till_o you_o bid_v he_o remove_v to_o another_o only_o when_o angle_n be_v very_a near_o you_o this_o labour_n may_v be_v spare_v 2._o when_o ever_o you_o have_v occasion_n to_o plant_v your_o instrument_n more_o than_o once_o as_o it_o will_v often_o fall_v out_o in_o the_o first_o method_n and_o ever_o in_o in_o the_o two_o latter_a you_o must_v be_v sure_a it_o stand_v just_a as_o it_o do_v the_o first_o time_n for_o situation_n for_o which_o your_o needle_n if_o well_o touch_v and_o hang_v will_v be_v good_a direction_n but_o be_v not_o think_v sufficient_a without_o back_n sight_n and_o foresight_n by_o some_o practical_a surveyor_n i_o shall_v therefore_o in_o due_a season_n show_v you_o that_o knack_n now_o for_o the_o first_o method_n i._o when_o you_o go_v about_o to_o plot_v your_o parcel_n of_o land_n find_v such_o a_o place_n in_o it_o if_o possible_a from_o whence_o you_o can_v see_v all_o the_o angle_n and_o in_o that_o place_n plant_v your_o instrument_n cover_v with_o a_o sheet_n of_o paper_n and_o turn_v it_o about_o till_o the_o needle_n play_v at_o liberty_n hang_v over_o the_o flower-de-luce_n or_o any_o other_o notable_a place_n that_o you_o make_v choice_n of_o screw_v it_o fast_o then_o choose_v any_o convenient_a place_n in_o your_o paper_n for_o a_o centre_n and_o to_o represent_v your_o station_n or_o place_n where_o you_o fix_v your_o instrument_n make_v a_o prick_n with_o the_o small_a point_n of_o your_o compass_n to_o which_o prick_n apply_v the_o fiducial_a edge_n of_o the_o index_n which_o be_v easy_o do_v if_o you_o keep_v the_o point_n of_o the_o compass_n rest_v in_o it_o direct_v the_o index_n by_o the_o sight_n to_o all_o the_o angle_n and_o when_o through_o the_o slit_n or_o long_a sight_n you_o see_v the_o opposite_a thread_n cut_v the_o mark_n in_o the_o angle_n draw_v a_o neat_a dry_a line_n along_o the_o fiducial_a edge_n to_o or_o from_o the_o centre_n then_o measure_v from_o the_o instrument_n to_o every_o angle_n set_v the_o measure_n by_o a_o scale_n and_o compass_n from_o the_o centre_n towards_o the_o angle_n upon_o the_o line_n that_o point_v at_o it_o make_v a_o prick_n in_o the_o line_n where_o the_o chain_n and_o link_n reckon_v from_o the_o centre_n do_v true_o end_v then_o shall_v line_n draw_v by_o a_o straight_a rule_n from_o prick_n to_o prick_v give_v you_o the_o perfect_a plot_n upon_o your_o paper_n which_o you_o may_v divide_v as_o have_v be_v before_o show_v into_o trapezla_n and_o triangle_n and_o to_o find_v the_o true_a content_a to_o make_v which_o plain_n mark_v this_o example_n fig._n 24_o suppose_v abcdefgh_o to_o be_v a_o field_n have_v plant_v my_o plain-table_n as_o before_o direct_v at_o a_o convenient_a advantage_n so_o as_o to_o see_v all_o the_o angle_n as_o at_o i_o i_o make_v a_o prick_n to_o represent_v my_o station_n in_o the_o little_a circle_n ☉_o mark_v with_o ay_o upon_o which_o lay_v the_o fiducial_a edge_n of_o my_o index_n and_o direct_v the_o sight_n to_o all_o the_o angle_n i_o draw_v dry_a line_n towards_o a_o and_o all_o the_o rest_n of_o the_o angle_n in_o order_n from_o the_o centre_n and_o then_o measure_v upon_o the_o ground_n from_o the_o instrument_n to_o the_o angle_n a_o i_o find_v it_o to_o be_v 3._o 45_o which_o i_o set_v by_o the_o help_n of_o my_o scale_n from_o the_o centre_n to_o the_o point_n a_o and_o so_o upon_o all_o the_o rest_n according_a to_o their_o due_a measure_n and_o then_o black_a line_n draw_v from_o point_n to_o point_v as_o from_o a_o to_o b_o from_o b_o to_z c_z etc._n etc._n limit_v the_o true_a figure_n of_o the_o field_n according_a to_o the_o scale_n i_o use_v viz._n of_o 400_o in_o a_o inch._n and_o now_o before_o i_o pass_v to_o further_a variety_n let_v my_o reader_n take_v notice_n of_o these_o follow_a thing_n 1._o from_o henceforth_o i_o shall_v forbear_v for_o brevity_n sake_n to_o take_v any_o notice_n of_o the_o measure_n of_o line_n measure_v from_o the_o instrument_n to_o the_o several_a angle_n have_v so_o often_o show_v how_o to_o measure_v by_o a_o scale_n 2._o when_o i_o speak_v of_o measure_v from_o or_o to_o the_o instrument_n i_o always_o mean_a from_o or_o to_o that_o part_n of_o ground_n that_o be_v perpendicular_o under_o the_o head_n of_o the_o instrument_n where_o you_o be_v to_o draw_v your_o plot_n which_o will_v ever_o be_v enclose_v with_o the_o three_o leg_n of_o your_o staff_n 3._o that_o it_o be_v usual_o the_o quick_a way_n to_o measure_v first_o from_o the_o instrument_n to_o the_o first_o angle_n and_o then_o back_o from_o the_o second_o angle_n to_o the_o instrument_n and_o so_o the_o rest_n in_o order_n still_o one_o from_o the_o instrument_n and_o the_o other_o to_o it_o 4._o it_o be_v no_o matter_n at_o all_o whether_o your_o plain-table_n be_v place_v towards_o the_o middle_n of_o a_o field_n as_o be_v represent_v in_o this_o figure_n or_o at_o a_o angle_n as_o will_v appear_v anon_o 5._o in_o all_o work_n by_o this_o instrument_n you_o must_v have_v a_o care_n that_o the_o instrument_n be_v not_o move_v out_o of_o its_o due_a place_n till_o you_o have_v finish_v the_o work_n of_o the_o present_a station_n for_o which_o purpose_n cast_v your_o eye_n now_o and_o then_o upon_o your_o needle_n observe_v whether_o it_o continue_v to_o hang_v direct_o over_o the_o same_o point_n you_o set_v it_o at_o when_o you_o begin_v your_o work_n and_o to_o rectify_v your_o instrument_n if_o you_o see_v cause_n but_o because_o all_o table_n have_v not_o needle_n and_o where_o needle_n be_v they_o be_v not_o account_v over-trusty_a make_v use_n of_o the_o follow_a help_n when_o you_o have_v plant_v your_o instrument_n and_o make_v a_o point_n or_o prick_v in_o your_o paper_n represent_v your_o station_n set_v the_o fiducial_a edge_n of_o your_o index_n to_o it_o and_o turn_v it_o soft_o about_o till_o you_o find_v one_o remarkable_a thing_n or_o other_o upon_o one_o side_n of_o the_o close_a and_o another_o on_o the_o opposite_a side_n as_o you_o look_v through_o the_o sight_n of_o your_o index_n which_o we_o call_v foresight_n and_o back-sight_n draw_v a_o remarkable_a line_n with_o ink_n or_o rather_o with_o a_o black-lead_a pen_n quite_o over_o your_o paper_n which_o in_o this_o figure_n be_v represent_v by_o the_o black_a line_n kl_n and_o then_o if_o you_o suspect_v that_o by_o any_o accidental_a jog_v or_o other_o casuality_n the_o instrument_n be_v any_o thing_n remove_v you_o may_v easy_o try_v and_o rectify_v it_o by_o apply_v the_o fiducial_a edge_n to_o the_o same_o line_n and_o make_v use_n of_o foresight_n and_o back-sight_n again_o upon_o the_o same_o mark_n which_o you_o before_o observe_v upon_o the_o opposite_a side_n of_o the_o close_a but_o if_o there_o be_v no_o convenient_a place_n for_o the_o place_n of_o your_o instrument_n whence_o you_o may_v see_v all_o the_o angle_n of_o the_o field_n more_o station_n must_v be_v make_v use_n of_o thus_o fig._n 25_o let_v abcdefghiklmn_n be_v a_o field_n who_o angle_n can_v be_v all_o see_v from_o any_o one_o angle_n or_o other_o place_n in_o it_o i_o plant_v my_o instrument_n at_o the_o angle_n a_o and_o if_o it_o have_v a_o needle_n i_o mark_v what_o degree_n of_o the_o chord_n it_o cut_v or_o turn_v about_o the_o table_n on_o the_o head_n of_o the_o staff_n till_o the_o needle_n hang_v over_o over_o some_o remarkable_a place_n as_o suppose_v the_o flower-de-luce_n and_o screw_v it_o fast_o then_o set_v up_o a_o stick_n with_o a_o white_a paper_n or_o cloth_n on_o the_o head_n of_o it_o where_o i_o intend_v my_o second_o sation_n as_o here_o at_o q._n i_o make_v a_o prick_n or_o point_n in_o my_o paper_n to_o signify_v the_o point_n a_o upon_o the_o paper_n on_o the_o table_n to_o which_o point_n i_o apply_v the_o fiducial_a edge_n of_o the_o index_n and_o when_o i_o see_v the_o white_a at_o q_o so_o as_o look_v through_o the_o slit_n i_o see_v the_o thread_n cut_v it_o i_o draw_v the_o line_n open_v quite_o through_o my_o paper_n with_o a_o black-lead_a pen_n and_o then_o keep_v the_o fiducial_a edge_n still_o upon_o the_o same_o point_n and_o turn_v it_o round_o by_o degree_n i_o look_v at_o the_o angles_n bcdeflmn_n still_o draw_v dry_a line_n with_o the_o point_n of_o my_o compass_n and_o set_v on_o the_o measure_n from_o the_o station_n a_o to_o every_o angle_n measure_v to_o or_o from_o as_o i_o do_v in_o the_o last_o example_n then_o i_o remove_v the_o instrument_n to_o the_o place_n of_o my_o second_o station_n have_v set_v up_o a_o mark_n at_o a_o and_o lay_v the_o fiducial_a edge_n to_o the_o line_n open_v i_o turn_v about_o the_o table_n upon_o the_o head_n of_o the_o staff_n till_o through_o
the_o instrument_n and_o also_o for_o measure_v the_o stationary-line_n on_o the_o ground_n and_o protract_v they_o on_o the_o paper_n as_o be_v manifest_a in_o this_o example_n fig._n 29_o let_v abcdef_n be_v a_o park-pond_n or_o close_a to_o be_v protract_v i_o first_o plant_v my_o instrument_n at_o a_o and_o direct_v the_o sight_n to_o a_o mark_n in_o the_o angle_n b_o draw_v a_o dry_a line_n from_o a_o convenient_a poinâ—_n on_o my_o paper_n towards_o b_o on_o the_o ground_n and_o have_v measure_v by_o my_o chain_n the_o distance_n ab_fw-la i_o set_v it_o by_o a_o scale_n upon_o the_o correspondent_a line_n from_o a_o to_o b_o drawing_z a_o black-line_n between_o they_o with_o ink_n or_o a_o lead-pen_n the_o extremity_n whereof_o be_v the_o point_n a_o and_o b_o on_o my_o paper_n and_o the_o little_a prick_v line_n that_o go_v beyond_o b_o represent_v the_o remainder_n of_o the_o dry_a line_n draw_v at_o random_n as_o to_o length_n with_o the_o point_n of_o the_o compass_n then_o set_v up_o a_o mark_n at_o a_o if_o there_o be_v none_o before_o i_o remove_v the_o instrument_n to_o b_o and_o lay_v the_o fiducial_a edge_n to_o the_o line_n ab_fw-la i_o turn_v about_o the_o instrument_n upon_o the_o saff_n till_o through_o the_o sight_n i_o perceive_v the_o thread_n cut_v the_o mark_n at_o a_o and_o my_o needle_n if_o i_o have_v one_o direct_o over_o the_o same_o point_n that_o it_o be_v when_o it_o be_v plant_v at_o a_o and_o so_o screw_v it_o fast_o my_o next_o work_n be_v to_o lay_v the_o fiducial_a edge_n to_o the_o point_n b_o and_o direct_v the_o sight_n to_o c_o draw_v a_o dry_a line_n towards_o it_o and_o set_v the_o distance_n bc_n measure_v by_o the_o chain_n from_o b_o to_o c._n in_o this_o manner_n i_o proceed_v surround_v the_o close_a till_o i_o come_v at_o last_o to_o a_o where_o i_o begin_v by_o plant_v the_o instrument_n at_o every_o angle_n use_v the_o help_n of_o back-sight_n and_o my_o needle_n as_o i_o do_v at_o b_o and_o then_o from_o the_o point_n represent_v my_o present_a station_n direct_v the_o sight_n to_o the_o next_o angle_n as_o i_o do_v from_o b_o to_o c._n in_o the_o second_o case_n we_o do_v not_o plant_v the_o instrument_n at_o every_o angle_n but_o at_o the_o more_o considerable_a take_v in_o the_o small_a by_o their_o perpendicular_o from_o the_o base_a as_o we_o pass_v along_o of_o which_o this_o follow_a figure_n may_v be_v a_o instance_n fig._n 30_o let_v abcdefghikl_n be_v a_o close_a to_o be_v measure_v by_o plant_v the_o instrument_n only_o at_o acf_n and_o k_n i_o have_v the_o main_a substance_n of_o the_o close_a in_o the_o trapezium_fw-la acfk_n and_o for_o the_o five_o small_a triangle_n which_o must_v be_v add_v to_o the_o trapezium_fw-la they_o may_v be_v easy_o protract_v by_o the_o help_n of_o such_o a_o little_a square_a as_o be_v mention_v towards_o the_o latter_a end_n of_o the_o ten_o chapter_n for_o thereby_o find_v at_o how_o many_o chain_n and_o link_n distance_n from_o a_o upon_o the_o ground_n the_o perpendicular_a b_o b_o fall_v upon_o the_o line_n ac_fw-la and_o have_v measure_v the_o length_n of_o that_o perpendicular_a and_o take_v it_o between_o my_o compass-point_n off_o my_o scale_n i_o erect_v a_o perpendicular_a of_o that_o length_n at_o b_o which_o be_v the_o point_n upon_o the_o paper_n where_o so_o many_o chain_n and_o link_n determine_v as_o be_v measure_v upon_o the_o ground_n from_o the_o angle_n a_o to_o the_o place_n where_o the_o perpendicular_a fall_v on_o ac_fw-la viz._n at_o b._n just_o in_o the_o same_o manner_n i_o raise_v the_o other_o perpendicular_o dd_v gg_n two_o and_o will_v and_o then_o by_o the_o help_n of_o the_o perpendicular_o i_o draw_v from_o and_o to_o the_o proper_a angle_n the_o boundary-line_n ab_fw-la bc_n cd_o de_fw-fr fg_n gh_o he_o ik_fw-mi k_o l_o la_fw-fr which_o together_o with_o the_o line_n of_o between_o the_o angle_n e_o and_o f_o give_v the_o true_a plot_n of_o the_o field_n in_o one_o large_a trapezium_fw-la and_o five_o small_a triangle_n ready_a for_o cast_v up_o the_o three_o case_n be_v so_o like_o the_o second_o that_o there_o need_v no_o new_a direction_n concern_v it_o but_o to_o annex_v one_o plain_a diagram_n all_o the_o difference_n consist_v in_o this_o that_o because_o we_o can_v go_v within_o it_o be_v suppose_v to_o be_v some_o pool_n bog_n or_o thicket_n we_o must_v of_o necessity_n go_v on_o the_o outside_n and_o consequent_o all_o the_o triangle_n make_v by_o inward_a angle_n and_o their_o line_n upon_o the_o measure_a base_n must_v be_v exclude_v by_o the_o boundary-line_n from_o be_v any_o part_n of_o the_o plot_n as_o here_o be_v manifest_a fig._n 31_o suppose_v abcdefghiklmn_n open_v to_o be_v a_o great_a pool_n though_o here_o be_v fifteen_o angle_n i_o plant_v my_o table_n only_o five_o time_n viz._n at_o aefh_n and_o m_n and_o upon_o the_o dry_a line_n ae_n fh_o he_o and_o ma_n i_o raise_v their_o perpendicular_o in_o due_a place_n according_a to_o measure_n and_o also_o of_o a_o right_a height_n by_o which_o and_o my_o five_o stationary_a angle_n i_o draw_v the_o bounding-line_n of_o the_o plot_n exclude_v all_o the_o triangle_n as_o foreign_a to_o it_o they_o be_v no_o resemblance_n of_o any_o part_n of_o the_o pool_n but_o of_o land_n adjacent_a where_o note_n 1._o that_o both_o in_o this_o and_o the_o former_a case_n such_o a_o little_a square_a as_o i_o mention_v in_o the_o second_o chapter_n will_v be_v very_o useful_a for_o speedy_a raise_n of_o perdendiculars_n but_o where_o the_o triangle_n be_v very_o small_a it_o need_v not_o be_v use_v not_o the_o other_o mention_a chap._n 10._o 2._o that_o if_o by_o reason_n of_o troublesome_a brush-wood_n gorse_n or_o bog_n etc._n etc._n i_o can_v not_o have_v measure_v close_o to_o the_o side_n of_o he_o or_o lm_o it_o will_v be_v the_o same_o thing_n if_o i_o go_v parallel_v to_o they_o and_o this_o be_v a_o shift_n that_o the_o practical_a surveyor_n will_v oft_o be_v put_v to_o make_v use_n of_o in_o other_o case_n as_o well_o as_o this_o chap._n xv._n concern_v the_o plot_v of_o many_o close_v together_o whether_o the_o ground_n be_v even_o or_o uneven_a though_o i_o design_v not_o so_o high_a in_o this_o manual_a as_o to_o make_v my_o reader_n able_a to_o survey_v lordship_n and_o forest_n much_o less_o to_o draw_v map_n of_o country_n but_o to_o measure_v a_o parcel_n of_o land_n with_o truth_n and_o judgement_n yet_o i_o will_v have_v he_o so_o expert_a as_o not_o to_o be_v puzzle_v if_o any_o shall_v desire_v he_o to_o draw_v as_o it_o be_v a_o true_a map_n of_o a_o tenement_n or_o small_a demesn_a consist_v of_o several_a close_n for_o which_o purpose_n let_v he_o that_o know_v no_o better_a observe_v this_o method_n fig._n 32_o suppose_v abcdefghiklm_n to_o be_v a_o tenement_n or_o small_a demesn_a divide_v into_o fourteen_o close_n to_o be_v measure_v and_o protract_v according_a to_o their_o several_a shape_n and_o situation_n i_o first_o draw_v the_o plot_n of_o the_o whole_a by_o the_o method_n of_o circuition_n plant_v my_o instrument_n either_o at_o every_o angle_n or_o only_o the_o most_o considerable_a either_o within_o or_o without_o as_o i_o find_v most_o convenient_a this_o be_v do_v a_o line_n from_o b_o to_o m_n give_v the_o triangle_n abm_n from_o the_o first_o close_n in_o the_o next_o place_n i_o go_v round_a the_o second_o close_a beginning_n at_o m_n then_o to_o b_o and_o so_o about_o cum_fw-la scle_n to_o m_n again_o and_o then_o for_o the_o three_o close_n i_o plant_v my_o table_n at_o c_o and_o etc_o round_o to_o b_o the_o line_n bc_n be_v protract_v already_o and_o so_o of_o all_o the_o rest_n still_o observe_v which_o be_v common_a line_n belong_v to_o several_a close_n represent_v the_o fence_n that_o i_o may_v avoid_v the_o trouble_n of_o measure_v â—hose_v line_n often_o than_o once_o and_o lay_v everâ—_n part_n of_o euâ—â—y_o close_a in_o its_o due_a place_n and_o that_o i_o be_v suâ—â—_n to_o keep_v the_o instrument_n throughout_o the_o whole_a work_n to_o its_o true_a position_n by_o needle_n foresight_n and_o back-sight_n there_o be_v i_o confess_v divers_a other_o way_n of_o do_v this_o work_n but_o none_o more_o sure_a or_o plain_a especial_o if_o the_o ground_n be_v uneven_a for_o in_o that_o case_n if_o you_o protract_v according_a to_o the_o length_n of_o line_n measure_v from_o your_o station_n to_o the_o angle_n you_o will_v put_v your_o close_n into_o unproportionable_a shape_n except_o you_o reduce_v hypothenusal_a line_n to_o horizontal_n by_o instrument_n or_o otherwise_o which_o be_v somewhat_o troublesome_a and_o the_o like_a may_v be_v say_v when_o you_o plot_n with_o the_o chain_n only_o indeed_o the_o method_n
of_o measure_v only_o the_o stationary_a distance_n be_v very_o proper_a for_o set_v out_o the_o figure_n of_o each_o particular_a close_a provide_v the_o distance_n of_o the_o station_n be_v large_a and_o take_v if_o possible_a upon_o pretty_a even_a ground_n which_o sometime_o may_v be_v do_v though_o most_o of_o the_o close_a be_v uneven_a and_o the_o work_n so_o order_v as_o not_o to_o make_v too_o acute_a angle_n but_o because_o this_o require_v skill_n and_o care_n i_o rather_o advise_v my_o young_a artist_n to_o use_v the_o circle_a way_n as_o ordinary_o most_o commodious_a in_o my_o poor_a judgement_n but_o not_o prejudice_v other_o man_n that_n may_v differ_v from_o i_o in_o opinion_n and_o where_o need_n require_v let_v he_o observe_v the_o direction_n in_o the_o 17_o chapter_n but_o which_o way_n soever_o you_o go_v to_o work_v ☞_o there_o be_v one_o very_o necessary_a rule_n to_o be_v observe_v if_o the_o ground_n be_v uneven_a considerable_o you_o must_v not_o give_v up_o the_o content_a by_o measure_v the_o base_n and_o perpendicular_o of_o the_o triangle_n on_o the_o paper_n by_o your_o scale_n but_o you_o must_v measure_v the_o line_n correspondent_a to_o they_o on_o the_o ground_n and_o cast_v up_o the_o content_a according_a to_o that_o measure_n and_o if_o it_o be_v desire_v that_o you_o shall_v adjoyn_v to_o your_o plot_n as_o be_v usual_a a_o scale_n of_o chain_n to_o measure_v distance_n by_o you_o must_v either_o by_o make_v the_o form_n of_o hill_n erect_v and_o reverse_v or_o some_o other_o note_n in_o writing_n mark_v out_o your_o uneven_a ground_n lest_o those_o that_o try_v it_o by_o the_o scale_n judge_v your_o work_n erroneous_a for_o though_o you_o make_v that_o scale_n exact_o correspondent_a to_o that_o you_o protract_v by_o as_o you_o ought_v to_o do_v the_o hill_n and_o dale_n in_o the_o ground_n true_o measure_v may_v make_v a_o considerable_a alteration_n it_o be_v convenient_a when_o you_o plant_v your_o table_n that_o the_o needle_n hang_v just_a over_o the_o north-point_n of_o the_o compass_n under_o it_o in_o the_o box_n then_o may_v you_o by_o the_o line_n overthwart_o the_o frame_n of_o the_o table_n easy_o draw_v two_o line_n quite_o through_o the_o plot_n cut_v one_o another_o at_o right_a angle_n the_o one_o point_v at_o north_n and_o south_n and_o the_o other_o at_o east_n and_o west_n and_o if_o your_o skill_n serve_v you_o to_o make_v the_o two_o and_o thirty_o point_n of_o the_o compass_n upon_o the_o place_n where_o they_o intersect_v and_o to_o draw_v the_o form_n of_o the_o house_n wood_n and_o other_o remarkable_a thing_n upon_o the_o demesn_a and_o the_o course_n of_o brook_n and_o river_n run_v through_o it_o it_o will_v add_v to_o your_o commendation_n and_o so_o it_o will_v also_o if_o you_o take_v in_o such_o parcel_n of_o land_n bound_v it_o whether_o common_a or_o peculiar_a to_o other_o man_n as_o will_v make_v your_o plot_n to_o look_v handsome_o like_o a_o perfect_a square_n or_o oblong_o but_o however_o that_o be_v you_o must_v be_v sure_a to_o protract_v true_o all_o lane_n go_v into_o it_o or_o through_o it_o and_o all_o close_v of_o other_o man_n mix_v with_o it_o and_o also_o all_o considerable_a pond_n way_n and_o outlet_n with_o the_o name_n of_o the_o close_n and_o quality_n of_o the_o ground_n whether_o meadow_n pasture_n arable_a etc._n etc._n chap._n xvi_o concern_v shift_n of_o paper_n in_o such_o work_n as_o that_o of_o the_o last_o chapter_n it_o may_v sometime_o fall_v out_o through_o the_o multitude_n and_o largeness_n of_o field_n that_o one_o sheet_n will_v not_o hold_v your_o whole_a plot_n in_o which_o case_n you_o may_v help_v yourself_o by_o shift_a paper_n as_o we_o call_v it_o thus_o fig._n 33_o let_v abcd_n represent_v our_o sheet_n of_o paper_n that_o cover_v the_o table_n upon_o which_o the_o plot_n of_o the_o large_a piece_n of_o land_n efghik_n shall_v be_v draw_v have_v make_v my_o first_o station_n at_o e_o and_o the_o second_o at_o f_o i_o find_v my_o paper_n will_v not_o receive_v the_o line_n fg_v but_o however_o i_o draw_v so_o far_o as_o it_o will_v go_v to_o the_o edge_n of_o the_o paper_n and_o plant_v my_o table_n again_o at_o e_z proceed_v in_o my_o circuition_n the_o contrary_a way_n to_o k_o and_o i_o where_o i_o find_v myself_o again_o at_o a_o loss_n for_o my_o line_n ih_v but_o draw_v it_o also_o to_o the_o edge_n of_o the_o paper_n then_o with_o the_o point_n of_o my_o compass_n strike_v the_o line_n po_n parallel_n to_o the_o edge_n of_o the_o paper_n bc_n and_o the_o line_n qo_n parallel_n to_o dc_o and_o cut_v po_n in_o o_o i_o throw_v aside_o that_o paper_n for_o a_o while_n cover_v the_o instrument_n with_o a_o new_a one_o which_o i_o mark_v with_o the_o figure_n 2_o for_o my_o second_o sheet_n fig._n 34_o upon_o which_o second_o sheet_n the_o lead_a part_n whereof_o be_v represent_v by_o the_o three_o line_n meet_v in_o the_o angular_a point_n a_o and_o b_o i_o draw_v po_n parallel_v to_o ab_fw-la the_o lead_a edge_n of_o the_o paper_n and_o cross_v it_o at_o right_a angle_n in_o the_o point_n o_o by_o a_o parallel_n to_o bc_n viz._n the_o line_n or_o be_v of_o the_o same_o distance_n from_o bc_n that_o qo_o in_o the_o former_a sheet_n be_v from_o dc_o then_o with_o a_o rule_n and_o a_o sharp_a penknife_n i_o cut_v off_o the_o end_n of_o the_o first_o sheet_n at_o the_o line_n po_n and_o apply_v the_o edge_n of_o it_o to_o the_o line_n po_n of_o the_o second_o sheet_n so_o as_o it_o may_v touch_v that_o line_n all_o along_o and_o the_o line_n qo_o of_o the_o former_a touch_v the_o line_n or_o in_o the_o latter_a so_o as_o to_o make_v one_o line_n with_o it_o i_o draw_v the_o line_n pg_n be_v the_o remainder_n of_o the_o line_n fg_v and_o the_o line_n oh_o being_n the_o remainder_n of_o the_o line_n ih_v and_o from_o their_o extremity_n the_o line_n gh_n and_o if_o the_o plot_n require_v it_o you_o may_v proceed_v on_o in_o the_o second_o sheet_n and_o annex_v a_o three_o and_o a_o four_o etc._n etc._n as_o there_o be_v occasion_n these_o sheet_n may_v be_v piece_v together_o with_o mouth-glew_a or_o fine_a paste_n apply_v the_o edge_n of_o the_o former_a as_o you_o do_v upon_o the_o table_n to_o the_o line_n po_n of_o the_o latter_a and_o note_v here_o once_o for_o all_o that_o when_o i_o speak_v of_o apply_v the_o edge_n of_o the_o paper_n to_o a_o line_n i_o mean_v the_o precise_a edge_n cut_v by_o the_o line_n po_n but_o when_o i_o speak_v of_o draw_v line_n to_o the_o edge_n of_o the_o paper_n upon_o the_o table_n i_o hope_v none_o will_v think_v i_o so_o absurd_a as_o to_o mean_v the_o edge_n that_o be_v couch_v under_o the_o frame_n but_o that_o my_o meaning_n be_v that_o the_o line_n must_v be_v continue_v on_o the_o paper_n till_o they_o touch_v the_o frame_n chap._n xvii_o concern_v the_o plot_v of_o a_o town-field_n where_o the_o several_a land_n butt_n or_o doles_n be_v very_o crooked_a with_o a_o note_n concern_v hypothenusal_a or_o sloap_a boundary_n common_a to_o this_o and_o the_o fiftâ—enth_o chapter_n fig._n 35_o suppose_v abcde_v divide_v in_o the_o manner_n of_o a_o common_a field_n into_o seven_o part_n or_o doles_n belong_v to_o seven_o several_a man_n first_o plot_v the_o whole_a as_o before_o have_v be_v teach_v then_o measure_v from_o a_o to_o b_o upon_o the_o land_n set_v one_o note_v down_o as_o you_o go_v along_o at_o how_o many_o chain_n or_o link_n or_o both_o the_o division_n be_v between_o dole_n and_o dole_n and_o according_o mark_v they_o out_o by_o the_o help_n of_o scale_n and_o compass_n in_o the_o line_n ab_fw-la on_o the_o paper_n plot_n in_o the_o very_a same_o manner_n you_o must_v measure_v and_o mark_v out_o the_o line_n oc_fw-fr and_o ed_z which_o be_v do_v take_v the_o paper_n off_o the_o instrument_n and_o lay_v it_o before_o you_o on_o a_o table_n with_o the_o side_n ae_n towards_o you_o the_o compass_n must_v be_v so_o open_v and_o place_v as_o by_o a_o few_o trial_n they_o may_v that_o one_o foot_n rest_v upon_o the_o table_n the_o other_o may_v pass_v through_o the_o point_n of_o division_n upon_o all_o the_o three_o line_n viz._n ab_fw-la oc_fw-la and_o ed_z as_o in_o this_o figure_n they_o do_v if_o the_o content_a of_o any_o one_o or_o more_o of_o these_o part_n butt_n or_o doles_n be_v desire_v without_o plot_v it_o may_v easy_o be_v do_v without_o your_o plain-table_n thus_o take_v the_o breadth_n by_o your_o chain_n at_o the_o head_n middle_a and_o low_a end_n and_o add_v these_o number_n together_o the_o three_o part_n of_o their_o sum_n be_v the_o equated_a breadth_n by_o which_o multiply_v the_o
length_n measure_v down_o the_o ridge_n or_o middle_a the_o product_n give_v the_o content_a but_o both_o in_o this_o case_n and_o that_o mention_v in_o the_o 15_o chapter_n the_o figure_n of_o a_o plot_n may_v be_v somewhat_o disorder_v not_o only_o by_o the_o unevenness_n of_o the_o ground_n within_o for_o which_o i_o have_v give_v due_a caution_n already_o that_o be_v both_o the_o more_o common_a and_o more_o considerable_a case_n but_o also_o by_o the_o great_a diclivity_n of_o the_o ground_n where_o the_o boundary-line_n go_v either_o of_o the_o whole_a plot_n or_o particular_a parcel_n for_o whereas_o in_o plot_v every_o line_n be_v presume_v to_o be_v horizontal_n or_o level_a that_o it_o may_v pass_v from_o angle_n to_o angle_v the_o short_a way_n and_o that_o every_o part_n may_v be_v due_o situate_v and_o none_o thrust_v another_o out_o of_o its_o right_a place_n if_o it_o be_v not_o level_a but_o fall_v down_o towards_o a_o valley_n or_o rise_v up_o hill_n or_o compound_v of_o both_o a_o line_n over_o such_o ground_n though_o true_a for_o the_o measure_n and_o for_o give_v up_o the_o content_a will_v be_v false_a as_o to_o the_o plot_n and_o therefore_o must_v be_v reduce_v to_o a_o level_n and_o so_o take_v off_o the_o scale_n and_o protract_v for_o the_o do_n of_o this_o there_o be_v several_a instrument_n very_o proper_a especial_o mr._n rathbourne'_v quadrant_n upon_o the_o head_n of_o his_o peractor_n though_o it_o be_v better_a to_o have_v a_o semicircle_n than_o a_o quadrant_n so_o place_v and_o divers_a other_o but_o suppose_v my_o country_n friend_n to_o have_v no_o other_o but_o such_o as_o i_o have_v already_o describe_v i_o shall_v show_v he_o a_o plain_a easy_a way_n much_o use_v by_o practical_a surveyor_n especial_o in_o ireland_n as_o some_o of_o themselves_o have_v tell_v i_o be_v the_o very_a same_o that_o he_o may_v meet_v with_o in_o mr._n leybourn_n book_n entitle_v the_o complete_a surveyor_n i_o mean_v the_o second_o way_n by_o he_o discover_v fig._n 36_o suppose_v abc_n to_o be_v part_n of_o a_o hill_n fall_v within_o my_o plot_n my_o boundary-line_n go_v crooked_o from_o a_o to_o b_o follow_v the_o surface_n of_o the_o ground_n to_o find_v the_o horizontal_n line_n equal_a to_o ac_fw-la i_o cause_v one_o to_o stand_v at_o the_o point_n a_o the_o foot_n of_o the_o hill_n and_o to_o hold_v up_o the_o end_n of_o the_o chain_n to_o a_o convenient_a height_n and_o gentle_o ascend_v the_o hill_n i_o draw_v it_o level_n and_o make_v a_o mark_n where_o it_o touch_v the_o hill_n observe_v the_o number_n of_o link_n betwixt_o my_o assistant's_a hand_n and_o that_o place_n where_o he_o must_v take_v his_o second_o stand_v and_o hold_v it_o up_o as_o before_o and_o so_o i_o draw_v it_o out_o level_a again_o till_o it_o touch_v the_o place_n where_o he_o must_v take_v his_o three_o stand_v note_v the_o link_n as_o before_o and_o so_o proceed_v till_o at_o last_o from_o his_o five_o stand_v i_o draw_v the_o chain_n level_v to_o the_o high_a point_n within_o my_o plot_n viz._n the_o point_n b._n and_o now_o as_o the_o prick_a line_n of_o this_o figure_n put_v together_o and_o evident_o equal_a to_o the_o line_n ac_fw-la so_o be_v the_o link_n note_v down_o at_o every_o station_n when_o sum_v up_o equal_a to_o the_o horizontal_n line_n of_o that_o part_n of_o the_o hill_n in_o the_o very_a same_o manner_n only_o invert_v the_o order_n you_o may_v find_v the_o horizontal_n line_n go_v downhill_o where_o that_o be_v most_o convenient_a and_o if_o there_o be_v both_o ascent_n and_o descent_n in_o one_o line_n betwixt_o two_o angle_n the_o horizontal_n line_n of_o both_o must_v be_v find_v and_o join_v together_o in_o protraction_n all_o this_o concern_v declivity_n of_o rise_v or_o fall_v ground_n be_v to_o be_v understand_v when_o they_o be_v considerable_a and_o a_o very_a exact_a plot_n require_v for_o small_a one_o especial_o when_o much_o exactness_n be_v not_o expect_v be_v not_o regardable_a chap._n xviii_o concern_v plot_v a_o piece_n of_o ground_n by_o the_o degree_n upon_o the_o frame_n of_o the_o plain-table_n several_a way_n and_o protract_v the_o same_o hitherto_o i_o have_v show_v the_o use_n of_o the_o plain-table_n as_o such_o and_o i_o think_v my_o direction_n have_v be_v near_o as_o plain_a as_o the_o instrument_n itself_o at_o which_o some_o quarrel_n for_o its_o over-plainness_n expose_v the_o art_n to_o proud_a ignorant_a people_n who_o judge_v the_o rest_n of_o the_o surveyor_n work_v to_o be_v as_o easy_a as_o look_v through_o sight_n at_o a_o mark_n and_o draw_v line_n by_o a_o rule_n be_v apt_a to_o undertake_v to_o use_v it_o or_o slight_v the_o skill_n of_o such_o as_o do_v other_o say_v and_o that_o true_o that_o for_o vast_a thing_n such_o as_o forest_n chase_n etc._n etc._n the_o circumferentor_n be_v more_o proper_a and_o every_o one_o must_v grant_v that_o in_o wet_a wether_n either_o that_o a_o peractor_n a_o theodolite_a or_o semicircle_n must_v needs_o be_v better_a than_o the_o plain-table_n cover_v with_o the_o paper_n which_o can_v endure_v wet_a hence_o it_o be_v that_o some_o artist_n have_v to_o good_a purpose_n show_v how_o the_o box_n screw_v to_o the_o index_n and_o that_o make_v to_o turn_v on_o the_o head_n of_o the_o three-legged_a staff_n become_v a_o circumferentor_n and_o if_o these_o thus_o fix_v be_v turn_v about_o upon_o the_o centre_n of_o the_o table_n they_o will_v say_v some_o with_o good_a reason_n mr._n leybourn_n for_o one_o perform_v the_o work_n of_o the_o peractor_n much_o better_a than_o the_o peractor_n itself_o other_o show_v as_o i_o shall_v brief_o that_o take_v the_o instrument_n as_o it_o be_v without_o the_o charge_n of_o further_a fit_v it_o or_o trouble_v of_o remove_v the_o box_n the_o index_n turn_v upon_o the_o centre_n will_v by_o help_n of_o the_o degree_n on_o the_o frame_n perform_v the_o work_n of_o the_o theodolite_a to_o which_o the_o semicircle_n be_v near_o of_o kin_n and_o though_o i_o may_v easy_o answer_v all_o these_o objection_n by_o say_v the_o first_o be_v frivolous_a such_o foolish_a arrogance_n be_v easy_o contemn_v or_o check_v if_o worth_a the_o while_n by_o put_v such_o conceit_a fool_n upon_o the_o hard_a part_n of_o the_o work_n the_o second_o impertinent_a to_o our_o purpose_n who_o design_v not_o to_o plot_v such_o vast_a parcel_n of_o land_n and_o the_o three_o concern_v only_o a_o extraordinary_a case_n and_o that_o well_o provide_v for_o otherways_o for_o sure_o no_o man_n that_o have_v not_o a_o body_n of_o the_o same_o metal_n with_o his_o instrument_n will_v ordinary_o measure_v land_n in_o continual_a rain_n a_o sudden_a shower_n may_v be_v fence_v against_o by_o a_o cover_n and_o if_o any_o be_v so_o eager_a upon_o his_o work_n i_o have_v show_v â—how_v it_o may_v be_v do_v in_o the_o former_a chapter_n of_o this_o book_n without_o plant_v any_o instrument_n at_o all_o by_o chain_n scale_n and_o compass_n alone_o yet_o i_o shall_v show_v how_o the_o plot_n of_o a_o field_n may_v be_v taâ—en_v by_o the_o degree_n on_o the_o frame_v not_o every_o way_n that_o i_o can_v imagine_v nor_o that_o i_o can_v transcribe_v for_o that_o will_v be_v tedious_a but_o two_o way_n only_o whereof_o the_o one_o be_v proper_a for_o a_o ordinary_a close_n where_o all_o the_o angle_n may_v be_v see_v from_o 〈◊〉_d station_n within_o it_o the_o other_o fit_v any_o parâ—â—l_n of_o land_n though_o much_o large_a whatever_o be_v the_o figure_n of_o it_o for_o the_o former_a take_v this_o example_n fig._n 37_o let_v abcde_v represent_v the_o figure_n of_o field_n to_o be_v plot_v by_o the_o plain-table_n in_o rain_n weather_n i_o put_v on_o the_o frame_n without_o a_o papâ—â—_n the_o graduated_a side_n upward_o and_o plant_v it_o iâ—_n some_o convenient_a place_n whence_o i_o can_v see_v aâ—â—_n the_o angles_n as_o at_o o_o then_o place_v the_o index_n upon_o thâ—_n table_n so_o as_o the_o fiducial_a edge_n do_v 〈◊〉_d the_o same_o time_n go_v through_o the_o centre_n upon_o the_o table_n and_o the_o line_n upon_o the_o frame_n of_o thâ—_n table_n cut_v it_o perpendicular_o at_o 360_o wheâ—â—_n the_o degree_n begin_v and_o end_v and_o 180_o the_o 〈◊〉_d act_v half_a i_o turn_v about_o the_o table_n upon_o the_o staâ—â—â—head_n till_o through_o the_o sight_n the_o side_n markeâ—_n with_o 180_o being_n next_o my_o eye_n i_o see_v thâ—â—_n angle_v a_o and_o then_o screw_v it_o fast_o observe_v where_o my_o needle_n cut_v and_o by_o back-sighâ—_a cause_v a_o mark_n to_o be_v set_v up_o in_o the_o line_n cd_o 〈◊〉_d the_o point_n f_o that_o the_o instrument_n may_v be_v keâ—â—_n firm_a from_o move_v or_o be_v rectify_v if_o it_o be_v move_v during_o the_o work_n and_o now_o the_o liâ—â—_n aof_o
polygonial_a figure_n but_o now_o methinks_v i_o see_v as_o it_o be_v my_o country_n student_n scratch_v his_o head_n ☞_o and_o wish_v for_o a_o opportunity_n to_o propound_v two_o doubt_n to_o i_o 1._o why_o i_o call_v the_o number_n correspondent_a to_o my_o line_n by_o divers_a denomination_n as_o inch_n foot_n yard_n rod_n and_o sometime_o by_o none_o at_o all_o but_o propound_v the_o number_n abstract_o 2._o how_o i_o come_v to_o know_v how_o many_o of_o those_o measure_n whatever_o they_o be_v be_v represent_v by_o the_o line_n give_v and_o perpendicular_o find_v to_o the_o former_a i_o answer_v i_o be_o not_o yet_o teach_v how_o to_o measure_v line_n that_o work_n be_v present_o to_o follow_v but_o what_o line_n of_o figure_n be_v to_o be_v measure_v and_o the_o measure_n of_o those_o line_n be_v know_v or_o suppose_a how_o the_o content_a upon_o those_o real_a or_o suppose_a ground_n may_v be_v find_v and_o to_o this_o purpose_n i_o may_v call_v the_o number_n represent_v by_o the_o line_n inches_n foot_n yard_n or_o any_o other_o measure_n at_o pleasure_n provide_v i_o call_v the_o square_n to_o which_o the_o area_n be_v equal_a by_o the_o same_o name_n for_o a_o inch_n in_o length_n bear_v the_o same_o proportion_n to_o a_o square_a inch_n have_v length_n and_o breadth_n that_o a_o mile_n in_o length_n bear_v to_o a_o square_a mile_n for_o this_o reason_n i_o profess_v not_o in_o the_o title_n of_o this_o chapter_n to_o teach_v how_o to_o measure_v figure_n much_o less_o how_o to_o measure_v the_o line_n of_o such_o figure_n but_o how_o to_o find_v the_o content_a the_o line_n be_v give_v and_o then_o to_o take_v away_o the_o second_o doubt_n know_v that_o the_o number_n represent_v by_o the_o line_n be_v either_o give_v by_o those_o learned_a artist_n from_o who_o i_o borrow_v the_o figure_n or_o suppose_v by_o myself_o as_o ground_n to_o go_v upon_o as_o in_o such_o case_n be_v ordinary_a or_o last_o find_v out_o to_o be_v agreeable_a thereto_o by_o some_o scale_n of_o small_a equal_a part_n which_o he_o be_v yet_o suppose_v ignorant_a of_o but_o now_o i_o be_o go_v to_o show_v he_o the_o nature_n and_o use_n of_o two_o or_o three_o plain_a and_o cheap_a instrument_n by_o the_o help_n whereof_o he_o may_v with_o much_o exactness_n 1._o measure_v the_o length_n of_o any_o line_n bound_v right-lined_n figure_n upon_o the_o ground_n 2._o draw_v lines_n and_o figure_n upon_o paper_n proportionable_a thereunto_o which_o we_o call_v protract_v 3._o find_v upon_o his_o paper-figure_n the_o true_a length_n of_o all_o the_o desire_a perpendicular_o which_o shall_v also_o be_v proportionable_a to_o those_o on_o the_o ground_n but_o much_o more_o easy_a to_o be_v obtain_v and_o withal_o i_o intend_v to_o give_v he_o such_o far_a instruction_n and_o caution_n for_o the_o application_n of_o the_o general_a and_o more_o particular_a rule_n of_o this_o chapter_n to_o his_o peculiar_a use_n as_o will_v render_v they_o especial_o some_o of_o they_o singular_o advantageous_a chap._n iu._n concern_v chain_n compass_n and_o scale_n 1._o among_o the_o many_o sort_n of_o chain_n use_v for_o measure_v land_n three_o be_v most_o famous_a bearing_n the_o name_n of_o their_o inventor_n mr._n rathborne_n mr._n gunter_n and_o mr._n wing_n all_o of_o they_o ingenious_o divide_v and_o useful_a in_o their_o kindâ—_n but_o my_o brievity_n will_v give_v i_o leave_v only_o to_o describe_v one_o and_o that_o shall_v be_v mr._n gunter_n be_v most_o in_o use_n and_o easy_a to_o be_v procure_v this_o chain_n contain_v in_o length_n four_o statute-pole_n or_o perch_n each_o perch_n contain_v 1â—_n foot_n and_o a_o half_a or_o 5_o yard_n and_o a_o half_a so_o that_o the_o whole_a chain_n be_v 66_o foot_n or_o 22_o yard_n long_o this_o whole_a chain_n be_v divide_v into_o 100_o equal_a part_n or_o link_n whereof_o 25_o be_v a_o just_a pole_n or_o perch_n and_o for_o ready_a count_a there_o be_v usual_o a_o remarkable_a distinction_n by_o some_o plate_n or_o large_a ring_n at_o the_o end_n of_o every_o 25_o link_n but_o especial_o at_o the_o precise_a middle_n of_o the_o chain_n which_o shall_v differ_v from_o the_o rest_n in_o greatness_n and_o conspicuousness_n also_o at_o the_o end_n of_o every_o ten_o link_n it_o be_v usual_a to_o hang_v a_o small_a curtain-ring_n and_o if_o there_o be_v at_o every_o five_o link_n end_v a_o piece_n oâ—_n wire_n make_v like_o the_o bow_n of_o a_o link_n with_o a_o little_a shank_n a_o inch_n or_o less_o long_o or_o some_o such_o distinction_n it_o be_v still_o better_a when_o you_o be_v to_o measure_v any_o line_n by_o this_o chain_n you_o need_v to_o regard_v no_o other_o denomination_n but_o only_a chain_n and_o link_n set_v down_o with_o a_o prick_n of_o your_o pen_n betwixt_o they_o e._n g._n if_o you_o find_v the_o side_n of_o a_o close_a to_o be_v 6_o chain_n and_o 35_o link_n long_o it_o be_v thus_o to_o be_v put_v down_o 6._o 35._o but_o if_o the_o link_n be_v under_o 10_o a_o cypher_n must_v be_v prefix_v so_o 7_o chain_n 9_o link_n must_v be_v thus_o set_v 7._o 09._o in_o the_o use_n of_o this_o or_o indeed_o of_o any_o chain_n care_n must_v be_v take_v both_o to_o go_v straight_o and_o to_o keep_v a_o true_a account_n for_o which_o purpose_n it_o be_v good_a that_o he_o which_o go_v before_o carry_v in_o his_o hand_n a_o bundle_n of_o rod_n to_o stick_v down_o one_o at_o the_o end_n of_o the_o chain_n which_o lead_v have_v first_o stretch_v it_o well_o and_o that_o he_o which_o follow_v do_v not_o only_o gather_v up_o the_o rod_n to_o keep_v the_o account_n but_o also_o at_o every_o remove_n mark_v whether_o he_o see_v the_o leader_n direct_o between_o his_o eye_n and_o the_o angle_n or_o other_o mark_n he_o aim_v to_o measure_v to_o and_o if_o need_v be_v call_v to_o the_o leader_n to_o move_v towards_o the_o right_n or_o left_a hand_n till_o he_o see_v he_o in_o a_o direct_a line_n to_o it_o ii_o compass_n be_v so_o well_o know_v that_o i_o need_v not_o describe_v they_o only_o they_o shall_v be_v of_o brass_n with_o steel_n point_v small_a and_o neat_o wrought_v nine_o or_o ten_o inch_n long_o from_o the_o joint_n to_o the_o point_n turn_v so_o true_o upon_o the_o rivet_n that_o they_o may_v be_v easy_o open_v and_o yet_o stand_v so_o firm_o that_o a_o arch_n or_o circle_n may_v be_v without_o their_o shrink_n describe_v upon_o a_o large_a radius_fw-la for_o the_o form_n i_o will_v commend_v above_o all_o those_o that_o have_v large_a bow_n so_o contrive_v that_o by_o press_v they_o with_o the_o hinder_a part_n of_o the_o hand_n they_o will_v gentle_o open_v and_o by_o the_o thumb_n and_o four_o finger_n be_v put_v together_o as_o other_o will_n so_o that_o they_o be_v manageable_a by_o one_o hand_n which_o be_v a_o great_a convenience_n for_o one_o that_o at_o the_o same_o time_n shall_v hold_v his_o rule_n with_o scale_n in_o the_o other_o these_o might_n also_o be_v contrive_v with_o a_o screw_n to_o take_v out_o one_o of_o the_o point_n to_o place_n in_o the_o room_n upon_o occasion_n a_o black-lead_a pen_n or_o any_o pen_n to_o draw_v circle_n with_o either_o black_a or_o otherwise_o colour_v and_o for_o a_o man_n that_o will_v be_v a_o artist_n indeed_o it_o be_v convenient_a he_o be_v furnish_v with_o divide_v campass_n beam_n compass_n and_o triangular_a one_o for_o several_a use_v not_o here_o to_o be_v mention_v but_o a_o country_n surveyor_n may_v make_v a_o good_a shift_n with_o such_o a_o plain_a pair_n as_o i_o first_o describe_v which_o mr._n wynn_n over_o against_o the_o roll_n in_o chancery-lane_n will_v help_v he_o to_o with_o the_o chain_n and_o scale_n for_o a_o small_a matter_n iii_o scale_n be_v certain_a line_n divide_v into_o equal_a part_n upon_o plate_n or_o broad_a rule_n of_o brass_n or_o box_n and_o they_o be_v of_o two_o sort_n 1._o plain_a 2._o diagonal_a 1._o plain_a scale_n be_v make_v up_o of_o two_o small_a line_n parallel_v to_o one_o another_o at_o a_o little_a distance_n and_o these_o be_v divide_v into_o great_a equal_a part_n which_o signify_v ten_o and_o be_v note_v 10_o 20_o 30_o 40_o 50_o etc._n etc._n according_a to_o the_o length_n of_o the_o line_n they_o may_v be_v of_o any_o convenient_a length_n but_o these_o great_a division_n be_v seldom_o more_o than_o inch_n or_o less_o than_o three_o part_n a_o piece_n again_o one_o of_o the_o great_a division_n or_o part_n be_v subdivide_v into_o ten_o equal_a part_n by_o short_a line_n whereof_o that_o in_o the_o middle_n stand_v for_o 5_o be_v long_a than_o the_o rest_n according_a to_o the_o number_n of_o these_o little_a part_n contain_v in_o a_o inch_n the_o scale_n be_v name_v a_o scale_n of_o
the_o opposite_a angle_n make_v a_o triangle_n of_o it_o and_o the_o first_o and_o second_o side_n 9.04_o and_o 6.72_o according_a to_o ch._n 2._o probl._n 6._o â—nd_v another_o after_o the_o same_o method_n of_o that_o diagonal_a and_o the_o three_o and_o four_o side_n 8.46_o and_o â—_o 28_o so_o have_v i_o the_o trapezium_fw-la abcd._n then_o by_o the_o help_n of_o my_o scale_n and_o compass_n 〈◊〉_d find_v the_o perpendicular_a of_o the_o triangle_n a_o b_o c_o 〈◊〉_d be_v 6.02_o and_o of_o the_o other_o viz._n cda_n 6.01_o which_o add_v be_v 12.03_o whereof_o the_o half_a sum_n 〈◊〉_d 6.01_o by_o which_o multiply_v the_o base_a 10.02_o and_o proceed_v as_o former_o have_v be_v show_v i_o â—nd_v the_o content_a of_o the_o field_n to_o be_v 6_o acre_n 0_o rood_n 3_o perch_n as_o be_v here_o apparent_a fi._n 16_o the_o base10_n 02_o half_n perpend_v 6.01_o 1002_o 60120_o 6â—02202_n 4_o â—08808_n 40_o 3â—52320_n before_o i_o pass_v any_o further_a let_v i_o tell_v you_o 1._o any_o quadrangular_a close_a or_o parcel_n ground_n whatsoever_o have_v right_a line_n 〈◊〉_d be_v thus_o measure_v protract_a and_o compute_v 2._o the_o odd_a measure_n above_o perch_n be_v 〈◊〉_d valuable_a here_o nor_o in_o the_o former_a computation_n be_v always_o under_o a_o square_a perch_n but_o in_o muâ—â—_n angular_n where_o there_o be_v many_o remainder_n thâ—â—â—_n must_v be_v sum_v up_o and_o the_o perch_v containâ—_n in_o they_o add_v to_o the_o content_a before_o found_v 3._o this_o last_o and_o the_o follow_a figure_n whâ—â—_n i_o use_v any_o scale_n at_o all_o be_v make_v that_o they_o migâ—â—_n not_o be_v too_o large_a by_o a_o scale_n of_o 400_o in_o a_o inâ—â—â—_n i._n e._n by_o the_o less_o diagonal_a scale_n each_o chain_n 〈◊〉_d link_n be_v count_v two_o fig._n 17_o iii_o if_o this_o multangular_a figure_n be_v conceive_v to_o represent_v a_o close_a of_o seven_o side_n which_o be_v 〈◊〉_d be_v measure_v i_o begin_v at_o the_o remarkable_a angle_n 〈◊〉_d and_o go_v round_o the_o close_a with_o the_o sun_n find_v the_o side_n to_o be_v in_o measure_n 3._o 11_o 2._o 49_o 2._o 4â—_n 1._o 77_o 4._o 11_o 2._o 29_o 4._o 37._o fi._n 17_o then_o i_o measure_v the_o four_o diagonal_n bd_o df_n â—b_n and_o bg_n in_o the_o order_n that_o i_o name_v they_o â—nd_v i_o find_v they_o to_o be_v 3.45_o 4.97_o 4.13_o and_o 4.36_o â—hich_v be_v as_o short_a a_o way_n as_o can_v be_v take_v to_o preâ—ent_v unnecessary_a walk_n but_o when_o i_o come_v to_o protract_v by_o the_o help_n of_o â—â—y_a scale_n and_o compass_n i_o first_o make_v the_o triangle_n bcd_v of_o the_o first_o diagonal_a and_o the_o second_o â—nd_n three_o side_n then_o the_o triangle_n def_n upon_o 〈◊〉_d second_o diagonal_n and_o four_o and_o five_o side_n 〈◊〉_d upon_o the_o same_o diagonal_a as_o a_o common_a base_a 〈◊〉_d triangle_n bdf_n of_o the_o first_o second_o and_o three_o diagonal_n next_o of_o the_o same_o three_o diagonal_a together_o â—ith_v the_o four_o and_o six_o side_n i_o make_v the_o triangle_n bfg_v and_o upon_o the_o four_o diagonal_a as_o â—pon_o a_o common_a base_a with_o the_o first_o and_o last_o side_n 〈◊〉_d triangle_n abg_n so_o be_v the_o whole_a close_o â—â—otted_v and_o now_o it_o stand_v visible_o reduce_v into_o two_o â—rapezia's_n abfg_n and_o bdef_n together_o with_o â—he_n triangle_n bcd_v which_o i_o shall_v not_o now_o cast_v 〈◊〉_d have_v so_o often_o show_v how_o such_o work_n be_v 〈◊〉_d be_v do_v but_o i_o must_v acknowledge_v that_o this_o sort_n of_o plot_v of_o parcel_n of_o land_n that_o have_v many_o angle_n require_v not_o only_o more_o care_n and_o pain_n but_o better_a skill_n and_o memory_n than_o to_o draw_v diagoâ—als_n upon_o paper_n when_o the_o plot_n be_v already_o take_v by_o the_o plain_a table_n or_o other_o stand_a instrument_n i_o shall_v therefore_o to_o help_v my_o young_a practitioner_n in_o this_o case_n advertise_v he_o of_o two_o easy_a way_n to_o help_v himself_o so_o as_o to_o be_v out_o of_o danger_n of_o mistake_n one_o way_n be_v to_o divide_v the_o multangular_a field_n into_o two_o or_o more_o part_n as_o the_o last_o may_v have_v be_v by_o the_o diagonal_a bf_n then_o may_v each_o paâ—â—_n have_v be_v measure_v several_o as_o if_o they_o have_v be_v separate_v by_o a_o pale_a or_o be_v sundry_a man_n land_n part_v by_o a_o boundary_a another_o way_n that_o much_o help_v both_o the_o understanding_n and_o memory_n be_v to_o draw_v a_o rude_a draughâ—_n of_o the_o figure_n of_o the_o land_n you_o intend_v to_o measure_v not_o only_o as_o to_o the_o side_n but_o also_o necessary_a diagonal_n then_o measure_v the_o line_n upoâ—_n the_o ground_n correspondent_a to_o those_o on_o the_o paper_n which_o by_o the_o help_n of_o the_o draught_n may_v be_v easy_o hit_v set_v the_o line_n as_o you_o measure_v they_o upon_o the_o line_n of_o the_o draught_n as_o if_o it_o be_v the_o true_a one_o and_o when_o you_o have_v finish_v your_o measure_n protract_v it_o true_o such_o as_o you_o see_v herâ—_n but_o it_o be_v better_a large_a will_v do_v your_o business_n for_o it_o be_v not_o a_o pin_n matter_n how_o rude_a or_o false_a the_o line_n or_o angle_n be_v resemblance_n be_v all_o that_o be_v desire_v chap._n vii_o concern_v the_o measure_n of_o circle_n and_o their_o part_n i_o have_v hitherto_o abstain_v of_o purpose_n from_o meddle_v with_o the_o circle_n and_o its_o part_n that_o i_o may_v lay_v those_o thing_n close_o together_o without_o unnecessary_a mixture_n that_o be_v of_o the_o great_a use_n it_o be_v wonderful_a rare_a if_o a_o land-meet_a ever_o have_v occasion_n to_o measure_v any_o field_n or_o parcel_n of_o land_n that_o will_v prove_v either_o circle_n semicircle_n quadrant_n or_o sector_n sometime_o indeed_o there_o will_v be_v a_o little_a crook_n in_o a_o old_a hedge_n bow_v like_o a_o arch_n but_o i_o have_v never_o see_v any_o offer_n to_o measure_v it_o as_o a_o segment_n but_o always_o take_v it_o as_o a_o angle_n or_o angles_n yet_o because_o it_o may_v be_v expect_v i_o shall_v say_v somewhat_o of_o those_o thing_n i_o shall_v brief_o do_v it_o 1._o to_o measere_fw-la a_o circle_n in_o the_o more_o exact_a way_n 〈◊〉_d to_o square_v the_o diameter_n and_o to_o multiply_v that_o square_n by_o 7854_o so_o shall_v the_o content_a be_v in_o integer_n and_o decimal_n but_o the_o more_o usual_a and_o quick_a way_n and_o near_o enough_o for_o any_o use_n we_o shall_v make_v of_o it_o be_v to_o multiply_v the_o half_a of_o the_o periphery_a or_o circumference_n by_o the_o semidiameter_n in_o like_a manner_n to_o find_v the_o content_a of_o a_o semicircle_n quadrant_n or_o sector_n make_v up_o of_o semidiameter_n and_o arch_a line_n multiply_v the_o half_a arch_n by_o the_o semidiameter_n give_v the_o content_a fi._n 19_o but_o that_o which_o fall_v out_o most_o frequent_o in_o mensuration_n though_o seldom_o much_o regard_v â—ave_n where_o a_o curious_a exactness_n be_v require_v be_v that_o particular_a sort_n of_o segment_n which_o we_o call_v 〈◊〉_d section_n less_o than_o a_o semicircle_n such_o as_o this_o figure_n abc_n and_o to_o find_v the_o content_a of_o it_o the_o centre_n of_o the_o circle_n whereof_o this_o be_v a_o section_n must_v be_v first_o fouâ—d_v out_o as_o here_o at_o o_o from_o which_o line_n draw_v to_o a_o and_o b_o make_v up_o the_o sector_n aobc_n which_o be_v measure_v according_a to_o the_o last_o rule_n and_o from_o the_o content_a thereof_o fi._n 19_o the_o content_a of_o the_o triangle_n aob_v subtract_v the_o difference_n or_o residue_n be_v the_o content_a of_o the_o section_n abc_n but_o two_o question_n may_v be_v here_o demand_v 1._o how_o may_v the_o centre_n be_v find_v 2._o how_o may_v such_o a_o portion_n of_o land_n be_v true_o protract_v and_o compute_v to_o the_o first_o i_o answer_v that_o the_o most_o exact_a and_o artificial_a way_n be_v by_o make_v a_o mark_v any_o where_o in_o the_o arch._n as_o for_o example_n at_o the_o point_n c_o and_o then_o by_o a_o problem_n know_v not_o only_o to_o every_o surveyor_n but_o to_o ordinary_a carpenter_n and_o joiner_n for_o find_v the_o centre_n of_o a_o circle_n who_o circumference_n will_v pass_v through_o 3_o give_v point_n that_o be_v not_o in_o a_o right_a line_n as_o acb_n to_o find_v the_o centre_n o._n but_o if_o you_o know_v not_o how_o to_o do_v it_o so_o across_o the_o line_n ab_fw-la in_o the_o middle_n as_o here_o it_o be_v do_v by_o the_o perpendicular_a oc_n so_o you_o may_v by_o a_o few_o trial_n find_v both_o the_o due_a extent_n of_o your_o compass_n and_o the_o point_n in_o the_o perpendicular_a that_o will_v fit_v your_o purpose_n near_o enough_o for_o if_o a_o little_a error_n be_v commit_v in_o make_v up_o the_o sector_n the_o most_o
of_o land_n where_o a_o strict_a proportion_n in_o quantity_n be_v to_o be_v observe_v you_o must_v have_v respect_n to_o the_o rule_n hereafter_o follow_v concern_v measure_v of_o uneven_a ground_n chapter_n 15._o especial_o if_o one_o part_n prove_v much_o more_o uneven_a than_o another_o and_o if_o there_o be_v any_o useful_a pond_n or_o well_o to_o draw_v your_o line_n of_o division_n through_o it_o but_o if_o it_o be_v a_o unuseful_a pond_n lake_n or_o puddle_n or_o if_o there_o be_v a_o boggy_a or_o barren_a ground_n that_o must_v be_v cast_v out_o in_o the_o division_n measure_v that_o first_o and_o subtract_v it_o from_o the_o content_a of_o the_o whole_a close_a and_o then_o lie_v the_o just_a proportion_n of_o the_o remainder_n on_o that_o side_n that_o be_v free_a from_o it_o that_o the_o other_o may_v have_v its_o just_a part_n also_o beside_o that_o which_o be_v useless_a what_o have_v be_v say_v with_o a_o ordinary_a measure_n of_o discretion_n may_v sufficient_o instruct_v a_o young_a artist_n to_o divide_v triangle_n parallellogram_n and_o regular_a polygonial_n in_o a_o artificial_a way_n but_o because_o many_o close_n and_o open_a ground_n be_v trapezia_n and_o many_o irregular_a polygon_n and_o even_o those_o that_o be_v regular_a enough_o may_v fall_v under_o a_o irregular_a division_n in_o regard_n of_o the_o quality_n of_o the_o land_n wood_n upon_o it_o or_o quarry_n in_o it_o or_o the_o convenience_n of_o way_n current_n of_o water_n situation_n in_o respect_n of_o adjacent_a land_n etc._n etc._n i_o shall_v propose_v a_o method_n which_o though_o it_o have_v somewhat_o of_o the_o mechanic_n in_o it_o will_v be_v singular_o useful_a in_o such_o case_n fig._n 23_o let_v abcd_n be_v a_o trapezium_fw-la to_o be_v divide_v betwixt_o a_o young_a heir_n and_o his_o mother_n so_o as_o his_o part_n may_v be_v double_a to_o she_o have_v by_o the_o diagonal_a bc_n divide_v it_o into_o two_o triangle_n i_o find_v the_o content_a of_o the_o triangle_n abc_n to_o be_v 138550_o square_a link_n and_o the_o triangle_n bcd_v to_o contain_v 103468_o in_o all_o 242018_o square_a link_n which_o if_o reduce_v as_o have_v be_v former_o teach_v will_v amount_v to_o 2_o acre_n 1_o rood_n and_o 27_o perch_n for_o which_o see_v chap._n 5._o but_o as_o to_o my_o present_a work_n they_o be_v in_o a_o better_a order_n already_o divide_v then_o 242018_o into_o three_o part_n each_o of_o they_o be_v 80676_o and_o 2_o 3_o fig._n 23_o two_o therefore_o of_o those_o three_o part_n must_v contain_v 161353_o and_o 1_o 3_o which_o 1_o 3_o be_v inconsiderable_a i_o regard_v not_o then_o resolve_v to_o lay_v out_o the_o double_a part_n towards_o the_o line_n bd_o i_o strike_v at_o adventure_n the_o line_n of_o and_o measure_v the_o trapezium_fw-la bound_v by_o that_o line_n and_o the_o opposite_a side_n bd_o together_o with_o the_o interjacent_a part_n of_o the_o line_n ab_fw-la and_o cd_o i_o find_v it_o to_o contain_v 119140_o square_a link_n but_o because_o it_o shall_v have_v be_v 161353_o i_o subtract_v 119140_o out_o of_o 161353_o and_o their_o difference_n be_v 42213_o and_o perceive_v that_o the_o line_n ab_fw-la and_o cd_o be_v very_o near_a parallel_n and_o find_v their_o distance_n where_o they_o be_v cut_v by_o the_o line_n of_o to_o be_v 326_o link_n or_o 3_o chain_n and_o 26_o link_n i_o divide_v 42213_o by_o 326_o and_o the_o quotient_n be_v 129_o link_n and_o almost_o half_a at_o which_o distance_n i_o draw_v the_o line_n gh_o parallel_n to_o of_o so_o shall_v the_o trapezium_fw-la gbdh_n be_v the_o heir_n part_n another_o way_n whereby_o this_o may_v be_v preform_v be_v thus_o find_v the_o triangle_n abc_n to_o contain_v 138550_o square_a link_n subtract_v it_o out_o of_o the_o heir_n part_n viz._n 161353_o the_o difference_n 22803_o show_v how_o many_o square_a link_n must_v be_v take_v out_o of_o the_o triangle_n bcd_v and_o add_v to_o the_o triangle_n abc_n which_o to_o perform_v with_o all_o necessary_a exactness_n suppose_v the_o side_n or_o line_v bd_o to_o be_v the_o base_a which_o by_o measure_n prove_v to_o be_v 344_o link_n or_o 3_o chain_n and_o 44_o link_n say_v by_o the_o rule_n of_o three_o direct_v if_o the_o whole_a content_a of_o the_o lesser_a triangle_n viz._n 103468_o give_v 344_o what_o shall_v 22803_o give_v so_o will_v the_o result_v be_v 75_o link_n and_o somewhat_o more_o than_o 4_o 5_o of_o a_o link_n for_o 22803_o multiply_v by_o 344_o give_v 7844232_o which_o be_v divide_v by_o 103468_o the_o quotient_n be_v 75_o 84132_o â—03468_n or_o according_a to_o decimal_a division_n 75.8131_o which_o be_v as_o i_o say_v before_o somewhat_o more_o than_o 75_o link_n and_o 4_o 5_o wherefore_o extend_v your_o compass_n upon_o the_o scale_n to_o almost_o '_o 76_o link_n set_v that_o distance_n upon_o the_o line_n bd_o from_o b_o to_o i_o and_o draw_v the_o line_n ci_o so_o shall_v the_o trapezium_fw-la abic_fw-la be_v double_a to_o the_o triangle_n icd_n within_o so_o small_a a_o matter_n as_o be_v not_o worth_a regard_n though_o the_o land_n be_v a_o rich_a meadow_n i_o hope_v i_o need_v not_o stand_v to_o tell_v any_o man_n of_o sense_n that_o if_o he_o please_v he_o may_v begin_v with_o the_o less_o part_n and_o take_v out_o that_o or_o if_o there_o be_v many_o partner_n he_o may_v divide_v betwixt_o any_o one_o and_o all_o the_o rest_n put_v their_o part_n together_o and_o then_o by_o the_o same_o method_n subdivide_v among_o they_o till_o each_o have_v his_o due_a share_n nor_o to_o spend_v many_o word_n in_o tell_v he_o he_o must_v subtract_v where_o he_o have_v by_o a_o separate_a line_n at_o adventure_n or_o by_o choose_v out_o a_o triangle_n take_v too_o much_o as_o i_o add_v when_o i_o take_v too_o little_a nor_o last_o that_o these_o method_n be_v not_o only_o applicable_a to_o trapezia_n but_o to_o any_o triangular_a figure_n whatsoever_o whether_o regular_a or_o irregular_a chap._n xii_o concern_v the_o boundary_n of_o land_n where_o the_o line_n to_o be_v measure_v must_v begin_v and_o end_v if_o there_o be_v no_o agreement_n between_o the_o party_n concern_v for_o if_o there_o be_v that_o must_v be_v observe_v reason_n and_o custom_n be_v the_o surveyor_n guide_n the_o farmer_n speak_v loud_o that_o when_o a_o piece_n of_o arable_a or_o meadow-land_n be_v let_v for_o a_o year_n to_o be_v sow_v or_o mow_v no_o more_o shall_v be_v measure_v nor_o expect_v to_o be_v pay_v for_o either_o to_o the_o letter_n or_o workman_n than_o the_o blow_n or_o since_o can_v go_v over_o so_o also_o when_o a_o parcel_n of_o land_n be_v let_v for_o pasture_n by_o measure_n to_o a_o farmer_n it_o seem_v very_o reasonable_a that_o all_o and_o only_o so_o much_o shall_v be_v measure_v as_o be_v useful_a to_o that_o purpose_n but_o commons_o to_o be_v enclose_v be_v usual_o measure_v except_o it_o be_v otherwise_o agree_v to_o the_o uttermost_a bound_n of_o every_o man_n particular_a proportion_n without_o any_o allowance_n for_o ditch_n or_o fence_n every_o man_n be_v to_o make_v they_o upon_o his_o own_o of_o what_o breadth_n he_o please_v nor_o be_v this_o unreasonable_a for_o it_o be_v as_o good_a for_o one_o as_o another_o and_o the_o rate_n pay_v to_o the_o lord_n be_v usual_o very_o little_a sometime_o nothing_o it_o be_v also_o very_o usual_a in_o measure_v betwixt_o lord_n and_o tenant_n in_o case_n of_o lease_n for_o life_n and_o long_a term_n of_o year_n to_o extend_v the_o line_n to_o the_o utmost_a bound_n of_o the_o tenant_n claim_v take_v in_o the_o very_a wall_n hedges_n and_o ditch_n but_o this_o be_v account_v very_o hard_o and_o oft_o prove_v very_o unequal_a among_o the_o tenant_n of_o a_o lordship_n some_o be_v force_v to_o make_v much_o more_o waste_n of_o their_o ground_n this_o way_n than_o other_o that_o hold_v as_o much_o or_o more_o but_o where_o the_o custom_n obtain_v the_o survey_n or_o must_v observe_v it_o for_o it_o be_v other_o work_n to_o appoint_v what_o must_v be_v measure_v and_o his_o only_a to_o measure_v true_o what_o be_v so_o appoint_v a_o good_a landlord_n may_v and_o will_v be_v apt_a to_o consider_v it_o in_o his_o rate_n and_o a_o bad_a one_o it_o be_v like_a will_v be_v tenacious_a of_o a_o custom_n to_o his_o own_o advantage_n last_o in_o case_n of_o sale_n by_o measure_n at_o a_o rate_n agree_v upon_o per_fw-la acre_n no_o boundary_n be_v specify_v in_o the_o bargain_n the_o rule_n as_o i_o have_v it_o from_o a_o old_a famous_a surveyor_n many_o year_n ago_o be_v to_o extend_v the_o line_n to_o the_o quick_a wood-row_n that_o be_v as_o reason_n prompt_v i_o to_o understand_v he_o to_o the_o place_n where_o the_o quick-wood_n actual_o grow_v or_o where_o according_a to_o custom_n it_o ought_v to_o be_v
know_v that_o to_o make_v a_o rhombus_fw-la or_o rhomboide_v like_o to_o another_o for_o figure_n or_o equal_a to_o it_o in_o content_a it_o be_v not_o sufficient_a to_o have_v the_o same_o side_n for_o the_o more_o oblique_a the_o angel_n 〈◊〉_d the_o far_a will_v the_o rhombus_fw-la differ_v from_o a_o 〈◊〉_d and_o the_o rhomboide_v from_o a_o long_a 〈◊〉_d be_v and_o the_o less_o will_v be_v the_o content_a but_o 〈◊〉_d must_v have_v a_o angle_n give_v which_o will_v proâ—â—â—e_v all_o the_o rest_n or_o else_o a_o diagonal_a line_n which_o 〈◊〉_d right_a line_n pass_v through_o the_o rhombus_fw-la or_o â—omboides_v from_o one_o opposite_a angle_n to_o another_o and_o divide_v the_o figure_n into_o two_o equal_a â—â—â—angles_n if_o the_o former_a viz._n a_o angle_n be_v â—â—n_fw-la i_o have_v show_v what_o use_n be_v to_o be_v make_v 〈◊〉_d if_o the_o latter_a i._n e._n a_o diagonal_a together_o with_o the_o length_n of_o the_o side_n you_o may_v by_o â—â—â—ng_v the_o length_n of_o the_o side_n with_o your_o comâ—â—es_n and_o set_v a_o foot_n in_o the_o end_n of_o the_o â—â—gonal_a line_n make_v a_o triangle_n on_o the_o one_o side_n â—he_v diagonal_a by_o probl._n 6._o and_o then_o another_o on_o the_o other_o side_n by_o the_o same_o problem_n the_o â—â—gonal_a be_v a_o common_a base_a to_o they_o both_o this_o will_v give_v the_o figure_n exact_o to_o make_v a_o rbomboide_n the_o side_n be_v give_v fi._n 9_o 〈◊〉_d neither_o angle_n nor_o diagonal_n be_v give_v 〈◊〉_d if_o either_o of_o they_o be_v limit_v the_o case_n be_v â—â—en_o to_o in_o the_o last_o problem_n make_v any_o angle_n adventure_n as_o here_o abc_n then_o suppose_v 〈◊〉_d line_n give_v to_o be_v open_a and_o qr_n set_v the_o 〈◊〉_d of_o the_o long_o upon_o the_o line_n bc_n from_o b_o 〈◊〉_d and_o the_o short_a on_o the_o line_n basilius_n to_o e_z 〈◊〉_d with_o the_o compass_n extend_v from_o b_o to_z e_z 〈◊〉_d one_o foot_n in_o d_o and_o describe_v the_o arch_n fg._n â—â—ewise_o with_o the_o compass_n extend_v to_o the_o 〈◊〉_d of_o the_o line_n open_v set_v one_o foot_n in_o e_o 〈◊〉_d the_o other_o describe_v the_o arch_n he_o intersect_v fig._n 9_o the_o former_a arch_n at_o k_o from_o which_o intersection_n line_n draw_v to_o d_o and_o e_o finish_v the_o rhomboide_n xii_o to_o make_v a_o trapezium_fw-la the_o diagonal_a and_o line_n in_o order_n be_v give_v fi._n 10_o let_v the_o line_n hl_n be_v the_o diagonal_a of_o a_o trapezium_fw-la who_o side_n be_v the_o line_n a_o b_o c_o d_o the_o side_n a_o be_v count_v the_o first_o as_o that_o which_o take_v its_o beginning_n from_o the_o point_n h_n and_o the_o rest_n in_o the_o order_n as_o they_o be_v mark_v alphabetical_o then_o with_o your_o compass_n set_v to_o the_o length_n of_o the_o line_n a_o place_n one_o foot_n in_o h_n and_o with_o the_o other_o describe_v the_o arch_n ef._n next_o take_v the_o length_n of_o the_o line_n b_o with_o the_o one_o foot_n oâ—_n your_o compass_n place_v in_o l_o with_o the_o other_o make_v the_o arch_n give_v intersect_v the_o former_a at_o k_o from_o which_o point_n of_o intersection_n line_n draw_v to_o h_n and_o l_o make_v the_o triangle_n hkl_n then_o with_o the_o extent_n of_o the_o line_n c_o set_v one_o of_o the_o foot_n of_o your_o compass_n at_o l_o and_o describe_v the_o arch_n open_v last_o set_v they_o to_o the_o length_n of_o the_o line_n d_o and_o place_v one_o foot_n of_o your_o compass_n in_o h_n with_o the_o other_o make_v the_o arch_a sir_n intersect_v the_o former_a at_o q_o 〈◊〉_d shall_v line_n draw_v from_o q_o to_o l_o and_o h_n make_v uâ—_n the_o triangle_n lqh_v and_o finish_v the_o trapezium_fw-la hklq_fw-la i_o can_v have_v be_v much_o brief_a in_o this_o problem_n by_o refer_v to_o the_o six_o but_o this_o be_v of_o very_o great_a and_o frequent_a use_n i_o desire_v to_o be_v very_o plain_a xiii_o to_o make_v a_o regular_a polygon_n otherwise_o call_v a_o regular_a multangular_a or_o multilateral_a figure_n consist_v of_o many_o equal_a side_n and_o angle_n viz._n above_o four_o apiece_o be_v satisfy_v what_o shall_v be_v the_o distance_n between_o the_o centre_n and_o every_o angle_n with_o that_o distance_n describe_v a_o circle_n which_o be_v equal_o divide_v into_o as_o many_o part_n as_o the_o figure_n must_v have_v angle_n or_o side_n for_o they_o be_v equal_a in_o number_n and_o line_n draw_v from_o the_o point_n of_o division_n within_o the_o circle_n from_o point_n to_o point_v ordinary_o call_v chord_n the_o polygon_n be_v finish_v as_o in_o this_o diagram_n fig._n 11_o suppose_v a_o heptagon_n or_o multangular_a figure_n of_o seven_o side_n and_o as_o many_o angles_n be_v to_o be_v describe_v every_o angle_n be_v design_v to_o be_v distant_a from_o the_o centre_n a_o seven_o eighth_n or_o three_o quarter_n and_o a_o half_a of_o a_o inch_n with_o that_o distance_n describe_v the_o circle_n bcdefgh_o which_o be_v divide_v into_o seven_o equal_a part_n and_o line_n draw_v from_o point_n to_o point_v the_o heptagon_n bcdefgh_o will_v be_v therein_o include_v i_o shall_v rather_o leave_v my_o unlearned_a reader_n to_o find_v out_o the_o point_n of_o division_n by_o many_o trial_n than_o to_o puzzle_v he_o with_o the_o geometrical_a way_n for_o find_v out_o chord_n to_o that_o purpose_n nor_o shall_v i_o busy_v myself_o to_o tell_v he_o at_o large_a how_o he_o may_v divide_v 360_o by_o the_o number_n of_o his_o angle_n or_o side_n and_o then_o find_v in_o his_o quotient_n the_o degree_n and_o part_n belong_v to_o every_o division_n set_v they_o ready_o out_o by_o a_o protractor_n or_o for_o want_n thereof_o by_o a_o line_n of_o chord_n for_o i_o suppose_v he_o yet_o ignorant_a of_o such_o thing_n i_o shall_v therefore_o only_o tell_v he_o thus_o much_o a_o line_n draw_v through_o the_o circle_n at_o the_o centre_n divide_v it_o into_o two_o equal_a part_n which_o be_v cross_v in_o the_o centre_n by_o another_o line_n the_o circle_n will_v be_v part_v into_o four_o equal_a part_n or_o quadrant_n and_o those_o by_o halve_v they_o into_o eight_o part_n the_o extent_n of_o the_o compass_n whereby_o the_o circle_n be_v draw_v usual_o call_v the_o radius_fw-la or_o semidiameter_n will_v divide_v it_o into_o six_o equal_a part_n two_o whereof_o must_v be_v a_o three_o part_n and_o half_a of_o one_o a_o twelve_o part_n and_o these_o still_o easy_o capable_a of_o far_a division_n fourteen_o have_v the_o side_n of_o the_o triangle_n whereof_o it_o consist_v orderly_o give_v to_o make_v a_o irregular_a multangler_n or_o multilateral_a figure_n this_o will_v be_v more_o full_o handle_v hereafter_o when_o i_o come_v to_o show_v the_o method_n of_o draw_v plot_n of_o ground_n in_o the_o interim_n i_o will_v give_v you_o a_o specimen_fw-la of_o a_o irregular_a pentagon_n fi._n 12_o have_v the_o line_n of_o three_o triangle_n give_v which_o by_o a_o rule_n hereafter_o to_o be_v mention_v be_v necessary_a to_o make_v up_o a_o five_o figure_n lay_v down_o the_o great_a of_o the_o first_o viz._n 20_o from_o a_o to_o b_o for_o a_o base_a and_o by_o probl._n 6._o make_v a_o triangle_n of_o it_o and_o the_o other_o line_n 16_o and_o 10._o viz._n the_o triangle_n abo_n second_o you_o find_v by_o the_o number_n o_o over_o the_o first_o line_n of_o the_o second_o triangle_n that_o it_o be_v the_o common_a base_a to_o they_o both_o and_o therefore_o by_o the_o same_o probl._n 6._o make_v the_o triangle_n a_o b_o p_o of_o the_o line_n 20_o 14_o 18._o fi._n 12_o last_o find_v the_o base_a of_o the_o three_o triangle_n to_o be_v the_o same_o with_o 18_o one_o of_o the_o side_n of_o the_o second_o make_v the_o triangle_n pbq_n of_o the_o line_n 18_o 11_o 12_o so_o be_v the_o quinquangular_a figure_n finish_v how_o every_o line_n be_v to_o be_v find_v in_o its_o due_a order_n in_o this_o or_o any_o other_o sort_n of_o multangular_a figure_n so_o as_o to_o give_v a_o true_a and_o exact_a account_n not_o only_o of_o the_o superficial_a content_a but_o also_o of_o the_o figure_n or_o shape_n and_o situation_n be_v to_o be_v teach_v hereafter_o in_o the_o doctrine_n and_o practice_n of_o protraction_n chap._n iii_o how_o to_o find_v the_o superficial_a content_n of_o any_o right-lined_n figure_n the_o line_n be_v give_v as_o a_o foundation_n to_o what_o i_o shall_v say_v upon_o this_o subject_a there_o be_v some_o few_o geometrical_a principle_n or_o theorem_n out_o of_o enclid_n and_o ramus_n which_o i_o desire_v may_v be_v remember_v and_o because_o understanding_n be_v a_o mighty_a help_n to_o memory_n i_o design_v for_o my_o country_n reader_n a_o kind_n of_o ocular_a demonstration_n which_o though_o not_o so_o strict_a and_o artificial_a as_o that_o which_o be_v to_o be_v find_v in_o