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two_o side_n apposite_a lie_n parallel_n to_o the_o line_n a_o c_o and_o the_o other_o two_o opposite_a side_n to_o the_o line_n b_o d_o and_o if_o you_o work_v by_o the_o help_n of_o the_o néedâ—â—_n beware_v that_o no_o one_o come_v about_o you_o but_o such_o as_o you_o know_v kind_a friend_n loost_n otherwise_o of_o purpose_n they_o bear_v a_o loadstone_n about_o they_o which_o may_v confound_v you_o in_o your_o work_n chap._n v._o to_o set_v the_o part_n of_o the_o topographicall_a glass_n together_o have_v now_o finish_v every_o part_n of_o this_o instrument_n and_o be_v ready_a to_o set_v he_o to_o work_v thus_o must_v the_o part_n be_v join_v together_o first_o upon_o the_o centre_n in_o the_o body_n of_o the_o instrument_n place_n the_o circle_n with_o the_o index_n f_o g_o h_o i_o and_o within_o this_o circle_n place_v the_o box_n with_o screw_a pin_n to_o keep_v down_o the_o circle_n in_o such_o sort_n as_o before_o be_v say_v and_o let_v the_o box_n be_v furnish_v with_o 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planisphere_n and_o a_o alhidada_n upon_o the_o planisphere_n there_o be_v describe_v a_o circle_n which_o be_v divide_v into_o 360._o degree_n etc._n etc._n within_o this_o circle_n there_o be_v inscribe_v a_o square_a which_o be_v part_v into_o a_o certain_a number_n of_o equal_a part_n which_o do_v represent_v part_n of_o the_o geometrical_a quadrant_n and_o no_o more_o division_n or_o graduation_n be_v in_o the_o planisphere_n of_o the_o theodelitus_n the_o alhidada_n be_v a_o straight_a ruler_n with_o a_o fiducial_a edge_n move_v equal_o and_o true_o upon_o the_o centre_n of_o the_o planisphere_n who_o length_n be_v equal_a with_o the_o diameter_n of_o the_o circle_n in_o the_o planisphere_n upon_o the_o two_o end_n of_o this_o index_n or_o alhidada_n as_o fix_v two_o fould_a sight_n instrument_n the_o description_n of_o the_o topographical_n instrument_n but_o if_o you_o make_v this_o instrument_n like_o to_o that_o which_o master_n digges_n call_v the_o topographicall_a 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more_o too_o i_o both_o for_o the_o needle_n who_o largeness_n be_v require_v and_o other_o circle_n needful_a and_o pleasant_a to_o be_v add_v hereunto_o as_o the_o mariner_n compass_n and_o other_o circle_n to_o tell_v the_o hour_n of_o the_o night_n by_o the_o moon_n and_o last_o touch_v the_o alteration_n of_o the_o planisphere_n look_v unto_o the_o 4_o index_n how_o requisite_a they_o be_v for_o the_o measure_n of_o ground_n and_o to_o what_o great_a purpose_n they_o stand_v you_o in_o as_o in_o the_o 33_o and_o 34_o chap._n touch_v the_o alteration_n of_o the_o demi-circle_n let_v every_o man_n acknowledge_v the_o necessity_n thereof_o for_o that_o you_o can_v not_o take_v any_o attitude_n of_o the_o sun_n or_o any_o other_o celestial_a body_n or_o object_n situate_v in_o the_o heaven_n or_o upon_o the_o earth_n if_o so_o the_o altitude_n thereof_o exceed_v 60_o degree_n for_o that_o you_o can_v look_v through_o the_o sight_n in_o the_o diameter_n of_o the_o semicircle_n by_o reason_n of_o the_o planisphere_n but_o in_o deed_n the_o same_o may_v be_v better_o deal_v with_o then_o any_o other_o thing_n whatsoever_o look_v also_o to_o she_o want_v of_o a_o plumbe_v to_o keep_v your_o instrument_n parallel_v and_o upright_o for_o which_o there_o be_v no_o convenient_a place_n in_o the_o theodelitus_n which_o this_o glass_n have_v sufficient_a though_o it_o be_v not_o needful_a by_o reason_n of_o the_o large_a cross_a needle_n which_o perform_v the_o same_o brief_o these_o impediment_n and_o defect_n well_o consider_v let_v any_o â—â—e_z of_o judgement_n speâ—â—_n iâ—_n there_o be_v not_o a_o necessity_n of_o reformation_n which_o 〈◊〉_d it_o be_v here_o do_v so_o i_o know_v it_o by_o practice_n and_o continual_a experience_n to_o be_v requisite_a to_o be_v do_v without_o offence_n be_v it_o speak_v to_o any_o friend_n of_o the_o composer_n of_o the_o theodellitus_n chap._n vii_o to_o search_v the_o proportion_n and_o symmitry_n of_o a_o country_n field_n or_o such_o like_a country_n to_o find_v the_o proportion_n of_o country_n in_o this_o he_o of_o worlbe_n we_o shall_v have_v no_o need_n of_o the_o needle_n or_o such_o like_a if_o you_o seek_v the_o proportion_n of_o a_o field_n or_o such_o like_a go_v into_o that_o part_n of_o it_o from_o which_o you_o may_v observe_v all_o the_o angle_n and_o it_o be_v convenient_a if_o white_a paper_n be_v fix_v in_o every_o angle_n and_o there_o plant_v your_o instrument_n begin_v at_o what_o angle_v you_o please_v place_v there_o for_o the_o index_n that_o bear_v the_o circular_a sight_n upon_o the_o o_o degree_n of_o the_o circle_n in_o the_o planisphere_n remain_v there_o erect_v the_o same_o by_o look_v through_o the_o sight_n unto_o the_o first_o angle_n than_o the_o instrument_n rest_v conucy_a the_o say_a index_n to_o the_o next_o angle_n upon_o your_o right_a hand_n and_o note_v down_o what_o degree_n the_o fiducial_a edge_n of_o your_o index_n do_v cut_v in_o your_o table_n book_n do_v so_o from_o angle_n to_o angle_v rightwards_o until_o you_o come_v unto_o the_o last_o and_o write_v they_o down_o in_o your_o table_n book_n in_o manner_n as_o follow_v the_o instrument_n rest_v unremoove_v convey_v your_o index_n towards_o your_o right_a hand_n at_o pleasure_n observe_v through_o that_o sight_n some_o mark_n a_o convenient_a distand_v from_o you_o according_a to_o the_o quantiy_n of_o the_o field_n and_o there_o must_v be_v your_o second_o place_n at_o this_o place_n plant_v your_o instrument_n by_o help_n of_o your_o back_n sight_n in_o such_o order_n that_o the_o line_n where_o the_o degree_n take_v beginning_n may_v point_v to_o your_o first_o station_n and_o here_o likewise_o you_o must_v begin_v at_o the_o angle_n which_o at_o the_o last_o station_n be_v your_o first_o angle_n and_o note_v the_o degree_n cut_v by_o the_o same_o index_n proceed_v from_o angle_n to_o angle_v rightwards_o until_o you_o come_v to_o the_o last_o still_o note_v
a_o excellent_a way_n you_o must_v find_v out_o two_o station_n in_o a_o know_a distance_n as_o you_o please_v where_o observe_v the_o angle_n of_o altitude_n and_o so_o get_v the_o complement_n of_o the_o tangent_n of_o both_o those_o angle_n by_o the_o seven_o book_n of_o my_o staff_n note_v the_o difference_n of_o the_o say_a compliment_n for_o as_o the_o difference_n be_v to_o the_o radius_fw-la so_o be_v the_o difference_n of_o the_o station_n to_o the_o altitude_n example_n we_o have_v observe_v the_o angle_n a_o b_o d_o to_o be_v 29._o degree_n 40._o min._n and_o a_o c_o d_o to_o be_v 46._o degree_n the_o tangent_fw-la of_o the_o complement_n of_o 29._o deg_fw-la 40._o min._n be_v 175556._o and_o of_o 46._o degree_n 96568._o now_o subtract_v 96568._o from_o 175556._o and_o there_o rest_v 78988._o then_o multiply_v 100000._o the_o total_a sign_n by_o 90._o the_o distance_n betwixt_o both_o your_o station_n for_o so_o many_o foot_n i_o find_v it_o by_o measure_n and_o there_o be_v 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find_v the_o distance_n betwixt_o window_n intteye_n etc._n etc._n to_o perform_v which_o you_o may_v first_o take_v the_o altitude_n of_o the_o one_o and_o the_o other_o and_o so_o consequent_o subtract_v the_o lesser_a out_o of_o the_o great_a tâ—e_v remainder_n be_v your_o desire_n but_o if_o you_o know_v not_o the_o whole_a altitude_n first_o observe_v the_o angle_n of_o altitude_n of_o the_o high_a and_o then_o of_o the_o low_a place_n and_z note_z the_o degree_n of_o both_o these_o angle_n next_o measure_v the_o distance_n of_o the_o tower_n from_o you_o and_o then_o conclude_v as_o the_o radius_fw-la be_v to_o the_o distance_n so_o be_v the_o difference_n of_o the_o tangent_n of_o each_o angle_n unto_o the_o longitude_n seek_v therefore_o subtract_v the_o lesser_a tangent_fw-la from_o the_o great_a the_o remainder_n increase_v by_o the_o distance_n of_o the_o tower_n the_o product_n whereof_o part_n by_o the_o total_a sign_n and_o the_o quotient_a iâ—_n your_o desire_n example_n 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at_o a_o take_v the_o angle_n z_o a_fw-fr c_o and_o note_v the_o part_n of_o the_o quadrant_n cut_v by_o the_o movable_a sight_n upon_o the_o back_n side_n the_o demicircle_n which_o be_v 20_o the_o glass_n rest_v parallel_n and_o equidistant_n to_o the_o horizon_n move_v the_o sight_n until_o i_o see_v through_o the_o same_o from_o a_o to_o b_o as_o at_z m_z and_o so_o do_v i_o find_v the_o part_n cut_v to_o be_v 43._o both_o upon_o the_o left_a side_n the_o scale_n k_o l_o which_o i_o perceive_v in_o my_o glass_n for_o that_o both_o the_o section_n be_v make_v in_o the_o 60._o part_n further_a from_o 90._o therefore_o by_o the_o first_o difference_n of_o this_o
point_n upon_o the_o paper_n which_o represent_v c_o and_o thereupon_o lie_v the_o fiducial_a edge_n of_o the_o rule_n move_v the_o other_o end_n until_o through_o the_o sight_n you_o seâ—_n c_o so_fw-ge wilt_fw-ge the_o edge_n of_o the_o ruler_n in_o the_o line_n upon_o the_o paper_n represent_v â—_o d_o thâ—â—_n kâ—â—ping_v the_o â—uler_a â—pon_n that_o point_n d_o i_o move_v the_o other_o 〈◊〉_d until_o it_o pâ—â—oâ—_n to_o 〈◊〉_d shall_v the_o fiducial_a edge_n of_o the_o rule_n intersectâ—_n witâ—_n the_o â—â—â—e_a 〈◊〉_d the_o papâ—â—_n represent_v a_o b_o from_o the_o point_n of_o which_o intersection_n to_o the_o point_n a_o be_v b_o the_o term_n of_o the_o line_n a_o b_o which_o be_v measure_v by_o your_o scale_n and_o compass_n be_v find_v 133_o perche_n chap._n xlix_o to_o take_v the_o distance_n of_o any_o two_o town_n or_o such_o like_a consider_v well_o the_o premise_n and_o this_o labour_n be_v already_o effect_v therefore_o plant_v your_o instrument_n at_o a_o latitude_n latitude_n as_o you_o be_v direct_v in_o the_o 29_o chapter_n and_o let_v the_o latitude_n require_v be_v d_o c_o noâ—â—raw_v line_n from_o a_o to_o point_n to_o d_o and_o c_o and_o also_o to_o b_o your_o second_o station_n now_o observe_v the_o former_a direction_n i_o remove_v my_o instrument_n to_o b_o and_o so_o draw_v line_n from_o b_o to_o point_n again_o to_o d_o and_o c_o then_o do_v i_o note_v the_o concourse_n or_o intersection_n of_o the_o say_a line_n which_o i_o measure_v by_o the_o scale_n and_o compass_n as_o before_o so_o will_v the_o stationary_a line_n a_o b_o be_v 316_o perch_n and_o the_o distance_n require_v d_o c_o 131_o perch_n distance_n a_o note_n for_o many_o distance_n and_o here_o note_v if_o you_o have_v seek_v more_o distance_n as_o the_o distance_n of_o f_o e_o e_o d_o d_o c_o etc._n etc._n the_o labour_n be_v no_o more_o but_o to_o draw_v line_n at_o every_o station_n to_o point_v â—nto_o the_o distance_n require_v and_o then_o to_o note_v the_o 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the_o sight_n upon_o the_o very_a edge_n of_o one_o of_o the_o side_n of_o the_o plaine-table_n turn_v the_o table_n about_o until_o through_o the_o sight_n you_o espy_v the_o mark_n who_o distance_n be_v require_v but_o with_o this_o proviso_n that_o the_o corner_n of_o the_o table_n where_o the_o division_n take_v begin_n be_v near_o unto_o you_o this_o do_v take_v the_o ruler_n with_o the_o sight_n the_o table_n unmon_v and_o place_v the_o same_o upon_o the_o right_a side_n the_o table_n as_o before_o and_o then_o look_v through_o the_o sight_n espy_v your_o second_o station_n in_o a_o know_a distance_n from_o your_o first_o station_n next_o shall_v you_o bear_v your_o instrument_n to_o your_o second_o station_n situate_a the_o instrument_n by_o help_n of_o the_o needle_n and_o back_n sight_n here_o in_o all_o respect_n as_o it_o be_v at_o the_o first_o which_o be_v do_v lay_v the_o ruler_n over_o the_o corner_n or_o both_o side_n of_o the_o instrument_n remove_v the_o same_o 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so_o draw_v shall_v represent_v the_o hedge_n of_o the_o field_n as_o in_o this_o demonstration_n your_o station_n be_v i_o the_o line_n draw_v from_o i_o to_o point_v to_o every_o angle_n be_v i_o a_o i_o b_o i_o c_o i_o d_o i_o k_o i_o e_o i_o f_o i_o g_o and_z i_z h_z which_o be_v measure_v as_o be_v note_v upon_o each_o line_n as_o i_o a_o 27_o perche_n i_o b_o 9_o ¾_n perche_n etc._n etc._n then_o from_o a_o to_o b_o i_o draw_v a_o line_n and_o so_o go_v round_o so_o have_v i_o make_v a_o figure_n proportional_a which_o be_v require_v chap._n lii_o to_o draw_v the_o plat_n of_o any_o field_n by_o the_o rule_n teach_v in_o the_o last_o chapter_n where_o you_o can_v from_o one_o place_n of_o the_o field_n see_v
the_o instrument_n of_o the_o staff_n staff_n the_o staff_n last_o unto_o this_o instrument_n there_o belong_v a_o staff_n 4_o foot_n long_o with_o a_o good_a steel_n pike_n in_o the_o foot_n thereof_o this_o staff_n serve_v to_o plant_v your_o instrument_n upon_o for_o which_o purpose_n in_o the_o top_n thereof_o be_v place_v a_o round_a pin_n of_o wood_n or_o brass_n and_o through_o the_o midst_n of_o the_o instrument_n be_v bore_v a_o hole_n to_o fit_v the_o say_a pin_n so_o when_o the_o instrument_n be_v place_v upon_o the_o say_a pin_n he_o will_v move_v round_o about_o but_o the_o best_a staff_n be_v that_o which_o be_v make_v with_o three_o staff_n join_v together_o like_a to_o a_o 3_o footed_a pair_n of_o compass_n chap._n lxii_o of_o the_o circumferentor_n his_o appellation_n and_o such_o thing_n as_o be_v to_o be_v consider_v general_o therein_o and_o of_o the_o protractor_n circumferentor_n the_o definition_n of_o the_o circumferentor_n what_o the_o intention_n of_o the_o 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sight_n hole_n and_o slit_v in_o the_o long_a sight_n and_o by_o the_o pin_n hear_v in_o the_o short_a sight_n you_o see_v the_o sun_n or_o star_n bring_v down_o the_o vane_n until_o through_o the_o hole_n therein_o and_o by_o the_o foresay_a pin_n head_n you_o see_v the_o say_a sun_n or_o star_n than_o the_o degree_n cut_v by_o the_o siâ—e_n of_o the_o â—ane_n show_v the_o almicanter_n or_o altitude_n of_o the_o sun_n and_o the_o degree_n in_o the_o card_n cut_v by_o the_o south_n end_n of_o the_o needle_n show_v the_o azimuth_n or_o the_o distance_n of_o the_o sun_n from_o the_o meridian_n but_o if_o the_o sun_n or_o star_n be_v high_o than_o 25_o degree_n so_o that_o you_o can_v bring_v down_o the_o vane_n to_o work_v upon_o the_o long_a sight_n than_o put_v the_o index_n upon_o the_o centre_n pin_n look_v through_o the_o sight_n in_o the_o index_n until_o through_o the_o same_o hole_n and_o by_o the_o centre_n pin_v you_o see_v the_o sun_n or_o star_n for_o the_o degr_n then_o cut_v upon_o the_o edge_n of_o the_o instrument_n by_o the_o edge_n of_o the_o index_n be_v the_o altitude_n and_o by_o this_o proposition_n may_v you_o observe_v all_o the_o star_n in_o the_o globe_n together_o with_o their_o motion_n in_o the_o heaven_n example_n the_o 6_o of_o october_n in_o the_o morning_n i_o make_v observation_n according_a unto_o the_o first_o difference_n where_o have_v plant_v my_o instrument_n parallel_n and_o spy_v the_o sun_n through_o the_o hole_n in_o the_o vane_n and_o by_o the_o pin_n head_n i_o find_v the_o vane_n to_o out_o 12_o degree_n upon_o the_o sight_n and_o the_o south_n end_n of_o the_o needle_n to_o cut_v 19_o â—_o 60_o degree_n which_o show_v i_o that_o the_o sun_n be_v 1_o degree_n high_a and_o that_o he_o waner_v 58_o degree_n of_o the_o meridian_n for_o the_o south_n point_n cut_v 29_o degree_n &_o 20_o minute_n i_o multiply_v the_o same_o by_o 3_o there_o come_v 58_o which_o show_v i_o there_o be_v so_o many_o degree_n include_v betwixt_o the_o sun_n and_o the_o meridian_n and_o so_o of_o the_o rest_n chap._n lxiiii_o to_o find_v in_o what_o point_n of_o the_o horizon_n any_o thing_n see_v lie_v by_o the_o old_a cirferentor_n lie_v to_o know_v in_o what_o point_n of_o the_o compass_n any_o thing_n lie_v here_o it_o be_v requisite_a first_o to_o understand_v that_o 120_o degree_n represent_v the_o south_n and_o that_o the_o degree_n be_v number_v into_o the_o east_n so_o that_o to_o find_v what_o point_n of_o the_o horizon_n any_o thing_n lie_v from_o you_o do_v thus_o let_v the_o instrument_n be_v place_v parallel_n upon_o the_o staff_n then_o cease_v not_o to_o move_v the_o same_o chapter_n with_o more_o ease_n see_v the_o 28_o chapter_n until_o through_o the_o hole_n in_o the_o vane_n and_o by_o the_o pin_n head_n you_o see_v the_o thing_n desire_v note_v the_o degree_n then_o cut_v by_o the_o south_n end_n of_o the_o needle_n with_o which_o resort_n unto_o this_o table_n so_o have_v you_o your_o demand_n 15_o 30_o 45_o 60_o sou_n east_n east_n nor_n east_n north_n 75_o 90_o 105_o 120_o nor_n west_n west_n sou_n west_n north_n example_n i_o find_v the_o south_n point_v cut_v 45_o degree_n i_o conclude_v the_o thing_n see_v be_v north-east_n chap._n lxv_o to_o find_v the_o hour_n of_o the_o day_n by_o sight_n of_o the_o sun_n day_n to_o know_v the_o hour_n of_o the_o day_n work_v the_o instrument_n lie_v parallel_n until_o the_o shadow_n of_o the_o pin_n head_n point_n or_o fall_v just_a in_o the_o slit_n in_o the_o longer_z sight_n &_o the_o intersection_n of_o the_o needle_n i_o mean_v the_o south_n part_n with_o the_o parallel_n of_o the_o month_n or_o sign_n take_v whether_o you_o please_v be_v the_o hour_n which_o you_o shall_v know_v by_o the_o hour_n line_n pass_v thereby_o and_o you_o must_v understand_v that_o those_o circle_n i_o call_v parallel_n be_v such_o as_o be_v describe_v about_o the_o centre_n of_o the_o card_n and_o those_o i_o call_v hour_n circle_n be_v those_o that_o pass_v as_o it_o be_v from_o the_o centre_n to_o the_o limb_n cross_v the_o parallel_n chap._n lxvi_o to_o find_v the_o hour_n of_o sun_n rise_v and_o set_v at_o any_o time_n propose_v and_o the_o length_n of_o the_o day_n and_o night_n here_o you_o must_v note_v that_o this_o card_n be_v make_v but_o for_o one_o latitude_n and_o therefore_o his_o work_n in_o that_o behalf_n can_v be_v general_a but_o it_o may_v serve_v without_o any_o notable_a error_n over_o the_o most_o part_n of_o england_n you_o shall_v observe_v where_o the_o parallel_n of_o the_o month_n cut_v the_o horizon_n for_o the_o hour_n circle_n pass_v thereby_o or_o the_o near_a thereunto_o show_v your_o demand_n remember_v to_o seek_v
the_o set_n upon_o the_o west_n side_n and_o the_o rise_n upon_o the_o east_n side_n of_o the_o card._n so_o shall_v you_o find_v the_o 11_o day_n of_o may_n the_o sun_n to_o rise_v near_o 4_o and_o set_v near_o 8_o then_o if_o you_o will_v know_v the_o length_n of_o the_o day_n and_o night_n you_o may_v repair_v unto_o the_o second_o book_n chap._n 10._o of_o the_o geodeticall_a staff_n chap._n lxvii_o to_o find_v the_o amplitude_n of_o the_o rise_n of_o the_o sun_n and_o star_n star_n to_o find_v the_o amplitude_n of_o the_o sun_n or_o star_n it_o be_v not_o unknown_a to_o any_o man_n though_o mean_o travel_v in_o astronomy_n that_o every_o horizon_n have_v four_o principal_a point_n viz._n east_n west_n north_n and_o south_n than_o you_o must_v understand_v that_o there_o be_v no_o star_n nor_o the_o sun_n that_o rise_v just_a east_n or_o set_v just_a west_n unless_o they_o be_v in_o the_o equinoctial_a which_o happen_v unto_o the_o sun_n but_o twice_o in_o the_o whole_a year_n but_o for_o star_n if_o they_o rise_v once_o east_n or_o set_v west_n so_o do_v they_o always_o whereof_o there_o be_v but_o a_o few_o the_o star_n in_o the_o pinion_n of_o the_o left_a wing_n of_o the_o virgin_n the_o star_n in_o antinous_n leave_v arm_n etc._n etc._n come_v near_o thereunto_o but_o as_o the_o amplitude_n of_o a_o star_n observe_v one_o day_n be_v certain_a and_o all_o one_o in_o any_o other_o day_n for_o that_o latitude_n so_o in_o the_o sun_n do_v it_o differ_v every_o day_n and_o be_v call_v amplitudo_fw-la ortus_fw-la this_o have_v observe_v the_o sun_n or_o star_n when_o they_o seem_v as_o it_o be_v to_o touch_v the_o earth_n as_o be_v at_o point_n of_o rise_v or_o set_v whereunto_o turn_v the_o instrument_n until_o through_o the_o slit_n in_o the_o long_a sight_n and_o by_o the_o pin_n head_n you_o see_v the_o sun_n or_o star_n then_o note_v the_o degr_n cut_v if_o you_o seek_v the_o set_n multiply_v the_o degr_n cut_v by_o the_o west_n end_n in_o 3_o which_o take_v from_o 90_o so_o have_v you_o your_o desire_n so_o the_o degr_n be_v under_o 30_o but_o if_o the_o degr_n cut_v be_v above_o 30_o multiply_v the_o degr_n cut_v by_o the_o east_n end_n in_o 3_o then_o from_o the_o total_a take_v 90_o so_o have_v you_o your_o desire_n and_o the_o set_n shall_v be_v north_n from_o the_o equinoctial_a but_o if_o you_o seek_v a_o rise_n you_o must_v consider_v whether_o the_o degree_n cut_v by_o the_o east_n end_v be_v under_o 30_o or_o above_o if_o they_o be_v under_o 30_o multiply_v they_o by_o 3_o so_o have_v you_o your_o demand_n and_o it_o be_v north_n if_o they_o be_v above_o 30_o see_v what_o degree_n the_o south_n end_n cut_v which_o multiply_v by_o 3_o subtract_v from_o 90_o to_o have_v you_o your_o desire_n and_o the_o rise_n be_v south_n from_o the_o equinoctial_a or_o thus_o with_o more_o ease_n have_v make_v your_o observation_n see_v how_o many_o degree_n be_v contain_v betwixt_o the_o west_n point_n of_o the_o card_n and_o the_o south_n end_n of_o the_o needle_n for_o arise_v but_o for_o a_o set_n see_v how_o many_o degree_n be_v include_v betwixt_o the_o east_n point_n of_o the_o card_n and_o the_o south_n end_n of_o the_o needle_n which_o treble_a so_o have_v you_o your_o desire_n but_o this_o chapter_n be_v perform_v with_o far_o more_o ease_n &_o truth_n by_o my_o topographicall_a glass_n chap._n lxviii_o of_o the_o opposite_a degree_n and_o how_o to_o find_v they_o degree_n opposite_a degree_n by_o a_o opposite_a degree_n be_v mean_v the_o opposite_a point_n of_o a_o diameter_n or_o the_o point_n opposite_a unto_o the_o degr_n cut_v by_o the_o south_n end_n of_o the_o needle_n that_o be_v the_o degr_n which_o the_o north_n end_n shall_v fall_v upon_o which_o be_v always_o the_o half_a of_o a_o circle_n distant_a from_o the_o south_n end_n in_o this_o instrument_n 60_o degree_n so_o that_o if_o the_o degree_n be_v less_o than_o 60_o add_v 60_o thereunto_o but_o if_o more_o than_o 60_o subtract_v 60_o from_o it_o and_o the_o total_a of_o the_o â—ne_n or_o the_o remainder_n of_o the_o other_o be_v your_o desire_n this_o need_v no_o example_n chap._n lxix_o to_o find_v the_o quantity_n of_o a_o angle_n angle_n to_o find_v the_o quantity_n of_o a_o angle_n the_o quantity_n of_o a_o angle_n be_v the_o portion_n of_o a_o circle_n include_v betwixt_o the_o 2_o side_n of_o any_o angle_n which_o be_v find_v upon_o this_o instrument_n by_o the_o cut_n of_o the_o needle_n at_o two_o observation_n in_o one_o place_n the_o lesser_a of_o which_o must_v be_v take_v from_o the_o great_a and_o the_o degree_n which_o remain_v after_o substraction_n be_v the_o quantity_n thereof_o but_o if_o the_o remainder_n after_o substraction_n excee_v 60_o then_o must_v the_o say_a remainder_n be_v take_v from_o 120_o so_o have_v you_o the_o quantity_n if_o your_o degree_n be_v not_o direct_v then_o must_v you_o work_v by_o the_o opposite_a degree_n as_o in_o the_o 9_o chapter_n take_v the_o lesser_a of_o those_o degree_n from_o the_o great_a and_o you_o must_v here_o note_v that_o all_o degree_n cut_v at_o diverse_a observation_n in_o one_o or_o more_o place_n be_v call_v direct_v and_o such_o degree_n as_o be_v opposite_a unto_o direct_a degree_n be_v call_v indirect_a and_o here_o note_v the_o tediousness_n of_o take_v a_o angle_n by_o this_o instrument_n inrespect_n of_o my_o staff_n chap._n lxx_o to_o take_v the_o distance_n of_o any_o mark_n by_o the_o old_a circumferentor_n distance_n to_o take_v a_o distance_n as_o i_o have_v often_o time_n say_v in_o the_o 2_o book_n of_o the_o geodeticall_a staff_n that_o there_o must_v be_v 3_o thing_n give_v as_o 2_o line_n and_o one_o angle_n or_o 2_o angle_n and_o one_o line_n by_o which_o all_o dimension_n be_v perform_v so_o in_o this_o kind_n of_o work_v you_o must_v always_o have_v two_o angle_n and_o one_o line_n give_v by_o help_n of_o which_o you_o may_v seek_v any_o distance_n propose_v thus_o plant_v your_o instrument_n at_o the_o place_n appoint_v whence_o you_o desire_v the_o distance_n and_o there_o look_v towards_o the_o say_a mark_n note_v the_o deg_fw-la cut_v by_o the_o south_n end_n of_o the_o needle_n then_o appoint_v another_o place_n for_o your_o second_o station_n to_o which_o bring_v the_o sight_n as_o before_o note_v the_o degr_n cut_v that_o do_v measure_v the_o distance_n betwixt_o the_o place_n you_o then_o stand_v at_o and_o the_o place_n appoint_v for_o your_o second_o station_n there_o again_o plant_v your_o instrument_n look_v through_o the_o fight_v unto_o the_o mark_n who_o distance_n be_v require_v then_o note_v the_o degr_n cut_v and_o so_o get_v the_o quantity_n of_o both_o the_o angle_n as_o in_o the_o last_o chapter_n when_o you_o have_v get_v these_o two_o angle_n add_v they_o both_o together_o which_o take_v from_o 60_o so_o have_v you_o the_o quantity_n of_o the_o angle_n at_o your_o mark_n then_o must_v you_o resort_v unto_o the_o table_n of_o sign_n place_v in_o the_o 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best_o to_o be_v wrought_v sinical_o so_o shall_v you_o place_n and_o situate_v the_o angle_n more_o true_o than_o you_o can_v by_o the_o intersection_n of_o line_n for_o because_o thereby_o you_o be_v teach_v to_o find_v out_o the_o true_a distance_n of_o every_o angle_n from_o your_o station_n in_o so_o much_o that_o if_o you_o do_v but_o observe_v the_o quantity_n of_o every_o angle_n and_o again_o protract_v the_o same_o true_o you_o can_v err_v any_o thing_n at_o all_o and_o for_o that_o it_o may_v be_v desire_v of_o many_o i_o will_v not_o leave_v for_o their_o sake_n to_o prosecute_v the_o same_o with_o a_o example_n example_n let_v there_o be_v a_o certain_a park_n c_o d_o e_o f_o g_o propose_v the_o proportion_n and_o quantity_n whereof_o you_o be_v require_v to_o deliver_v at_o your_o stand_v a_o or_o b_o which_o be_v certain_a hill_n from_o whence_o you_o may_v well_o view_v all_o the_o angle_n and_o corner_n of_o the_o say_a park_n in_o performance_n whereof_o i_o first_o 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b_o a_o e_o 65_o ½_n  _fw-fr b_o a_o g_o 84_o 2_o 4_o  _fw-fr b_o a_o f_o 87_o ½_n the_o angle_n a_o b_o d_o be_v 128._o degree_n b_o a_o d_o 44._o degree_n which_o add_v together_o and_o the_o total_a take_v from_o 180._o leave_v 8._o degree_n the_o angle_n b_o d_o a._n now_o i_o say_v by_o the_o say_v second_o axioma_fw-la as_o the_o sign_n of_o the_o angle_n a_o d_o b_o 13917_o be_v to_o the_o sign_n of_o the_o angle_n a_o b_o d_o 78801._o so_o be_v the_o side_n a_o b_o to_z the_o side_z a_o d_o or_o as_o the_o sign_n of_o a_o d_o b_o be_v to_o the_o line_n a_o b_o so_o be_v the_o sign_n a_o b_o d_o to_o the_o line_n a_o d._n therefore_o multiply_v 78801._o the_o sign_n of_o b_o by_o 65._o so_o be_v the_o product_n 5122065._o which_o part_n by_o 13917._o the_o sign_n of_o the_o angle_n d_o so_o be_v the_o quotient_a 368_o 609_o 13917_o perche_n the_o line_n a_o d_o which_o be_v one_o mile_n one_o quarter_n of_o a_o mile_n 8._o perche_n and_o odd_a in_o like_a manner_n must_v you_o 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