for_o the_o elevation_n of_o london_n these_o dial_n though_o vertical_a and_o direct_a as_o pass_v through_o our_o zenith_n and_o face_v also_o two_o cardinal_n point_n or_o quarter_n of_o the_o world_n be_v very_o different_a from_o the_o former_a nor_o have_v any_o body_n i_o believe_v teach_v yet_o their_o description_n by_o the_o globe_n to_o perform_v therefore_o this_o operation_n you_o must_v by_o the_o help_n premise_v of_o your_o string_n or_o compass_n describe_v on_o your_o globe_n with_o chalk_n or_o the_o like_a matter_n a_o arch_n as_o in_o sch._n 11._o which_o have_v its_o pole_n at_o k_o the_o east-point_n for_o example_n sake_n of_o the_o aequinoctial_a cut_v somewhere_o or_o other_o the_o 11_o a_o clock_n northern_a hour_n circle_n i_o mean_v the_o 11_o a_o clock_n hour_n circle_n on_o the_o northern_a or_o black_a part_n of_o the_o globe_n and_o this_o arch_n by_o reach_v from_o the_o point_n c_o in_o the_o aequinoctial_a colour_n or_o 6_o a_o clock_z circle_n to_o h_n in_o the_o horizon_n on_o the_o say_v northern_a side_n of_o the_o globe_n will_v be_v a_o piece_n of_o a_o little_a circle_n parallel_n to_o the_o meridian_n contain_v the_o degree_n of_o the_o elevation_n of_o the_o pole_n and_o cut_v all_o the_o hour-circle_n also_o from_o 6_o to_o 11._o but_o if_o this_o be_v think_v too_o troublesome_a a_o work_n the_o globe-maker_n may_v avoid_v it_o by_o put_v 6_o prick_n or_o asterisk_v upon_o the_o globe_n where_o the_o say_a arch_n and_o hour-circle_n will_v intersect_v as_o may_v be_v see_v in_o the_o say_v 11_o scheme_n at_o c_o o_o s_o t_o v_o and_o z_o so_o that_o if_o beyond_o c_z he_o add_v one_o prick_v more_o viz._n at_o r_o to_o give_v you_o from_o h_n the_o radius_fw-la or_o 60_o degree_n of_o the_o say_a arch_n you_o need_v nothing_o else_o this_o be_v premise_v describe_v on_o a_o sheet_n of_o paper_n hr_n or_o 60_o degree_n of_o the_o say_a arch_n be_v radius_fw-la a_o blind_a circle_n dial._n as_o in_o sch._n 12_o and_o draw_v the_o line_n h_o h_z how_o you_o please_v throu_fw-fr '_o k_o its_o centre_n to_o represent_v the_o intersection_n of_o the_o horizon_n open_v your_o compass_n to_o the_o say_a arch_n full_a extent_n to_o wit_n from_o h_n to_o c_o and_o put_v one_o foot_n on_o the_o blind_a circle_n at_o h_n and_o the_o other_o mark_v there_o at_o c_o draw_v the_o line_n pc_n Ï€_n throu_fw-fr '_o the_o centre_n k_o and_o it_o will_v represent_v the_o intersection_n of_o the_o aequinoctial_a colour_n or_o 6_o a_o clock_z hour_n circle_n with_o your_o say_a blind_a circle_n or_o plane_n so_o that_o if_o you_o take_v from_o off_o your_o globe_n the_o distance_n between_o the_o point_n c_o and_o the_o several_a intersection_n of_o the_o hour_n circle_n with_o the_o say_a arch_n ch_z and_o place_v they_o on_o your_o blind_a circle_n on_o the_o right_a hand_n side_n of_o pc_n Ï€_n as_o well_o below_o the_o horizon_n h_o h_o as_o above_o it_o and_o draw_v line_n through_o they_o viz._n o_o ο_n s_o σ_n t_o Ï„_n five_o Ï…_n and_o z_o ζ_n you_o will_v have_v a_o complete_a east_n dial_n describe_v after_o you_o have_v draw_v 2_o line_n more_o on_o the_o left_a side_n of_o the_o say_v c_o Ï€_n to_o wit_n the_o line_n n_o ν_fw-gr distant_a from_o it_o as_o be_v o_o ο_n and_o the_o line_n m_o μ_n as_o be_v saint_n σ._n as_o for_o the_o figure_v each_o hour_n line_n it_o must_v be_v according_a to_o the_o figure_n of_o the_o correspond_v hour-circle_n cut_v by_o the_o aforesaid_a arch_n ch_z and_o thus_o you_o will_v find_v they_o figure_v in_o the_o forementioned_a scheme_n 12_o which_o show_v you_o too_o how_o the_o border_n or_o parallel_n be_v draw_v for_o the_o say_a figure_n to_o lie_v in_o as_o be_v only_o double_a line_n equidistant_a at_o pleasure_n on_o both_o side_n of_o the_o horizon_n h_o h_z and_o here_o also_o by_o the_o blind_a line_n and_o by_o the_o fair_a one_o you_o have_v before_o your_o eye_n what_o be_v necessary_a to_o be_v express_v on_o your_o fair_a plane_n and_o what_o not_o nor_o be_v there_o any_o difference_n in_o the_o construction_n of_o a_o west-dial_n dial._n except_o it_o be_v in_o turn_v on_o your_o draught_n the_o hour-line_n or_o parallel_n the_o other_o way_n to_o the_o end_n they_o may_v all_o point_n northwards_o on_o their_o respective_a plane_n for_o thus_o in_o sch._n 11._o do_v the_o prick_v line_n m_z 8_o n_o 7_o c_o 6_o o_z 5_o s_z 4_o t_o 3_o u_z 2_o and_o z_o 1._o which_o will_v true_o represent_v this_o dial_n if_o they_o be_v produce_v in_o the_o say_a scheme_n now_o for_o the_o substilar_n it_o be_v the_o 6_o a_o clock_n hour_n line_n since_o that_o substilar_n hour_n circle_n fall_v on_o the_o plane_n at_o right_a angle_n and_o as_o for_o the_o cock_n it_o may_v be_v a_o gallow_n style_v as_o in_o scheme_n 13_o or_o a_o pin_n as_o in_o scheme_n 14_o so_o it_o be_v place_v on_o the_o substilar_a and_o perpendicular_a to_o it_o have_v its_o height_n equal_a to_o the_o distance_n between_o the_o prick_n or_o asterisk_n c_o and_o p_o in_o the_o say_v 11_o scheme_n or_o which_o be_v all_o one_o to_o the_o distance_n between_o k_o and_o x._o viz._n the_o near_a distance_n between_o the_o substilar_n and_o the_o 9_o a_o clock_n hour_n line_n in_o a_o east-dial_n and_o the_o substilar_a and_o the_o 3_o a_o clock_n line_n in_o a_o west_n dial._n but_o here_o you_o be_v to_o remember_v that_o when_o i_o say_v that_o the_o height_n of_o the_o style_n be_v to_o be_v equal_a to_o the_o distance_n between_o c_o and_o p._n i_o mean_v in_o rigour_n equal_a to_o the_o sine_fw-la and_o not_o the_o chord_n of_o that_o arch_n but_o see_v the_o chord_n of_o 10_o degree_n differ_v not_o sensible_o from_o the_o sine_fw-la and_o by_o the_o way_n the_o arch_n cp_n on_o the_o globe_n will_v not_o be_v above_o 10_o degree_n from_o the_o meridian_n the_o interval_n between_o c_o and_o p_o will_v serve_v the_o turn_n but_o if_o you_o will_v be_v more_o exact_a take_v between_o your_o compass_n the_o distance_n of_o double_a cp_n to_o wit_v the_o interval_n of_o suppose_v 20_o degree_n and_o half_a of_o it_o be_v the_o require_a distance_n for_o half_a the_o chord_n of_o 20_o deg._n be_v equal_a to_o the_o sine_fw-la of_o 10._o or_o if_o you_o please_v you_o may_v erect_v a_o needle_n at_o c_o parallel_n to_o p_o the_o elevate_a pole_n of_o the_o globe_n and_o the_o distance_n between_o they_o will_v be_v the_o true_a height_n of_o your_o style_n to_o conclude_v you_o may_v contract_v and_o enlarge_v these_o dial_n as_o you_o please_v by_o draw_v the_o hour-line_n twice_o or_o thrice_o or_o according_a to_o any_o other_o proportion_n near_o or_o far_a asunder_o and_o so_o abate_v or_o heighten_v in_o the_o like_a manner_n your_o style_n the_o demonstration_n be_v obvious_a for_o since_o the_o point_n m_o n_o c_o o_o demonstration_n s_o t_o v_o and_o z_o in_o the_o upper_a part_n of_o the_o blindcircle_n or_o plane_n and_o the_o point_n μ_n ν_fw-gr Ï€_n ο_n σ_n Ï„_n â—_o ζ_n on_o the_o low_a part_n of_o it_o be_v by_o be_v equal_a in_o distance_n to_o those_o on_o the_o arch_n the_o intersection_n of_o the_o morning_n hour_n circle_n of_o 4_o 5_o 6_o 7_o 8_o 9_o 10_o 11_o with_o the_o edge_n of_o the_o say_a plane_n it_o follow_v that_o the_o line_n draw_v from_o the_o correspond_v point_n must_v be_v the_o true_a hour_n line_n of_o this_o dial_n since_o the_o hour_n line_n as_o we_o say_v of_o all_o dial_n be_v only_o the_o intersection_n of_o the_o respective_a hour_n circle_n with_o the_o plane_n again_o the_o shade_n of_o the_o axis_n the_o axis_n be_v a_o part_n of_o all_o the_o hour_n circle_n fall_v ever_o on_o the_o hour-line_n or_o interfection_n of_o this_o or_o that_o hour_n circle_n as_o often_o as_o the_o sun_n come_v into_o the_o plane_n of_o that_o hour-circle_n therefore_o the_o style_n of_o this_o dial_n represent_v true_o the_o axis_n since_o it_o be_v above_o the_o plane_n and_o distant_a from_o it_o as_o it_o be_v on_o the_o globe_n will_v cast_v its_o shade_n every_o hour_n on_o the_o
hour_n circle_n i._n e._n that_o which_o correspond_v with_o the_o time_n of_o the_o day_n will_v be_v just_o interpose_v between_o your_o eye_n and_o the_o sun_n but_o since_o the_o whole_a axis_n be_v the_o common_a section_n of_o the_o hour-circle_n let_v your_o eye_n be_v but_o in_o any_o part_n of_o it_o the_o same_o interposition_n must_v happen_v so_o that_o see_v the_o sun_n ray_n by_o reason_n of_o the_o blue_a colour_n penetrate_v not_o the_o glass_n his_o picture_n must_v needs_o be_v on_o the_o outside_n of_o it_o where_o the_o say_a ray_n will_v have_v otherways_o past_a now_o the_o ray_n that_o go_v from_o your_o eye_n throu_fw-fr '_o the_fw-fr two_o holes_n be_v the_o axis_n therefore_o whilst_o your_o eye_n remain_v in_o this_o posture_n it_o will_v follow_v that_o wheresoever_o you_o see_v the_o sun_n picture_n on_o the_o glass_n there_o his_o place_n must_v be_v and_o consequent_o his_o say_a picture_n must_v show_v the_o hour_n operation_n xxxi_o how_o to_o make_v a_o horizontal_n concave_a dial_n by_o the_o globe_n and_o geometrical_o also_o compose_v so_o your_o globe_n in_o the_o concavity_n give_v suppose_v construction_n bac_n in_o scheme_n 37._o that_o a_o the_o centre_n of_o the_o say_a concavity_n shall_v concur_v with_o the_o centre_n of_o the_o say_a globe_n then_o draw_v your_o string_n over_o each_o necessary_a hour_n circle_n on_o the_o globe_n to_o the_o side_n of_o the_o concavity_n mark_v as_o many_o point_n as_o shall_v be_v convenient_a for_o the_o describe_v the_o correspond_v hour_n circle_n and_o the_o pin_n ad_fw-la erect_v in_o the_o nadir_n at_o d_o as_o high_a as_o the_o say_a centre_n a_o i_o mean_v a_o pin_n equal_a to_o the_o semi-diameter_n of_o the_o concavity_n will_v with_o its_o top_n always_o show_v you_o the_o hour_n though_o the_o former_a way_n be_v impracticable_a when_o the_o hole_n be_v less_o way_n than_o the_o globe_n yet_o it_o serve_v to_o illustrate_v and_o make_v easy_a the_o geometrical_a operation_n for_o you_o have_v nothing_o you_o see_v to_o do_v but_o to_o draw_v hour_n circle_n within_o as_o you_o will_v without_o be_v the_o say_a concavity_n a_o whole_a sphere_n and_o then_o the_o top_n of_o its_o semi-diameter_n i._n e._n the_o point_n which_o lie_v in_o the_o centre_n a_o will_v perform_v the_o style_n demonstration_n part_n for_o since_o the_o sun_n be_v every_o hour_n as_o we_o have_v before_o show_v you_o in_o the_o same_o plane_n of_o the_o true_a hour_n circle_n and_o since_o a_o the_o top_n of_o the_o semi-diameter_n be_v in_o the_o centre_n of_o the_o concavity_n be_v part_n of_o the_o axis_n or_o common_a section_n of_o all_o the_o hour-circle_n it_o follow_v that_o its_o shadow_n must_v fall_v on_o the_o true_a hour_n operation_n xxxii_o how_o to_o describe_v geometrical_o a_o ceiling_n dial._n see_v the_o glass_n which_o reflect_v the_o sun_n ray_n to_o show_v we_o the_o hour_n be_v common_o fix_v in_o the_o corner_n and_o by-place_n of_o window_n the_o globe_n can_v seldom_o be_v so_o well_o order_v by_o reason_n of_o its_o bulk_n as_o to_o help_v we_o in_o the_o construction_n of_o this_o dial_n therefore_o i_o shall_v only_o give_v you_o the_o geometrical_a way_n which_o be_v as_o i_o take_v it_o both_o short_a and_o new_a and_o because_o these_o dial_n have_v common_o the_o window_n or_o inlet_n for_o the_o sun_n southerly_a for_o otherwise_o they_o will_v show_v but_o very_o few_o hour_n we_o will_v suppose_v we_o also_o in_o the_o follow_a example_n to_o stand_v thus_o and_o afterward_o you_o shall_v see_v the_o difference_n between_o such_o a_o dial_n and_o those_o who_o window_n have_v another_o aspect_n first_o make_v on_o any_o pasteboard_n trencher_n etc._n etc._n a_o horizontal_n construction_n dial_n as_o in_o scheme_n 38._o and_o fix_v in_o o_o its_o centre_n a_o thread_n of_o a_o good_a length_n to_o wit_n open_v then_o fasten_v the_o say_a dial_n so_o with_o a_o nail_n to_o a_o long_a mason_n ruler_n that_o its_o fiducial_a edge_n kl_n may_v lie_v upon_o the_o meridian_n or_o 12_o a_o clock_n line_n and_o have_v cement_v and_o place_v level_v a_o piece_n of_o look_a glass_n of_o the_o bigness_n of_o a_o three_o penny_n in_o the_o window_n or_o what_o convenient_a place_n else_o you_o please_v of_o your_o chamber_n which_o we_o will_v suppose_v to_o be_v g_z find_v by_o the_o plumet_n ae_n the_o point_v a_o in_o the_o ceiling_n wxyz_n be_v the_o point_n in_o scheme_n 39_o direct_o over_o the_o say_v g_z and_o draw_z throu_fw-fr '_o it_o a_o meridian_n line_n viz._n the_o line_n al._n in_o the_o next_o place_n fix_v one_o end_n of_o a_o piece_n of_o packthread_n on_o g_o the_o centre_n of_o the_o glass_n and_o the_o other_o on_o some_o point_n of_o your_o meridian_n line_n in_o such_o manner_n that_o it_o make_v a_o angle_n with_o it_o of_o 51._o 30′_n i_o e._n the_o angle_n of_o the_o elevation_n which_o may_v be_v easy_o perform_v by_o the_o application_n of_o the_o side_n of_o a_o quadrant_n to_o the_o say_v extend_v packthread_n and_o when_o it_o be_v right_a let_v the_o point_n thus_o find_v in_o your_o meridian_n line_n be_v call_v b._n last_o take_v the_o distance_n between_o the_o aforesaid_a point_n a_o and_o b_o and_o mark_v it_o suppose_v at_o c_o on_o the_o edge_n of_o your_o ruler_n from_o o_o the_o centre_n or_o fasten_v of_o the_o horizontal_n place_v so_o the_o say_a ruler_n fiducial_a edge_n kcl_n along_o the_o meridian_n line_n on_o the_o ceiling_n that_o the_o point_n c_o may_v lie_v just_a on_o a_o and_o all_o be_v do_v for_o than_o if_o you_o draw_v but_o the_o thread_n open_v straight_o over_o each_o hour-line_n of_o the_o horizontal_n it_o show_v you_o where_o you_o be_v to_o draw_v all_o the_o fair_a line_n of_o the_o require_a dial._n sch._n 40._o as_o for_o the_o truth_n of_o this_o demonstration_n dial_n it_o appear_v in_o scheme_n 40._o by_o the_o right_a angle_n triangle_n ogh_n and_o ghf_n where_o hf_n be_v part_n of_o he_o a_o suppose_a meridian_n line_n on_o the_o floor_n under_o that_o in_o the_o ceiling_n g_o the_o station_n of_o the_o glass_n in_o the_o window_n h_n the_o point_n under_o the_o say_a station_n as_o former_o a_o be_v the_o point_n over_o it_o and_o to_o facilitate_v the_o demonstration_n let_v we_o imagine_v gh_o equal_a to_o give_v i._n e._n that_o the_o glass_n lie_v in_o the_o middle_n between_o the_o floor_n and_o ceiling_n this_o be_v so_o suppose_v that_o gh_a instead_o of_o represent_v a_o perpendicular_a line_n in_o the_o wall_n as_o here_o we_o conceive_v it_o have_v be_v a_o perpendicular_a stick_n and_o that_o you_o be_v to_o describe_v a_o horizontal_n dial_n on_o the_o floor_n who_o style_n be_v to_o be_v the_o say_a stick_n i_o say_v suppose_v this_o you_o must_v you_o know_v to_o perform_v the_o operation_n produce_v the_o meridian_n line_n mh_o to_o suppose_v n_o and_o fasten_v a_o string_n on_o g_o find_v in_o it_o the_o point_n v._n g._n o_o for_o the_o centre_n of_o the_o dial_n i_o mean_v a_o point_n to_o which_o a_o string_n be_v extend_v from_o g_o make_v with_o the_o meridian_n oh_o the_o angle_n of_o the_o elevation_n and_o so_o draw_v the_o several_a hour-line_n from_o the_o say_v o_o according_a to_o their_o respective_a angle_n and_o distance_n all_o which_o be_v express_v at_o large_a in_o the_o three_o 73._o scheme_n or_o first_o horizontal_n dial_n for_o there_o you_o see_v gh_n be_v a_o perpendicular_a style_n show_v the_o hour_n with_o its_o top_n and_o that_o o_o be_v the_o centre_n of_o the_o dial_n have_v a_o line_n draw_v to_o it_o from_o g_z make_v the_o angle_n of_o the_o elevation_n with_o the_o meridian_n oh_o now_o since_o o_o in_o our_o present_a case_n be_v a_o point_n without_o the_o chamber_n and_o consequent_o the_o line_n mh_o can_v be_v produce_v to_o it_o you_o must_v draw_v your_o thread_n from_o g_o to_o the_o say_a meridian_n line_n hm_n within_o the_o chamber_n and_o find_v in_o it_o the_o point_n f_o to_o wit_v the_o point_n where_o the_o say_a thread_n gf_n make_v with_o it_o a_o angle_n equal_a to_o that_o of_o the_o elevation_n for_o thereby_o you_o will_v have_v the_o distance_n of_o o_o your_o true_a centre_n from_o h_n as_o be_v the_o distance_n of_o f_o from_o h_n see_v the_o side_n gh_n be_v common_a and_o the_o angle_n in_o both_o triangle_n equal_a this_o be_v so_o if_o you_o put_v out_o of_o the_o chamber_n a_fw-fr horizontal_n dial_n who_o centre_n shall_v lie_v on_o o_o and_o its_o meridian_n line_n concur_v with_o hf_n it_o be_v but_o produce_v all_o its_o hour-line_n on_o the_o floor_n and_o it_o must_v necessary_o follow_v that_o g_o the_o top_n of_o the_o perpendicular_a style_n will_v show_v you_o true_o the_o time_n of_o