equal_a 2._o if_o any_o right_a line_n fall_v upon_o two_o parallel_n right_a line_n it_o make_v the_o outward_a angle_n on_o the_o one_o equal_a to_o the_o inward_a angle_n on_o the_o other_o and_o the_o two_o inward_a opposite_a angle_n on_o contrary_a side_n of_o the_o fall_a line_n also_o equal_a 3._o if_o any_o side_n of_o a_o triangle_n be_v produce_v the_o outward_a angle_n be_v equal_a to_o the_o two_o inward_a opposite_a angle_n and_o all_o the_o three_o angle_n of_o any_o triangle_n be_v equal_a to_o two_o right_a angle_n 4._o in_o equiangle_v triangle_n all_o their_o side_n be_v proportional_a as_o well_o such_o as_o contain_v the_o equal_a angle_n as_o also_o the_o subtendent_fw-la side_n 5._o if_o any_o four_o quantity_n be_v proportional_a the_o first_o multiply_v in_o the_o four_o produce_v a_o quantity_n equal_a to_o that_o which_o be_v make_v by_o multiplication_n of_o the_o second_o in_o the_o three_o 6._o in_o all_o right_a angle_a triangle_n the_o square_a of_o 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it_o be_v require_v to_o find_v the_o centre_n of_o a_o circle_n who_o circumference_n shall_v pass_v through_o the_o three_o point_n give_v first_o open_v your_o compass_n to_o any_o distance_n great_a than_o half_a bc_n place_n one_o foot_n in_o the_o point_n b_o and_o with_o the_o other_o describe_v the_o arch_a fg_n then_o the_o compass_n remain_v at_o the_o same_o distance_n place_z one_o foot_n in_o c_o and_o with_o the_o other_o turn_v about_o make_v the_o mark_n f_o and_o g_o in_o the_o former_a arch_n and_o draw_v the_o line_n fg_v at_o length_n if_o need_v be_v again_o open_v the_o compass_n to_o any_o distance_n great_a than_o half_a ab_fw-la place_n one_o foot_n in_o
to_o reduce_v acre_n into_o perch_n and_o the_o contrary_a 248._o 19_o the_o use_n of_o a_o scale_n of_o reduction_n necessary_a for_o find_v the_o fraction_n part_n of_o a_o acre_n 250_o 20._o divers_a compendious_a rule_n for_o the_o ready_a cast_v up_o of_o any_o plain_a superficies_n with_o divers_a other_o compendium_n in_o survey_v by_o the_o line_n of_o number_n 251._o 21._o of_o statute_n and_o customary_a measure_n to_o reduce_v one_o to_o the_o other_o at_o pleasure_n 254._o 22._o of_o the_o lay_n out_o of_o common_a field_n into_o furlong_n 255._o 23._o of_o hill_n and_o mountain_n how_o to_o find_v the_o length_n of_o the_o horizontall_a line_n on_o which_o they_o stand_v several_a way_n 257_o 24._o of_o mountainous_a and_o uneven_a ground_n how_o to_o protract_v or_o lay_v the_o same_o down_o in_o plano_fw-la after_o the_o best_a manner_n give_v the_o area_n or_o content_n thereof_o 258._o 25._o how_o to_o take_v the_o plot_n of_o a_o whole_a manner_n by_o the_o plain_a 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for_o the_o due_a exact_a and_o speedy_a performance_n of_o any_o thing_n belong_v to_o the_o art_n of_o survey_v theodolite_a the_o plain_a table_n use_v as_o the_o theodolite_a for_o the_o frame_n of_o the_o table_n be_v graduate_v according_a to_o that_o description_n will_v be_v a_o absolute_a theodolite_n and_o perform_v the_o work_n thereof_o with_o the_o same_o facility_n and_o exactness_n and_o whatsoever_o may_v be_v do_v by_o the_o limb_n of_o the_o theodolite_a the_o same_o the_o degree_n on_o the_o frame_n of_o the_o table_n will_v as_o well_o perform_v circumferentor_n the_o plain_a table_n use_v as_o a_o circumferentor_n likewise_o the_o index_n and_o sight_n together_o with_o the_o box_n and_o needle_n be_v take_v from_o the_o table_n and_o screw_v to_o the_o staff_n as_o in_o the_o description_n thereof_o it_o be_v so_o convenient_o order_v will_v be_v a_o absolute_a circumferentor_n and_o in_o some_o respect_v better_a than_o the_o ordinary_a one_o hereafter_o describe_v because_o the_o sight_n thereof_o stand_v at_o a_o great_a distance_n so_o that_o thereby_o the_o visual_a line_n may_v be_v the_o better_o direct_v instrument_n the_o plain_a table_n not_o one_o but_o all_o instrument_n and_o this_o instrument_n as_o now_o contrive_v though_o it_o be_v call_v the_o plain_a table_n only_o yet_o you_o see_v that_o it_o contain_v both_o the_o other_o and_o therefore_o in_o advise_v any_o man_n to_o the_o use_n thereof_o chief_o i_o do_v not_o confine_v he_o to_o one_o but_o to_o all_o instrument_n and_o therefore_o do_v not_o contradict_v my_o former_a expression_n beside_o there_o be_v another_o great_a convenience_n which_o do_v ensue_v by_o the_o degree_n on_o the_o table_n frame_v for_o in_o take_v the_o plot_n of_o a_o field_n according_a to_o the_o follow_a direction_n by_o the_o plain_a table_n you_o may_v at_o the_o same_o time_n perform_v the_o same_o work_n by_o the_o degree_n on_o the_o frame_n of_o the_o table_n if_o at_o the_o draw_v
according_a to_o the_o scale_n of_o 10_o in_o a_o inch_n take_v in_o your_o compass_n the_o length_n of_o the_o line_n ab_fw-la and_o apply_v it_o to_o your_o scale_n of_o 10_o in_o a_o inch_n you_o shall_v find_v the_o extent_n of_o the_o compass_n to_o reach_v from_o 5_o of_o the_o great_a division_n to_o fix_v of_o the_o lesser_a division_n wherefore_o the_o line_n ab_fw-la contain_v 5_o chain_n and_o 60_o link_n the_o like_a must_v be_v do_v for_o any_o other_o line_n and_o also_o by_o any_o of_o the_o other_o scale_n upon_o the_o ruler_n there_o be_v beside_o the_o several_a scale_n of_o equal_a part_n a_o line_n or_o scale_n of_o chord_n which_o be_v number_v by_o 10_o 20_o 30_o etc._n etc._n to_o 90_o and_o this_o line_n serve_v to_o protract_v or_o lay_v down_o angle_n but_o in_o all_o the_o prectise_n of_o survey_v a_o protractor_n be_v much_o more_o convenient_a yet_o for_o other_o use_v this_o line_n may_v be_v very_o serviceable_a and_o when_o a_o protractor_n be_v want_v it_o may_v supply_v that_o defect_n the_o manner_n how_o to_o use_v it_o be_v thus_o 3._o how_o to_o lay_v down_o upon_o paper_n a_o angle_n contain_v any_o number_n of_o degree_n and_o minute_n by_o the_o line_n of_o chord_n draw_v a_o line_n at_o pleasure_n as_o ab_fw-la and_o from_o the_o point_n a_o let_v it_o be_v require_v to_o protract_v a_o angle_n of_o 40_o degree_n 20_o minute_n first_o extend_v your_o compass_n upon_o the_o line_n of_o chord_n from_o the_o begin_n thereof_o to_o 60_o degree_n always_o and_o with_o this_o distance_n set_v one_o foot_n upon_o the_o point_n a_o with_o the_o other_o describe_v the_o prick_v arch_a bc_n then_o with_o your_o compass_n take_v 40_o degree_n 20_o minute_n which_o be_v the_o quantity_n of_o the_o inquire_v angle_n out_o of_o the_o line_n of_o chord_n from_o the_o begin_n thereof_o to_o 40_o degree_n 20_o minute_n than_o the_o compass_n so_o rest_v if_o you_o set_v one_o foot_n thereof_o upon_o b_o the_o other_o will_v reach_v upon_o the_o arch_n to_o c._n last_o draw_v the_o line_n ac_fw-la so_o the_o angle_n cab_n shall_v contain_v 40_o degree_n 20_o minute_n 4._o any_o angle_n be_v give_v to_o find_v what_o number_n of_o degree_n and_o minute_n be_v contain_v therein_o suppose_v cab_n be_v a_o angle_n give_v and_o that_o it_o be_v require_v to_o find_v the_o quantity_n thereof_o open_v your_o compass_n as_o before_o to_o 60_o degree_n of_o your_o chord_n and_o place_v one_o foot_n in_o 〈◊〉_d with_o the_o other_o describe_v the_o arch_n cb_n then_o take_v in_o your_o compass_n the_o distance_n cb_n and_o measure_v that_o extent_n upon_o the_o little_a of_o chord_n from_o the_o begin_n thereof_o you_o shall_v find_v it_o to_o reach_v to_o 40_o degree_n 20_o minute_n which_o be_v the_o quantity_n of_o the_o require_a angle_n if_o any_o angle_n give_v or_o require_v shall_v contain_v above_o 20_o degree_n you_o must_v then_o protract_v it_o at_o twice_o by_o take_v first_o the_o whole_a line_n and_o then_o the_o remainder_n chap._n ii_o of_o the_o use_n of_o the_o protractor_n although_o the_o chief_a use_n of_o the_o protractor_n may_v be_v perform_v by_o the_o line_n of_o chord_n last_o speak_v of_o yet_o for_o avoid_v of_o superfluous_a line_n and_o arch_n which_o must_v otherwise_o be_v draw_v all_o over_o your_o plot_n the_o protractor_n be_v far_o more_o convenient_a the_o 〈◊〉_d â—ereof_o be_v 1._o to_o lay_v down_o upon_o paper_n a_o angle_n of_o any_o quantity_n first_o draw_v a_o right_a line_n at_o length_n as_o ab_fw-la then_o on_o any_o part_n thereof_o as_o on_o c_o place_n the_o centre_n of_o the_o protractor_n in_o which_o point_n also_o fix_v your_o protract_n pin_n and_o turn_v the_o protractor_n about_o upon_o the_o centre_n till_o the_o meridian_n line_n of_o the_o protractor_n note_v in_o the_o description_n thereof_o with_o of_o lie_v direct_o on_o this_o line_n ab_fw-la the_o semicircle_n of_o the_o protractor_n lie_v upward_o or_o from_o you_o then_o close_o to_o the_o 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a_o line_n into_o such_o equal_a part_n so_o that_o your_o stationarie_a distance_n kl_n may_v contain_v 800_o of_o they_o your_o scale_n be_v thus_o make_v take_v in_o your_o compass_n the_o distance_n between_o any_o two_o mark_n or_o place_n here_o describe_v and_o apply_v it_o to_o your_o scale_n so_o shall_v it_o exact_o show_v you_o the_o true_a distance_n between_o the_o two_o place_n so_o take_v in_o the_o same_o part_n as_o the_o the_o line_n kl_n be_v divide_v in_o this_o manner_n may_v you_o with_o speed_n and_o exactness_n attein_v the_o true_a distance_n and_o situation_n of_o any_o mark_n or_o mark_n far_o remote_a without_o approach_v near_o any_o of_o they_o and_o thus_o in_o overgrow_a land_n where_o you_o can_v neither_o go_v about_o it_o nor_o measure_n within_o it_o this_o chapter_n will_v be_v of_o excellent_a use_n chap._n xvi_o how_o to_o take_v the_o true_a plot_n of_o a_o field_n at_o one_o station_n take_v within_o the_o same_o field_n so_o that_o from_o thence_o you_o may_v see_v all_o the_o angle_n of_o the_o same_o field_n by_o the_o plain_a table_n when_o you_o enter_v any_o field_n to_o survey_v your_o first_o work_n must_v be_v to_o set_v up_o some_o visible_a mark_n at_o each_o angle_n thereof_o or_o let_v one_o go_v continual_o before_o you_o to_o every_o angle_n hold_v up_o a_o white_a cloth_n or_o the_o like_a to_o direct_v you_o which_o be_v do_v make_v choice_n of_o some_o convenient_a place_n about_o the_o middle_n of_o the_o field_n from_o whence_o you_o may_v behold_v all_o your_o mark_n and_o there_o place_v your_o table_n cover_v with_o a_o sheet_n of_o paper_n the_o needle_n hang_v direct_o over_o the_o meridian_n line_n of_o the_o card_n which_o you_o must_v always_o have_v regard_n unto_o especial_o when_o you_o be_v to_o survey_v many_o field_n together_o then_o make_v a_o mark_n about_o the_o middle_n of_o your_o paper_n which_o shall_v represent_v that_o part_n of_o the_o field_n where_o your_o table_n stand_v and_o lay_v the_o index_n unto_o this_o point_n direct_v your_o sight_n to_o the_o several_a angle_n where_o you_o before_o place_v your_o mark_n and_o draw_v line_n by_o the_o side_n of_o the_o index_n upon_o the_o paper_n then_o measure_v the_o distance_n of_o every_o of_o these_o mark_n from_o your_o table_n and_o by_o your_o scale_n set_v the_o same_o distance_n upon_o the_o line_n draw_v upon_o the_o table_n make_v small_a mark_n with_o your_o protract_n pin_n or_o compass_n point_n at_o the_o end_n of_o every_o of_o they_o then_o line_n be_v draw_v from_o one_o to_o another_o of_o these_o point_n you_o shall_v have_v upon_o your_o table_n the_o exact_a plot_n of_o your_o field_n all_o the_o line_n and_o angle_n upon_o the_o table_n be_v proportional_a to_o those_o of_o the_o field_n suppose_v you_o be_v to_o take_v the_o plot_n of_o the_o field_n abcdef_n have_v place_v mark_n in_o the_o several_a angle_n thereof_o make_v choice_n of_o some_o convenient_a place_n about_o the_o middle_n of_o the_o field_n as_o at_o l_o from_o whence_o you_o may_v behold_v all_o the_o mark_n before_o place_v in_o the_o several_a angle_n and_o there_o place_v your_o table_n then_o turn_v your_o instrument_n about_o till_o the_o needle_n hang_v over_o the_o meridian_n line_n of_o the_o card_n the_o north_n end_n of_o which_o line_n be_v note_v with_o a_o flower-de-luce_n and_o be_v represent_v in_o this_o figure_n by_o the_o line_n n_v your_o table_n be_v thus_o place_v with_o a_o sheet_n of_o paper_n thereupon_o make_v a_o mark_n about_o the_o middle_n of_o your_o table_n which_o shall_v represent_v that_o place_n in_o the_o field_n where_o your_o table_n stand_v then_o apply_v your_o index_n to_o this_o point_n direct_v the_o sight_n to_o the_o first_o mark_n at_o a_o and_o the_o index_n rest_v there_o draw_v a_o line_n by_o the_o side_n thereof_o to_o the_o point_n l_o then_o with_o your_o chain_n measure_v the_o distance_n from_o l_o the_o place_n where_o your_o table_n stand_v to_o a_o your_o first_o mark_n which_o suppose_v to_o be_v 8_o chain_n 10_o link_n then_o take_v 8_o chain_n 10_o link_n from_o any_o scale_n and_o set_v that_o distance_n upon_o your_o table_n from_o l_o to_o a_o and_o at_o a_o make_v a_o mark_n then_o direct_v the_o sight_n to_o b_o your_o second_o mark_n draw_v a_o line_n by_o the_o side_n of_o your_o index_n as_o before_o and_o measure_v the_o distance_n from_o your_o table_n at_o l_o to_o your_o mark_n at_o b_o which_o suppose_v 8_o chain_n 75_o link_n this_o distance_n must_v be_v take_v from_o your_o scale_n and_o set_v upon_o your_o table_n from_o l_o to_o b_o and_z at_z b_o make_v another_o mark_n then_o direct_v the_o sight_n to_o the_o three_o mark_n c_o and_o draw_v a_o line_n by_o the_o side_n of_o the_o index_n measure_v the_o distance_n from_o l_o to_o c_o which_o suppose_v 10_o chain_n 65_o link_n this_o distance_n be_v take_v from_o your_o scale_n and_o apply_v to_o your_o table_n from_o l_o to_o c_o shall_v give_v you_o the_o point_n c_o represent_v your_o three_o mark_n in_o this_o manner_n you_o must_v deal_v with_o the_o rest_n of_o the_o mark_n at_o d_o e_z and_o f_o and_o more_o if_o the_o field_n have_v consist_v of_o more_o angle_n last_o when_o you_o have_v make_v observation_n of_o all_o the_o mark_n round_o the_o field_n and_o find_v the_o point_n a_o b_o c_o d_o e_o and_o f_o upon_o your_o table_n you_o must_v draw_v line_n frnm_fw-la one_o point_n to_o another_o till_o you_o conclude_v where_o you_o first_o begin_v as_o draw_v a_o line_n from_o a_o to_o b_o from_z b_o to_z c_z from_z c_z to_z d_o from_z d_o to_z e_z from_z e_z to_o f_o and_o from_o f_o to_o a_o where_o you_o begin_v then_o will_v abcdef_n be_v the_o exact_a figure_n of_o your_o field_n the_o side_n and_o angle_n of_o the_o say_a figure_n bear_v a_o exact_a proportion_n to_o those_o in_o the_o field_n and_o the_o line_n n_n in_o this_o and_o the_o follow_a figure_n always_o represent_v the_o meridian_n line_n chap._n xvii_o how_o to_o take_v the_o plot_n of_o a_o field_n at_o one_o station_n take_v in_o the_o middle_n thereof_o by_o the_o theodolite_a place_v mark_n at_o the_o several_a angle_n of_o the_o field_n as_o before_o and_o make_v choice_n of_o some_o convenient_a place_n about_o the_o middle_n thereof_o as_o l_o from_o whence_o you_o may_v see_v all_o the_o mark_n and_o there_o place_v your_o instrument_n the_o needle_n hang_v direct_o over_o the_o meridian_n line_n in_o the_o card._n this_o do_v direct_v your_o sight_n to_o the_o first_o mark_n at_o a_o note_v what_o degree_n the_o index_n cut_v which_o let_v be_v 36_o degree_n 45_o minute_n these_o 36_o degree_n 45_o minute_n must_v be_v note_v down_o in_o your_o field-book_n in_o the_o first_o and_o second_o column_n thereof_o then_o measure_v the_o distance_n from_o l_o the_o place_n of_o your_o instrument_n to_o a_o your_o first_o mark_n which_o let_v contain_v 8_o chain_n 10_o link_n these_o 8_o chain_n 10_o link_n must_v be_v place_v in_o the_o three_o and_o four_o column_n of_o your_o field-book_n as_o have_v be_v direct_v in_o the_o description_n thereof_o then_o direct_v the_o sight_n to_o b_o your_o second_o mark_n and_o note_v the_o degree_n cut_v by_o the_o index_n which_o let_v be_v 99_o degree_n 15_o minute_n and_o the_o distance_n lb_n 8_o chain_n 75_o link_n the_o 99_o degree_n 15_o minute_n must_v be_v note_v in_o the_o first_o and_o second_o column_n of_o your_o field-book_n and_o the_o 8_o chain_n 75_o link_n in_o the_o three_o and_o four_o column_n then_o direct_v your_o sight_n to_o c_o your_o three_o mark_n and_o note_v the_o degree_n cut_v by_o the_o index_n which_o let_v be_v 163_o degree_n 15_o minute_n and_o let_v the_o distance_n lc_n be_v 10_o chain_n 65_o link_n the_o 163_o degree_n 15_o minute_n must_v be_v note_v in_o the_o first_o and_o second_o column_n of_o your_o field-book_n and_o the_o 10_o chain_n 65_o link_n in_o the_o three_o and_o four_o column_n thereof_o then_o direct_v your_o sight_n to_o d_o your_o four_o mark_n and_o note_v the_o degree_n cut_v by_o the_o index_n which_o let_v be_v 212_o degree_n ¶_o and_o here_o you_o must_v note_v that_o in_o use_v the_o degree_n on_o the_o frame_n of_o the_o table_n that_o after_o the_o index_n have_v pass_v 180_o degree_n which_o be_v at_o the_o line_n n_v represent_v always_o the_o meridian_n line_n you_o must_v then_o count_v the_o degree_n backward_o according_a as_o they_o be_v number_v on_o the_o frame_n of_o the_o table_n from_o 190_o to_o 360._o then_o measure_v the_o distance_n ld_n which_o let_v be_v 8_o chain_n 53_o link_n the_o 212_o degree_n must_v be_v note_v in_o
and_o through_o it_o draw_v the_o line_n bc_n contain_v 6_o chain_n 83_o link_n 3._o place_v the_o centre_n of_o the_o protractor_n on_o the_o point_n c_o the_o meridian_n line_n thereof_o lie_v parallel_n to_o one_o of_o the_o prick_v meridian_n draw_v on_o the_o paper_n than_o the_o degree_n cut_v by_o the_o needle_n at_o your_o three_o observation_n at_o c_o being_n above_o 180_o namely_o 216_o degree_n 30_o minute_n therefore_o must_v the_o semicircle_n lie_v downward_o then_o make_v a_o mark_n against_o 216_o degree_n 30_o minute_n through_o it_o draw_v the_o line_n cd_o contain_v 7_o chain_n 82_o link_n 4._o lay_v the_o centre_n of_o the_o protractor_n upon_o the_o point_n d_o the_o degree_n cut_v by_o the_o needle_n at_o that_o angle_n be_v 325_o which_o be_v above_o 180_o lay_v the_o semicircle_n of_o the_o protractor_n downward_o and_o against_o 325_o degree_n make_v a_o mark_n with_o your_o protract_n pin_n through_o which_o point_n and_o the_o angle_n d_o draw_v the_o line_n de_fw-fr make_v it_o to_o contain_v 6_o chain_n 96_o link_n 5._o remove_v your_o protractor_n to_o e_o lay_v the_o meridian_n line_n thereof_o upon_o or_o parallel_n to_o one_o of_o the_o meridian_n draw_v upon_o your_o paper_n and_o because_o the_o degree_n cut_v by_o the_o needle_n at_o this_o angle_n be_v less_o than_o 180_o namely_o 12_o degree_n 30_o minute_n therefore_o lay_v the_o semicircle_n of_o the_o protractor_n upward_o and_o make_v a_o mark_n against_o 12_o degree_n 30_o minute_n through_o which_o draw_v the_o line_n of_o contain_v 9_o chain_n 71_o link_n 6._o lay_v the_o centre_n of_o the_o protractor_n upon_o the_o point_n f_o and_o because_o the_o degree_n to_o be_v protract_v be_v above_o 180_o viz._n 342_o degree_n 30_o minute_n lay_v the_o semicircle_n of_o the_o protractor_n downward_o and_o make_v a_o mark_n against_o 342_o degree_n 30_o minute_n draw_v the_o line_n fg_v which_o contain_v 7_o chain_n 54_o link_n and_o in_o this_o manner_n must_v you_o protract_v all_o the_o other_o angle_n g_o h_o and_o k_o and_o more_o if_o the_o field_n have_v consist_v of_o more_o angle_n always_o observe_v this_o for_o a_o general_a rule_n to_o lay_v the_o meridian_n line_n of_o the_o protractor_n upon_o or_o parallel_n to_o one_o of_o the_o meridian_n draw_v upon_o your_o paper_n which_o the_o small_a division_n at_o each_o end_n of_o the_o scale_n of_o the_o protractor_n will_v help_v you_o to_o do_v and_o if_o the_o degree_n you_o be_v to_o protract_v be_v less_o than_o 180_o as_o those_o at_o g_z h_n and_o k_n be_v to_o lay_v the_o semicircle_n of_o the_o protractor_n upward_o or_o from_o you_o and_o if_o they_o be_v above_o 180_o degree_n as_o those_o at_o a_o b_o c_o and_o d_o be_v to_o lay_v the_o semicircle_n downward_o as_o you_o see_v do_v in_o the_o figure_n chap._n xxxvii_o how_o to_o take_v the_o plot_n of_o any_o park_n forrest_n chase_n wood_n ot_fw-mi other_o large_a champion_n plain_a by_o the_o index_n and_o needle_n together_o with_o the_o degree_n on_o the_o frame_n of_o the_o table_n most_o commodious_o supply_v the_o use_n of_o the_o peractor_n the_o use_n of_o the_o plain_a table_n theodolite_n and_o circumferentor_n have_v be_v sufficient_o teach_v in_o the_o precede_a chapter_n and_o their_o agreement_n in_o all_o kind_n of_o practice_n full_o intimate_v so_o that_o you_o may_v perceive_v by_o what_o have_v be_v hitherto_o deliver_v that_o for_o some_o kind_n of_o work_n one_o instrument_n be_v better_a than_o another_o and_o for_o large_a and_o spacious_a business_n the_o circumferentor_n be_v the_o best_a the_o needle_n be_v good_a and_o no_o impediment_n near_o to_o hinder_v the_o play_v or_o virtue_n thereof_o there_o be_v only_o this_o objection_n to_o be_v make_v against_o it_o viz._n that_o the_o degree_n in_o the_o card_n be_v for_o the_o most_o part_n so_o small_a that_o they_o can_v be_v true_o estimate_v and_o so_o may_v occasion_v the_o great_a error_n in_o protraction_n for_o the_o salve_v of_o this_o grand_a inconvenience_n master_n rathborn_a have_v a_o contrivance_n in_o his_o book_n of_o survey_v by_o a_o instrument_n which_o he_o call_v a_o peractor_n which_o be_v no_o other_o than_o a_o theodolite_a only_o the_o box_n and_o needle_n be_v so_o fit_v to_o the_o centre_n of_o the_o instrument_n that_o when_o the_o instrument_n be_v fix_v in_o any_o position_n whatsoever_o the_o index_n may_v be_v turn_v about_o and_o yet_o the_o box_n and_o needle_n remain_v immovable_a the_o benefit_n of_o this_o contrivance_n be_v that_o whereas_o in_o the_o circumferentor_n the_o degree_n be_v cut_v by_o the_o needle_n here_o the_o same_o degree_n be_v cut_v by_o the_o index_n and_o therefore_o be_v large_a the_o use_n whereof_o be_v thus_o place_v the_o peractor_n at_o any_o angle_n of_o a_o field_n and_o turn_v it_o about_o till_o the_o needle_n hang_v direct_o over_o the_o meridian_n line_n in_o the_o card_n then_o fix_v the_o instrument_n there_o and_o turn_v the_o index_n about_o till_o through_o the_o sight_n you_o espy_v the_o mark_n or_o angle_v you_o will_v look_v at_o then_o shall_v the_o index_n cut_v the_o same_o degree_n and_o minute_n upon_o the_o limb_n of_o the_o peractor_n as_o the_o needle_n will_v have_v cut_v upon_o the_o card_n of_o the_o circumferentor_n if_o use_v as_o be_v before_o teach_v yet_o notwithstanding_o this_o contrivance_n you_o see_v you_o must_v be_v behold_v to_o the_o needle_n the_o convenience_n only_o be_v that_o the_o degree_n which_o you_o be_v to_o note_v in_o your_o field-book_n be_v large_a upon_o the_o limb_n of_o the_o instrument_n then_o in_o the_o card_n which_o i_o confess_v be_v something_o considerable_a let_v abcde_v be_v a_o field_n to_o be_v measure_v by_o the_o index_n and_o needle_n on_o the_o plain_a table_n supply_v the_o use_n of_o the_o peractor_n 1._o place_v your_o instrument_n at_o a_o lay_v the_o index_n and_o sight_n with_o the_o box_n and_o needle_n screw_v thereto_o upon_o the_o diameter_n of_o the_o table_n than_o the_o index_n so_o lie_v turn_v the_o whole_a instrument_n about_o till_o the_o needle_n hang_v direct_o over_o the_o meridian_n line_n in_o the_o card_n then_o screw_v the_o instrument_n fast_o and_o turn_v the_o index_n about_o upon_o the_o centre_n till_o through_o the_o sight_n you_o espy_v your_o second_o angle_n at_o b_o than_o you_o shall_v see_v that_o the_o south_n end_n of_o the_o needle_n will_v cut_v upon_o the_o card_n in_o the_o box_n about_o 218_o degree_n and_o the_o index_n at_o the_o same_o time_n upon_o the_o table_n will_v cut_v 218_o degree_n 10_o minute_n which_o must_v be_v note_v down_o in_o your_o field_n book_n as_o have_v be_v several_a time_n before_o teach_v and_o measure_v the_o distance_n ab_fw-la 9_o chain_n 65_o link_n which_o you_o must_v note_v down_o in_o your_o field-book_n also_o ¶_o by_o this_o you_o may_v see_v the_o convenience_n of_o count_v the_o degree_n cut_v by_o the_o index_n rather_o than_o by_o the_o needle_n as_o 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and_o dale_n as_o before_o and_o to_o this_o perpendicular_a ch_n set_v the_o number_n as_o you_o find_v it_o by_o the_o chain_n then_o find_v the_o perpendicular_a je_n and_o measure_n that_o with_o your_o chain_n also_o all_o which_o line_n in_o respect_n of_o the_o hill_n and_o valley_n will_v be_v find_v much_o long_o than_o if_o they_o be_v measure_v by_o your_o scale_n then_o by_o the_o measure_a line_n bd_o ch_n and_o je_n cast_v up_o the_o content_a of_o the_o trapezia_n bcde_v in_o this_o manner_n you_o must_v cast_v up_o the_o content_a of_o the_o trapezia_n abeg_n and_o the_o triangle_n gef_n and_o this_o be_v the_o exact_a way_n i_o can_v prescribe_v for_o the_o mensuration_n of_o uneven_a ground_n which_o be_v well_o and_o careful_o perform_v will_v not_o vary_v much_o of_o the_o true_a content_n for_o it_o be_v apparent_a that_o if_o such_o mountainous_a ground_n be_v plot_v true_o according_a to_o their_o area_n in_o plano_fw-la the_o figure_n thereof_o will_v not_o be_v contain_v within_o its_o proper_a limit_n and_o be_v lay_v down_o among_o other_o ground_n will_v swell_v beyond_o the_o bound_n and_o force_v the_o adjoin_a ground_n out_o of_o their_o place_n now_o for_o distinction_n in_o your_o plot_n you_o may_v shadow_v they_o off_o with_o hill_n as_o in_o this_o figure_n lest_o any_o man_n see_v your_o plot_n shall_v measure_v by_o your_o scale_n and_o find_v your_o work_n to_o differ_v chap._n xlviii_o how_o to_o take_v the_o plot_n of_o a_o whole_a manor_n or_o of_o divers_a parcel_n of_o land_n lie_v together_o whether_o wood-land_n or_o champion_n plain_n by_o the_o plain_a table_n although_o practice_n in_o the_o performance_n hereof_o be_v better_o than_o many_o word_n and_o that_o the_o rule_v already_o deliver_v be_v of_o sufficient_a extent_n to_o perform_v the_o work_n of_o this_o chapter_n yet_o for_o far_a satisfaction_n in_o this_o particular_a i_o will_v herein_o deliver_v the_o most_o sure_a and_o compendious_a way_n i_o can_v 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passage_n you_o ought_v to_o take_v special_a notice_n of_o all_o eminent_a thing_n lie_v in_o your_o way_n as_o church_n house_n mill_n highway_n river_n etc._n etc._n which_o will_v much_o help_v you_o also_o in_o this_o your_o passage_n it_o be_v necessary_a to_o take_v notice_n of_o some_o convenient_a place_n to_o begin_v your_o work_n as_o follow_v have_v make_v choice_n of_o some_o convenient_a place_n in_o the_o peripherie_n or_o outward_a part_n of_o the_o manor_n as_o at_o a_o place_n there_o your_o table_n turn_v it_o about_o till_o the_o needle_n hang_v over_o the_o meridian_n line_n in_o the_o card_n and_o there_o fix_v it_o then_o upon_o the_o table_n with_o most_o convenience_n assign_v any_o point_n at_o pleasure_n as_o a_o unto_o which_o point_n lie_v the_o index_n and_o turn_v it_o about_o till_o through_o the_o sight_n you_o see_v a_o mark_n set_v up_o at_o the_o next_o angle_n at_o l_o then_o by_o the_o side_n of_o the_o index_n draw_v the_o line_n all_o which_o 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as_o before_o and_o place_v the_o length_n thereof_o upon_o your_o table_n from_o m_n unto_o n._n 4._o place_v your_o instrument_n at_o n_n lay_v the_o index_n upon_o the_o line_n nm_n and_o turn_v the_o table_n about_o till_o through_o the_o sight_n you_o see_v a_o mark_n set_v up_o at_o your_o former_a station_n at_o m_n and_o there_o fix_v the_o table_n so_o will_v the_o needle_n hang_v over_o the_o meridian_n line_n as_o before_o then_o turn_v the_o index_n about_o upon_o the_o point_n n_n till_o through_o the_o sight_n you_o espy_v the_o next_o angle_n at_o p_o and_o draw_v a_o line_n by_o the_o side_n thereof_o then_o measure_v the_o distance_n np_v 9_o chain_n 32_o link_n which_o take_v from_o the_o scale_n and_o set_v it_o upon_o your_o table_n from_o n_n unto_o p._n in_o this_o manner_n must_v you_o go_v round_o about_o the_o whole_a manor_n make_v observation_n at_o every_o angle_n thereof_o as_o at_o p_o q_o s_o t_o y_fw-fr x_o g_o h_n and_o k_n and_o set_v down_o the_o 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apprehend_v at_o the_o first_o sight_n i_o will_v therefore_o instance_n in_o the_o circumferentor_n as_o be_v most_o general_a let_v the_o example_n of_o the_o last_o chapter_n serve_v where_o the_o figure_n almnpqstuxghk_v represent_v part_n of_o a_o manor_n then_o have_v provide_v your_o field-book_n ready_o rule_v you_o must_v at_o the_o head_n of_o one_o of_o the_o leave_v thereof_o write_v the_o title_n of_o the_o manor_n the_o county_n in_o which_o it_o be_v and_o who_o be_v lord_n thereof_o as_o the_o manor_n of_o elsmore_n in_o the_o county_n of_o s._n for_o the_o honourable_a r._n b._n lord_n thereof_o then_o beginning_n with_o your_o first_o close_n write_v over_o the_o head_n of_o your_o field-book_n the_o tenant_n name_n the_o name_n of_o the_o close_a and_o the_o tenor_n by_o which_o he_o hold_v the_o same_o so_o for_o the_o first_o close_n henry_n grey_n casbey_n close_n pasture_n free_n under_o this_o draw_v a_o line_n quite_o through_o your_o book_n then_o begin_v to_o 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in_o your_o field-bok_a banton_n plain_a and_o because_o you_o be_v now_o to_o leave_v the_o hedge_n or_o bounder_n of_o banton_n plain_a draw_v a_o line_n quite_o through_o your_o field-book_n 6._o place_v your_o instrument_n at_o c_o and_o direct_v the_o sight_n to_o b_o the_o needle_z cut_v 54_o degree_n 00_o minute_n and_o the_o distance_n cb_n be_v 8_o chain_n 5_o link_n the_o degree_n and_o minute_n must_v be_v note_v in_o the_o first_o and_o second_o column_n of_o your_o field-book_n and_o the_o chain_n and_o link_n in_o the_o three_o and_o four_o 7._o remove_v your_o instrument_n to_o b_o and_o direct_v the_o sight_n to_o a_o the_o needle_n cut_v 19_o degree_n 30_o minute_n and_o the_o distance_n basilius_n be_v 6_o chain_n 43_o link_n the_o degree_n and_o minute_n must_v be_v note_v in_o the_o first_o and_o second_o column_n of_o your_o field-book_n and_o the_o chain_n and_o link_n in_o the_o three_o and_o four_o now_o because_o at_o these_o two_o last_o observation_n you_o 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at_o c_o which_o be_v 54_o degree_n and_o 8_o chain_n 5_o link_n therefore_o against_o that_o number_n make_v this_o ☉_o or_o the_o like_a mark_n and_o write_v the_o title_n for_o your_o second_o close_a thus_o samuel_n white_a bay-wood_n by_o lease_n begin_v at_o ☉_o by_o this_o mean_v you_o shall_v ready_o know_v when_o you_o come_v to_o protraction_n where_o to_o begin_v with_o this_o prcell_n and_o in_o the_o margin_n place_n 2_o for_o the_o number_n of_o your_o second_o parsell_n and_o then_o proceed_v in_o your_o work_n of_o survey_v this_o parcel_n as_o before_o you_o do_v for_o the_o other_o till_o you_o have_v go_v round_o about_o the_o same_o end_n at_o a_o where_o you_o first_o begin_v note_v down_o all_o your_o observation_n both_o of_o line_n and_o angle_n with_o the_o particular_a bounder_n as_o you_o go_v along_o in_o your_o field-book_n in_o all_o respect_n as_o you_o do_v those_o of_o the_o first_o close_n and_o in_o thus_o do_v you_o shall_v find_v that_o at_o your_o 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needle_n cut_v when_o you_o make_v observation_n at_o n_n in_o the_o survey_v of_o gosby_n close_n and_o leave_v the_o bounder_n of_o wisby_n common_a which_o degree_n you_o shall_v find_v to_o be_v 355_o degree_n 40_o minute_n and_o 4_o chain_n 45_o link_n therefore_o at_o the_o end_n of_o that_o line_n where_o you_o find_v 355_o degree_n 40_o minute_n and_o 4_o chain_n 45_o link_n make_v this_o +_o or_o some_o other_o mark_n for_o a_o remembrance_n when_o you_o come_v to_o protraction_n then_o for_o the_o next_o parcel_n write_v in_o your_o field-book_n george_n burton_n banton_n plain_a for_o two_o life_n begin_v at_o ✚_o this_o be_v do_v place_v your_o instrument_n at_o n_n and_o direct_v the_o sight_n to_o p_o the_o needle_n cut_v 220_o degree_n 20_o minute_n and_o the_o line_n np_v contain_v 9_o chain_n 32_o link_n which_o note_n in_o your_o field-book_n and_o because_o at_o this_o observation_n you_o go_v by_o the_o hedge_n or_o bounder_n of_o wisby_n common_a and_o be_v now_o to_o leave_v it_o therefore_o draw_v a_o line_n and_o write_v wisby_n common_a and_o in_o this_o manner_n must_v you_o go_v about_o this_o parcel_n also_o till_o you_o come_v to_o close_v at_o d_o and_o have_v finish_v draw_v a_o double_a line_n then_o consider_v that_o church_n field_n be_v next_o fit_a to_o be_v survey_v and_o that_o it_o be_v most_o convenient_a to_o begin_v the_o same_o at_o q_o therefore_o look_v what_o degree_n the_o needle_n cut_v at_o q_o in_o the_o survey_v of_o banton_n plain_n which_o be_v 15_o degree_n 40_o minute_n â—nd_v 10_o chain_n 75_o link_n against_o which_o in_o your_o fild-book_n make_v this_o ♓_o or_o the_o like_a mark_n for_o your_o remembrance_n and_o for_o your_o next_o close_a â—rite_n in_o your_o field-book_n as_o
on_o the_o frame_n of_o the_o table_n which_o supply_v the_o use_n thereof_o three_o when_o i_o mention_v or_o make_v use_n of_o the_o circumferentor_n i_o mean_v the_o index_n with_o the_o box_n and_o needle_n screw_v to_o the_o staff_n ¶_o having_n thus_o give_v you_o a_o sufficient_a description_n of_o the_o several_a instrument_n and_o their_o part_n i_o come_v now_o to_o the_o use_n of_o they_o show_v how_o any_o angle_n in_o the_o field_n may_v be_v measure_v by_o any_o of_o they_o and_o 1._o how_o to_o observe_v a_o angle_n in_o the_o field_n by_o the_o plain_a table_n suppose_v eke_o and_o kg_o to_o be_v two_o hedge_n or_o two_o side_n of_o a_o field_n include_v the_o angle_n ekg_v and_o that_o it_o be_v require_v to_o draw_v upon_o your_o table_n a_o angle_n equal_a thereunto_o first_o place_v your_o instrument_n as_o near_o the_o angular_a point_n k_o as_o conveniency_n will_v permit_v turn_v it_o about_o till_o the_o north_n end_n of_o the_o needle_n hang_v direct_o over_o the_o flower-de-luce_n in_o the_o box_n and_o then_o screw_v the_o table_n fast_o then_o upon_o your_o table_n with_o your_o protract_n pin_n or_o compass_n point_n assign_v any_o point_n at_o pleasure_n upon_o the_o table_n and_o to_o that_o point_n apply_v the_o edge_n of_o the_o index_n turn_v the_o index_n about_o upon_o that_o point_n till_o through_o the_o sight_n thereof_o you_o espy_v a_o mark_n set_v up_o at_o e_o or_o parallel_v to_o the_o line_n eke_o and_o then_o with_o your_o protract_n pin_n or_o compass_n point_n or_o black-lead_a draw_v a_o line_n by_o the_o side_n of_o the_o index_n to_o the_o assign_a point_n upon_o the_o table_n then_o the_o table_n remain_v immovable_a turn_v the_o index_n about_o upon_o the_o same_o point_n and_o direct_v the_o sight_n to_o a_o mark_n set_v up_o at_o g_o or_o parallel_v thereto_o that_o be_v so_o far_o distant_a from_o g_z as_o your_o instrument_n be_v place_v from_o k_o and_o then_o by_o the_o side_n of_o the_o index_n draw_v another_o line_n to_o the_o assign_a point_n so_o shall_v you_o have_v draw_v upon_o your_o table_n two_o line_n which_o shall_v represent_v the_o two_o hedge_n eke_o and_o kg_v and_o those_o line_n shall_v include_v a_o angle_n equal_a to_o the_o angle_n ekg_v and_o although_o you_o know_v not_o the_o quantity_n of_o this_o angle_n yet_o you_o may_v by_o the_o 1_o or_o 2_o chapter_n of_o this_o book_n find_v the_o quantity_n thereof_o if_o there_o be_v any_o need_n for_o in_o work_v by_o this_o instrument_n it_o be_v sufficient_a only_a to_o give_v the_o symmetry_n or_o proportion_n of_o angle_n and_o not_o their_o quantity_n as_o in_o work_v by_o the_o theodolite_a or_o circumferentor_n it_o be_v also_o in_o work_v by_o the_o plain_a table_n there_o need_v no_o protraction_n at_o all_o for_o you_o shall_v have_v upon_o your_o table_n the_o true_a figure_n of_o any_o angle_n or_o angle_n which_o you_o observe_v in_o the_o field_n in_o their_o true_a position_n without_o any_o far_a trouble_n 2._o how_o to_o find_v the_o quantity_n of_o a_o angle_n in_o the_o field_n by_o the_o theodolite_a let_v it_o be_v require_v to_o find_v the_o quantity_n of_o the_o angle_n ekg_v by_o the_o theodolite_a place_n your_o instrument_n at_o k_o lay_v the_o index_n on_o the_o diameter_n thereof_o then_o turn_v the_o whole_a instrument_n about_o the_o index_n still_o rest_v on_o the_o diameter_n till_o through_o the_o sight_n you_o espy_v the_o mark_n at_o e_o then_o screw_v the_o instrument_n fast_o there_o turn_v the_o index_n about_o upon_o the_o centre_n till_o through_o the_o sight_n you_o espy_v the_o mark_n at_o g_o then_z note_z what_o degree_n on_o the_o frame_n of_o the_o table_n be_v cut_v by_o the_o index_n which_o you_o will_v find_v to_o be_v 114_o degree_n and_o that_o be_v the_o quantity_n of_o the_o angle_n ekg_v 3._o how_o to_o find_v the_o quantity_n of_o any_o angle_n in_o the_o field_n by_o the_o circumferentor_n if_o it_o be_v require_v to_o find_v the_o quantity_n of_o the_o former_a angle_n ekg_v by_o the_o circumferentor_n first_o place_v your_o instrument_n as_o before_o at_o k_o with_o the_o flower-de-luce_n in_o the_o card_n towards_o you_o then_o direct_v your_o sight_n to_o e_o and_o observe_v what_o degree_n in_o the_o card_n be_v cut_v by_o the_o south_n end_n of_o the_o needle_n which_o let_v be_v 296_o then_o turn_v the_o instrument_n about_o the_o staff_n the_o flower-de-luce_n always_o towards_o you_o direct_v the_o sight_n to_o g_o note_v then_o also_o what_o degree_n be_v cut_v by_o the_o south_n end_n of_o the_o needle_n which_o suppose_v 182_o this_o do_v always_o subtract_v the_o lesser_a number_n of_o degree_n out_o of_o the_o great_a as_o in_o this_o example_n 182_o from_o 296_o and_o the_o remainder_n be_v 114_o degree_n which_o be_v the_o true_a quantity_n of_o the_o angle_n ekg_v again_o the_o instrument_n stand_v at_o k_o and_o the_o sight_n be_v direct_v to_o e_o as_o before_z suppose_v that_o the_o south_n end_n of_o the_o needle_n have_v cut_v 79_o degree_n and_o then_o direct_v the_o sight_n to_o g_o the_o same_o end_n of_o the_o needle_n have_v cut_v 325_o degree_n now_o if_o from_o 325_o you_o subtract_v 79_o the_o remainder_n be_v 246_o but_o because_o this_o remainder_n 246_o be_v great_a than_o 180_o you_o must_v therefore_o subtract_v 246_o the_o remainder_n from_o 360_o and_o there_o will_v remain_v 114_o the_o true_a quantity_n of_o the_o inquire_v angle_n and_o thus_o you_o must_v always_o do_v when_o the_o remainder_n exceed_v 180_o degree_n ¶_o this_o add_v and_o substract_n for_o the_o find_n of_o angle_n may_v seem_v tedious_a to_o some_o but_o here_o the_o reader_n be_v desire_v to_o take_v notice_n that_o for_o quick_a dispatch_n the_o circumferentor_n be_v as_o good_a a_o instrument_n as_o the_o best_a for_o in_o go_v round_o a_o field_n or_o in_o survey_v of_o a_o whole_a manor_n you_o be_v not_o to_o take_v notice_n of_o the_o quantity_n of_o any_o angle_n but_o only_o to_o observe_v what_o degree_n the_o needle_n cut_v which_o in_o those_o case_n be_v sufficient_a as_o will_v appear_v hereafter_o but_o in_o take_v of_o distance_n by_o the_o circumferentor_n it_o be_v altogether_o necessary_a as_o may_v appear_v by_o the_o 7_o chap._n follow_v and_o for_o that_o reason_n i_o have_v here_o show_v how_o to_o find_v a_o angle_n by_o the_o circumferentor_n and_o also_o that_o you_o may_v thereby_o perceive_v what_o congruity_n and_o harmony_n there_o be_v in_o all_o the_o three_o instrument_n 4._o how_o to_o set_v the_o index_n and_o label_n horizontall_a upon_o the_o staff_n when_o you_o have_v screw_v the_o index_n and_o sight_n to_o the_o staff_n as_o a_o circumferentor_n before_o you_o put_v the_o label_n upon_o the_o brass_n pin_n or_o wire_n you_o must_v hang_v a_o line_n and_o plummet_n upon_o that_o pin_n and_o then_o put_v on_o the_o label_n then_o move_v the_o index_n up_o and_o down_o till_o the_o thread_n and_o plummet_n hang_v direct_o upon_o a_o line_n which_o be_v gage_v from_o under_o the_o pin_n all_o along_o the_o sight_n and_o then_o do_v the_o instrument_n stand_v horizontall_a or_o level_n which_o it_o must_v always_o do_v when_o you_o take_v a_o altitude_n therewith_o 5._o how_o to_o observe_v a_o angle_n of_o altitude_n the_o label_n which_o be_v to_o be_v hang_v on_o one_o of_o the_o sight_n of_o the_o circumferentor_n as_o be_v intimate_v in_o the_o description_n thereof_o and_o the_o tangent_fw-la line_n on_o the_o edge_n of_o the_o index_n be_v only_o for_o the_o find_n of_o angle_n of_o altitude_n and_o be_v therefore_o only_o useful_a in_o take_v of_o height_n and_o in_o survey_v of_o mountainous_a and_o uneven_a ground_n the_o manner_n how_o to_o observe_v a_o angle_n of_o altitude_n by_o this_o label_n and_o the_o tangent_fw-la line_n on_o the_o index_n be_v thus_o suppose_v ca_n to_o be_v a_o tree_n tower_n or_o hill_n who_o height_n be_v require_v your_o instrument_n be_v place_v at_o b_o exact_o level_v direct_v the_o sight_n thereof_o towards_o ca_n and_o there_o fix_v it_o hang_v the_o label_n on_o the_o farthermost_a fight_n upon_o a_o pin_n for_o that_o purpose_n then_o move_v the_o label_n too_o and_o fro_o along_o the_o side_n of_o the_o index_n till_o through_o the_o sight_n at_o the_o end_n of_o the_o label_n and_o by_o the_o pin_n on_o which_o the_o label_n hang_v you_o espy_v the_o very_a top_n of_o the_o object_n to_o be_v measure_v at_o c_o then_z note_z what_o degree_n of_o the_o tangent_fw-la line_n be_v cut_v by_o the_o label_n which_o suppose_v 30_o and_o that_o be_v the_o quantity_n of_o the_o angle_n of_o altitude_n it_o be_v equal_a to_o the_o angle_n cba_n thus_o by_o the_o rule_n in_o this_o chapter_n