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 the_o side_n subtend_v the_o right_a angle_n be_v equal_a to_o both_o the_o square_n of_o the_o contain_v side_n 7._o all_o parallellogram_n be_v double_a to_o the_o triangle_n that_o be_v describe_v upon_o their_o base_n their_o altitude_n be_v equal_a 8._o all_o triangle_n that_o have_v one_o and_o the_o same_o base_a and_o lie_v between_o two_o parallel_a line_n be_v equal_a one_o to_o the_o other_o geometrical_a problem_n problem_n i._o upon_o a_o right_a line_n give_v how_o to_o erect_v another_o right_a line_n which_o shall_v be_v perpendicular_a to_o the_o right_a line_n give_v the_o right_a line_n give_v be_v ab_fw-la upon_o which_o from_o the_o point_n e_o it_o be_v require_v to_o erect_v the_o perpendicular_a eh_n open_v your_o compass_n at_o pleasure_n to_o any_o convenient_a distance_n place_n one_o foot_n in_o the_o assign_a point_n e_o and_o with_o the_o other_o make_v the_o mark_n c_o and_o d_o equidistant_n on_o each_o side_n the_o give_v point_n e._n then_o open_v your_o compass_n again_o to_o any_o other_o convenient_a distance_n wide_o than_o the_o former_a place_n one_o foot_n in_o c_o and_o with_o the_o other_o describe_v the_o arch_a gg_n also_o the_o compass_n remain_v at_o the_o same_o distance_n place_v one_o foot_n in_o the_o point_n d_o and_o with_o the_o other_o describe_v the_o arch_a ff_n then_o from_o the_o point_n where_o these_o two_o arch_n intersect_v or_o cut_v each_o other_o which_o be_v at_o h_n draw_v the_o right_a line_n he_o which_o shall_v be_v perpendicular_a to_o the_o give_v right_a line_n ab_fw-la which_o be_v the_o thing_n require_v to_o be_v do_v prob._n ii_o how_o to_o erect_v a_o perpendicular_a on_o the_o end_n of_o a_o right_a line_n give_v let_v or_o be_v a_o line_n give_v and_o let_v it_o be_v require_v to_o erect_v the_o perpendicular_a rs._n first_o upon_o the_o line_n or_o with_o your_o compass_n open_v to_o any_o small_a distance_n make_v five_o small_a division_n begin_v at_o r_n note_v with_o 1_o 2_o 3_o 4_o 5._o then_o take_v with_o your_o compass_n the_o distance_n from_o r_n to_o 4_o and_o place_v one_o foot_n in_o r_o with_o the_o other_o describe_v the_o arch_n pp_n then_o take_v the_o distance_n r_o 5_o and_o place_v one_o foot_n of_o the_o compass_n in_o 3_o with_o the_o other_o foot_n describe_v the_o arch_n bb_n cut_v the_o former_a arch_n in_o the_o point_n s._n last_o from_o the_o point_n s_o draw_v the_o line_n r_n which_o shall_v be_v perpendicular_a to_o the_o give_v line_n or_o prob._n iii_o how_o to_o let_v fall_v a_o perpendicular_a from_o any_o point_n assign_v upon_o a_o right_a line_n give_v the_o point_n give_v be_v c_o from_o which_o point_n it_o be_v require_v to_o draw_v a_o right_a line_n which_o shall_v be_v perpendicular_a to_o the_o give_v right_a line_n ab_fw-la first_o from_o the_o give_v point_n c_o to_o the_o line_n ab_fw-la draw_v a_o line_n by_o chance_n as_o ce_fw-fr which_o divide_v into_o two_o equal_a part_n in_o the_o point_n d_o then_z placing_z one_o foot_n of_o the_o compass_n in_o the_o point_n d_o with_o the_o distance_n dc_o describe_v the_o semicircle_n cfe_n cut_v the_o give_v line_n ab_fw-la in_o the_o point_n f._n last_o if_o from_o the_o point_n c_o you_o draw_v the_o right_a line_n cf_n it_o shall_v be_v a_o perpendicular_a to_o the_o give_v line_n ab_fw-la which_o be_v require_v prob._n iu._n how_o to_o make_v a_o angle_n equal_a to_o a_o angle_n give_v let_v the_o angle_n give_v be_v acb_n and_o let_v it_o be_v require_v to_o make_v another_o angle_n equal_a thereunto_o first_o draw_v the_o line_n of_o at_o pleasure_n then_o upon_o the_o give_v angle_n at_o c_o the_o compass_n open_v to_o any_o distance_n describe_v the_o ark_n ab_fw-la also_o upon_o the_o point_n f_o the_o compass_n un-altered_n describe_v the_o ark_n de_fw-fr than_o take_v with_o your_o compass_n the_o distance_n ab_fw-la and_o set_v the_o same_o distance_n from_o e_z to_z d._n last_o draw_v the_o line_n df_n so_o shall_v the_o angle_n dfe_n be_v equal_a to_o the_o give_v angle_n acb_n prob._n v._o a_o right_a line_n be_v give_v how_o to_o draw_v another_o right_a line_n which_o shall_v be_v parallel_n to_o the_o former_a at_o any_o distance_n require_v the_o line_n give_v be_v ab_fw-la unto_o which_o it_o be_v require_v to_o draw_v another_o right_a line_n parallel_n thereunto_o at_o the_o distance_n ac_fw-la or_o bd._n first_o open_v your_o compass_n to_o the_o distance_n ac_fw-la or_o ad_fw-la then_o place_v one_o foot_n in_o a_o with_o the_o other_o describe_v the_o ark_n c_o also_o place_n one_o foot_n in_o b_o and_o with_o the_o other_o describe_v the_o arch_n d._n last_o draw_v the_o line_n cd_o so_o that_o it_o may_v only_o touch_v the_o ark_n c_o and_o d_o so_fw-mi shall_v the_o line_n cd_o be_v parallel_n to_o the_o line_n ab_fw-la and_o at_o the_o distance_n require_v prob._n vi_o to_o divide_v a_o right_a line_n give_v into_o any_o number_n of_o equal_a part_n let_v ab_fw-la be_v a_o line_n give_v and_o let_v it_o be_v require_v to_o divide_v the_o same_o into_o four_o equal_a part_n first_o from_o the_o end_n of_o the_o give_v line_n a_o draw_v the_o line_n ac_fw-la make_v any_o angle_n then_o from_o the_o other_o end_n of_o the_o give_v line_n which_o be_v at_o the_o point_n b_o draw_v the_o line_n bd_o parallel_v to_o ac_fw-la or_o make_v the_o angle_n abdella_n equal_a to_o the_o angle_n cab_n then_o upon_o the_o line_n ac_fw-la and_z bd_o set_v off_o any_o three_o equal_a part_n which_o be_v one_o less_o than_o the_o number_n of_o part_n into_o which_o the_o line_n ab_fw-la be_v to_o be_v divide_v on_o â—ace_n line_n as_o 1_o 2_o 3_o then_o draw_v line_n from_o 1_o to_o 3_o from_z 2_o to_z 2_o and_o from_o 3_o to_o 1_o which_o line_n cross_v the_o give_v line_n ab_fw-la shall_v divide_v it_o into_o four_o equal_a part_n as_o be_v require_v prob._n vii_o a_o right_a line_n be_v give_v how_o to_o draw_v another_o right_a line_n parallel_n thereunto_o which_o shall_v also_o pass_v through_o a_o point_n assign_v let_v ab_fw-la be_v a_o line_n give_v and_o let_v it_o be_v require_v to_o draw_v another_o line_n parallel_n thereunto_o which_o shall_v pass_v through_o the_o give_v point_n c._n first_o take_v with_o your_o compass_n the_o distance_n from_o a_o to_o c_o and_o place_v one_o foot_n thereof_o in_o b_o with_o the_o other_o describe_v the_o ark_n de_fw-fr then_o take_v in_o your_o compass_n the_o whole_a line_n ab_fw-la and_o place_v one_o foot_n in_o the_o point_n c_o with_o the_o other_o describe_v the_o ark_n fg_v cross_v the_o former_a ark_n de_fw-fr in_o the_o point_n h._n last_o if_o you_o draw_v the_o line_n ch_n it_o shall_v be_v parallel_n to_o ab_fw-la prob._n viii_o have_v any_o three_o point_n give_v which_o be_v not_o situate_a in_o a_o right_a line_n how_o to_o find_v the_o centre_n of_o a_o arch_n of_o a_o circle_n which_o shall_v pass_v direct_o through_o the_o three_o give_v point_n the_o three_o point_n give_v be_v a_o b_o and_o c_o now_o 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
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 survey_v this_o close_a place_v your_o instrument_n at_o a_o and_o direct_v your_o sight_n to_o l_o note_v the_o degree_n there_o cut_v which_o let_v be_v 160_o degree_n 45_o minute_n which_o 160_o degree_n 45_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 then_o measure_v the_o distance_n all_o 8_o chain_n 68_o link_n which_o place_n in_o the_o three_o &_o four_o column_n 2._o remove_v your_o instrument_n to_o l_o and_o direct_v the_o sight_n to_o m_n the_o needle_n cut_v 181_o degree_n 30_o min._n and_o the_o line_n lm_o contain_v 6_o chain_n 55_o link_n which_o note_v down_o in_o your_o field-book_n 3._o place_v your_o instrument_n at_o m_n and_o direct_v the_o sight_n to_o n_n the_o needle_n cut_v 233_o degree_n and_o the_o line_n mn_v 7_o chain_n 27_o link_n which_o note_n in_o your_o field-book_n and_o in_o regard_n you_o be_v to_o leave_v the_o hedge_n or_o bounder_n almn_n adjoin_v to_o wisby_n common_a which_o appertain_v to_o another_o manor_n and_o therefore_o only_a the_o name_n insert_v for_o your_o remembrance_n when_o you_o come_v to_o protraction_n you_o must_v draw_v a_o line_n quite_o through_o your_o field_n book_n and_o in_o the_o last_o column_n thereof_o write_v wisby_n common_a which_o denote_v unto_o you_o that_o you_o be_v to_o leave_v the_o bounder_n of_o wisby_n common_a 4._o place_v your_o instrument_n at_o n_n and_o direct_v the_o sight_n to_o o_o the_o needle_n cut_v 355_o deg_fw-la 40_o min._n and_o the_o distance_n no_o be_v 4_o chain_n 45_o link_n which_o note_n in_o your_o field-book_n as_o before_o 5._o place_v your_o instrument_n at_o o_o and_o direct_v the_o sight_n to_o c_o the_o needle_n cut_v 309_o degree_n 30_o minute_n and_o the_o line_n oc_fw-fr contain_v 6_o chain_n 64_o link_n which_o note_n in_o your_o field-book_n now_o because_o at_o these_o two_o observation_n you_o go_v against_o the_o hedge_n or_o bounder_n of_o banton_n plain_a you_o must_v against_o they_o write_v 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 go_v against_o the_o hedge_n or_o bounder_n of_o bay_a wood_n you_o must_v therefore_o against_o they_o write_v bay_a wood_n and_o because_o you_o have_v now_o finish_v your_o first_o close_a you_o must_v draw_v a_o double_a line_n through_o your_o book_n for_o your_o remembrance_n then_o consider_v which_o parcel_n be_v next_o fit_a to_o be_v take_v in_o hand_n which_o let_v be_v bay_fw-mi wood_n and_o withal_o at_o what_o angle_n thereof_o it_o be_v most_o meet_a to_o begin_v which_o suppose_v c_o and_o here_o for_o your_o help_n when_o you_o come_v to_o protraction_n you_o must_v express_v in_o the_o title_n of_o this_o second_o close_a at_o what_o angle_n you_o begin_v the_o same_o unless_o you_o have_v begin_v it_o where_o you_o end_v the_o last_o at_o a_o and_o then_o it_o be_v not_o material_a wherefore_o see_v you_o be_v best_a to_o begin_v at_o c_o look_v in_o your_o field-book_n on_o the_o work_n of_o the_o last_o close_n what_o degree_n and_o minute_n the_o needle_n cut_v 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 first_o observation_n from_o c_o to_o e_z that_o you_o go_v partly_o by_o the_o hedge_n or_o bounder_n of_o banton_n plain_a and_o partly_o by_o the_o hedge_n or_o bounder_n of_o church-field_n and_o therefore_o against_o the_o degree_n of_o that_o observation_n write_v banton_n plain_a and_o church-field_n there_o draw_v a_o line_n then_o at_o your_o two_o next_o observation_n at_o e_o and_o f_o you_o go_v along_o the_o hedge_n or_o bounder_n of_o church-field_n and_o at_o the_o three_o last_o observation_n at_o g_o h_n and_o k_n you_o go_v against_o the_o hedge_n or_o bounder_n of_o wisby_n common_a there_o finish_v your_o second_o parsell_n wherefore_o draw_v a_o double_a line_n quite_o through_o your_o field-book_n these_o two_o parcel_n be_v finish_v consider_v which_o be_v next_o fit_a to_o be_v take_v in_o hand_n and_o where_o to_o begin_v it_o which_o suppose_v banton_n plain_a and_o to_o begin_v at_o n_n wherefore_o look_v in_o your_o field-book_n what_o degree_n the_o 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
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 table_n three_o several_a way_n 260._o circumferentor_n 266._o or_o peractor_n 266._o with_o the_o keep_v a_o account_n in_o your_o field-book_n after_o the_o best_a and_o most_o certain_a manner_n 270._o and_o to_o protract_v any_o observation_n so_o take_v 271._o 26._o of_o enlarge_n or_o diminish_n of_o plot_n according_a to_o any_o possible_a proportion_n by_o two_o semicircle_n mr._n rathborn_v ruler_n a_o line_n into_o 100_o part_n the_o parallelogram_n 273._o 27_o of_o convey_v of_o water_n 276._o forasmuch_o as_o the_o whole_a art_n of_o survey_v of_o land_n be_v perform_v by_o instrument_n of_o several_a kind_n and_o that_o the_o exact_a and_o careful_a make_n and_o divide_v of_o all_o such_o instrument_n be_v chief_o to_o be_v aim_v at_o i_o think_v good_a to_o intimate_v to_o such_o as_o be_v desirous_a to_o practice_v this_o art_n and_o do_v not_o ready_o know_v where_o to_o be_v furnish_v with_o necessary_a instrument_n for_o the_o performance_n thereof_o that_o all_o or_o any_o of_o the_o instrument_n use_v or_o mention_v in_o this_o book_n or_o any_o mathematical_a instrument_n whatsoever_o be_v exact_o make_v by_o mr._n anthony_n thompson_n in_o hosier_n lane_n near_o smithfield_n london_n the_o complete_a surveyor_z the_o first_o book_n the_o argument_n this_o first_o book_n consist_v of_o divers_a definition_n &_o problem_n geometrical_a extract_v out_o of_o the_o write_n of_o divers_a ancient_a and_o modern_a geometrician_n as_o euclid_n ramus_n clavius_n etc._n etc._n and_o be_v here_o so_o methodical_o dispose_v that_o any_o man_n may_v gradual_o proceed_v from_o problem_n to_o problem_n without_o interruption_n or_o be_v refer_v to_o any_o other_o author_n for_o the_o practical_a performance_n of_o any_o of_o they_o only_o the_o demonstration_n be_v whole_o omit_v partly_o because_o those_o book_n out_o of_o which_o they_o be_v extract_v be_v very_o large_a in_o that_o particular_a and_o also_o for_o the_o avoid_n of_o many_o other_o proposition_n and_o theorem_n which_o have_v the_o ensue_a problem_n be_v demonstrate_v must_v of_o necessity_n have_v be_v insert_v also_o the_o figure_n will_v have_v be_v so_o encumber_v with_o multiplicity_n of_o line_n that_o the_o intend_a problem_n will_v have_v be_v thereby_o much_o darken_v and_o beside_o it_o be_v not_o my_o intent_n in_o this_o place_n to_o make_v a_o absolute_a or_o entire_a treatise_n of_o geometry_n and_o therefore_o i_o have_v only_o make_v choice_n of_o such_o problem_n as_o i_o conceive_v most_o useful_a for_o my_o present_a purpose_n and_o come_v most_o in_o use_n in_o the_o practice_n of_o survey_v and_o aught_o of_o necessity_n to_o be_v know_v by_o every_o man_n that_o intend_v to_o exercise_v himself_o in_o the_o practice_n thereof_o and_o those_o be_v chief_o such_o as_o concern_v the_o reduce_n of_o plot_n from_o one_o form_n to_o another_o and_o to_o enlarge_v or_o diminish_v they_o according_a to_o any_o assign_a proportion_n also_o divers_a of_o the_o problem_n in_o this_o book_n will_v abundant_o help_v the_o surveyor_n in_o the_o division_n and_o separation_n of_o land_n and_o in_o the_o lay_n out_o of_o any_o assign_a quantity_n whereby_o large_a parcel_n may_v be_v ready_o divide_v into_o divers_a several_n and_o those_o again_o subdivide_v if_o need_v be_v also_o for_o the_o better_a satisfaction_n of_o the_o reader_n i_o have_v perform_v divers_a of_o the_o follow_a problem_n both_o arithmetical_o and_o geometrical_o geometrical_a definition_n 1._o a_o point_n be_v that_o which_o can_v be_v divide_v a_o point_n or_o sign_n be_v that_o which_o be_v void_a of_o all_o magnitude_n and_o be_v the_o least_o thing_n that_o by_o mind_n and_o understanding_n can_v be_v imagine_v and_o conceive_v than_o which_o there_o can_v be_v nothing_o less_o as_o the_o point_n or_o prick_v note_v with_o the_o letter_n a_o which_o be_v neither_o quantity_n nor_o part_n of_o quantity_n but_o only_o the_o term_n or_o end_n of_o quantity_n and_o herein_o a_o point_n in_o geometry_n differ_v from_o unity_n in_o number_n 2._o a_o line_n be_v a_o length_n without_o breadth_n or_o thickness_n a_o line_n be_v create_v or_o make_v by_o the_o move_a or_o draw_v out_o of_o a_o point_n from_o one_o place_n to_o another_o so_o the_o line_n ab_fw-la be_v make_v by_o move_v of_o a_o point_n from_o a_o to_o b_o and_o according_a as_o this_o motion_n be_v so_o be_v the_o line_n thereby_o create_v whether_o straight_o or_o crooked_a and_o of_o the_o three_o kind_n of_o magnitude_n in_o geometry_n viz._n length_n breadth_n and_o thickness_n a_o line_n be_v the_o first_o consist_v of_o length_n only_o and_o therefore_o the_o line_n ab_fw-la be_v capable_a of_o division_n in_o length_n only_o and_o may_v be_v divide_v equal_o in_o the_o point_n c_o or_o unequal_o in_o d_o and_o the_o like_a but_o will_v admit_v of_o no_o other_o dimension_n 3._o the_o end_n or_o bound_n of_o a_o line_n be_v point_n this_o be_v to_o be_v understand_v of_o a_o finite_a line_n only_o as_o be_v the_o line_n ab_fw-la the_o end_n or_o bound_n whereof_o be_v the_o point_v a_o and_o b_o but_o in_o a_o circular_a line_n it_o be_v otherwise_o for_o there_o the_o point_n in_o its_o motion_n return_v again_o to_o the_o place_n where_o it_o first_o begin_v and_o so_o make_v the_o line_n infinite_a and_o the_o end_n or_o bound_n thereof_o undeterminate_a 4._o a_o right_a line_n be_v that_o which_o lie_v equal_o between_o his_o point_n as_o the_o right_a line_n ab_fw-la lie_v straight_a and_o equal_a between_o the_o point_v a_o and_z b_o which_o be_v the_o bound_n thereof_o without_o bow_v and_o be_v the_o short_a of_o all_o other_o line_n that_o can_v be_v draw_v between_o those_o two_o point_n 5._o a_o superficies_n be_v that_o which_o have_v only_a length_n and_o breadth_n as_o the_o motion_n of_o a_o point_n produce_v a_o line_n the_o first_o kind_n of_o magnitude_n so_o the_o motion_n of_o a_o line_n produce_v a_o superficies_n which_o be_v the_o second_o kind_n of_o magnitude_n and_o be_v capable_a of_o two_o dimension_n namely_o length_n and_o breadth_n and_o so_o the_o superficies_n abcd_n may_v be_v divide_v in_o length_n from_o a_o to_o b_o and_o also_o in_o breadth_n from_o a_o to_o c._n 6._o the_o extreme_n of_o a_o superficies_n be_v line_n as_o the_o extreme_n or_o end_n of_o a_o line_n be_v point_n so_o the_o extreme_n or_o bound_n of_o a_o superficies_n be_v line_n and_o so_o the_o extreme_n or_o end_n of_o the_o superficies_n abcd_n be_v the_o line_n ab_fw-la bd_o dc_o and_o ca_n which_o be_v the_o term_n or_o limit_n thereof_o 7._o a_o plain_a superficies_n be_v that_o which_o lie_v equal_o between_o his_o line_n so_o the_o superficies_n abcd_n lie_v direct_a and_o equal_o between_o his_o line_n and_o whatsoever_o be_v say_v of_o a_o right_a line_n the_o same_o be_v also_o to_o be_v understand_v of_o a_o plain_a superficies_n 8._o a_o plain_a angle_n be_v the_o inclination_n or_o bow_v of_o two_o line_n the_o one_o to_o the_o other_o the_o one_o touch_v the_o other_o &_o not_o be_v direct_o join_v together_o as_o the_o two_o line_n ab_fw-la and_z bc_n incline_v the_o one_o to_o the_o other_o and_o touch_v one_o another_o in_o the_o point_n b_o in_o which_o point_n by_o reason_n of_o the_o inclination_n of_o the_o say_a line_n be_v make_v the_o angle_n abc_n but_o if_o the_o two_o line_n which_o touch_v each_o other_o be_v without_o inclination_n and_o be_v draw_v direct_o one_o to_o the_o other_o than_o they_o make_v no_o angle_n at_o all_o as_o the_o line_n cd_o and_o de_fw-fr touch_v each_o other_o in_o the_o point_n d_o and_o yet_o they_o make_v no_o angle_n but_o one_o continue_v right_a line_n ¶_o and_o here_o note_n that_o a_o angle_n common_o be_v sign_v by_o three_o letter_n the_o middlemost_a whereof_o show_v
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
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
the_o first_o column_n of_o your_o field-book_n and_o the_o 8_o chain_n 53_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 e_o the_o index_n cut_v 287_o degree_n 15_o minute_n and_o the_o distance_n le_z be_v 8_o chain_n 15_o link_n these_o must_v be_v note_v in_o your_o field-book_n as_o before_o the_o 287_o degree_n 15_o minute_n in_o the_o first_o and_o second_o column_n and_o the_o 8_o chain_n 15_o link_n in_o the_o three_o and_o four_o last_o direct_v the_o sight_n to_o f_o your_o last_o mark_n the_o index_n cut_v 342_o degree_n and_o the_o distance_n lf_o be_v 9_o chain_n 55_o link_n these_o must_v be_v note_v down_o in_o your_o field-book_n in_o all_o respect_n as_o the_o former_a viz_o the_o 342_o degree_n in_o the_o first_o column_n and_o the_o 9_o chain_n 55_o link_n in_o the_o three_o and_o four_o then_o will_v your_o observation_n note_v in_o your_o field-book_n stand_v as_o in_o this_o table_n follow_v  _fw-fr degree_n minute_n chain_n link_n a_o 36_o 45_o 8_o 10_o b_o 99_o 15_o 8_o 75_o c_o 163_o 15_o 10_o 65_o d_o 212_o 00_o 8_o 53_o e_z 287_o 15_o 8_o 15_o f_o 342_o 00_o 9_o 55_o chap._n xviii_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 circumferentor_n there_o be_v little_a difference_n between_o the_o work_n of_o this_o and_o the_o last_o chapter_n for_o the_o mark_n be_v place_v in_o the_o several_a angle_n of_o the_o field_n and_o the_o station_n appoint_v at_o l_o place_n there_o the_o instrument_n and_o turn_v it_o about_o direct_v the_o sight_n to_o a_o the_o flower-de-luce_n of_o the_o card_n be_v always_o towards_o you_o the_o south_n end_n of_o the_o needle_n cut_v 36_o degree_n 45_o minute_n the_o same_o which_o the_o index_n of_o the_o theodolite_n do_v in_o the_o last_o chapter_n then_o measure_v the_o distance_n from_o l_o to_o a_o you_o will_v find_v it_o to_o contain_v as_o before_o 8_o chain_n 10_o link_n which_o you_o must_v note_v down_o in_o your_o field-book_n as_o in_o the_o last_o chapter_n then_o turn_v the_o whole_a instrument_n about_o as_o before_o direct_v the_o sight_n to_o b_o the_o south_n end_n of_o the_o needle_n cut_v 99_o degree_n 15_o minute_n and_o the_o distance_n lb_n will_v contain_v 8_o chain_n 75_o link_n which_o note_v down_o in_o your_o book_n also_o in_o this_o manner_n must_v you_o direct_v the_o sight_n to_o all_o the_o other_o angle_n c_o d_o e_o and_o f_o and_o you_o shall_v find_v the_o south_n end_n of_o the_o needle_n always_o to_o cut_v the_o same_o degree_n in_o the_o card_n as_o the_o index_n of_o the_o theodolite_n do_v and_o the_o measure_a line_n lc_a ld_n le_z and_o lf_a will_v be_v likewise_o the_o same_o so_o that_o the_o table_n of_o observation_n in_o the_o last_o chapter_n will_v serve_v to_o protract_v either_o this_o or_o the_o other_o work_n as_o be_v teach_v in_o the_o next_o chapter_n chap._n xix_o how_o to_o protract_v any_o observation_n take_v according_a to_o the_o direction_n in_o the_o last_o chapter_n first_o draw_v upon_o your_o paper_n or_o parchment_n a_o line_n at_o length_n which_o shall_v represent_v the_o meridian_n line_n n_n in_o the_o figure_n then_o make_v choice_n of_o some_o point_n or_o other_o in_o that_o line_n which_o shall_v represent_v your_o station_n or_o place_n of_o stand_v in_o the_o field_n as_o k_o upon_o this_o point_n place_v the_o centre_n of_o your_o protractor_n so_o that_o the_o meridian_n line_n of_o of_o the_o protractor_n may_v lie_v direct_o upon_o the_o meridian_n line_n n_n of_o this_o figure_n then_o lay_v your_o field-book_n before_o you_o see_v that_o at_o your_o first_o observation_n at_o a_o the_o index_n of_o the_o theodolite_a or_o the_o needle_n of_o the_o circumferentor_n cut_v 36_o degree_n 45_o minute_n you_o must_v therefore_o against_o 36_o degree_n 45_o minute_n of_o your_o protractor_n make_v a_o mark_n upon_o your_o paper_n 2._o see_v the_o degree_n cut_v at_o your_o second_o observation_n be_v 99_o degree_n 15_o minute_n you_o must_v make_v a_o mark_n upon_o your_o paper_n against_o 99_o degree_n 15_o minute_n of_o your_o protractor_n 3._o the_o degree_n cut_v at_o your_o three_o observation_n be_v 163_o degree_n 15_o minute_n therefore_o agaig_v 163_o degree_n 15_o minute_n make_v a_o mark_n upon_o your_o paper_n 4._o the_o degree_n cut_v by_o the_o index_n or_o needle_n at_o your_o four_o observation_n be_v 212_o degree_n ¶_o now_o because_o 212_o degree_n be_v great_a than_o 180_o degree_n you_o must_v therefore_o turn_v the_o semicircle_n of_o the_o protractor_n downward_o yet_o the_o line_n of_o thereof_o must_v lie_v direct_o upon_o the_o meridian_n line_n n_n as_o before_o you_o must_v against_o 212_o degree_n of_o the_o protractor_n make_v a_o mark_n upon_o your_o paper_n 5._o see_v the_o degree_n cut_v at_o your_o five_o observation_n be_v 287_o deg_fw-la 15_o minute_n therefore_o make_v a_o mark_n against_o 287_o degree_n 15_o minute_n of_o the_o protractor_n last_o the_o degree_n cut_v at_o your_o last_o observation_n be_v 342_o therefore_o against_o 342_o degree_n of_o your_o protractor_n make_v a_o mark_n with_o your_o protract_n pin_n as_o before_o this_o do_v you_o must_v observe_v by_o your_o field-book_n the_o length_n of_o every_o line_n as_o the_o line_n la_fw-fr at_o your_o first_o observation_n be_v 8_o chain_n 10_o link_n therefore_o 8_o chain_n 10_o link_n be_v take_v from_o your_o scale_n and_o set_v upon_o your_o paper_n from_o l_o to_o a_o it_o shall_v give_v you_o the_o point_n a_o upon_o your_o paper_n 2._o the_o length_n of_o your_o second_o line_n be_v 8_o chain_n 75_o link_n you_o must_v take_v 8_o chain_n 75_o link_n from_o your_o scale_n and_o set_v it_o upon_o your_o paper_n from_o l_o to_z b._n 3._o the_o line_n lc_n be_v 10_o chain_n 65_o link_n you_o must_v therefore_o take_v 10_o chain_n 65_o link_n from_o your_o scale_n and_o set_v it_o upon_o your_o paper_n from_o l_o to_z c._n and_o thus_o must_v you_o deal_v with_o all_o the_o rest_n of_o the_o line_n as_o ld_n le_z and_o lf_a last_o draw_v the_o line_n ab_fw-la bc_n cd_o de_fw-fr of_o and_o favorina_n so_o shall_v you_o have_v the_o exact_a figure_n of_o the_o field_n upon_o your_o paper_n ¶_o in_o these_o four_o last_o chapter_n you_o be_v teach_v how_o to_o take_v the_o plot_n of_o any_o field_n at_o one_o station_n take_v in_o the_o midst_n thereof_o both_o by_o the_o plain_a table_n theodolite_n and_o circumferentor_n and_o also_o how_o to_o protract_v the_o same_o this_o way_n of_o plot_v of_o a_o field_n be_v seldom_o or_o never_o use_v in_o survey_v of_o divers_a parcel_n but_o for_o one_o particular_a field_n it_o be_v as_o good_a as_o any_o but_o divers_a other_o variety_n will_v appear_v in_o the_o follow_a chapter_n chap._n xx._n 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 any_o angle_n thereof_o from_o whence_o all_o the_o other_o angle_n may_v be_v see_v by_o the_o plain_a table_n place_v your_o table_n in_o some_o convenient_a angle_n in_o the_o field_n to_o be_v measure_v 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 and_o there_o fix_v it_o then_o draw_v a_o line_n parallel_n to_o the_o side_n of_o your_o table_n as_o n_n in_o which_o line_n assign_v any_o point_n at_o pleasure_n as_o h_n which_o shall_v represent_v your_o station_n or_o place_n of_o stand_v unto_o this_o point_n apply_v the_o index_n and_o direct_v the_o sight_n to_o a_o and_o draw_v a_o line_n upon_o your_o paper_n as_o ha_o and_o measure_v the_o distance_n ha_o as_o be_v direct_v before_o in_o chap._n 16._o then_o direct_v the_o sight_n to_o b_o your_o second_o mark_n and_o there_o likewise_o draw_v a_o line_n hb_n measure_v the_o distance_n hb_n as_o be_v teach_v in_o the_o forementioned_a chapter_n in_o like_a manner_n direct_v the_o sight_n to_o c_o d_o e_o f_o and_o g_o draw_v line_n by_o the_o side_n of_o your_o index_n at_o every_o observation_n and_o measure_n with_o your_o chain_n the_o distance_n from_o h_n the_o place_n where_o your_o instrument_n stand_v to_o the_o several_a angle_n of_o the_o field_n a_o b_o c_o d_o e_o f_o and_o g_o which_o distance_n be_v take_v in_o your_o compass_n from_o any_o scale_n and_o set_v upon_o your_o table_n from_o h_n upon_o the_o several_a line_n ha_o hb_n hc_fw-la hd_n he_o hf_n and_o hg_v so_o shall_v you_o have_v upon_o your_o table_n the_o point_n a_o b_o c_o d_o e_o f_o and_o g_o by_o which_o mark_n draw_v the_o line_n ha_o ab_fw-la bc_n cd_o de_fw-fr of_o fg_v and_o gh_a which_o line_n
and_o in_o protract_v you_o must_v turn_v the_o semicircle_n of_o the_o protractor_n the_o contrary_a way_n to_o what_o you_o do_v in_o protract_v of_o other_o angle_n chap._n xxxiv_o how_o to_o know_v whether_o you_o have_v take_v the_o angle_n of_o a_o field_n true_o in_o go_v round_o about_o the_o same_o with_o the_o theodolite_a as_o in_o chap._n 33_o whereby_o you_o may_v know_v whether_o your_o plot_n will_v close_v or_o not_o the_o side_n be_v true_o measure_v have_v make_v observation_n of_o all_o the_o angle_n in_o the_o field_n with_o your_o instrument_n and_o note_v they_o down_o in_o your_o field-book_n as_o be_v do_v in_o the_o latter_a end_n of_o chap._n 32._o collect_v the_o quantity_n of_o all_o the_o angle_n find_v at_o your_o several_a observation_n into_o one_o sum_n and_o multiply_v 180_o degree_n by_o a_o number_n less_o by_o two_o then_o the_o number_n of_o angle_n in_o the_o field_n and_o if_o the_o product_n of_o this_o multiplication_n be_v equal_a to_o the_o total_a sum_n of_o your_o angle_n then_o be_v your_o work_n true_a otherwise_o not_o example_n in_o the_o work_n of_o the_o 32_o chap._n the_o angle_v find_v be_v as_o in_o the_o margin_n the_o sum_n of_o they_o be_v 900_o degree_n 00_o minute_n now_o because_o the_o field_n consist_v of_o 7_o angle_n you_o must_v therefore_o multiply_v 180_o degree_n by_o 5_o which_o be_v a_o number_n less_o by_o two_o then_o the_o number_n of_o angle_n in_o the_o field_n and_o the_o product_n will_v be_v 900_o deg_fw-la min._n 130_o 00_o 120_o 30_o 137_o 30_o 120_o 30_o 121_o 30_o 126_o 30_o 143_o 30_o 900_o 00_o which_o exact_o agree_v with_o the_o sum_n of_o all_o the_o angle_n in_o the_o field_n as_o you_o find_v they_o by_o observation_n you_o may_v conclude_v that_o your_o work_n be_v exact_o perform_v chap._n xxxv_o how_o to_o take_v the_o plot_n of_o any_o wood_n park_n or_o other_o large_a champion_n plain_a by_o go_v about_o the_o same_o and_o make_v observation_n at_o every_o angle_n thereof_o by_o the_o circumferentor_n suppose_v then_o that_o abcdefghk_n be_v a_o large_a field_n or_o other_o enclosure_n to_o be_v plot_v by_o the_o circumferentor_n 1._o place_v your_o instrument_n at_o a_o the_o flower-de-luce_n towards_o you_o direct_v the_o sight_n to_o b_o the_o south_n end_n of_o the_o needle_n cut_v 191_o degree_n and_o the_o ditch_n wall_n or_o hedge_n ab_fw-la contain_v 10_o chain_n 75_o link_n the_o degree_n cut_v and_o the_o line_n measure_v must_v be_v note_v down_o in_o your_o field-book_n as_o in_o the_o forego_n example_n 2._o place_v your_o instrument_n at_o b_o and_o direct_v the_o sight_n to_o c_o the_o south_n end_n of_o the_o needle_n cut_v 279_o degree_n and_o the_o line_n bc_n contain_v 6_o chain_n 83_o link_n which_o note_v down_o in_o your_o field-book_n as_o before_o 3._o place_v the_o instrument_n at_o c_o and_o direct_v the_o sight_n to_o d_o the_o needle_n cut_v 216_o degree_n 30_o minute_n and_o the_o line_n cd_o contain_v 7_o chain_n 82_o link_n 4._o place_v the_o instrument_n at_o d_o and_o direct_v the_o sight_n to_o e_o the_o needle_z cut_v 325_o degree_n and_o the_o line_n de_fw-fr contain_v 6_o chain_n 96_o link_n 5._o place_v the_o instrument_n at_o e_o and_o direct_v the_o sight_n to_o f_o the_o needle_n cut_v 12_o degree_n 30_o minute_n and_o the_o line_n of_o contain_v 9_o chain_n 71_o link_n 6._o place_v the_o instrument_n at_o f_o and_o direct_v the_o sight_n to_o g_o the_o needle_n cut_v 342_o degree_n 30_o minute_n and_o the_o line_n fg_v contain_v 7_o chain_n 54_o link_n 7._o place_v the_o instrument_n at_o g_o and_o direct_v the_o sight_n to_o h_n the_o needle_n cut_v 98_o degree_n 30_o minute_n and_o the_o line_n gh_o contain_v 7_o chain_n 52_o link_n 8._o place_v the_o instrument_n at_o h_n and_o direct_v the_o sight_n to_o k_o the_o needle_n cut_v 71_o degree_n and_o the_o line_n hk_v contain_v 7_o chain_n 78_o link_n 9_o place_v the_o instrument_n at_o k_o and_o direct_v the_o sight_n to_o a_o where_o you_o begin_v the_o needle_n cut_v 161_o degree_n 30_o minute_n and_o the_o line_n ka_o contain_v 8_o chain_n 22_o link_n have_v go_v round_o the_o field_n in_o this_o manner_n and_o collect_v the_o degree_n cut_v and_o the_o line_n measure_v in_o the_o several_a column_n of_o your_o field_n book_n according_a to_o former_a direction_n you_o shall_v find_v they_o to_o stand_v as_o follow_v by_o which_o you_o may_v protract_v and_o draw_v the_o plot_n of_o your_o field_n as_o in_o the_o next_o chapter_n  _fw-fr degree_n minute_n chain_n link_n a_o 191_o 00_o 10_o 75_o b_o 279_o 00_o 6_o 83_o c_o 216_o 30_o 7_o 82_o d_o 325_o 00_o 6_o 96_o e_z 12_o 30_o 9_o 71_o f_o 342_o 30_o 7_o 54_o g_z 98_o 30_o 7_o 54_o h_n 71_o 00_o 7_o 78_o k_o 161_o 30_o 8_o 22_o in_o go_v about_o a_o field_n in_o this_o manner_n you_o may_v perceive_v a_o wonderful_a quick_a dispatch_n for_o you_o be_v only_o to_o take_v notice_n of_o the_o degree_n cut_v once_o at_o every_o angle_n and_o not_o to_o use_v any_o back-sight_n as_o in_o the_o before_o go_v work_n of_o the_o theodolite_a but_o to_o use_v back-sight_n with_o the_o circumferentor_n be_v best_a for_o to_o confirm_v your_o work_n for_o when_o you_o stand_v at_o any_o angle_n of_o a_o field_n and_o direct_v your_o sight_n to_o the_o next_o and_o observe_v what_o degree_n the_o south_n end_n of_o the_o needle_n cut_v if_o you_o remove_v your_o instrument_n from_o this_o angle_n to_o the_o next_o and_o look_v to_o the_o mark_n or_o angle_v where_o it_o last_o stand_v with_o your_o back-sight_n the_o needle_n will_v there_o also_o cut_v the_o same_o degree_n as_o before_o which_o ought_v to_o be_v do_v and_o may_v be_v without_o much_o loss_n of_o time_n so_o the_o instrument_n be_v place_v at_o a_o if_o you_o direct_v the_o sight_n to_o b_o you_o shall_v find_v the_o needle_n to_o cut_v 191_o degree_n then_o remove_v your_o instrument_n to_o b_o if_o you_o direct_v the_o back-sight_n to_o a_o the_o needle_n will_v then_o also_o cut_v 191_o degree_n now_o for_o dispatch_n and_o exactness_n if_o the_o needle_n be_v good_a the_o card_n well_o divide_v and_o the_o degree_n by_o a_o good_a eye_n true_o estimate_v the_o circumferentor_n for_o large_a and_o spacious_a ground_n be_v as_o good_a as_o any_o and_o therefore_o observe_v well_o the_o manner_n of_o protract_v chap._n xxxvi_o how_o to_o protract_v any_o observation_n take_v by_o the_o circumferentor_n according_a to_o the_o doctrine_n of_o the_o last_o chapter_n according_a to_o the_o largeness_n of_o your_o plot_n provide_v a_o sheet_n of_o paper_n or_o skin_n of_o parchment_n as_o lmno_n upon_o which_o draw_v the_o line_n lm_o and_o parallel_v thereto_o draw_v divers_a other_o line_n quite_o through_o the_o whole_a paper_n or_o parchment_n as_o the_o prick_a line_n in_o the_o figure_n draw_v between_o lm_o and_o no_o and_o let_v the_o distance_n of_o each_o of_o these_o parallel_v one_o from_o another_o be_v somewhat_o less_o than_o the_o breadth_n of_o the_o scale_n of_o your_o protractor_n these_o parallel_a line_n thus_o draw_v do_v represent_v meridian_n and_o be_v hereafter_o so_o call_v upon_o one_o or_o other_o of_o these_o line_n or_o parallel_n to_o one_o of_o they_o the_o meridian_n line_n of_o your_o protractor_n note_v in_o the_o figure_n thereof_o pa._n 51_o with_o of_o must_v always_o be_v lay_v when_o you_o protract_v any_o observation_n take_v by_o the_o circumferentor_n as_o in_o the_o chapter_n before_o go_v your_o paper_n or_o parchment_n be_v thus_o prepare_v assign_v any_o point_n upon_o any_o of_o the_o meridian_n as_o a_o upon_o which_o point_n place_n the_o centre_n of_o your_o protractor_n lay_v the_o meridian_n line_n thereof_o just_a upon_o the_o meridian_n line_n draw_v upon_o your_o paper_n as_o you_o see_v it_o lie_v in_o the_o figure_n annex_v then_o look_v in_o your_o field-book_n what_o degree_n the_o needle_n cut_v at_o a_o which_o be_v 191_o degree_n now_o because_o the_o degree_n be_v more_o than_o 180_o you_o must_v therefore_o lay_v the_o semicircle_n of_o the_o protractor_n downward_o and_o hold_v it_o there_o with_o your_o protract_n pin_n make_v a_o mark_n against_o 191_o degree_n through_o which_o point_n from_o a_o draw_v the_o line_n ab_fw-la which_o contain_v 10_o chain_n 75_o link_n 2._o lay_v the_o centre_n of_o the_o protractor_n on_o the_o point_n b_o with_o the_o meridian_n line_n thereof_o parallel_v to_o one_o of_o the_o prick_v meridian_n draw_v upon_o the_o paper_n and_o see_v the_o degree_n cut_v at_o b_o be_v more_o than_o 180_o viz._n 279_o therefore_o the_o semicircle_n must_v lie_v downward_o and_o so_o hold_v it_o make_v a_o mark_n against_o 279_o degree_n
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 imagine_v suppose_v therefore_o that_o the_o follow_a figure_n almnpqstyxgh_n and_o k_o be_v part_n of_o a_o manor_n or_o divers_a parcel_n of_o land_n lie_v together_o and_o that_o it_o be_v require_v to_o take_v the_o plot_n thereof_o upon_o your_o plain_a table_n now_o the_o best_a way_n in_o my_o opinion_n be_v first_o to_o go_v round_o about_o the_o whole_a quantity_n to_o be_v measure_v and_o draw_v upon_o your_o table_n a_o perfect_a plot_n thereof_o as_o if_o it_o be_v one_o entire_a field_n which_o you_o may_v do_v by_o the_o 31_o chap._n of_o this_o book_n and_o then_o to_o make_v separation_n and_o division_n thereof_o in_o a_o orderly_a way_n as_o be_v teach_v in_o this_o chapter_n but_o before_o you_o begin_v your_o work_n it_o will_v be_v very_o necessary_a to_o ride_v or_o walk_v about_o the_o whole_a manor_n or_o at_o least_o so_o much_o as_o you_o be_v to_o survey_v that_o you_o may_v be_v the_o better_o acquaint_v with_o the_o several_a bounder_n and_o in_o your_o 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 suppose_v to_o contain_v 8_o chain_n 68_o link_n take_v these_o 8_o chain_n 68_o link_n from_o any_o scale_n and_o place_v that_o length_n upon_o your_o table_n from_o a_o to_o l._n 3._o remove_v your_o table_n to_o m_n and_o lay_v the_o index_n upon_o the_o line_n ml_o turn_v the_o table_n about_o till_o through_o the_o sight_n you_o espy_v a_o mark_n set_v up_o at_o the_o angle_n l_o where_o your_o table_n last_o stand_v and_o there_o fix_v it_o you_o shall_v still_o find_v the_o needle_n to_o hang_v direct_o over_o the_o meridian_n line_n if_o you_o proceed_v true_o in_o your_o work_n then_o lay_v the_o index_n to_o the_o point_n m_o turn_v it_o about_o till_o through_o the_o sight_n you_o espy_v some_o mark_n set_v up_o at_o the_o next_o angle_n at_o n_n and_o draw_v a_o line_n by_o the_o side_n of_o the_o index_n then_o measure_v with_o your_o chain_n from_o m_n to_o n_n you_o shall_v find_v it_o to_o contain_v 7_o chain_n 27_o link_n which_o take_v from_o the_o same_o scale_n 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 length_n of_o every_o line_n upon_o your_o table_n as_o you_o find_v it_o by_o measure_v with_o your_o chain_n you_o shall_v have_v upon_o your_o table_n the_o figure_n of_o one_o large_a plain_a which_o must_v include_v all_o the_o rest_n of_o the_o work_n and_o in_o thus_o go_v about_o you_o shall_v if_o you_o have_v true_o wrought_v all_o the_o way_n find_v your_o plot_n to_o close_v exact_o in_o the_o point_n a_o where_o you_o begin_v but_o if_o it_o do_v not_o go_v over_o your_o work_n again_o for_o otherwise_o all_o that_o you_o do_v afterward_o within_o the_o same_o will_v be_v false_a ¶_o here_o note_n that_o if_o one_o sheet_n of_o paper_n will_v not_o contain_v your_o whole_a plot_n you_o must_v then_o shift_v your_o paper_n in_o this_o manner_n when_o any_o line_n fall_v off_o of_o your_o table_n draw_v two_o line_n at_o right_a angle_n across_o your_o paper_n which_o the_o equal_a division_n on_o the_o frame_n will_v help_v you_o to_o do_v then_o lay_v another_o clean_a sheet_n of_o paper_n upon_o your_o table_n and_o by_o the_o same_o parallel_a division_n at_o the_o contrary_a end_n of_o the_o table_n draw_v two_o other_o line_n at_o right_a angle_n and_o upon_o they_o note_v what_o part_n of_o your_o plot_n cross_v the_o two_o other_o line_n before_o draw_v and_o at_o those_o point_n begin_v to_o go_v forward_o with_o the_o rest_n of_o your_o work_n and_o thus_o may_v you_o shift_v divers_a paper_n one_o after_o another_o if_o need_v be_v have_v thus_o draw_v the_o true_a plot_n of_o the_o outward_a bound_n or_o peripherie_n of_o the_o whole_a manor_n upon_o your_o table_n as_o the_o figure_n almnpqstyxgh_n and_o k_o and_o exact_o close_v your_o plot_n at_o a_o where_o you_o begin_v you_o may_v proceed_v now_o to_o lay_v out_o the_o several_a close_n therein_o contain_v in_o this_o manner_n 1._o place_v your_o table_n at_o a_o lay_v the_o index_n and_o sight_n upon_o the_o line_n all_o before_o draw_v and_o turn_v it_o about_o till_o through_o the_o sight_n you_o espy_v the_o angle_n l_o and_o there_o fix_v it_o the_o needle_n will_v hang_v direct_o over_o the_o meridian_n line_n in_o the_o card_n then_o turn_v the_o index_n about_o upon_o the_o point_n a_o till_o through_o the_o sight_n you_o espy_v a_o mark_n set_v up_o at_o the_o angle_n b_o and_o by_o the_o side_n of_o the_o index_n draw_v the_o line_n ab_fw-la contain_v 6_o chain_n 43_o link_n 2._o remove_v the_o table_n to_o b_o lay_v the_o index_n on_o the_o line_n basilius_n and_o turn_v the_o table_n about_o till_o through_o the_o sight_n you_o see_v the_o angle_n a_o then_o fix_v it_o and_o turn_v the_o index_n about_o upon_o b_o till_o you_o see_v the_o next_o
the_o angular_a point_n as_o in_o this_o figure_n when_o we_o say_v the_o angle_n abc_n you_o be_v to_o understand_v the_o very_a point_n at_o b_o and_o note_v also_o that_o the_o length_n of_o the_o side_n contain_v any_o angle_n as_o the_o side_n ab_fw-la and_z bc_n do_v not_o make_v the_o angle_n abc_n either_o great_a or_o lesser_a but_o the_o angle_n still_o retain_v the_o same_o quantity_n be_v the_o contain_v side_n thereof_o either_o long_o or_o short_a 9_o and_o if_o the_o line_n which_o contain_v the_o angle_n be_v right_a line_n then_o be_v it_o call_v a_o right_n line_v angle_n so_o the_o angle_n abc_n be_v a_o right_n line_v angle_n because_o the_o line_n ab_fw-la and_z bc_n which_o contain_v the_o say_a angle_n be_v right_a line_n and_o of_o right_n line_v angle_n there_o be_v three_o sort_n who_o definition_n follow_v 10._o when_o a_o right_a line_n stand_v upon_o a_o right_a line_n make_v the_o angle_n on_o either_o side_n equal_a then_o either_o of_o those_o angle_n be_v a_o right_a angle_n and_o the_o right_a line_n which_o stand_v erect_v be_v call_v a_o perpendicular_a line_n to_o that_o whereon_o it_o stand_v as_o upon_o the_o right_a line_n cd_o suppose_v there_o do_v stand_v another_o right_a line_n ab_fw-la in_o such_o sort_n that_o it_o make_v the_o angle_n on_o either_o side_n thereof_o equal_a namely_o the_o angle_n abdella_n on_o the_o one_o side_n equal_a to_o the_o angle_n abc_n on_o the_o other_o side_n then_o be_v either_o of_o the_o two_o angle_n abc_n and_o abdella_n right_a angle_n and_o the_o right_a line_n ab_fw-la which_o stand_v erect_v upon_o the_o right_a line_n cd_o without_o incline_v to_o either_o part_n thereof_o be_v a_o perpendicular_a to_o the_o line_n cd_o 11._o a_o obtuse_a angle_n be_v that_o which_o be_v great_a than_o a_o right_a angle_n so_o the_o angle_n cbe_n be_v a_o obtuse_a angle_n because_o it_o be_v great_a than_o the_o angle_n abc_n which_o be_v a_o right_a angle_n for_o it_o do_v not_o only_o contain_v that_o right_a angle_n but_o the_o angle_n abe_n also_o and_o therefore_o be_v obtuse_a 12._o a_o acute_a angle_n be_v less_o than_o a_o right_a angle_n so_o the_o angle_n ebb_v be_v a_o acute_a angle_n for_o it_o be_v less_o than_o the_o right_a angle_n abdella_n in_o which_o it_o be_v contain_v by_o the_o other_o acute_a angle_n abe_n 13._o a_o limit_n or_o term_n be_v the_o end_n of_o every_o thing_n as_o a_o point_n be_v the_o limit_n or_o term_v of_o a_o line_n because_o it_o be_v the_o end_n thereof_o so_o a_o line_n likewise_o be_v the_o limit_n and_o term_v of_o a_o superficies_n and_o a_o superficies_n be_v the_o limit_n and_o term_v of_o a_o body_n 14._o a_o figure_n be_v that_o which_o be_v contain_v under_o one_o limit_n or_o term_n or_o many_o as_o the_o figure_n a_o be_v contain_v under_o one_o limit_n or_o term_n which_o be_v the_o round_a line_n also_o the_o figure_n b_o be_v contain_v under_o three_o right_a line_n which_o be_v the_o limit_n or_o term_n thereof_o likewise_o the_o figure_n c_o be_v contain_v under_o four_o right_a line_n the_o figure_n e_o under_o five_o right_a line_n and_o so_o of_o all_o other_o figure_n ¶_o and_o here_o note_n that_o in_o the_o follow_a work_n we_o call_v any_o plain_a superficies_n who_o side_n be_v unequal_a as_o the_o figure_n e_z a_o plot_n as_o of_o a_o field_n wood_n park_n forrest_n and_o the_o like_a 15._o a_o circle_n be_v a_o plain_a figure_n contain_v under_o one_o line_n which_o be_v call_v a_o circumference_n unto_o which_o all_o line_n draw_v from_o one_o point_n within_o the_o figure_n and_o fall_v upon_o the_o circumference_n thereof_o be_v equal_a one_o to_o the_o other_o as_o the_o figure_n abcde_v be_v a_o circle_n contain_v under_o the_o crooked_a line_n bcde_v which_o line_n be_v call_v the_o circumference_n in_o the_o middle_n of_o this_o figure_n be_v a_o point_n a_o from_o which_o point_n all_o line_n draw_v to_o the_o circumference_n thereof_o be_v equal_a as_o the_o line_n ab_fw-la ac_fw-la of_o ad_fw-la and_o this_o point_n a_o be_v call_v the_o centre_n of_o the_o circle_n 16._o a_o diameter_n of_o a_o circle_n be_v a_o right_a line_n draw_v by_o the_o centre_n thereof_o and_o end_v at_o the_o circumference_n on_o either_o side_n divide_v the_o circle_n into_o two_o equal_a part_n so_o the_o line_n bid_v in_o the_o former_a figure_n be_v the_o diameter_n thereof_o because_o it_o pass_v from_o the_o point_n b_o on_o the_o one_o side_n of_o the_o circumference_n to_o the_o point_n d_o on_o the_o other_o side_n of_o the_o circumference_n and_o pass_v also_o by_o the_o point_n a_o which_o be_v the_o centre_n of_o the_o circle_n and_o moreover_o it_o divide_v the_o circle_n into_o two_o equal_a part_n namely_o bcd_v be_v on_o one_o side_n of_o the_o diameter_n equal_a to_o bed_n on_o the_o other_o side_n of_o the_o diameter_n and_o this_o observation_n be_v first_o make_v by_o thales_n miletius_n for_o say_v he_o if_o a_o line_n draw_v by_o the_o centre_n of_o any_o circle_n do_v not_o divide_v it_o equal_o all_o the_o line_n draw_v from_o the_o centre_n of_o that_o circle_n to_o the_o circumference_n can_v be_v equal_a 17._o a_o semicircle_n be_v a_o figure_n contain_v under_o the_o diameter_n and_o that_o part_n of_o the_o circumference_n cut_v off_o by_o the_o diameter_n as_o in_o the_o former_a circle_n the_o figure_n bed_n be_v a_o semicircle_n because_o it_o be_v contain_v of_o the_o right_a line_n bad_a which_o be_v the_o diameter_n and_o of_o the_o crooked_a line_n bed_n be_v that_o part_n of_o the_o circumference_n which_o be_v cut_v off_o by_o the_o diameter_n also_o the_o part_n bcd_n be_v a_o semicircle_n 18._o a_o section_n or_o portion_n of_o a_o circle_n be_v a_o figure_n contain_v under_o a_o right_a line_n and_o a_o part_n of_o the_o circumference_n great_a or_o less_o than_o a_o semicircle_n so_o the_o figure_n abc_n which_o consist_v of_o the_o part_n of_o the_o circumference_n abc_n and_o the_o right_a line_n ac_fw-la be_v a_o section_n or_o portion_n of_o a_o circle_n great_a than_o a_o semicircle_n also_o the_o other_o figure_n acd_v which_o be_v contain_v under_o the_o right_a line_n ac_fw-la and_o the_o part_n of_o the_o circumference_n adc_n be_v a_o section_n of_o a_o circle_n less_o than_o a_o semicircle_n ¶_o and_o here_o note_n that_o by_o a_o section_n segment_n portion_n or_o part_n of_o a_o circle_n be_v mean_v the_o same_o thing_n and_o signify_v such_o a_o part_n as_o be_v either_o great_a or_o lesser_a than_o a_o semicircle_n so_o that_o a_o semicircle_n can_v proper_o be_v call_v a_o section_n segment_n or_o part_n of_o a_o circle_n 19_o right_o line_v figure_n be_v such_o as_o be_v contain_v under_o right_a line_n  _fw-fr 20._o three_o side_v figure_n be_v such_o as_o be_v contain_v under_o three_o right_a line_n  _fw-fr 21._o four_o side_v figure_n be_v such_o as_o be_v contain_v under_o four_o right_a line_n  _fw-fr 22._o many_o side_v figure_n be_v such_o as_o have_v more_o side_n than_o four_o  _fw-fr 23._o all_o three_o side_v figure_n be_v call_v triangle_n and_o such_o be_v the_o triangle_n bcd_v 24._o of_o four_o side_v figure_n a_o quadrat_fw-la or_o square_n be_v that_o who_o side_n be_v equal_a and_o his_o angle_n right_a as_o the_o figure_n a._n 25._o a_o long_a square_n be_v that_o which_o have_v right_a angle_n but_o unequal_a side_n as_o the_o figure_n b_o 26._o a_o rhombus_fw-la be_v a_o figure_n have_v four_o equal_a side_n but_o not_o right_a angle_n as_o the_o figure_n c._n 27._o a_o rhomboide_n be_v a_o figure_n who_o opposite_a side_n be_v equal_a and_o who_o opposite_a angle_n be_v also_o equal_a but_o it_o have_v neither_o equal_a side_n nor_o equal_a angle_n as_o the_o figure_n d._n 28._o all_o other_o figure_n of_o four_o side_n beside_o these_o be_v call_v trapezias_n such_o be_v all_o figure_n of_o four_o side_n in_o which_o be_v observe_v no_o equality_n of_o side_n or_o angle_n as_o the_o figure_n a_o and_o b_o which_o have_v neither_o equal_a side_n nor_o equal_a angle_n but_o be_v describe_v by_o all_o adventure_n without_o the_o observation_n of_o any_o order_n 29._o parallel_n or_o equidistant_a right_a line_n be_v such_o which_o be_v in_o one_o and_o the_o same_o superficies_n and_o produce_v infinite_o on_o both_o side_n do_v never_o in_o any_o part_n concur_v as_o the_o right_a line_n ab_fw-la and_o cd_o be_v parallel_n one_o to_o the_o other_o and_o if_o they_o be_v infinite_o extend_v on_o either_o side_n will_v never_o meet_v or_o concur_v together_o but_o still_o retain_v the_o same_o distance_n geometrical_a theorem_n 1._o any_o two_o right_a line_n cross_v one_o another_o make_v the_o contrary_a or_o vertical_a angle_n
colour_n you_o must_v always_o work_v with_o one_o end_n of_o the_o chain_n from_o you_o this_o chain_n be_v thus_o divide_v and_o mark_v you_o have_v every_o whole_a pole_n equal_a to_o ten_o prime_n or_o 100_o second_o every_o three_o quarter_n of_o a_o pole_n equal_a to_o seven_o prime_n and_o a_o half_a or_o 75_o second_o every_o half_a pole_n equal_a to_o five_o prime_n or_o 50_o second_o and_o last_o every_o quarter_n of_o a_o pole_n equal_a to_o two_o prime_n and_o a_o half_a or_o 25_o second_o and_o here_o be_v to_o be_v note_v that_o in_o the_o ordinary_a use_n of_o this_o chain_n for_o measure_v and_o plat_v you_o need_v take_v notice_n only_o of_o unite_v and_o prime_n which_o be_v exact_a enough_o for_o ordinary_a use_n but_o in_o case_n that_o separation_n or_o division_n of_o land_n into_o several_a part_n you_o may_v make_v use_n of_o second_o of_o mr._n gunter_n chain_n as_o every_o pole_n of_o master_n rathborn_v chain_n be_v divide_v into_o 100_o link_n so_o master_n gunter'_v whole_a chain_n which_o be_v always_o make_v to_o contain_v four_o pole_n be_v divide_v into_o 100_o link_n one_o of_o these_o link_n be_v four_o time_n the_o length_n of_o the_o other_o now_o if_o this_o chain_n be_v make_v according_a to_o the_o statute_n each_o perch_n to_o contain_v 16½_n foot_n than_o each_o link_n of_o this_o chain_n will_v contain_v 7_o inch_n and_o 92_o 100_o of_o a_o inch_n and_o the_o whole_a chain_n 729_o inch_n or_o 66_o foot_n in_o measure_v with_o this_o chain_n you_o be_v to_o take_v notice_n only_o of_o chain_n and_o link_n as_o say_v such_o a_o line_n measure_v by_o the_o chain_n contain_v 72_o chain_n 48_o link_n which_o you_o may_v express_v more_o brief_o thus_o 72,48_o and_o these_o be_v all_o the_o denomination_n which_o be_v necessary_a to_o be_v take_v notice_n of_o in_o survey_v of_o land_n for_o the_o ready_a count_v of_o the_o link_n of_o this_o chain_n there_o ought_v to_o be_v these_o distinction_n namely_o in_o the_o middle_n thereof_o which_o be_v at_o two_o pole_n end_n let_v there_o be_v hang_v a_o large_a ring_n or_o rather_o a_o plate_n of_o brass_n like_o a_o rhombus_fw-la so_o be_v the_o whole_a chain_n by_o this_o plate_n divide_v into_o two_o equal_a part_n second_o let_v each_o of_o these_o two_o part_n be_v divide_v into_o two_o other_o equal_a part_n by_o small_a ring_n or_o circular_a plate_n of_o brass_n so_o shall_v the_o whole_a chain_n be_v divide_v into_o four_o equal_a part_n or_o perch_n each_o perch_n contain_v 25_o link_n three_o at_o every_o ten_o link_n let_v be_v fasten_v a_o lesser_a ring_n than_o the_o former_a or_o else_o a_o plate_n of_o some_o other_o fashion_n as_o a_o semicircle_n or_o the_o like_a and_o last_o at_o every_o five_o link_n if_o you_o please_v may_v be_v fasten_v other_o mark_n so_o by_o this_o mean_v you_o shall_v most_o easy_o and_o exact_o count_v the_o link_n of_o your_o chain_n without_o any_o trouble_n the_o chain_n be_v thus_o distinguish_v it_o matter_v not_o which_o end_n thereof_o be_v carry_v forward_o because_o the_o note_n of_o distinction_n proceed_v alike_o on_o both_o side_n from_o the_o middle_n of_o the_o chain_n ¶_o here_o note_n that_o in_o all_o the_o example_n in_o this_o book_n the_o line_n be_v suppose_v to_o be_v measure_v by_o this_o four_o pole_n chain_n of_o master_n gunter_n it_o be_v the_o best_a of_o any_o other_o the_o manner_n how_o to_o cast_v up_o the_o content_a of_o any_o plot_n measure_v therewith_o shall_v be_v hereafter_o teach_v in_o its_o due_a place_n caution_n to_o be_v observe_v in_o the_o use_n of_o any_o chain_n in_o measure_v a_o large_a distance_n with_o your_o chain_n you_o may_v casual_o mistake_v or_o miss_v a_o chain_n or_o two_o in_o keep_v your_o account_n from_o whence_o will_v ensue_v a_o considerable_a error_n also_o in_o measure_v of_o distance_n when_o you_o go_v not_o along_o by_o a_o hedge_n side_n you_o can_v hardly_o keep_v your_o instrument_n chain_n and_o mark_v in_o a_o right_a line_n which_o if_o you_o do_v not_o you_o must_v necessary_o make_v your_o measure_a distance_n great_a than_o in_o reality_n it_o be_v for_o the_o avoid_n of_o either_o of_o these_o mistake_n you_o ought_v to_o provide_v ten_o small_a stick_n or_o arrow_n which_o let_v he_o that_o lead_v the_o chain_n carry_v in_o his_o hand_n before_o and_o at_o the_o end_n of_o every_o chain_n stick_v one_o of_o these_o arrow_n into_o the_o ground_n which_o let_v he_o that_o follow_v the_o chain_n take_v up_o so_o go_v on_o till_o the_o whole_a number_n of_o arrow_n be_v spend_v and_o then_o you_o may_v conclude_v that_o you_o have_v measure_v ten_o chain_n without_o any_o further_a trouble_n and_o these_o ten_o chain_n if_o the_o distance_n you_o be_v to_o measure_n be_v large_a you_o may_v call_v a_o change_n and_o so_o you_o may_v denominate_v every_o large_a distance_n by_o change_n chain_n and_o link_n or_o you_o may_v at_o the_o end_n of_o every_o ten_o chain_n set_v up_o another_o kind_n of_o stick_n by_o which_o stand_v at_o the_o instrument_n you_o may_v see_v whether_o your_o eye_n the_o stick_n and_o the_o mark_n to_o which_o you_o be_v to_o measure_n be_v in_o a_o right_a line_n or_o not_o and_o according_o guide_v those_o that_o carry_v the_o chain_n with_o the_o more_o exactness_n to_o direct_v it_o to_o the_o mark_v intend_v how_o to_o reduce_v any_o number_n of_o chain_n and_o link_n into_o foot_n in_o the_o practice_n of_o many_o geometrical_a conclusion_n as_o in_o the_o take_n of_o height_n and_o distance_n hereafter_o teach_v it_o be_v requisite_a to_o give_v your_o measure_n in_o such_o case_n in_o foot_n or_o yard_n and_o not_o in_o pole_n or_o perch_n yet_o because_o your_o chain_n be_v the_o most_o necessary_a instrument_n to_o measure_v withal_o i_o think_v it_o convenient_a in_o this_o place_n to_o show_v you_o how_o to_o reduce_v any_o number_n of_o chain_n and_o link_n into_o foot_n which_o be_v thus_o multiply_v your_o number_n of_o chain_n and_o link_n together_o as_o one_o whole_a number_n by_o 66_o cut_v off_o from_o the_o product_n the_o two_o last_o figure_n towards_o the_o right_a hand_n so_o shall_v the_o rest_n of_o the_o product_n be_v foot_n and_o the_o two_o figure_n cut_v off_o shall_v be_v hundred_o part_n of_o a_o foot_n example_n let_v it_o be_v require_v to_o know_v how_o many_o foot_n be_v contain_v in_o 5_o chain_n 32_o link_n first_o set_v down_o your_o 5_o chain_n 32_o link_n as_o be_v before_o teach_v and_o as_o you_o see_v in_o the_o first_o example_n with_o a_o comma_n between_o the_o chain_n and_o link_n then_o multiply_v this_o 5_o chain_n 32_o link_n by_o 66_o the_o product_n will_v be_v 35112_o from_o which_o cut_v off_o the_o two_o last_o figure_n towards_o the_o right_a hand_n with_o a_o comma_n then_o will_v the_o number_n be_v 351,12_o which_o be_v 351_o foot_n and_o 12_o 100_o part_n of_o a_o foot_n and_o so_o many_o foot_n be_v contain_v in_o 5_o chain_n 32_o link_n example_n i._n 5,32_o 66_o 3192_o 3192_o 351,12_o example_n ii_o 9,05_o 66_o 5430_o 5430_o 597,30_o but_o let_v the_o number_n of_o chain_n be_v what_o they_o will_v if_o the_o number_n of_o link_n be_v less_o than_o 10_o as_o in_o the_o second_o example_n it_o be_v 9_o chain_n 5_o link_n you_o must_v place_v a_o cypher_n before_o the_o five_o link_n as_o there_o you_o see_v and_o then_o multiply_v that_o number_n viz._n 9,05_o by_o 66_o the_o product_n will_v be_v 59730_o from_o which_o take_v the_o two_o last_o figure_n there_o will_v remain_v 597_o foot_n and_o â—…_n 100_o part_n of_o a_o foot_n the_o like_a may_v be_v do_v for_o any_o other_o number_n of_o chain_n and_o link_n whatsoever_o according_a to_o these_o example_n be_v make_v the_o table_n follow_v which_o show_v how_o many_o foot_n be_v contain_v in_o any_o number_n of_o chain_n and_o link_n from_o 5_o link_n to_o 10_o chain_n for_o every_o five_o link_n which_o be_v sufficient_a for_o ordinary_a use_n by_o which_o table_n you_o may_v see_v that_o in_o 6_o chain_n 40_o link_n be_v contain_v 422_o foot_n and_o 40_o 100_o of_o a_o foot_n also_o in_o 5_o chain_n 55_o link_n be_v contain_v 366_o foot_n and_o 30_o 100_o part_n of_o a_o foot_n and_o so_o of_o any_o other_o a_o table_n show_v how_o many_o foot_n and_o part_n of_o a_o foot_n be_v contain_v in_o any_o number_n of_o chain_n and_o link_n between_o five_o link_n and_o eight_o chain_n  _fw-fr 0_o 1_o 2_o 3_o 4_o 5_o 6_o 7_o 0_o  _fw-fr 66,00_o 132,00_o 198,00_o 264,00_o 330,00_o 396,00_o 462,00_o 5_o 3,30_o 69,30_o 135,30_o 201,30_o 267,30_o 333,30_o 399,30_o 465,30_o 10_o 6,60_o 72,60_o 138,60_o 204,60_o 270,60_o 336,60_o 402,60_o
through_o the_o sight_n and_o then_o by_o some_o know_a sign_n or_o sound_n cause_v he_o to_o take_v notice_n what_o number_n of_o foot_n inch_n and_o part_n of_o a_o inch_n be_v cut_v by_o the_o say_a paper_n which_o will_v he_o also_o to_o keep_v in_o mind_n or_o note_n in_o a_o paper_n as_o your_o first_o assistant_n do_v this_o do_v require_v your_o first_o assistant_n to_o bring_v his_o station_n staff_n from_o the_o spring_n head_n and_o cause_v your_o second_o assistant_n to_o take_v that_o staff_n and_o carry_v it_o forward_o towards_o the_o place_n to_o which_o the_o water_n be_v to_o be_v convey_v 30_o 40_o 60_o or_o 100_o yard_n and_o there_o to_o erect_v it_o perpendicular_a as_o before_o let_v your_o first_o assistant_n stand_v at_o that_o staff_n where_o your_o second_o assistant_n before_o stand_v then_o in_o the_o mid_a way_n between_o your_o two_o assistant_n place_v your_o water-levell_a exact_o horizontall_a and_o look_v through_o the_o sight_n thereof_o cause_n your_o first_o assistant_n to_o move_v a_o paper_n up_o and_o down_o and_o when_o you_o give_v he_o a_o sign_n to_o note_v what_o number_n of_o foot_n inch_n and_o part_n of_o a_o inch_n be_v cut_v by_o the_o paper_n and_o note_v they_o down_o then_o go_v to_o the_o other_o end_n of_o your_o water-levell_a look_v through_o the_o sight_n and_o cause_v your_o second_o assistant_n to_o move_v a_o paper_n along_o the_o staff_n and_o to_o note_v the_o foot_n inch_n and_o part_n of_o a_o inch_n as_o before_o then_o cause_n your_o first_o assistant_n to_o bring_v away_o his_o station-staffe_n and_o cause_v your_o second_o assistant_n to_o take_v it_o and_o carry_v it_o 30_o 40_o 60_o or_o 100_o yard_n forward_a towards_o the_o place_n to_o which_o the_o water_n be_v to_o be_v convey_v and_o leave_v your_o first_o assistant_n at_o the_o place_n where_o your_o second_o assistant_n last_o stand_v place_v your_o water-levell_a again_o in_o the_o mid_a way_n between_o your_o two_o assistant_n and_o look_v through_o the_o sight_n as_o before_o cause_n each_o of_o they_o to_o move_v a_o leaf_n of_o paper_n up_o and_o down_o their_o station_n staff_n and_o note_v down_o in_o their_o several_a paper_n the_o number_n of_o foot_n inch_n and_o part_n of_o a_o inch_n cut_v when_o you_o look_v through_o the_o sight_n of_o your_o water-levell_n in_o this_o manner_n you_o must_v go_v along_o from_o the_o spring_n head_n to_o the_o place_n unto_o which_o you_o will_v have_v the_o water_n convey_v and_o if_o there_o be_v never_o so_o many_o several_a station_n you_o must_v in_o all_o of_o they_o observe_v this_o manner_n of_o work_n precise_o so_o by_o compare_v the_o note_n of_o your_o two_o assistant_n together_o you_o may_v easy_o know_v whether_o the_o water_n may_v be_v convey_v from_o the_o spring_n head_n to_o the_o desire_a place_n or_o not_o ¶_o here_o note_n that_o in_o your_o passage_n between_o the_o spring_n head_n and_o the_o appoint_a place_n from_o station_n to_o station_n you_o must_v observe_v this_o order_n otherwise_o great_a error_n will_v ensue_v viz._n that_o your_o first_o assistant_n must_v at_o every_o station_n stand_v between_o the_o spring_n head_n and_o your_o water-levell_a and_o your_o second_o assistant_n must_v always_o stand_v between_o your_o water-levell_a and_o the_o place_n to_o which_o the_o water_n be_v to_o be_v convey_v thus_o by_o observe_v this_o order_n in_o your_o work_n you_o shall_v have_v no_o confusion_n neither_o shall_v one_o of_o your_o assistant_n take_v more_o pain_n than_o the_o other_o have_v thus_o orderly_o proceed_v from_o the_o spring_n head_n to_o the_o place_n appoint_v call_v both_o your_o assistant_n together_o and_o cause_v they_o to_o give_v in_o their_o note_n of_o the_o observation_n at_o each_o station_n and_o add_v they_o together_o several_o then_o if_o the_o note_n of_o the_o second_o assistant_n exceed_v or_o be_v great_a than_o the_o note_n of_o the_o first_o assistant_n take_v the_o lesser_a out_o of_o the_o great_a and_o the_o remainder_n will_v show_v you_o how_o much_o the_o appoint_a place_n to_o which_o the_o water_n be_v to_o be_v bring_v be_v low_a than_o the_o spring_n head_n the_o first_o assistant_n note_v station_n foot_n inch_n part_n 1_o 15_o 3_o ½_n 2_o 2_o 1_o ¼_n 3_o 1_o 6_o 0_o sum_n 18_o 10_o ¾_n the_o second_o assistant_n note_v station_n foot_n inch_n part_n 1_o 3_o 2_o ¾_n 2_o 14_o 0_o ¼_n 3_o 3_o 11_o 0_o sum_n 21_o 2_o 0_o by_o this_o table_n you_o may_v perceive_v that_o the_o note_n of_o the_o first_o assistant_n collect_v at_o his_o several_a station_n be_v add_v together_o amount_v to_o 18_o foot_n 10_o inch_n and_o ¾_n of_o a_o inch_n and_o the_o note_n of_o your_o second_o assistant_n at_o his_o several_a station_n be_v add_v together_o amount_v to_o 21_o foot_n and_o 2_o inch_n so_o the_o number_n of_o the_o first_o assistant_n observation_n be_v take_v from_o the_o number_n of_o the_o second_o there_o will_v remain_v 2_o foot_n 3_o inch_n and_o ¼_n of_o a_o inch_n and_o so_o much_o be_v the_o place_n to_o which_o the_o water_n be_v to_o be_v bring_v low_o than_o the_o spring_n head_n according_a to_o the_o straight_a water-levell_a and_o therefore_o the_o water_n may_v easy_o be_v convey_v thither_o ¶_o here_o note_n that_o when_o you_o have_v call_v your_o two_o assistant_n together_o and_o examine_v their_o several_a note_n and_o add_v they_o together_o if_o then_o you_o shall_v find_v the_o sum_n of_o your_o first_o assistant_n note_v to_o be_v great_a than_o the_o sum_n of_o your_o second_o assistant_n note_v that_o then_o it_o be_v impossible_a to_o bring_v the_o water_n from_o that_o spring_n head_n to_o the_o intend_a place_n but_o if_o the_o sum_n of_o the_o note_n of_o your_o two_o assistant_n do_v exact_o agree_v there_o be_v then_o a_o possibility_n of_o effect_v it_o if_o the_o distance_n be_v but_o short_a though_o with_o more_o charge_n and_o difficulty_n ¶_o note_v 2_o that_o the_o most_o approve_a author_n concern_v this_o particular_a do_v aver_v that_o at_o every_o mile_n end_v there_o ought_v to_o be_v allow_v 4½_n inch_n more_o than_o the_o straight_a level_n for_o the_o current_n of_o the_o water_n ¶_o note_v 3_o if_o there_o be_v any_o hill_n lie_v in_o the_o way_n between_o the_o spring_n head_n and_o the_o place_n to_o which_o the_o water_n be_v to_o be_v convey_v you_o must_v then_o cut_v a_o trench_n by_o the_o side_n of_o the_o hill_n in_o which_o you_o must_v lay_v your_o pipe_n equal_a with_o the_o straight_a water_n level_v with_o the_o former_a allowance_n and_o in_o case_n there_o be_v a_o valley_n you_o must_v then_o make_v a_o trunk_n of_o strong_a wood_n well_o underproped_n with_o strong_a piece_n of_o timber_n and_o well_o pitch_v or_o lead_v as_o be_v do_v in_o diverse_a place_n between_o ware_n and_o london_n ¶_o note_v 4_o that_o in_o your_o convey_n of_o water_n to_o a_o appoint_a place_n it_o be_v not_o convenient_a to_o bring_v it_o from_o the_o spring_n head_n by_o the_o near_a distance_n or_o in_o a_o straight_a line_n but_o by_o a_o crooked_a or_o wind_a way_n and_o you_o ought_v also_o to_o lay_v the_o pipe_v one_o up_o and_o another_o down_o but_o this_o be_v to_o be_v observe_v but_o in_o some_o case_n only_o where_o the_o water_n will_v have_v too_o violent_a a_o current_n another_o way_n there_o be_v another_o way_n whereby_o you_o may_v know_v whether_o water_n will_v be_v bring_v to_o any_o place_n or_o not_o which_o in_o very_o large_a distance_n ought_v to_o be_v consider_v take_v the_o distance_n between_o the_o spring_n head_n and_o the_o place_n to_o which_o the_o water_n be_v to_o be_v bring_v which_o multiply_v in_o itself_o add_v the_o product_n thereof_o to_o the_o square_n of_o the_o earth_n semidiameter_n viz._n to_o the_o square_n of_o 3436_o 4_o 11_o italian_a mile_n than_o out_o of_o the_o product_n thereof_o extract_v the_o square_a root_n and_o then_o from_o that_o square_a root_n take_v 3436_o 4_o 11_o mile_n the_o remainder_n be_v the_o difference_n between_o the_o line_n of_o level_n and_o the_o water_n or_o circular_a level_n thus_o have_v i_o finish_v my_o intend_a discourse_n of_o survey_v of_o land_n in_o which_o i_o have_v study_v rather_o to_o make_v every_o particular_a therein_o contain_v plain_a and_o perspicuous_a to_o the_o mean_a capacity_n then_o with_o too_o much_o brevity_n to_o obscure_v that_o which_o i_o chief_o aim_v at_o namely_o to_o instruct_v the_o ignorant_a i_o confess_v i_o may_v be_v just_o blame_v by_o those_o who_o be_v master_n of_o the_o art_n or_o have_v a_o considerable_a knowledge_n thereof_o already_o for_o use_v too_o many_o circumlocution_n but_o i_o answer_v it_o be_v not_o write_v for_o their_o sake_n yet_o i_o hope_v it_o will_v not_o be_v reject_v by_o they_o and_o although_o i_o do_v not_o attempt_v to_o teach_v such_o more_o than_o they_o know_v already_o yet_o possible_o they_o may_v herein_o find_v something_o worth_a their_o perusal_n and_o practice_n or_o at_o least_o it_o may_v be_v a_o remembrancer_n unto_o they_o to_o bring_v to_o mind_n what_o otherwise_o they_o may_v have_v forget_v but_o cease_v to_o apologise_v any_o more_o for_o my_o book_n let_v it_o now_o speak_v for_o itself_o finis_fw-la