follow_v this_o azimuth_n to_o the_o finitor_n there_o be_v nonagesimus_fw-la gradus_fw-la and_o the_o altitude_n thereof_o 42_o degree_n count_v from_o the_o limb_n here_o horizon_n the_o azimuth_n thereof_o lie_v in_o the_o limb_n between_o the_o finitor_n and_o the_o meridian_n 36_o ⅓_n as_o before_o equal_a to_o the_o amplitude_n of_o the_o ascendent_n i_o number_v also_o from_o ♓_o 25_o ½_n in_o the_o meridian_n 23._o 41_o minute_n to_o the_o left_a hand_n still_o and_o there_o i_o have_v ♈_o 19_o 11_o minute_n the_o sun_n place_n which_o cut_v on_o the_o label_n 41_o ⅔_n for_o the_o altitude_n of_o the_o sun_n there_o and_o the_o label_n at_o the_o same_o time_n cut_v in_o the_o limb_n about_o 29._o from_o south_n eastward_o for_o the_o azimuth_n of_o the_o sun_n and_o after_o the_o same_o manner_n you_o have_v before_o you_o the_o altitude_n and_o azimuth_n of_o every_o other_o degree_n of_o the_o ecliptic_a for_o the_o time_n propose_v chap._n lviii_o to_o do_v the_o same_o by_o the_o nonagesimal_n projection_n if_o the_o altitude_n of_o nonagesimus_fw-la gradus_fw-la be_v first_o give_v instead_o of_o the_o altitude_n of_o culmen_fw-la caeli_fw-la set_v your_o planisphear_n in_o the_o nonagesimal_n projection_n by_o book_n 2.3_o that_o be_v make_v the_o limb_n now_o to_o represent_v the_o circle_n of_o longitude_n or_o azimuth_n for_o it_o be_v both_o which_o cut_v the_o nonagesimus_fw-la gradus_fw-la and_o make_v the_o equinoctial_a line_n here_o to_o be_v horizon_n and_o from_o the_o equinectial_a line_n number_n in_o the_o limb_n the_o altitude_n of_o nonagesimus_fw-la gradus_fw-la and_o thereto_o set_v the_o finitor_n so_o shall_v the_o finitor_n be_v ecliptic_a the_o nonagesimus_fw-la gradus_fw-la at_o the_o limb_n the_o ascendent_n and_o descendent_a at_o the_o centre_n and_o because_o the_o equinoctial_a line_n be_v horizon_n in_o this_o projection_n therefore_o the_o meridian_n become_v azimuth_n and_o the_o parallel_n almicantars_n show_v the_o altitude_n and_o azimuth_n of_o every_o degree_n of_o the_o ecliptic_a if_o you_o reckon_v as_o you_o ought_v in_o this_o manner_n reckon_v in_o the_o equinoctial_a line_n here_o horizon_n from_o the_o centre_n the_o amplitude_n of_o the_o ascendent_n to_o the_o right_a hand_n if_o it_o be_v a_o north_n sign_n and_o contrary_o if_o it_o be_v a_o south_n sign_n where_o this_o amplitude_n end_n be_v the_o east_n point_n from_o whence_o you_o shall_v reckon_v all_o your_o azimuth_n count_n thence_o to_o the_o limb_n and_o back_n again_o if_o need_v be_v in_o the_o say_v equinoctial_a line_n till_o you_o have_v make_v 90_o degree_n there_o be_v your_o meridian_n as_o far_o distant_a from_o the_o limb_n as_o the_o east_n point_n be_v from_o the_o ascendent_n follow_v this_o meridian_n to_o the_o finitor_n and_o there_o he_o show_v you_o culmen_fw-la caeli_fw-la and_o the_o parallel_n there_o cut_v show_v the_o altitude_n thereof_o now_o may_v you_o find_v every_o degree_n of_o the_o ecliptic_a above_o the_o horizon_n if_o you_o know_v but_o what_o ascend_v or_o descend_v or_o culminate_v and_o of_o every_o such_o degree_n the_o parallel_n show_v you_o the_o altitude_n and_o the_o meridian_n show_n his_o azimuth_n if_o you_o begin_v your_o number_n from_o the_o east_n or_o south_n azimuth_n example_n when_o ♋_o 24_o degree_n be_v ascend_v as_o in_o the_o example_n before_o use_v as_o by_o consequence_n ♈_o 24._o in_o nonagisimo_fw-la gradu_fw-la ♂_o be_v in_o ♉_o 4._o 45_o minute_n and_o have_v but_o 3._o or_o 4._o minute_n south_n latitude_n i_o will_v know_v ♂_o his_o altitude_n and_o azimuth_n set_v go_v the_o finitor_n above_o the_o equinoctial_a line_n 42_o degree_n which_o be_v the_o altitude_n of_o nonagesimus_fw-la gradus_fw-la i_o say_v because_o the_o nonagesimus_fw-la gradus_fw-la at_o the_o end_n of_o the_o finitor_n in_o the_o limb_n be_v ♈_o 24._o therefore_o i_o must_v count_v back_o 10._o 45_o minute_n towards_o the_o ascendent_n for_o mars_n and_o there_o the_o parallel_n 41_o degree_n with_o 10_o minute_n cut_v the_o finitor_n for_o the_o altitude_n of_o ♂_o and_o the_o 14_o meridian_n eastward_o from_o the_o limb_n give_v i_o his_o azimuth_n which_o if_o i_o begin_v to_o reckon_v from_o the_o east_n point_n fall_v out_o to_o be_v almost_o the_o 40th_o azimuth_n from_o the_o east_n mars_n his_o latitude_n here_o be_v not_o regard_v chap._n lix_n the_o nonagesimus_fw-la gradus_fw-la and_o his_o altitude_n and_o azimuth_n give_v as_o in_o the_o former_a chapter_n how_o in_o the_o same_o projection_n to_o get_v the_o altitude_n and_o azimuth_n of_o any_o planet_n or_o star_n by_o his_o longitude_n and_o latitude_n your_o palnisphear_n set_v as_o in_o the_o former_a chapter_n you_o shall_v number_v the_o longitude_n of_o the_o star_n upon_o the_o finitor_n here_o ecliptic_a beginning_n at_o the_o descendent_a or_o nonagesimus_fw-la gardus_fw-la and_o in_o the_o azimuth_n serve_v his_o longitude_n count_v his_o latitude_n by_o the_o almicantars_n at_o the_o end_n of_o which_o account_n be_v the_o star_n place_n for_o this_o time_n the_o parallel_n cut_v there_o show_v his_o altitude_n and_o the_o meridian_n cut_v there_o show_v his_o azimuth_n if_o you_o count_v from_o the_o east_n point_n as_o you_o be_v teach_v in_o the_o former_a chapter_n example_n lucida_n pleiadum_fw-la be_v in_o longitude_n ♉_o 25._o 10_o minute_n latitude_n 4_o degree_n 00_o minute_n north._n therefore_o from_o the_o nonagesimus_fw-la gradus_fw-la ♈_o 24._o i_o number_n in_o the_o finitor_n towards_o the_o ascendent_n 31._o 10_o minute_n and_o there_o be_v the_o longitude_n of_o lucida_n pleiaedum_n in_o the_o azimuth_n that_o cut_v here_o i_o go_v up_o northward_o 4_o degree_n and_o there_o i_o make_v a_o prick_n for_o lucida_n pleiadum_fw-la now_o the_o parallel_n 38_o ½_n show_v i_o his_o altitude_n and_o the_o 48th_o ½_n meridian_n from_o the_o centre_n show_v i_o that_o lucida_n pleiadum_fw-la be_v go_v 48_o ½_n in_o azimuth_n from_o the_o ascendent_n but_o from_o the_o east_n point_n only_o 12_o degree_n 10_o minute_n chap._n lx._n the_o altitude_n and_o azimuth_n of_o any_o star_n take_v and_o either_o the_o ascendent_n nonagesimus_fw-la gradus_fw-la or_o culmen_fw-la caeli_fw-la know_v how_o by_o the_o same_o nonagesimal_a projection_n to_o find_v the_o star_n longitude_n and_o latitude_n if_o you_o know_v either_o the_o ascendent_n nonagesimus_fw-la gradus_fw-la or_o culmen_fw-la caeli_fw-la you_o have_v enough_o to_o put_v your_o planisphear_n in_o the_o nonagesimal_n projection_n by_o the_o former_a chapter_n and_o your_o planisphear_n so_o set_v you_o shall_v seek_v out_o the_o meridian_n which_o stand_v for_o the_o azimuth_n in_o which_o you_o observe_v the_o star_n and_o therein_o number_n from_o the_o equinoctial_a line_n the_o altitude_n observe_v the_o azimuth_n and_o almicantar_n cut_v there_o show_v the_o longitude_n and_o latitude_n of_o the_o star_n inquire_v if_o the_o azimuth_n reach_v not_o the_o place_n of_o the_o star_n turn_v the_o reet_a half_a round_n and_o let_v the_o zenith_n and_o nadir_n point_v change_v place_n and_o your_o turn_n be_v serve_v example_n febr._n 13_o 1657_o 8._o i_o observe_v somewhat_o near_o that_o ♃_o be_v go_v westward_o from_o the_o meridian_n in_o azimuth_n 14_o degree_n and_o that_o his_o altitude_n be_v 61_o degree_n sirius_n be_v then_o in_o the_o meridian_n by_o which_o i_o have_v the_o ascendent_n culmen_fw-la and_o nonagesimus_fw-la gradus_fw-la any_o or_o all_o of_o they_o give_v for_o when_o in_o the_o equinoctial_a projection_n i_o bring_v sirius_n to_o the_o meridian_n line_n it_o be_v all_o one_o as_o if_o i_o have_v set_v the_o sun_n place_n to_o the_o hour_n of_o the_o night_n by_o chapter_n 46._o and_o i_o see_v there_o culminate_v with_o sirius_n ♋_o 7._o 10_o minute_n who_o meridian_n altitude_n by_o the_o 46._o be_v 61._o 5_o minute_n and_o i_o see_v ♎_o 5_o ½_n ascend_v in_o my_o horizon_n and_o ♈_o 5_o ½_n descend_v therefore_o ♋_o 5_o ½_n be_v nonagesimus_fw-la gradus_fw-la which_o be_v 90_o degree_n distant_a both_o from_o the_o ascendent_n and_o descendent_a his_o altitude_n by_o chapter_n 55._o 61._o 10_o minute_n almost_o therefore_o i_o set_v the_o finitor_n 61._o 10_o minute_n above_o meridies_n as_o chapter_n 58._o and_o in_o the_o finitor_n at_o the_o limb_n i_o count_v ♋_o 5_o ½_n nonagesimus_fw-la gradus_fw-la thence_o i_o go_v inward_o in_o the_o finitor_n 1._o 40_o minute_n where_o i_o come_v to_o ♋_o 7._o 10._o the_o degree_n of_o culmination_n this_o degree_n be_v cut_v by_o the_o four_o meridian_n from_o the_o limb_n whereby_o i_o learn_v that_o this_o four_o meridian_n will_v be_v the_o meridian_n of_o my_o place_n and_o that_o the_o amplitude_n of_o the_o nonagesimus_fw-la gradus_fw-la and_o likewise_o of_o the_o ascendent_n be_v 4_o degree_n now_o to_o place_v ♃_o in_o the_o mater_fw-la i_o count_v his_o azimuth_n first_o beginning_n from_o the_o meridian_n of_o my_o
30_o degree_n i_o say_v here_z begins_z â™’_o and_o go_v on_o 26._o 22._o minute_n further_o i_o say_v thus_o far_o be_v the_o star_n go_v in_o longitude_n now_o here_o cut_v the_o finiter_n by_o this_o account_n the_o azimuth_n 35_o â…“_n from_o the_o limb_n in_o this_o azimuth_n i_o number_v the_o star_n latitude_n by_o the_o almicantars_n 22.07_o ½_n and_o at_o the_o end_n of_o that_o number_n in_o the_o say_a azimuth_n i_o prick_v the_o star_n place_n and_o here_o i_o see_v the_o 8_o parallel_v of_o north_n declination_n upon_o the_o mater_n cut_v he_o and_o the_o meridian_n 51_o â…“_n from_o the_o limb_n show_v the_o excess_n of_o his_o right_a ascension_n above_o 270._o which_o i_o keep_v before_o therefore_o i_o conclude_v the_o right_a ascension_n of_o eniph_n alpharat_n anno_fw-la dom._n 1600_o be_v 321._o 20_o minute_n and_o his_o declination_n 8._o deg_fw-la north._n past_o this_o on_o fol._n 102_o so_o as_o it_o may_v lie_v open_a while_o that_o chapter_n be_v read_v another_o way_n to_o place_v the_o star_n in_o the_o mater_fw-la by_o their_o declination_n and_o horary-distance_n from_o the_o meridian_n see_v hereafter_o chapter_n 52._o chap._n xxxvi_o the_o latitude_n and_o declination_n of_o a_o star_n give_v to_o find_v his_o longitude_n and_o right_a ascension_n set_v your_o planisphear_n in_o the_o second_o mode_n of_o the_o meridional_a projection_n turn_v the_o zenith_n northward_o or_o southward_o as_o the_o star_n latitude_n happen_v to_o be_v north_n or_o south_n then_o look_v where_o the_o parallel_n of_o the_o star_n latitude_n in_o the_o reet_n cut_v the_o parallel_n of_o the_o star_n declination_n on_o the_o mater_n the_o azimuth_n cut_v that_o intersection_n show_v the_o longitude_n of_o the_o star_n and_o the_o meridian_n there_o cut_v show_v his_o right_a ascension_n example_n the_o declination_n of_o spica_fw-la â™_o anno_fw-la dom._n 1670._o will_v be_v 9_o ½_n south_n the_o latitude_n be_v always_o 1._o 59_o minute_n south_n now_o where_o the_o second_o almicantar_n cut_v the_o 9_o ½_n parallel_v of_o south_n declination_n there_o pass_v the_o 19_o ¼_n azimuth_n from_o the_o axis_n towards_o my_o left_a hand_n show_v spica_n longitude_n ♎_o 19_o ¼_n and_o the_o 17_o meridian_n from_o the_o axis_n to_o which_o i_o add_v a_o semicircle_n because_o ♎_o 0._o be_v at_o the_o centre_n and_o i_o make_v 197_o degree_n the_o right_a ascension_n of_o spica_fw-la for_o 1670._o chap._n xxxvii_o the_o longitude_n and_o latitude_n of_o two_o star_n give_v to_o find_v their_o distance_n make_v one_o of_o the_o pole_n of_o the_o mater_n to_o be_v pole_n of_o the_o ecliptic_a for_o this_o turn_n and_o set_v the_o star_n which_o have_v most_o latitude_n at_o his_o distance_n in_o the_o limb_n and_o turn_v the_o zenith_n to_o he_o count_v thence_o by_o the_o meridian_n the_o difference_n of_o longitude_n till_o you_o come_v to_o the_o other_o side_n of_o your_o triangle_n and_o in_o that_o side_n number_n either_o the_o latitude_n from_o the_o equator_fw-la or_o his_o compliment_n from_o the_o pole_n at_o the_o end_n of_o this_o number_n be_v the_o other_o star_n and_o the_o azimuth_n pass_v from_o he_o to_o the_o zenith_n show_v the_o distance_n this_o be_v do_v by_o the_o second_o problem_n of_o obliquangled_a triangle_n book_n 3.15_o example_n in_o tycho'es_n table_n for_o 1600._o aldebarans_n longitude_n be_v ♊_o 4.12_o ½_n latitude_n 5._o 31._o min._n a._n sirius_n longitude_n ♋_o 8._o 35_o ½_n latitude_n 39_o 30_o ½_n a._n difference_n of_o longitude_n 34._o 23._o i_o number_v therefore_o 39_o 30_o minute_n ½_n the_o latitude_n of_o sirius_n from_o the_o equator_fw-la in_o the_o limb_n or_o the_o compliment_n thereof_o from_o the_o pole_n all_o be_v one_o there_o i_o set_v the_o zenith_n to_o stand_v for_o sirius_n then_o because_o aldebaran_n be_v distant_a from_o sirius_n in_o longitude_n 34._o 23._o minute_n i_o take_v the_o 34_o ½_n meridian_n from_o the_o zenith_n and_o where_o the_o 5_o ½_n parallel_n cut_v he_o there_o say_v i_o be_v aldebaran_n and_o c_o of_o my_o triangle_n and_o the_o azimuth_n pass_v thence_o to_o the_o zenith_n measure_v the_o distance_n of_o the_o star_n 46_o degree_n almost_o chap._n xxxviii_o the_o declination_n and_o right_a ascension_n of_o any_o two_o star_n give_v to_o find_v their_o distance_n do_v here_o with_o the_o right_a ascension_n and_o declination_n as_o you_o shall_v do_v with_o the_o longitude_n and_o latitude_n by_o the_o former_a chapter_n for_o the_o case_n be_v like_a and_o require_v the_o same_o manner_n of_o work_v chap._n thirty-nine_o the_o declination_n of_o a_o star_n or_o planet_n and_o his_o distance_n from_o a_o know_a star_n give_v to_o find_v his_o right_a ascension_n because_o this_o case_n be_v the_o converse_n of_o the_o precedent_n and_o soluble_a by_o the_o first_o problem_n of_o obliquangled_a triangle_n book_n 3._o 14._o a_o example_n or_o two_o shall_v suffice_v past_o this_o on_o fol._n 105_o so_o as_o it_o may_v lie_v open_a while_o that_o chapter_n be_v read_v a_o b_o the_o distance_n of_o mandibulae_fw-la from_o the_o pole_n 87._o 20_o minute_n i_o set_v between_o the_o pole_n and_o nadir_n in_o the_o limb_n because_o b_o c_o will_n reach_n beyond_o the_o finitor_n for_o a_o c_o the_o distance_n of_o the_o star_n i_o seek_v the_o 13_o parallel_v from_o the_o pole_n and_o for_o b_o c_o i_o seek_v the_o 94._o 50_o minute_n almicantar_n count_v from_o the_o nadir_n that_o be_v the_o 5_o almost_o above_o the_o finitor_n and_o where_o the_o say_a parallel_n and_o almicantar_n cross_v there_o be_v cor_fw-la caeti_fw-la and_o c_o of_o my_o triangle_n through_o it_o there_o cut_v the_o azimuth_n 10_o â…”_n show_v the_o difference_n of_o the_o right_a ascension_n of_o the_o star_n which_o difference_n i_o subtract_v out_o of_o the_o right_a ascension_n of_o mandibula_fw-la because_o he_o be_v further_a east_n and_o there_o remain_v the_o right_a ascension_n of_o cor_fw-la caeti_fw-la 30._o 16_o minute_n or_o rather_o 13_o minute_n and_o i_o have_v here_o also_o number_v by_o the_o meridian_n the_o angle_n a_o at_o mandibula_fw-la 120_o degr_fw-la though_o un-required_n another_o example_n january_n 7._o 1656_o 7_o i_o observe_v by_o my_o brass_n quadrant_n of_o 12_o inch_n in_o radius_fw-la the_o meridian_n altitude_n of_o jupiter_n 56._o 20_o minute_n out_o of_o which_o subtract_v the_o height_n of_o the_o equator_fw-la here_o at_o ecton_n 37._o 45_o minute_n i_o find_v his_o declination_n 18._o 35_o minute_n north_n his_o distance_n then_o from_o lucida_n pleiadum_fw-la i_o observe_v by_o my_o crossstaff_n 5._o 12_o minute_n and_o from_o aldebaran_n 10.07_o minute_n the_o compliment_n of_o decli_n of_o lucida_n pleiadum_fw-la be_v 67.00_o mi._n the_o compliment_n of_o ♃_o his_o declination_n be_v observe_v 71._o 25._o and_o these_o two_o compliment_n with_o the_o distance_n of_o ♃_o and_o lucida_n pleiadum_fw-la 5._o 12_o minute_n make_v a_o triangle_n soluble_a by_o the_o first_o problem_n of_o obliquangled_a triangle_n whereby_o you_o may_v find_v the_o angle_n of_o the_o difference_n of_o right_a ascension_n of_o lucida_n pleiadum_fw-la and_o ♃_o be_v 2._o 56_o minute_n which_o add_v to_o the_o right_a ascension_n of_o lucida_n pleiadum_fw-la because_o ♃_o be_v eastward_o make_v 54._o 44_o minute_n the_o right_a ascension_n of_o jupiter_n chap._n xl._n the_o latitude_n of_o a_o star_n or_o planet_n and_o his_o distance_n from_o a_o know_a star_n give_v to_o find_v his_o longitude_n do_v here_o with_o the_o longitude_n and_o latitude_n as_o you_o be_v teach_v to_o do_v with_o the_o right_a ascension_n and_o declination_n in_o the_o former_a chapter_n chap._n xli_o to_o find_v the_o distance_n of_o two_o star_n by_o their_o altitude_n and_o their_o difference_n of_o azimuth_n observe_v at_o the_o same_o time_n the_o compliment_n of_o the_o altitude_n be_v the_o distance_n of_o the_o star_n from_o the_o zenith_n set_v one_o of_o the_o star_n at_o the_o pole_n and_o set_v the_o zenith_n as_o much_o from_o he_o in_o the_o limb_n as_o the_o compliment_n of_o his_o altitude_n come_v to_o then_o consider_v what_o difference_n of_o azimuth_n the_o star_n have_v take_v the_o azimuth_n of_o like_a distance_n from_o the_o limb_n begin_v from_o that_o side_n of_o the_o limb_n where_o the_o pole_n aforesaid_a be_v and_o in_o that_o azimuth_n reckon_v from_o the_o finitor_n the_o altitude_n of_o the_o other_o star_n or_o the_o compliment_n of_o his_o altitude_n from_o the_o zenith_n all_o be_v one_o at_o the_o end_n thereof_o be_v c_o and_o the_o other_o star_n and_o the_o meridian_n that_o pass_v from_o he_o to_o the_o pole_n show_v the_o distance_n of_o the_o star_n this_o case_n be_v so_o like_a that_o of_o chapter_n 37._o that_o he_o who_o know_v one_o may_v know_v the_o other_o also_o chap._n xlii_o to_o find_v the_o angle_n of_o
london_n from_o jerusalem_n chap._n lxx_o the_o latitude_n and_o distance_n of_o two_o place_n give_v to_o find_v the_o difference_n of_o longitude_n the_o triangle_n will_v stand_v as_o in_o the_o former_a chapter_n there_o by_o two_o side_n and_o the_o angle_n comprehend_v you_o seek_v the_o three_o side_n by_o problem_n 2._o obliquangled_a triangle_n here_o by_o three_o side_n give_v you_o seek_v a_o angle_n by_o problem_n 1_o obliquangled_a triangle_n make_v the_o pole_n pole_n and_o set_v the_o zenith_n to_o the_o latitude_n of_o one_o of_o the_o place_n as_o you_o do_v london_n chapter_n 69._o 38._o 28_o minute_n from_o the_o pole_n than_o number_n the_o compliment_n of_o the_o latitude_n of_o the_o other_o place_n from_o the_o pole_n by_o the_o parallel_n and_o the_o distance_n of_o the_o two_o place_n from_o the_o zenith_n by_o the_o almicantars_n and_o where_o the_o last_o parallel_n and_o last_o almicantar_n meet_v be_v c_o of_o your_o triangle_n see_v book_n 3._o 14._o now_o count_v how_o many_o meridian_n there_o be_v between_o c_o and_z the_o limb_n so_o many_o degree_n be_v the_o angle_n at_o the_o pole_n seek_v for_o the_o difference_n of_o longitude_n example_n have_v the_o distance_n of_o london_n from_o the_o pole_n 38._o 28_o minute_n and_o of_o jerusalem_n from_o the_o pole_n 58._o 5_o minute_n and_o the_o distance_n of_o london_n from_o jerusalem_n 2300._o common_a english_a mile_n of_o which_o 60._o make_v a_o degree_n i_o set_v the_o zenith_n for_o london_n 38._o 28_o minute_n from_o the_o pole_n in_o the_o limb_n then_o because_o jerusalem_n be_v distant_a from_o the_o pole_n 58._o 5_o minute_n i_o go_v to_o the_o 58th_o parallel_n from_o the_o pole_n and_o lay_v one_o finger_n or_o the_o point_n of_o a_o bodkin_n on_o he_o and_o because_o london_n be_v distant_a from_o jerusalem_n 38_o degree_n 20_o minute_n i_o count_v from_o the_o zenith_n to_o the_o almicantar_n 38._o 20_o minute_n now_o where_o this_o almicantar_n cross_v the_o parallel_n last_o find_v there_o be_v c_o of_o the_o triangle_n and_o the_o place_n of_o jerusalem_n and_o you_o may_v see_v that_o you_o must_v cross_v 46._o meridian_n before_n you_o can_v go_v thence_o to_o the_o zenith_n in_o the_o limb_n which_o show_v that_o the_o angle_n at_o the_o pole_n for_o the_o difference_n of_o longitude_n be_v 46._o chap._n lxxi_o to_o find_v what_o degree_n of_o the_o ecliptic_a culminate_v in_o another_o country_n at_o any_o time_n propose_v if_o the_o difference_n of_o longitude_n be_v know_v in_o the_o equinoctial_a projection_n bring_v the_o sun_n place_n to_o the_o hour_n propose_v by_o help_n of_o the_o label_n and_o in_o the_o noon-line_n you_o see_v present_o what_o degree_n culminate_v in_o your_o country_n as_o chapter_n 46_o be_v show_v now_o to_o know_v this_o for_o another_o town_n set_v the_o label_n so_o many_o degree_n from_o the_o noon-line_n as_o the_o difference_n of_o longitude_n require_v and_o that_o eastward_o if_o the_o place_n propose_v be_v east_n or_o westward_o if_o it_o bear_v west_n and_o so_o the_o label_n shall_v cut_v the_o degree_n of_o culmination_n for_o the_o place_n propose_v example_n if_o it_o be_v demand_v what_o degree_n be_v culminate_v at_o jerusalem_n march_v 10._o at_o 10._o a_o clock_n before_o noon_n i_o will_v set_v the_o sun_n place_n ♈_o 0._o to_o the_o hour_n and_o i_o see_v upon_o the_o noon_n line_n which_o be_v our_o meridian_n there_o culminate_v ♒_o 28_o almost_o now_o for_o the_o meridian_n of_o jerusalem_n i_o must_v lay_v the_o label_n 46_o degree_n eastward_o that_o be_v from_o meridies_n towards_o oriens_fw-la and_o look_v what_o star_n or_o degree_n of_o the_o ecliptic_a be_v then_o cut_v by_o the_o label_n that_o be_v then_o culminate_v in_o the_o meridian_n at_o jerusalem_n as_o here_o i_o find_v ♈_o 17_o ½_n for_o in_o this_o projection_n the_o label_n lay_v he_o where_o you_o will_v be_v a_o meridian_n chap._n lxxii_o to_o find_v what_o a_o clock_n it_o be_v in_o another_o country_n by_o know_v the_o hour_n at_o home_n and_o the_o difference_n of_o longitude_n this_o be_v do_v easy_o enough_o without_o a_o instrument_n for_o if_o you_o turn_v the_o difference_n of_o longitude_n into_o hour_n and_o minute_n and_o add_v the_o same_o to_o your_o hour_n for_o any_o place_n which_o lie_v eastward_o or_o subtract_v the_o same_o for_o any_o place_n which_o lie_v westward_o you_o shall_v make_v the_o hour_n of_o the_o place_n example_n the_o difference_n of_o longitude_n between_o london_n and_o jerusalem_n be_v 46._o or_o be_v convert_v into_o time_n 3_o hour_n 4_o minute_n therefore_o add_v this_o to_o the_o time_n at_o london_n i_o say_v when_o it_o be_v noon_n at_o london_n it_o be_v 4_o minute_n past_o 3_o a_o clock_n after_o noon_n at_o jerusalem_n and_o when_o it_o be_v 2_o a_o clock_n at_o london_n it_o be_v 5._o and_o 4_o minute_n at_o jerusalem_n if_o you_o will_v do_v it_o by_o the_o planisphear_n you_o shall_v do_v it_o in_o the_o equinoctial_a projection_n thus_o whereas_o the_o limb_n of_o your_o rect_a be_v graduate_v into_o 360_o degree_n if_o you_o distinguish_v the_o hour_n also_o at_o every_o 15_o degree_n begin_v at_o the_o zenith_n which_o shall_v be_v 12_o and_o number_v thence_o in_o the_o limb_n of_o your_o reet_n to_o your_o right_a hand_n or_o westward_o 1_o 2_o 3_o etc._n etc._n then_o shall_v you_o need_v to_o do_v no_o more_o but_o set_v the_o zenith_n to_o the_o difference_n of_o longitude_n east_n or_o west_n from_o your_o meridian_n as_o the_o strange_a place_n happen_v to_o be_v situate_a for_o then_o the_o label_n lay_v to_o the_o hour_n of_o your_o country_n in_o the_o limb_n of_o the_o mater_n shall_v show_v the_o hour_n of_o the_o other_o country_n in_o the_o limb_n of_o the_o reet_n and_o so_o the_o zenith_n be_v lay_v to_o 60_o degree_n westward_o which_o be_v the_o meridian_n of_o the_o isle_n of_o barbados_n the_o label_n lay_v to_o meridies_n shall_v cut_v in_o the_o limb_n of_o the_o reet_n 8_o of_o the_o clock_n before_o noon_n which_o show_v i_o that_o when_o it_o be_v noon_n with_o we_o it_o be_v at_o barbados_n but_o eight_o in_o the_o morning_n the_o end_n of_o the_o four_o book_n chap._n lxxiii_o the_o longitude_n and_o latitude_n of_o one_o place_v know_v and_o the_o rumb_n and_o distance_n of_o a_o second_o place_n to_o find_v both_o the_o longitude_n and_o latitude_n of_o the_o second_o place_n set_v the_o zenith_n to_o the_o latitude_n of_o the_o first_o place_n then_o seek_v the_o azimuth_n which_o serve_v for_o the_o rumb_n of_o the_o second_o place_n and_o in_o that_o azimuth_n count_v his_o distance_n from_o the_o zenith_n where_o this_o distance_n end_v there_o be_v the_o second_o place_n whole_a latitude_n be_v show_v you_o by_o the_o parallel_n which_o cut_v he_o and_o the_o meridian_n cut_v there_o also_o show_v his_o longitude_n example_n let_v z_o be_n london_n and_o because_o jerusalem_n bear_v from_o london_n almost_o s_n b_o e_o or_o 77_o ½_n from_o south_n eastward_o therefore_o i_o choose_v the_o azimuth_n 77_o ½_n z_o k._n therein_o i_o number_v jerusalem_n distance_n from_o london_n z_o i_o 2300._o mile_n or_o minute_n that_o be_v 38._o 20._o minute_n now_o in_o the_o triangle_n z_o p_o i_o i_o may_v find_v p_o i_o the_o compliment_n of_o jerusalem_n latitude_n 58._o 05._o minute_n and_o z_o p_o i_o the_o difference_n of_o longitude_n 46_o which_o must_v be_v add_v to_o the_o longitude_n of_o london_n to_o make_v the_o longitude_n of_o jerusalem_n chap._n lxxiv_o the_o latitude_n and_o distance_n of_o two_o place_n give_v to_o find_v the_o rumb_n and_o the_o difference_n of_o longitude_n count_n in_o the_o meridian_n from_o p_o the_o pole_n the_o compliment_n of_o the_o latitude_n of_o the_o first_o place_n and_o thereto_o set_v z_o the_o zenith_n count_n also_o from_o p_o the_o compliment_n of_o the_o latitude_n of_o the_o second_o place_n and_o lay_v your_o finger_n on_o the_o parallel_n at_o which_o your_o number_n end_v count_n also_o from_o z_o the_o distance_n of_o the_o place_n in_o degree_n and_o minute_n and_o note_v the_o almicantar_n at_o which_o this_o number_n end_v where_o this_o almicantar_n cross_v the_o aforesaid_a parallel_n there_o be_v c_o of_o your_o triangle_n but_o here_o mark_v i_o look_v what_o azimuth_n cut_v here_o it_o show_v the_o rumb_n and_o the_o meridian_n that_o cut_v here_o if_o you_o count_v his_o distance_n from_o the_o limb_n show_v the_o difference_n of_o the_o longitude_n of_o the_o place_n this_o be_v so_o plain_a from_o chapter_n 69_o 70_o and_o 73_o that_o it_o need_v no_o example_n the_o same_o scheam_n serve_v these_o 4_o chapter_n the_o end_n of_o the_o four_o book_n the_o five_o book_n show_v the_o way_n to_o resolve_v all_o gnomonical_a
to_o take_v your_o point_n in_o the_o tropique_n at_o the_o large_a distance_n as_o i_o have_v here_o do_v if_o there_o be_v room_n enough_o on_o the_o ceiling_n but_o because_o it_o often_o happen_v that_o part_n of_o your_o dyal_n fall_v beside_o the_o ceiling_n and_o the_o plain_a of_o the_o ceiling_n and_o of_o the_o wall_n be_v often_o interrupt_v and_o make_v irregular_a by_o beam_n wal-plate_n corrish_n wainscot_n chimney-peece_n and_o such_o like_a body_n i_o will_v â—hew_v you_o one_o absolute_a device_n to_o carry_v on_o your_o hour_n line_n over_o all_o extend_v the_o thread_n for_o any_o hour_n line_n to_o the_o tropic_n of_o cancerâ—n_n â—n_z the_o ceiling_n as_o you_o where_o teach_v before_o and_o fix_v it_o there_o and_o extend_v another_o thread_n in_o like_a manner_n to_o the_o tropic_n of_o copricorn_n where_o ever_o it_o shall_v happen_v as_o perhaps_o beyond_o the_o middle_a beam_n or_o quite_o beyond_o the_o ceiling_n upon_o the_o wall_n and_o fix_v that_o thread_n also_o then_o place_v your_o ey_fw-mi so_o behind_o these_o thread_n that_o one_o of_o they_o may_v cover_v the_o other_o and_o at_o the_o same_o instant_n where_o the_o upper_a line_n to_o your_o sight_n or_o imagination_n cut_v the_o ceiling_n beam_n wall_n or_o any_o regular_a or_o irregular_a body_n above_o the_o end_n of_o the_o low_a line_n there_o shall_v the_o hour_n line_n pass_v from_o tropic_n to_o tropic_n direct_v any_o by-stander_n to_o make_v mark_n as_o many_o as_o you_o shall_v need_v and_o by_o these_o mark_n draw_v the_o hour_n line_n according_a to_o your_o desire_n if_o the_o arch_n of_o the_o horizon_n between_o the_o tropique_n be_v within_o view_n of_o your_o window_n you_o shall_v draw_v the_o same_o on_o the_o wall_n to_o bound_v the_o parallel_n the_o orison_n altitude_n you_o know_v be_v nothing_o and_o therefore_o he_o will_v be_v a_o level_a line_n and_o the_o sun_n azimuth_n when_o he_o rise_v common_o call_v amplitude_n and_o ortive_a latitude_n be_v in_o cancer_n 40.40_o minute_n east_n northward_o and_o in_o capricorn_n as_o much_o southward_n and_o these_o will_v be_v reflect_v to_o the_o contrary_a coast_n on_o the_o dyal_n the_o end_n of_o the_o five_o book_n a_o brief_a description_n of_o a_o crossstaff_n the_o crossstaff_n consist_v of_o two_o rule_n join_v by_o a_o socket_n or_o else_o pin_v in_o the_o form_n of_o a_o roman_a t_n and_o three_o sight_n or_o more_o the_o long_a ruler_n be_v call_v radius_fw-la index_n and_o the_o yard_n as_o a_o b_o of_o which_o i_o call_v a_o the_o near_a end_n b_o the_o further_a end_n the_o breadth_n will_v be_v ¾_n of_o a_o inch_n the_o depth_n a_o inch_n and_o half_a the_o length_n 70_o or_o 80._o inch_n and_o every_o of_o those_o inch_n will_v be_v divide_v by_o parallel_n and_o diagonal_a line_n into_o 100_o equal_a part_n the_o short_a ruler_n e_o f_o be_v call_v the_o transom_n it_o will_v be_v half_a a_o inch_n or_o three_o quarter_n both_o in_o breadth_n and_o depth_n and_o in_o length_n about_o 2._o foot_n for_o the_o sight_n there_o if_o i_o may_v advise_v you_o will_v never_o be_v set_v above_o 20_o inch_n asunder_o this_o transom_n will_v be_v divide_v into_o whole_a inch_n only_o begin_v in_o the_o midst_n at_o b_o in_o the_o visual_a line_n ☉_o b._n and_o number_v to_o 10_o both_o way_n the_o sight_n c_o and_o d_o must_v have_v socket_n at_o the_o bottom_n through_o which_o the_o transom_n must_v pass_v so_o that_o the_o sight_n may_v be_v set_v to_o any_o division_n of_o the_o transom_n the_o vane_n or_o top_n of_o those_o sight_n must_v have_v only_o two_o edge_n on_o their_o side_n visible_a to_o your_o eye_n namely_o those_o edge_n which_o touch_v the_o transom_n and_o the_o two_o other_o edge_n must_v be_v pare_v away_o the_o middle_a sight_n at_o b_o will_v have_v half_a his_o head_n cut_v away_o and_o a_o shoulder_n leave_v as_o in_o the_o figure_n and_o a_o tenon_n at_o the_o bottom_n fit_v to_o a_o mortess_n make_v in_o the_o middle_n of_o the_o transom_n that_o you_o may_v stick_v he_o in_o and_o take_v he_o out_o when_o you_o please_v for_o to_o this_o mortess_n you_o shall_v do_v well_o to_o fit_v two_o other_o movable_a sight_n very_o narrow_a for_o observe_v the_o diameter_n of_o the_o moon_n or_o the_o distance_n of_o star_n which_o be_v very_o near_o one_o may_v be_v about_o half_a a_o inch_n broad_a and_o the_o other_o about_o a_o quarter_n this_o crossstaff_n be_v exact_o make_v by_o mr._n anthony_n thomson_n in_o hosier_n lane_n london_n when_o you_o will_v use_v this_o staff_n you_o shall_v first_o set_v the_o sight_n of_o the_o transom_n to_o like_a inch_n as_o at_o 10_o and_o 10._o if_o the_o angle_n be_v great_a or_o at_o 5_o and_o 5._o as_o in_o the_o figure_n they_o be_v place_v always_o set_v they_o at_o whole_a inch_n and_o at_o like_a number_n on_o both_o side_n from_o the_o middle_n of_o the_o transom_n and_o choose_v to_o place_v those_o sight_n so_o that_o your_o eyesight_n may_v be_v far_o distant_a from_o they_o in_o observe_v for_o so_o you_o may_v the_o more_o distinct_o observe_v the_o minute_n and_o second_n of_o the_o angle_n inquire_v then_o rest_v the_o further_a end_n of_o the_o index_n upon_o a_o wall_n or_o some_o device_n fit_v for_o that_o purpose_n put_v the_o near_a end_n over_o your_o right_a shoulder_n and_o set_v your_o ey_fw-mi to_o the_o ey-hole_n slip_v the_o index_n backward_o or_o forward_o till_o you_o see_v the_o object_n by_o the_o side_n of_o the_o sight_n of_o the_o transom_n and_o mark_v what_o number_n the_o backside_n of_o the_o eyesight_n cut_v upon_o the_o index_n for_o that_o shall_v give_v you_o the_o angle_n seek_v in_o this_o manner_n example_n the_o sight_n of_o the_o transom_n be_v set_v at_o 5_o and_z 5_o that_o be_v 10._o inch_n asunder_o i_o observe_v two_o steeple_n by_o their_o edge_n and_o the_o eyesight_n then_o cut_v upon_o the_o index_n 6625._o that_o be_v inch_n 66_o ¼_n from_o the_o transom_n i_o say_v therefore_o as_o c_o b_o 500_o to_o b_o g_z 6625._o so_z c_o b_o radius_fw-la or_o 100000._o to_o b_o g_o the_o co-tangent_a of_o half_a the_o angle_n here_o i_o have_v no_o more_o to_o do_v then_o to_o divide_v 662500000._o by_o 500_o or_o 6625000._o by_o 5._o which_o be_v a_o easy_a work_n and_o the_o quotient_a 1325000._o be_v the_o co-tangent_a of_o 4._o degree_n 18._o minute_n 57_o second_o 43._o three_o for_o half_a the_o angle_n note_v here_o that_o if_o the_o sight_n have_v stand_v at_o 10_o and_o 10._o then_o have_v the_o number_n 6625._o be_v the_o very_a co-tangent_a of_o half_a the_o angle_n and_o remember_v that_o your_o radius_fw-la on_o the_o transom_n have_v but_o 1000_o actual_a part_n go_v to_o the_o canon_n and_o cut_v off_o so_o many_o place_n as_o may_v leave_v the_o radius_fw-la there_o but_o 1000_o you_o shall_v find_v your_o number_n 6625_o to_o be_v the_o co-tangent_a of_o 8._o 35_o minute_n note_v also_o that_o you_o may_v observe_v the_o angle_n between_o the_o middle_a 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hour_n 34._o minute_n during_o the_o great_a part_n of_o which_o time_n the_o moon_n be_v quite_o lose_v though_o the_o sky_n be_v clear_a when_o the_o moon_n begin_v to_o recover_v light_n she_o be_v in_o the_o foremost_a foot_n of_o apollo_n between_o the_o two_o star_n of_o the_o three_o magnitude_n a_o line_n draw_v between_o those_o star_n do_v cut_v off_o the_o low_a part_n of_o the_o moon_n body_n to_o ⅙_n of_o her_o diameter_n and_o set_v the_o distance_n of_o the_o star_n in_o 12._o part_n the_o moon_n have_v go_v 7_o ½_n of_o those_o part_n towards_o the_o easterly_a star_n which_o be_v in_o calce_fw-la apollinis_fw-la hence_o i_o compute_v the_o apparent_a longitude_n of_o the_o moon_n at_o the_o time_n of_o emergence_n ♊_o 29._o 36._o minute_n 19_o second_o and_o her_o apparent_a latitude_n 0._o 44._o minute_n south_n 2._o at_o easton_n macodit_n who_o longitude_n be_v west_n from_o london_n 0._o 43._o minute_n of_o space_n that_o be_v almost_o 3_o minute_n of_o time_n the_o latitude_n 52._o 13._o minute_n anno_fw-la dom._n 1641._o upon_o friday_n october_n 8._o i_o observe_v the_o end_n of_o the_o total_a eclipse_n of_o the_o moon_n when_o lyra_n have_v altitude_n 48._o 48._o minute_n that_o be_v at_z 8_o hour_n 38._o minute_n 08._o second_o after_o noon_n 3._o at_o ecton_n who_o longitude_n be_v west_n from_o london_n 45._o minute_n of_o space_n or_o 3._o minute_n of_o time_n latitude_n 52._o 15._o minute_n anno_fw-la dom._n 1645_o upon_o monday_n angust_n 11._o i_o observe_v the_o eclipse_n of_o the_o sun_n end_v when_o the_o centre_n of_o the_o sun_n be_v in_o azimuch_o 0._o 55._o minute_n past_o the_o south_n that_o be_v 0._o hour_n 2_o ½_n minute_n after_o noon_n this_o eclipse_n hevelius_n observe_v to_o end_v at_o danizick_n at_o 1._o hour_n 53_o minute_n as_o he_o write_v in_o his_o selenographia_fw-la 4._o at_o ecton_n aforesaid_a anno_fw-la dom._n 1649._o upon_o wednesday_n may_v 16._o before_o noon_n i_o observe_v in_o the_o company_n 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0._o ⅛_n 0._o 41.56_o 4._o 1.47.28_o 1._o  _fw-fr 49.48_o 3._o 2.03.28_o 2._o  _fw-fr 59.44_o 2._o 15.32_o 3._o 1._o 09.44_o 1._o 22.40_o 4._o  _fw-fr 26.12_o 0._o 31.04_o 4._o ⅛_n 33.32_o  _fw-fr  _fw-fr 6._o at_o easton_n macodit_fw-la anno_fw-la domi._n 1651_o 2._o on_o monday_n march_v 15._o in_o the_o morning_n i_o observe_v with_o dr_n twysden_n that_o the_o moon_n be_v eclipse_v about_o one_o digit_fw-la when_o alkair_o be_v in_o azimuth_n 79._o 40._o minute_n from_o the_o south_n eastward_o more_o we_o can_v not_o see_v for_o cloud_n 7._o at_o ecton_n anno_fw-la dom._n 1652._o on_o monday_n march_v 29._o before_o noon_n i_o observe_v the_o great_a eclipse_n of_o the_o sun_n by_o a_o telescope_n and_o a_o minute-watch_n rectify_v by_o the_o azimuth_n of_o the_o sun_n take_v both_o before_o and_o
projection_n the_o concurrent_a circle_n meet_v in_o the_o pole_n a_o and_o b_o be_v meridian_n those_o meridian_n be_v 180_o in_o number_n and_o divide_v the_o equator_fw-la c_o d_o into_o 360._o degree_n because_o every_o one_o of_o they_o cut_v it_o twice_o that_o be_v once_o in_o each_o hemisphere_n by_o these_o be_v number_v the_o right_a ascension_n of_o the_o star_n and_o planet_n and_o the_o hour_n and_o minute_n of_o day_n and_o night_n for_o every_o 15_o of_o these_o meridian_n number_v from_o the_o limb_n be_v a_o hour_n circle_n as_o have_v be_v show_v book_n 1.6_o they_o be_v number_v from_o d_o to_z c_z that_o be_v from_o septentrio_fw-la to_o meridies_n 1.2.3_o etc._n etc._n for_o the_o morning_n hour_n and_o back_o again_o from_o c_z to_z d_o in_o like_a manner_n for_o the_o afternoon_n the_o axletree_n line_n a_o b_o fall_v out_o to_o be_v the_o six_o a_o clock_n line_v both_o way_n by_o those_o meridian_n also_o be_v number_v the_o longitude_n of_o town_n and_o 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azimuth_n shall_v be_v almicanter_n or_o circle_n of_o altitude_n the_o diameter_n cross_v the_o axletree_n of_o the_o reet_n at_o right_a angle_n shall_v be_v the_o horizon_n or_o finiter_n who_o graduation_n be_v set_v to_o he_o in_o a_o border_n below_o the_o centre_n and_o from_o he_o be_v the_o almicanter_n reckon_v upward_o to_o the_o zenith_n the_o azimuth_n may_v be_v reckon_v from_o the_o north_n or_o south_n semicircle_n of_o the_o meridian_n or_o from_o the_o axtree_n line_n of_o the_o reet_n which_o be_v the_o east_n or_o west_n azimuth_n common_o call_v the_o prime_n vertical_a when_o i_o bid_v you_o set_v the_o vertex_fw-la of_o the_o reet_n to_o the_o latitude_n of_o your_o place_n you_o must_v first_o know_v what_o your_o latitude_n be_v it_o be_v the_o near_a distance_n of_o your_o place_n from_o the_o terrestrial_a equinoctial_a number_v in_o degree_n and_o minute_n of_o a_o great_a circle_n the_o latitude_n of_o london_n be_v 31_o degr_n 32_o min._n north._n the_o 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the_o mater_n or_o the_o innermost_a circle_n of_o the_o ring_n now_o be_v the_o upper_a semicircle_n of_o your_o meridian_n divide_v into_o four_o notable_a part_n from_o the_o zenith_n southward_o to_o the_o equator_fw-la be_v the_o latitude_n 51._o degree_n 32_o minute_n from_o thence_o to_o the_o horizon_n be_v the_o compliment_n of_o the_o latitude_n 38._o degree_n 28._o minute_n make_v up_o a_o quadrant_n again_o from_o the_o zenith_n northerly_a to_o the_o pole_n be_v the_o compliment_n of_o latitude_n 38._o degr_n 28._o minute_n as_o before_o and_o from_o thence_o to_o the_o north_n of_o the_o horizon_n be_v the_o elevation_n of_o the_o pole_n above_o your_o horizon_n which_o be_v always_o equal_a to_o the_o latitude_n of_o your_o place_n for_o where_o in_o a_o right_a sphere_n the_o poles_o in_o the_o horizon_n and_o have_v on_o elevation_n there_o the_o equator_fw-la pass_v through_o the_o zenith_n and_o if_o you_o go_v from_o such_o a_o country_n northward_o till_o the_o 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ecliptic_a line_n of_o the_o mater_n so_o the_o azimuth_n shall_v in_o this_o posture_n become_v circle_n of_o longitude_n and_o the_o almicanters_n circle_n of_o latitude_n and_o in_o this_o mode_n your_o planisphear_n be_v fit_v to_o resolve_v all_o question_n of_o the_o longitude_n latitude_n right_a ascension_n and_o declination_n of_o the_o star_n 3_o the_o three_o mode_n of_o the_o meridional_a projection_n number_v the_o altitude_n of_o culmen_fw-la caeli_fw-la that_o be_v the_o sothe_v point_n of_o the_o ecliptic_a in_o the_o ring_n from_o the_o north_n pole_n towards_o meridies_n if_o the_o ascendant_n be_v a_o north_n sign_n or_o towards_o septentrio_fw-la if_o the_o ascendant_n be_v a_o south_n sign_n to_o the_o end_n of_o this_o numeration_n place_n the_o finiter_fw-la reckon_v also_o upon_o the_o finiter_n from_o the_o centre_n towards_o septentrie_n the_o amplitude_n of_o the_o ascendant_n the_o meridian_n cut_v there_o give_v you_o
he_o in_o his_o proper_a line_n go_v to_o the_o mater_n of_o your_o planisphear_n and_o take_v he_o there_o in_o the_o first_o projection_n there_o number_n 60_o the_o sun_n longitude_n in_o the_o ecliptic_a line_n of_o the_o mater_n from_o the_o centre_n outward_a where_o 60_o end_v there_o be_v c_o of_o your_o triangle_n and_o the_o meridian_n that_o meet_v you_o there_o be_v c_o a_o the_o arch_n of_o declination_n follow_v he_o to_o the_o equator_fw-la and_o you_o shall_v find_v by_o his_o graduation_n he_o be_v 20_o degr_n 12_o min._n long._n thence_o turn_v in_o the_o equator_fw-la to_o the_o centre_n and_o you_o make_v b_o a_o the_o right_a ascension_n 57_o degr_n 48_o min._n so_o have_v you_o the_o true_a picture_n of_o your_o triangle_n in_o his_o proper_a place_n observe_v your_o triangle_n now_o and_o you_o may_v see_v a_o be_v a_o right_a angle_n for_o at_o such_o angle_n all_o the_o meridian_n cut_n the_o equator_fw-la b_o be_v 23_o ½_n for_o such_o a_o angle_n the_o ecliptic_a daily_o make_v with_o the_o equator_fw-la as_o the_o arch_n in_o the_o limb_n comprehend_v between_o they_o show_v now_o take_v for_o give_v any_o of_o the_o three_o side_n and_o you_o have_v the_o rest_n take_v the_o longitude_n for_o give_v and_o be_v it_o 60_o degr_n as_o before_o or_o 70_o degr_n or_o what_o you_o will_v and_o you_o may_v find_v the_o declination_n and_o right_a ascension_n as_o before_o let_v the_o right_a ascension_n be_v give_v then_o set_v a_o needle_n point_n in_o the_o end_n thereof_o a_o you_o may_v thence_o in_o a_o meridian_n trace_v out_o the_o declination_n c_o a_o to_o the_o ecliptic_a and_o the_o longitude_n b_o c_o thence_o to_o the_o centre_n every_o side_n be_v divide_v into_o his_o whole_a part_n or_o degree_n if_o the_o declination_n be_v give_v say_v because_o the_o 20_o parallel_n almost_o must_v cut_v off_z c_o a_o the_o arch_n of_o declination_n in_o c_o therefore_o i_o follow_v the_o parallel_n 20_o ⅕_n to_o the_o place_n where_o he_o cut_v the_o ecliptic_a and_o there_o come_v the_o meridian_n that_o serve_v my_o turn_n and_o i_o may_v go_v down_o by_o he_o to_o the_o equator_fw-la as_o you_o will_v go_v down_o a_o ladder_n count_v the_o round_n or_o degree_n as_o you_o go_v and_o so_o on_o round_o my_o triangle_n and_o i_o need_v no_o more_o for_o observe_v it_o when_o you_o will_v in_o the_o use_n of_o this_o planisphear_n if_o you_o can_v find_v the_o way_n to_o go_v round_o your_o triangle_n you_o have_v all_o the_o side_n measure_v to_o your_o hand_n and_o evermore_o one_o angle_n also_o most_o common_o two_o and_o the_o angle_n c_o only_a leave_v unknown_a but_o admit_v the_o sun_n be_v in_o ♌_o 0_o then_o be_v his_o longitude_n 120_o degree_n and_o he_o be_v come_v back_o from_o the_o solstice_n in_o your_o planisphear_n as_o many_o degr_n as_o he_o want_v of_o it_o before_o here_o the_o triangle_n be_v equal_a to_o the_o former_a and_o resolve_v in_o like_a manner_n the_o declination_n be_v the_o same_o as_o before_o but_o the_o arch_n of_o longitude_n and_o right_a ascension_n in_o the_o triangle_n be_v supplement_n of_o the_o true_a longitude_n and_o right_a ascension_n show_v what_o the_o sun_n want_v of_o the_o longitude_n and_o right_a ascension_n 180_o in_o ♎_o 0._o wherefore_o subtract_v the_o base_a of_o the_o triangle_n 57_o degr_n 48_o min._n from_o a_o semicircle_n or_o 180_o degr_n and_o you_o shall_v leave_v 122_o degr_n 12_o min._n the_o right_a ascension_n of_o ♌_o 0._o or_o number_n in_o the_o equator_fw-la from_o the_o centre_n the_o way_n in_o which_o the_o right_a ascension_n have_v increase_v that_o be_v first_o to_o the_o limb_n which_o here_o be_v colurus_n solstitiorum_fw-la 90_o degr_n then_o back_o again_o to_o a_o the_o right_a angle_n of_o your_o triangle_n and_o you_o have_v 32_o degr_n 12_o min._n to_o be_v add_v thereto_o the_o sum_n be_v 122_o degr_n 12_o min._n the_o right_a ascension_n as_o before_o if_o you_o observe_v this_o example_n you_o will_v easy_o perceive_v that_o when_o the_o sun_n be_v pass_v ♎_o 0._o the_o triangle_n will_v be_v on_o the_o other_o side_n the_o centre_n and_o between_o ♎_o and_o ♑_o you_o must_v add_v to_o the_o right_a ascension_n and_o longitude_n find_v within_o the_o triangle_n 180_o degr_n and_o in_o the_o last_o quadrant_n between_o ♑_o and_o ♈_o where_o the_o right_a ascension_n again_o increase_v inward_o you_o must_v add_v 270_o degr_n to_o the_o compliment_n of_o right_a ascension_n find_v in_o the_o triangle_n and_o take_v the_o sum_n or_o else_o subduct_v the_o right_a ascension_n find_v in_o the_o triangle_n from_o 360_o degr_n and_o take_v the_o residue_n for_o the_o right_a ascension_n chap._n vii_o to_o do_v the_o same_o in_o the_o second_o projection_n more_o easy_o in_o the_o second_o projection_n where_o the_o centre_n be_v the_o pole_n of_o the_o world_n and_o the_o limb_n equator_fw-la you_o shall_v find_v the_o ecliptic_a fair_o draw_v upon_o the_o reet_n and_o distinguish_v into_o his_o quarter_n and_o degree_n remember_v now_o from_o the_o former_a chap._n that_o the_o ecliptic_a equator_fw-la and_o a_o meridian_n must_v make_v your_o triangle_n and_o know_v that_o the_o label_n supply_v the_o place_n of_o the_o meridian_n if_o the_o longitude_n or_o right_a ascension_n be_v give_v lay_v the_o label_n on_o the_o degree_n give_v in_o the_o ecliptic_a for_o longitude_n or_o in_o the_o limb_n of_o the_o reet_n for_o right_a ascension_n and_o your_o triangle_n be_v make_v and_o you_o may_v present_o see_v your_o desire_n if_o the_o declination_n be_v give_v consider_v in_o what_o quarter_n of_o the_o ecliptic_a the_o sun_n be_v than_o number_n the_o declination_n give_v upon_o the_o label_n inward_o and_o where_o the_o number_n end_v make_v a_o prick_n on_o your_o label_n then_o move_v the_o label_n into_o the_o quarter_n where_o the_o sun_n be_v and_o lay_v the_o prick_n on_o the_o ecliptic_a there_o and_o your_o triangle_n be_v make_v wherein_o you_o may_v see_v the_o longitude_n and_o right_a ascension_n desire_v this_o need_v no_o example_n chap._n viii_o to_o find_v the_o angle_n at_o the_o sun_n make_v between_o the_o ecliptic_a and_o meridian_n this_o be_v the_o angle_n c_o of_o the_o former_a triangle_n and_o be_v the_o only_a part_n which_o can_v be_v find_v in_o the_o former_a posture_n of_o the_o triangle_n neither_o in_o chap._n 6_o nor_o 7_o but_o be_v easy_o have_v by_o conversion_n of_o the_o triangle_n as_o you_o may_v remember_v out_o of_o the_o three_o book_n take_v the_o triangle_n of_o chap._n 6_o and_o make_v the_o cathetus_n base_a for_o this_o turn_n and_o by_o the_o 1_o or_o 2_o problem_n of_o rectangled_a triangle_n you_o may_v find_v this_o angle_n to_o be_v 77_o degr_n 43_o min._n chap._n ix_o to_o find_v the_o say_a angle_n of_o the_o ecliptic_a with_o the_o meridian_n by_o the_o longitude_n declination_n or_o right_a ascension_n divers_a other_o way_n in_o the_o meridional_a projection_n do_v thus_o if_o you_o have_v the_o longitude_n give_v count_v the_o distance_n of_o the_o sun_n in_o that_o longitude_n from_o the_o next_o equinoctial_a point_n and_o count_v so_o many_o degree_n in_o the_o arctic_a circle_n from_o the_o limb_n inward_o to_o the_o end_n of_o this_o number_n lay_v the_o label_n and_o between_o the_o label_n and_o equator_fw-la you_o have_v upon_o the_o limb_n the_o lesser_a angle_n make_v between_o the_o ecliptic_a and_o meridian_n the_o great_a angle_n be_v the_o supplement_n thereof_o also_o between_o the_o arctic_a circle_n and_o the_o limb_n you_o may_v find_v the_o declination_n on_o the_o label_n which_o be_v more_o than_o be_v require_v if_o you_o have_v the_o declination_n give_v count_v it_o on_o the_o label_n inward_o and_o make_v a_o prick_n where_o the_o number_n end_v then_o turn_v this_o prick_n upon_o the_o arctic_a circle_n and_o the_o label_n show_v the_o lesser_a angle_n in_o the_o limb_n as_o before_o example_n i_o will_v know_v what_o angle_n the_o meridian_n that_o cut_v the_o sun_n in_o ♉_o 9_o degr_n make_v with_o the_o ecliptic_a i_o number_v therefore_o in_o the_o arctic_a circle_n from_o the_o limb_n inward_o 39_o deg_fw-la and_o to_o the_o 39th_o degr_n i_o say_v the_o label_n and_o it_o show_v in_o the_o limb_n the_o angle_n seek_v 71_o degr_n 20_o min._n and_o in_o the_o label_n the_o declination_n of_o ♉_o 9_o degr_n viz._n 14._o 32_o minute_n this_o be_v a_o good_a way_n but_o that_o the_o label_n at_o this_o 39th_o degr_n cut_v the_o pole_n of_o the_o ecliptic_a as_o mr._n blagrave_n say_v book_n 3_o 40._o be_v not_o true_a either_o mr._n blagrave_n or_o the_o printer_n here_o mistake_v for_o the_o pole_n of_o the_o ecliptic_a lie_n 14._o 24_o minute_n near_a the_o axletree_n as_o you_o shall_v
find_v in_o the_o next_o rule_n 2._o another_o way_n mark_v what_o be_v the_o right_a ascension_n of_o the_o point_n propose_v be_v count_v from_o the_o next_o equinoctial_a point_n as_o of_o ♉_o 9_o degr_n the_o right_a ascension_n be_v 36.36_o min._n count_v so_o many_o degree_n in_o the_o arctic_a circle_n from_o the_o axletree_n at_o the_o end_n of_o this_o number_n be_v the_o pole_n of_o the_o ecliptic_a lay_v the_o label_n to_o he_o and_o you_o shall_v make_v a_o quadrantal_a triangle_n who_o side_n shall_v be_v equal_a to_o the_o angle_n of_o the_o former_a triangle_n which_o be_v make_v of_o the_o longitude_n declination_n and_o right_a ascension_n of_o the_o point_n propose_v for_o the_o right_a angle_n you_o have_v a_o radius_fw-la or_o quadrant_n of_o the_o axis_n for_o the_o angle_n of_o the_o great_a declination_n between_o the_o equator_fw-la and_o ecliptic_a 23_o ½_n you_o have_v the_o arch_n of_o a_o meridian_n between_o the_o pole_n of_o the_o equator_fw-la and_o the_o pole_n of_o the_o ecliptic_a for_o the_o angle_n seek_v you_o have_v the_o arch_n of_o the_o label_n between_o the_o pole_n of_o the_o ecliptic_a and_o the_o centre_n 71.20_o minute_n as_o before_o the_o least_o angle_n of_o this_o quadrantal_a triangle_n be_v at_o the_o centre_n and_o you_o shall_v find_v his_o measure_n in_o the_o limb_n 14.32_o minute_n that_o be_v the_o measure_n of_o the_o least_o side_n of_o the_o former_a triangle_n viz._n the_o declination_n of_o the_o point_n propose_v here_o you_o see_v if_o the_o declination_n have_v be_v give_v you_o shall_v have_v set_v it_o in_o the_o limb_n between_o the_o pole_n and_o the_o label_n and_o so_o have_v you_o make_v the_o same_o quadrantal_a triangle_n and_o may_v have_v find_v on_o the_o label_n between_o the_o arctic_a circle_n and_o the_o centre_n the_o measure_n of_o the_o angle_n seek_v and_o likewise_o in_o the_o arctic_a circle_n between_o the_o label_n and_o the_o axtree-line_n the_o right_a aseension_n though_o it_o be_v more_o than_o be_v require_v the_o reason_n hereof_o you_o may_v learn_v from_o book_n 3.7_o chap._n x._o to_o find_v the_o point_n of_o the_o ecliptic_a in_o which_o the_o longitude_n and_o right_a ascension_n have_v great_a difference_n move_v the_o label_n on_o the_o polar_a circle_n till_o you_o find_v the_o degree_n of_o the_o label_n between_o the_o polar_a circle_n and_o the_o limb_n to_o be_v equal_a to_o the_o degr_n of_o the_o limb_n between_o the_o label_n and_o the_o pole_n so_o have_v you_o a_o rectangle_v aeqaicrurall_a triangle_n make_v by_o the_o limb_n label_n and_o the_o meridian_n 46_o ¼_n like_v to_o that_o in_o the_o second_o variety_n book_n 3.10_o here_o the_o angle_n b_o at_o the_o pole_n between_o the_o 46_o ¼_n meridian_n and_o the_o limb_n be_v equal_a to_o the_o longitude_n of_o the_o point_n seek_v 46¼_n and_o either_o leg_n be_v equal_a to_o the_o declination_n thereof_o 16_o ¼_n therefore_o i_o conclude_v that_o when_o the_o sun_n be_v 46_o ¼_n in_o longitude_n that_o be_v in_o ♉_o 16_o ¼_n than_o his_o longitude_n have_v further_a out_o run_v the_o right_a ascension_n subtract_v now_o the_o right_a ascension_n of_o ♉_o 16_o ¼_n which_o be_v 43_o ¾_n out_o of_o the_o longitude_n 46_o ¼_n there_o remain_v 2_o deg_fw-la ½_n which_o be_v convert_v into_o time_n be_v 10_o min._n the_o great_a inequality_n of_o ascension_n in_o a_o right_a sphere_n chap._n ii_o to_o find_v the_o latitude_n of_o your_o place_n or_o the_o elevation_n of_o the_o pole_n above_o your_o horizon_n by_o the_o meridional_a altitude_n and_o declination_n of_o the_o sun_n meridional_a projection_n geographer_n call_v the_o distance_n of_o a_o place_n from_o the_o near_a point_n of_o the_o equator_fw-la upon_o earth_n the_o latitude_n of_o that_o place_n as_o the_o latitude_n of_o london_n be_v 51_o deg_fw-la 32_o min._n from_o the_o equator_fw-la northward_o the_o latitude_n of_o st_n thomas_n island_n upon_o the_o coast_n of_o africa_n be_v 0_o deg_fw-la 0_o min._n because_o the_o middle_n of_o that_o island_n lie_v under_o the_o equator_fw-la and_o because_o the_o latitude_n of_o your_o place_n and_o the_o elevation_n of_o the_o pole_n above_o your_o horizon_n be_v always_o equal_a therefore_o the_o elevation_n of_o the_o pole_n be_v oft_o call_v latitude_n of_o the_o place_n or_o latitude_n simple_o and_o so_o for_o brevity_n sake_n we_o shall_v often_o call_v it_o but_o when_o we_o speak_v of_o the_o latitude_n of_o the_o moon_n or_o star_n you_o must_v understand_v astronomer_n thereby_o mean_v their_o distance_n from_o the_o near_a point_n of_o the_o ecliptic_a to_o find_v the_o latitude_n of_o your_o place_n get_v the_o sun_n declination_n by_o the_o 6_o or_o seven_o and_o his_o meridian_n altitude_n by_o the_o second_o of_o this_o book_n then_o find_v the_o parallel_n of_o the_o sun_n declination_n north_n or_o south_n as_o the_o declination_n be_v and_o where_o it_o touch_v the_o limb_n here_o meridian_n there_o be_v the_o point_n where_o you_o observe_v the_o sun_n at_o noon_n set_v the_o south_n end_n of_o the_o finiter_n so_o many_o degr_n below_o this_o point_n as_o the_o meridian_n altitude_n have_v then_o be_v your_o finiter_n set_v to_o your_o latitude_n and_o you_o shall_v find_v the_o measure_n of_o it_o between_o the_o equator_fw-la and_o the_o zenith_n which_o be_v proper_o the_o latitude_n and_o the_o same_o measure_n shall_v you_o find_v between_o the_o north_n point_n of_o the_o finiter_n and_o the_o north_n pole_n where_o it_o be_v more_o proper_o call_v the_o elevation_n of_o the_o pole_n example_n june_n 20_o 1651._o i_o observe_v the_o meridian_n altitude_n of_o the_o sun_n here_o at_o ecton_n four_o mile_n eastward_o from_o northampton_n 60_o degr_n 59_o min._n the_o longitude_n of_o the_o sun_n be_v then_o ♋_o 8_o degr_n 19_o min._n ½_n his_o declination_n 23_o degr_v 14_o min._n northward_o therefore_o have_v find_v in_o the_o limb_n the_o point_n where_o the_o parallel_n 23_o degr_n 14_o min._n touch_v above_o the_o equator_fw-la i_o put_v the_o south_n end_n of_o the_o finiter_fw-la 60_o degr_n 59_o min._n below_o that_o point_n towards_o the_o south_n pole_n which_o do_v i_o see_v the_o north_n pole_n elevate_v above_o the_o finiter_fw-la 52_o degr_n 15_o min._n and_o the_o zenith_n of_o my_o horizon_n likewise_o to_o be_v remove_v from_o the_o equator_fw-la northward_o 52_o degr_n 15_o min._n which_o be_v the_o latitude_n of_o ecton_n note_v that_o you_o may_v best_o observe_v the_o latitude_n when_o the_o sun_n be_v near_o the_o summer_n tropic_n for_o than_o you_o shall_v not_o be_v trouble_v with_o refraction_n and_o then_o the_o declination_n vary_v slow_o which_o vary_v almost_o one_o minute_n every_o hour_n near_o the_o equinoctial_a chap._n xii_o to_o do_v the_o same_o by_o the_o meridian_n altitude_n of_o the_o star_n about_o the_o pole_n many_o of_o the_o star_n near_o the_o northern_a pole_n may_v be_v see_v with_o we_o twice_o in_o the_o meridian_n in_o one_o winter_n night_n that_o be_v one_o while_o above_o the_o pole_n and_o 12_o hour_n after_o again_o below_o the_o pole_n as_o for_o example_n the_o polestar_n call_v alrucabe_n about_o december_n 18_o will_n be_v in_o the_o meridian_n above_o the_o pole_n at_o 6_o of_o the_o clock_n at_o night_n and_o at_o 6_o next_o morning_n he_o will_v be_v in_o the_o meridian_n below_o the_o pole_n observe_v both_o the_o meridian_n altitude_n and_o add_v they_o together_o half_o that_o sum_n be_v the_o elevation_n of_o the_o pole_n example_n i_o observe_v at_o ecton_n the_o great_a altitude_n of_o the_o polestar_n to_o be_v 54_o deg_fw-la 45_o min._n and_o his_o least_o altitude_n 49_o degr_n 45_o min._n the_o sum_n be_v 104_o deg_fw-la 30_o min._n the_o half_a 52_o degr_n 15_o min._n the_o latitude_n of_o ecton_n and_o here_o i_o have_v get_v also_o the_o pole-star_n distance_n from_o the_o pole_n and_o consequent_o his_o declination_n which_o be_v the_o compliment_n thereof_o for_o the_o latitude_n be_v subduct_v from_o the_o great_a altitude_n leave_v the_o star_n distance_n from_o the_o pole_n 2_o degr_n 30_o min._n and_o consequent_o show_v his_o declination_n to_o be_v 87_o degr_n 30_o min._n which_o be_v 39_o min._n more_o than_o gemma_fw-la frisius_n observe_v it_o anno_fw-la dom._n 1547._o for_o in_o our_o age_n the_o polestar_n approach_v about_o 1_o min._n near_o the_o pole_n in_o every_o 3_o year_n note_v that_o these_o star_n which_o be_v distant_a from_o the_o pole_n less_o than_o the_o latitude_n and_o more_o than_o the_o compliment_n thereof_o have_v their_o less_o meridian_n altitude_n in_o the_o north_n part_n of_o the_o meridian_n and_o their_o great_a meridian_n altitude_n in_o the_o southern_a part_n of_o the_o meridian_n beyond_o the_o zenith_n wherefore_o for_o they_o you_o shall_v take_v the_o compliment_n of_o