imply_v that_o the_o figure_n i_o speak_v of_o be_v in_o that_o very_a page_n and_o so_o it_o be_v in_o my_o copy_n but_o the_o printer_n and_o graver_n have_v otherwise_o contrive_v they_o for_o convenience_n in_o copper_n cut_v by_o themselves_o and_o to_o give_v they_o their_o due_a they_o be_v general_o do_v with_o great_a accuracy_n and_o none_o of_o they_o have_v any_o such_o error_n as_o be_v like_a to_o beget_v trouble_n or_o mistake_v to_o the_o reader_n save_v only_o that_o fig._n 19_o have_v d_o instead_o of_o o_o at_o the_o centre_n and_o the_o line_n ol_n in_o the_o margin_n of_o fig._n 14._o shall_v be_v of_o the_o length_n from_o l_o to_o the_o uppermost_a o_fw-mi in_o the_o scale_n and_o the_o figure_n on_o the_o side_n shall_v be_v make_v 1_o less_o than_o they_o be_v viz._n 2_o shall_v be_v 1_o 3_o made_z 2_o etc._n etc._n and_o last_o as_o to_o the_o errata_fw-la though_o i_o have_v not_o be_v so_o anxious_o careful_a as_o to_o correct_v every_o literal_a mistake_n i_o have_v very_o diligent_o peruse_v all_o from_o p._n 1_o to_o p._n 224_o inclusive_a and_o hope_v i_o have_v sufficient_o restore_v the_o sense_n to_o the_o place_n wrong_v when_o thou_o have_v do_v they_o right_o by_o the_o pen_n according_a to_o the_o direction_n of_o the_o errata_fw-la follow_v next_o after_o the_o content_n and_o that_o you_o continue_v the_o line_n in_o the_o margin_n of_o p._n 34._o to_o the_o length_n of_o the_o line_n ol_n in_o fig._n 14._o the_o content_n of_o the_o chapter_n chapt._n 1_o of_o geometrical_a definition_n division_n and_o remark_n p._n 1._o chapt._n 2._o of_o geometrical_a problem_n p._n 6._o chapt._n 3_o to_o find_v the_o superficial_a content_n of_o any_o right_n line_v figure_n the_o line_n be_v give_v p._n 17._o chapt._n 4._o concern_v chain_n compass_n and_o scale_n p._n 26._o chapt._n 5._o how_o to_o cast_v up_o the_o content_a of_o a_o figure_n the_o line_n be_v give_v in_o chain_n and_o link_n p._n 35._o chapt._n 6._o how_o to_o measure_v a_o close_a or_o parcel_n of_o land_n and_o to_o protract_v it_o and_o give_v up_o the_o content_a p._n 41._o chapt._n 7._o concern_v the_o measure_n of_o circle_n and_o their_o part_n p._n 48._o chapt._n 8._o concern_v customary_a measure_n and_o how_o it_o may_v be_v reduce_v to_o statute_n measure_n &_o e_fw-la contra_fw-la either_o by_o the_o rule_n of_o three_o or_o a_o more_o compendious_a may_v by_o multiplication_n only_o p._n 52._o chapt._n 9_o how_o a_o man_n may_v become_v a_o ready_a measurer_n by_o practice_n in_o his_o private_a study_n without_o any_o one_o assistance_n or_o observation_n till_o he_o design_v to_o practice_v abroad_o p._n 65._o chapt._n 10._o how_o to_o measure_v a_o piece_n of_o land_n with_o any_o chain_n of_o what_o length_n soever_o and_o howsoever_o divide_v yea_o with_o a_o cord_n or_o cart-rope_n be_v a_o good_a expedient_a when_o instrument_n be_v not_o at_o hand_n of_o a_o more_o artificial_a â—ake_z p._n 67._o chapt._n 11._o concern_v divide_n of_o land_n artificial_o and_o mechanical_o p._n 70_o chapt._n 12._o concern_v the_o boundary_n of_o land_n where_o the_o â—ines_n to_o be_v measure_v must_v begin_v and_o end_v p._n 80._o chapt._n 13._o contain_v a_o description_n of_o the_o plain-table_n the_o protractor_n and_o line_n of_o chord_n p._n 82._o chapt._n 14._o how_o to_o take_v the_o true_a plot_n of_o a_o field_n by_o the_o â—lain-table_n upon_o the_o paper_n that_o cover_v it_o at_o one_o or_o â—ore_a station_n p._n 85._o chapt._n 15._o concern_v the_o plot_v of_o many_o close_v together_o â—hether_o the_o ground_n be_v even_o or_o uneven_a p._n 99_o chapt._n 16._o concern_v shift_n of_o paper_n p._n 102._o chapt._n 17._o concern_v the_o plot_v of_o a_o town_n field_n where_o 〈◊〉_d several_a land_n butt_n or_o doles_n be_v very_o crooked_a â—â—th_v a_o note_n concern_v hypothenusual_a or_o slope_v boundary_n common_a to_o this_o and_o the_o fifteen_o chapter_n â—_o 104._o chapt._n 18._o concern_v taking_n the_o plot_n of_o a_o piece_n of_o ground_n 〈◊〉_d the_o degree_n upon_o the_o frame_n of_o the_o plain-table_n seâ—â—â—al_a way_n and_o protract_v the_o same_o p._n 108._o chapt._n 19_o concern_v taking_n inaccessible_a distance_n by_o the_o â—â—ain-table_n and_o accessible_a altitude_n by_o the_o protractor_n â—_o 121._o chapt._n 20._o of_o cast_v up_o the_o content_a of_o land_n by_o a_o table_n â—_o 193._o errata_fw-la page_n 3_o line_n 16_o read_v trilateral_n p._n 4_o 〈◊〉_d geodates_n p._n 5_o l._n 29_o eneagon_n p._n 10_o l._n 6_o belong_v as_o the_o other_o two_o p._n 16_o l._n 6_o centre_n at_o right_a aâ—â—gles_n p._n 28_o l._n 1_o forefinger_n p._n 36_o l._n 20_o pole_n or_o râ—â—_n p._n 47_o l._n 15_o four_o diagonal_a and_o the_o six_o side_n p._n 〈◊〉_d l._n 28_o as_o in_o this_o figure_n be_v abc_n p._n 56_o l._n 23_o 〈◊〉_d and_o l._n 24_o â—_o 22_o ½_o p._n 58_o l._n 11_o 28._o p._n 69_o l._n 5_o side_n 74_o l._n 25_o fg._n p._n 77_o l._n 27_o 138562_o and_o l._n 28_o 〈◊〉_d 33_o r._n 242030._o p._n 79_o l._n 33_o triangulate_v p._n 80_o l_o former_a p._n 82_o l._n 24_o fit_v p._n 86_o l._n 2_o stationary_a â—â—â—stances_n p._n 90_o l._n 15_o chartley_n or_o card._n p._n 95_o l._n â—_o park_n pond_n p._n 103_o l._n 22_o line_n p._n 104._o l._n 19_o 〈◊〉_d fig._n 1._o fig._n 2._o fig._n 3._o fig._n 4._o fig._n 5._o fig._n 6._o fig._n 7._o fig._n 8._o fig._n 9_o fig._n 10._o fig._n 11._o fig._n 12._o fig._n 13._o fig._n 14_o fig._n 15._o fig._n 16._o fig._n 17._o fig._n 18._o fig._n 19_o fig._n 20._o fig._n 21._o fig._n 22._o fig._n 23._o fig._n 24._o fig._n 25._o fig._n 26._o fig._n 27._o fig._n 28._o fig._n 29._o fig._n 30._o fig._n 31._o fig._n 32._o fig._n 33._o fig._n 34._o fig._n 35._o fig._n 36._o fig._n 37._o fig._n 38._o fig._n 39_o the_o country_n survey-book_n or_o land-meter's_a vade-mecum_a chap._n i._n of_o geometrical_a definition_n division_n and_o remark_n i._o a_o point_n be_v that_o which_o have_v no_o part_n either_o of_o longitude_n or_o latitude_n but_o be_v indivisible_a ordinary_o express_v with_o a_o small_a prick_n like_o a_o period_n at_o the_o end_n of_o a_o sentence_n ii_o a_o line_n have_v length_n but_o no_o breadth_n nor_o depth_n who_o limit_n or_o extremity_n be_v point_n this_o be_v either_o right_a or_o crooked_a iii_o a_o right_a line_n lie_v straight_o and_o equal_a between_o its_o extreme_a point_n be_v the_o short_a extension_n between_o they_o the_o crock_v or_o circular_a not_o so_o iv._o a_o superficies_n have_v length_n and_o breadth_n but_o no_o depth_n of_o this_o line_n be_v the_o limit_n v._o a_o plain_a superficies_n be_v that_o which_o lie_v equal_o or_o even_o between_o its_o line_n vi_o a_o angle_n be_v the_o meeting_n or_o two_o line_n in_o one_o point_n so_o as_o not_o to_o make_v one_o straight_a line_n and_o if_o draw_v on_o past_o that_o point_n they_o will_v intersect_v or_o cross_v one_o another_o this_o be_v vulgar_a english_a may_v be_v call_v a_o corner_n of_o which_o there_o be_v two_o sort_n one_o right_a the_o other_o oblique_a vii_o a_o right_a angle_n be_v that_o which_o be_v make_v by_o two_o right_a line_n cross_v or_o touch_v one_o another_o perpendicular_o or_o square_o like_o a_o ordinary_a cross_n or_o carpenter_n square_a viii_o a_o oblique_a angle_n be_v that_o which_o be_v either_o great_a or_o less_o than_o a_o right_a angle_n and_o this_o be_v of_o two_o sort_n obtuse_a and_o acute_a ix_o a_o obtuse_a angle_n be_v great_a than_o a_o right_a angle_n like_o the_o left_a and_o right_a corner_n of_o a_o roman_a x._o x._o a_o acute_a angle_n be_v less_o than_o a_o right_a angle_n like_o the_o high_a and_o low_a corner_n of_o the_o same_o letter_n xi_o a_o figure_n be_v that_o which_o be_v comprehend_v under_o one_o line_n or_o many_o of_o this_o there_o be_v two_o kind_n a_o circle_n and_o a_o right-lined_n figure_n xii_o a_o circle_n be_v a_o perfect_a round_a figure_n such_o as_o be_v draw_v with_o a_o pair_n of_o compass_n the_o one_o foot_n be_v turn_v round_o in_o a_o point_n and_o the_o other_o wheel_v about_o it_o the_o point_n in_o the_o precise_a middle_n be_v call_v the_o centre_n the_o round_a line_n the_o circumference_n or_o peripheri_n a_o line_n go_v through_o the_o centre_n and_o divide_v the_o circle_n into_o two_o equal_a part_n be_v call_v the_o diameter_n half_a of_o that_o line_n be_v a_o somidiameter_n or_o radius_fw-la half_a the_o circle_n be_v style_v a_o semicircle_n the_o quarter_n a_o quadrant_n any_o portion_n of_o it_o cut_v off_o by_o a_o right_a line_n not_o touch_v the_o centre_n be_v call_v a_o segment_n xiii_o right-lined_n figure_n be_v such_o as_o be_v limit_v by_o three_o
right_a line_n or_o more_o and_o be_v either_o triangle_n or_o triangulate_v that_o be_v such_o as_o be_v compound_v of_o and_o resolvable_a into_o triangle_n fourteen_o triangle_n be_v figure_n comprehend_v under_o three_o right_a line_n and_o as_o ramus_n think_v for_o a_o reason_n that_o he_o give_v lib._n 6._o pr._n 6._o may_v be_v better_o call_v trilateral_n but_o the_o name_n triangle_n from_o the_o number_n of_o the_o angles_n have_v obtain_v also_o from_o the_o nature_n and_o quantity_n of_o their_o angle_n these_o triangle_n be_v distinguish_v into_o three_o sort_n 1._o rectangle_v have_v one_o right_a angle_n 2_o obtuse-angled_n have_v one_o obtuse_a angle_n and_o 3._o acute-angled_n have_v all_o acute_a angle_n for_o no_o triangle_n can_v have_v more_o right_a or_o obtuse_a angle_n than_o one_o because_o by_o by_o a_o old_a rule_n easy_a to_o be_v demonstrate_v no_o triangle_n upon_o a_o plain_a superficies_n can_v consist_v of_o three_o great_a angle_n than_o such_o as_o be_v joint_o take_v be_v equal_a to_o two_o right_a these_o three_o sort_n of_o triangle_n may_v according_a to_o the_o length_n and_o proportion_n of_o their_o side_n be_v subdistinguish_v into_o seven_o for_o each_o of_o they_o may_v have_v either_o two_o equal_a side_n or_o none_o and_o the_o acute-angled_n may_v have_v all_o three_o side_n or_o line_n equal_a to_o all_o which_o kind_n learned_a man_n give_v distinct_a greek_a name_n which_o if_o my_o english_a reader_n have_v a_o mind_n to_o see_v they_o be_v to_o be_v find_v in_o 〈…〉_z practice_n book_n 1._o page_n 6._o for_o my_o present_a purpose_n the_o abovementioned_a â—rimembred_v distinction_n will_v abundant_o suffice_v for_o be_v triangle_n of_o what_o name_n or_o kind_n soever_o they_o be_v all_o capable_a of_o be_v exact_o measure_v by_o one_o plain_a rule_n as_o hereafter_o shall_v full_o appear_v xv._n triangulare_a figure_n be_v such_o as_o have_v more_o angles_n and_o consequent_o more_o side_n or_o line_n then_o three_o and_o these_o be_v either_o quadrangular_a or_o multangular_a xvi_o quadrangular_a figure_n be_v such_o as_o have_v foâ—â—_n angles_n and_o as_o many_o side_n and_o these_o be_v either_o parallellogram_n or_o trapezia_n xvii_o parallellogram_n be_v figure_n that_o be_v bound_v with_o parallel_a line_n that_o be_v such_o line_n as_o be_v every_o where_o of_o the_o same_o distance_n one_o from_o another_o so_o as_o if_o they_o be_v infinite_o extend_v they_o will_v never_o meet_v like_o the_o upright_a line_n of_o he_o roman_a h._n these_o parallellogram_n be_v either_o rectangular_a or_o obliquangular_a xviii_o rectangular_a parallellogram_n be_v such_o as_o have_v four_o right_a angle_n viz._n the_o square_a or_o quadrat_fw-la and_o the_o long_a square_n otherwise_o call_v the_o oblong_a xix_o the_o square_n be_v that_o figure_n that_o have_v four_o right_a angle_n and_o four_o equal_a side_n like_o any_o of_o the_o six_o face_n of_o a_o die_v xx._n the_o long_a square_n have_v also_o four_o right_a angle_n and_o the_o oposite_a side_n be_v equal_a but_o the_o adjoin_a side_n meet_v at_o each_o angle_n differ_v in_o length_n of_o this_o figure_n be_v a_o well_o print_v page_n in_o a_o book_n and_o the_o superficies_n of_o a_o well_o cut_v sheet_n of_o paper_n or_o a_o ordinary_a pane_n of_o glass_n xxi_o obliquangled_a parallellogram_n be_v such_o as_o have_v oblique_a angle_n viz._n two_o acute_a and_o two_o obtuse_a of_o these_o there_o be_v two_o kind_n the_o rhombus_fw-la and_o the_o rhomboide_n xxii_o the_o rhombus_fw-la be_v a_o figure_n that_o have_v equal_a side_n but_o no_o right_a angle_n like_o the_o form_n of_o a_o diamond_n on_o the_o card_n or_o the_o most_o ordinary_a cut_v of_o glass_n in_o window_n who_o oposite_a angle_n be_v equal_a xxiii_o the_o rhomboide_n be_v as_o it_o be_v a_o defective_a rbombus_n for_o if_o from_o any_o side_n of_o a_o rhombus_fw-la we_o cut_v off_o a_o part_n with_o a_o parallel_n line_n the_o remainder_n will_v be_v a_o rhomboide_n which_o have_v neither_o equal_a side_n nor_o angle_n but_o yet_o the_o opposite_a side_n and_o angle_n be_v equal_a xxiv_o the_o trapezium_fw-la be_v a_o figure_n that_o be_v neither_o parallellogram_n nor_o consequent_o have_v equal_a side_n or_o angle_n but_o be_v irregular_o quadrangular_a as_o if_o draw_v at_o adventure_n of_o this_o shape_n most_o field_n prove_v that_o seem_v to_o the_o eye_n to_o be_v square_n or_o oblong_v xxv_o multangular_a figure_n be_v such_o as_o contain_v more_o side_n and_o angle_n than_o four_o and_o they_o be_v either_o regular_a or_o irregular_a xxvi_o regular_a multangular_n take_v their_o name_n from_o their_o number_n of_o angles_n so_o a_o pentagon_n hexagon_n heptagon_n octogon_n encagon_fw-mi decagon_n signify_v a_o multangular_a figure_n of_o five_o six_o seven_o eight_o nine_o ten_o angle_n and_o consequent_o side_n xxvii_o a_o irregular_a polygon_n or_o multangular_a figure_n be_v that_o which_o have_v more_o angle_n and_o side_n than_o four_a the_o side_n and_o angle_n be_v unequal_a to_o one_o another_o chap._n ii_o of_o geometrical_a problem_n i._o to_o draw_v a_o line_n parallel_n to_o another_o at_o any_o distance_n assign_v fig._n 1_o open_v your_o compass_n to_o the_o distance_n give_v and_o choose_v two_o point_n convenient_o distant_a in_o the_o line_n give_v as_o here_o at_o a_o and_o b_o describe_v the_o arch_n c_o and_o d_o to_o who_o convixity_n if_o you_o apply_v a_o rule_n the_o parallel_a line_n be_v easy_o draw_v ii_o to_o raise_v a_o perpendicular_a upon_o a_o line_n give_v or_o to_o cross_v that_o line_n at_o right_a angle_n in_o a_o point_n assign_v fig._n 2_o suppose_v the_o point_n c_o in_o the_o line_n ab_fw-la be_v assign_v for_o the_o perpendicular_a open_v the_o compass_n to_o a_o convenient_a distance_n and_o mark_v out_o the_o two_o point_n e_z and_o f_o in_o the_o line_n ab_fw-la then_o open_v they_o some_o what_o wide_a you_o may_v by_o set_v one_o foot_n in_o e_o 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line_n exact_o in_o the_o middle_n at_o right_a angle_n note_v that_o when_o one_o point_n of_o your_o compass_n stand_v in_o a_o you_o may_v make_v both_o the_o arch_n belong_v to_o that_o centre_n above_o and_o below_o the_o line_n and_o then_o remove_v the_o compass_n to_o b_o you_o may_v cross_v they_o both_o iii_o to_o raise_v a_o perpendicular_a at_o the_o end_n of_o a_o line_n fig._n 3_o let_v or_o be_v the_o line_n give_v then_o to_o raise_v a_o perpendicular_a at_o r_o make_v five_o little_a equal_a division_n and_o take_v four_o of_o they_o with_o your_o compass_n set_v one_o foot_n of_o your_o compass_n in_o r_o and_o with_o the_o other_o describe_v the_o arch_n pp_n then_o take_v the_o distance_n from_o r_z to_z 5_o and_o place_v one_o foot_n in_o 3_o with_o the_o other_o describe_v the_o arch_n bb_n intersect_v the_o former_a in_o the_o point_n s_o then_o shall_v the_o line_n sir_n be_v draw_v by_o a_o straight_a rule_n be_v a_o perpendicular_a to_o the_o line_n or_o iv._o to_o let_v fall_v a_o perpendicular_a upon_o a_o give_v line_n from_o any_o point_n assign_v open_v your_o compass_n so_o as_o one_o foot_n be_v set_v in_o the_o assign_a point_n the_o other_o may_v go_v clear_a over_o the_o line_n give_v and_o thereby_o describe_v a_o arch_n cut_v the_o line_n at_o two_o point_n then_o shall_v the_o half_a distance_n between_o those_o two_o point_n be_v the_o point_n to_o which_o the_o perpendicular_a may_v be_v draw_v from_o the_o point_n assign_v but_o if_o you_o think_v it_o too_o much_o pain_n to_o find_v the_o point_n of_o half_a distance_n by_o trial_n you_o may_v help_v yourself_o by_o the_o second_o problem_n for_o if_o you_o describe_v two_o arch_n intersect_v one_o another_o on_o the_o far_a side_n of_o the_o line_n from_o the_o assign_a point_n place_v to_o
upon_o measure_v a_o piece_n of_o land_n whereupon_o i_o take_v four_o or_o five_o of_o my_o scholar_n to_o the_o heath_n with_o i_o that_o have_v only_o be_v exercise_v within_o the_o wall_n of_o the_o school_n and_o never_o see_v that_o i_o know_v of_o so_o much_o as_o a_o chain_n lay_v on_o the_o ground_n and_o to_o the_o admiration_n of_o the_o spectator_n and_o especial_o of_o a_o skilful_a surveyor_n then_o live_v in_o the_o town_n they_o go_v about_o their_o work_n as_o regular_o and_o dispatch_v it_o with_o as_o much_o expedition_n and_o exactness_n as_o if_o they_o have_v be_v old_a land-meter_n chap._n x._o how_o to_o measure_v a_o piece_n of_o land_n with_o any_o chain_n of_o what_o length_n soever_o and_o howsoever_o divide_v yea_o with_o a_o cord_n or_o cart-rope_n be_v a_o good_a expedient_a when_o instrument_n be_v not_o at_o hand_n of_o a_o more_o artificial_a make_v if_o you_o can_v procure_v a_o chain_n and_o find_v it_o be_v not_o divide_v as_o before_o have_v be_v show_v but_o into_o foot_n or_o quarter_n of_o yard_n or_o any_o such_o vulgar_a division_n make_v no_o reckon_n of_o the_o division_n at_o all_o but_o measure_v it_o as_o exact_o as_o you_o can_v to_o find_v out_o the_o true_a length_n of_o the_o whole_a chain_n and_o if_o it_o fit_v none_o of_o those_o length_n mention_v in_o the_o 8_o chapter_n nor_o any_o of_o their_o half_n make_v it_o to_o fit_v by_o take_v off_o a_o link_n or_o two_o or_o piece_v it_o out_o with_o a_o string_n then_o divide_v the_o length_n of_o that_o chain_n by_o 100_o or_o the_o half_a of_o it_o by_o 50_o find_v the_o true_a length_n of_o a_o link_n according_a to_o our_o artificial_a division_n and_o have_v get_v a_o long_a stick_n or_o rod_n set_v as_o many_o of_o those_o link-length_n upon_o it_o as_o it_o will_v hold_v then_o may_v you_o measure_v all_o the_o whole_a chain_n by_o your_o regulate_v chain_n and_o the_o odd_a link_n of_o every_o line_n by_o your_o divide_a stick_n or_o rod_n as_o be_v manifest_a in_o this_o example_n follow_v be_v far_o from_o my_o instrument_n and_o request_v by_o a_o friend_n to_o measure_v he_o a_o close_a i_o procure_v a_o pair_n of_o compass_n a_o ordinary_a carpenter_n rule_n of_o two_o foot_n divide_v into_o inch_n and_o quarter_n and_o meet_v also_o with_o a_o piece_n of_o a_o old_a chain_n seem_o divide_v into_o foot_n i_o measure_v it_o by_o the_o rule_n and_o find_v it_o to_o be_v 45_o foot_n long_o and_o some_o odd_a measure_n i_o piece_v it_o out_o with_o a_o pretty_a strong_a cord_n that_o will_v not_o stretch_v much_o to_o 48_o foot_n exact_o than_o it_o will_v serve_v i_o for_o half_a a_o chain_n of_o 24_o foot_n to_o the_o pole_n this_o 48_o i_o multiply_v by_o 12_o the_o number_n of_o inch_n in_o a_o foot_n and_o that_o product_v be_v 576_o i_o divide_v by_o 50_o the_o number_n of_o link_n in_o half_a a_o decimal_n chain_n and_o the_o quotient_n be_v 1166-50_a inch_n or_o 11_o inch_n and_o a_o half_a and_o a_o trifle_n over_o so_o then_o divide_v a_o long_o stick_v throughout_o into_o such_o part_n each_o contain_v 11_o inch_n and_o a_o half_a beside_o the_o breadth_n of_o the_o nick_n i_o be_o provide_v of_o tool_n to_o measure_v line_n to_o a_o link_n with_o exactness_n enough_o in_o like_a manner_n will_v i_o proceed_v with_o a_o cord_n or_o rope_n have_v fit_v they_o to_o some_o know_a length_n or_o other_o and_o then_o for_o protraction_n it_o be_v easy_a with_o the_o compass_n to_o make_v a_o plain_a scale_n of_o a_o large_a sort_n either_o upon_o paper_n or_o a_o even_a piece_n of_o wood_n this_o for_o once_o may_v serve_v a_o man_n turn_n well_o enough_o beside_o there_o be_v a_o way_n of_o measure_v the_o perpendicular_o of_o triangle_n and_o trapezia`s_n upon_o the_o ground_n itself_o so_o as_o to_o prevent_v the_o necessity_n of_o a_o scale_n for_o if_o you_o have_v a_o little_a square_n with_o a_o hole_n in_o it_o to_o turn_v upon_o the_o head_n of_o a_o little_a stick_n which_o you_o may_v fix_v where_o you_o please_v as_o you_o be_v measure_v the_o base_a of_o a_o triangle_n or_o the_o diagonal_a of_o a_o trapezium_fw-la you_o may_v by_o a_o very_a few_o trial_n find_v the_o place_n where_o the_o one_o leg_n will_v be_v just_a in_o the_o line_n which_o you_o be_v measure_v and_o the_o other_o point_n at_o the_o angle_n from_o which_o the_o perpendicular_a fall_n on_o it_o and_o then_o the_o space_n between_o your_o stick_n and_o that_o angle_n true_o measure_v be_v the_o perpendicular_a if_o you_o have_v not_o such_o a_o square_a a_o square_a trencher_n or_o any_o end_n of_o a_o board_n that_o have_v one_o right_a angle_n and_o two_o true_a side_v will_v supply_v the_o want_n of_o it_o and_o now_o that_o i_o be_o mention_v this_o way_n of_o measure_v ☜_o i_o shall_v make_v bold_a to_o add_v that_o this_o be_v a_o good_a way_n and_o as_o such_o ordinary_o use_v by_o that_o general_a scholar_n and_o reverend_a minister_n mr._n samuel_n langley_n of_o tamworth_n in_o staffordshire_n who_o ancient_a acquaintance_n i_o have_v long_o esteem_v both_o my_o happiness_n and_o honour_n to_o measure_v a_o trapezium_fw-la thus_o though_o it_o be_v protract_v afterward_o for_o by_o measure_v the_o perpendicular_o as_o aforesaid_a and_o observe_v at_o how_o many_o chain_n and_o link_n end_v the_o say_v perpendicular_o meet_v the_o common_a base_a the_o whole_a trapezium_fw-la may_v be_v true_o protract_v without_o go_v about_o it_o this_o little_a square_n competent_o supply_v the_o place_n of_o a_o instrument_n which_o be_v usual_o call_v a_o cross_n or_o square_a make_v up_o as_o it_o be_v of_o two_o small_a indices_fw-la like_o those_o for_o a_o plain-table_n but_o much_o less_o with_o foresight_n and_o back-sight_n and_o cut_v one_o another_o at_o right_a angle_n put_v together_o and_o have_v a_o hole_n at_o the_o centre_n like_o those_o thing_n which_o here_o in_o cheshire_n we_o call_v yarndle_n be_v use_v by_o country_n housewife_n in_o wind_a of_o their_o yarn_n chap._n xi_o concern_v divide_n of_o land_n artificial_o and_o mechanical_o be_v it_o suitable_a to_o my_o design_n or_o humour_n to_o be_v copious_a or_o curious_a i_o have_v here_o a_o fait_fw-fr opportunity_n for_o four_o or_o five_o modern_a survey-book_n of_o the_o best_a account_n lie_v open_a before_o i_o will_v tempt_v i_o to_o transcribe_v abundance_n of_o ingenious_a thing_n but_o for_o reason_n often_o hint_v before_o i_o shall_v confine_v myself_o to_o a_o few_o plain_a thing_n that_o will_v competent_o do_v this_o business_n 1._o to_o divide_v a_o triangle_n into_o any_o part_n require_v divide_v the_o base_a as_o the_o demand_n import_v then_o shall_v line_n draw_v from_o the_o point_n of_o division_n to_o the_o opposite_a angle_n finish_v the_o division_n of_o the_o triangle_n example_n fi._n 20_o ac_fw-la the_o base_a of_o the_o triangle_n abc_n be_v divide_v into_o 12_o equal_a part_n a_o line_n draw_v from_o the_o angular_a point_n b_o to_o the_o point_n 6_o divide_v the_o triangle_n into_o two_o equal_a part_n 2._o line_n draw_v to_o 4_o and_o 8_o divide_v it_o into_o three_o equal_a part_n 3._o line_n draw_v to_o the_o point_n note_v with_o 3_o 6_o and_o 9_o divide_v it_o into_o four_o equal_a part_n and_o so_o line_n draw_v to_o 2_o 4_o 6_o 8_o 10_o divide_v it_o into_o six_o equal_a part_n also_o it_o be_v very_o obvious_a that_o if_o the_o same_o triangle_n be_v so_o to_o be_v divide_v that_o the_o one_o part_n shall_v be_v double_a to_o the_o other_o a_o line_n draw_v from_o b_o to_z 4_o or_o 8_o do_v the_o work_n or_o if_o it_o be_v require_v to_o divide_v it_o into_o two_o part_n so_o as_o the_o one_o shall_v be_v triple_a to_o the_o other_o a_o line_n draw_v from_o b_o to_z 3_o or_o 9_o complete_v the_o work_n so_o also_o a_o line_n from_o b_o to_o 2_o or_o 10_o divide_v it_o into_o two_o part_n whereof_o the_o one_o be_v quintuple_a or_o fivefold_a to_o the_o other_o and_o a_o line_n from_o b_o to_o 1_o or_o 11_o divide_v it_o into_o two_o part_n whereof_o the_o one_o be_v 11_o time_n as_o large_a as_o the_o other_o further_o yet_o if_o it_o be_v require_v this_o triangle_n shall_v be_v so_o divide_v that_o the_o two_o part_n shall_v in_o quantity_n bear_v proportion_n as_o 5_o and_o 7_o a_o line_n from_o b_o to_z 5_o or_o 7_o do_v that_o feat_n but_o to_o deal_v plain_o with_o you_o i_o must_v confess_v that_o sometime_o the_o division_n will_v be_v a_o little_a more_o intricate_a than_o thus_o yet_o not_o such_o but_o that_o the_o seem_a difficulty_n may_v be_v easy_o overcome_v by_o observe_v the_o method_n wherein_o i_o shall_v satisfy_v the_o follow_a demand_n
suppose_v a_o large_a triangle_n of_o common_a land_n be_v to_o be_v divide_v among_o three_o tenant_n a_o b_o and_o c_o according_a to_o the_o quantity_n of_o their_o tenement_n a_o have_v 19_o acre_n of_o land_n to_o his_o tenement_n b13_n and_o c7_n the_o base_a of_o the_o triangle_n be_v find_v by_o measure_n to_o be_v 17_o chain_n and_o 27_o link_n and_o the_o dem_n and_o be_v where_o the_o point_n of_o division_n must_v be_v place_v in_o the_o base_a so_o as_o line_n draw_v from_o thence_o to_o the_o opposite_a angle_n shall_v true_o limit_v each_o man_n part_n to_o answer_v this_o let_v we_o add_v 13_o and_o 07_o to_o 19_o as_o in_o the_o margin_n and_o they_o give_v 39_o so_o be_v the_o work_n plain_o reduce_v to_o the_o rule_n of_o fellowship_n and_o therefore_o to_o find_v every_o man_n distinct_a portion_n we_o need_v only_o to_o multiply_v the_o base_a by_o his_o 19_o 13_o 07_o 39_o particular_a number_n and_o divide_v that_o product_n by_o 39_o the_o sum_n of_o all_o their_o number_n as_o here_o be_v plain_a a_o 39_o 17._o 27_o ∷_o 19_o 19_o 15543_o 1727_o 39_o 32813_o 841_o 14_o 39_o 312_o 161_o 156_o 53_o 39_o 14_o b_o 39_o 17._o 27_o ∷_o 13_o 13_o 5181_o 1727_o 39_o 22451_o 575_o 2d_o 3â—_n 195_o 295_o 273_o 221_o 195_o 26_o c_o 39_o 17._o 27_o ∷_o 7_o 7_o 39_o 12089_o 309_o 38_o 39_o 117_o 389_o 351_o 38_o from_o these_o operation_n it_o be_v plain_a that_o if_o we_o set_v off_o from_o the_o angular_a point_n where_o the_o base_a begin_v 8_o chain_n 41_o link_n and_o a_o little_a above_o the_o three_o part_n of_o a_o link_n upon_o the_o base_a for_o a_o and_o where_o that_o end_n 5_o chain_n and_o 75_o link_n and_o 2_o 3_o of_o a_o link_n for_o b_o and_o consequent_o leave_v between_o this_o second_o division_n and_o the_o other_o end_n of_o the_o base_a 3_o chain_n and_o almost_o 10_o link_n for_o c_o line_n draw_v from_o those_o point_n of_o division_n to_o the_o opposite_a angle_n will_v give_v each_o man_n his_o due_n what_o i_o have_v say_v touch_v the_o division_n of_o triangle_n upon_o their_o base_n ☜_o will_v with_o a_o little_a variation_n serve_v for_o the_o divide_n of_o all_o sort_n of_o parallellogram_n whether_o square_a long-squares_a rhombus_n or_o rhomboides_n all_o the_o difference_n be_v that_o in_o stead_n of_o draw_v line_n from_o point_n in_o the_o base_a to_o the_o opposite_a angle_n you_o must_v draw_v parallel_a line_n from_o point_n in_o one_o opposite_a side_n to_o another_o as_o will_v be_v sufficient_o plain_a by_o this_o one_o instance_n fig._n 7_o suppose_v the_o square_a figure_n in_o the_o 8_o prop._n of_o the_o second_o chapter_n to_o represent_v a_o close_a of_o six_o acre_n and_o i_o be_o to_o cut_v off_o a_o acre_n at_o the_o side_n ac_fw-la have_v set_v off_o the_o 6_o part_n of_o the_o line_n cd_o from_o c_o towards_z d_o and_o also_o from_o a_o towards_o n_o a_o parallel_n draw_v between_o those_o point_n take_v off_o exact_o a_o 6_o part_n or_o a_o acre_n if_o it_o be_v not_o think_v convenient_a as_o in_o some_o case_n it_o be_v not_o to_o cut_v off_o a_o piece_n so_o long_o and_o narrow_a you_o may_v by_o the_o rule_n of_o three_o find_v what_o other_o length_n of_o any_o great_a breadth_n will_v limit_v a_o equal_a quantity_n to_o it_o or_o you_o may_v multiply_v the_o breadth_n by_o 2_o 3_o or_o any_o other_o and_o divide_v the_o length_n by_o the_o same_o number_n that_o you_o multiply_v the_o breadth_n by_o or_o last_o if_o you_o set_v out_o a_o double_a proportion_n that_o be_v 2_o 6_o or_o 1_o 3_o from_o c_z towards_z d_o and_o from_o the_o point_n where_o it_o fall_v draw_v a_o line_n to_o the_o angle_n a_o you_o will_v have_v a_o triangle_n equal_a to_o 1_o 6_o of_o the_o square_a acdn._n but_o to_o return_v to_o triangle_n the_o most_o simple_a and_o primitive_a of_o all_o rectilinear_n and_o therefore_o the_o most_o considerable_a in_o this_o case_n of_o partition_n as_o give_v law_n often_o to_o the_o rest_n it_o may_v fall_v out_o that_o a_o triangle_n must_v be_v divide_v convenience_n so_o require_v by_o a_o line_n from_o some_o point_n in_o a_o side_n so_o as_o that_o line_n may_v either_o be_v parallel_n to_o some_o other_o side_n or_o not_o parallel_v to_o any_o for_o the_o former_a case_n take_v this_o example_n follow_v out_o of_o mr._n wing_n lib._n 5._o prob._n 5._o fig._n 21_o let_v abc_n be_v a_o triangle_n give_v and_o it_o be_v require_v to_o cut_v off_o 3_o 5_o by_o a_o line_n parallel_n to_o ab_fw-la first_o on_o the_o line_n ac_fw-la describe_v the_o semicircle_n aec_fw-la who_o diameter_n ca_n divide_v into_o five_o equal_a part_n according_a to_o the_o great_a term_n and_o upon_o three_o of_o those_o part_n the_o lesser_a term_n erect_v the_o perpendicular_a de_fw-fr which_o cut_v the_o arch_a line_n in_o e_z then_o set_v the_o line_n ce_fw-fr from_fw-la c_o to_o f_o and_o from_o thence_o draw_v the_o line_n eglantine_n parallel_n to_o ab_fw-la so_o will_v the_o triangle_n cgf_n contain_v 3_o 5_o of_o the_o triangle_n abc_n as_o be_v require_v fig._n 22_o now_o for_o the_o latter_a case_n when_o the_o line_n of_o partition_n go_v not_o parallel_v with_o any_o side_n take_v this_o example_n let_v abc_n be_v a_o triangle_n give_v to_o be_v divide_v into_o two_o part_n which_o shall_v bear_v proportion_n to_o one_o another_o as_o 3_o and_o 2_o by_o a_o line_n draw_v from_o the_o point_n d_o in_o the_o base_a or_o line_n ac_fw-la from_o the_o limit_a point_n d_o draw_v a_o line_n to_o the_o angle_n b_o then_o divide_v the_o base_a ac_fw-la into_o five_o equal_a part_n and_o from_o the_o three_o point_n of_o division_n draw_v the_o line_n to_o e_o parallel_n to_o bd._n last_o from_o e_o draw_v the_o line_n ed._n so_o shall_v the_o trapezium_fw-la abed_o be_v in_o content_n as_o 3_o to_o 2_o to_o the_o new_a triangle_n dec_n i_o have_v now_o do_v with_o the_o division_n of_o triangle_n when_o i_o have_v add_v these_o three_o advertisement_n 1._o you_o must_v be_v sure_a to_o take_v very_o exact_o the_o distance_n of_o every_o point_n where_o a_o divide_v line_n cut_v any_o side_n to_o one_o of_o the_o end_n of_o the_o same_o side_n as_o in_o this_o last_o figure_n the_o distance_n be_v and_o ad_fw-la which_o distance_n be_v apply_v to_o the_o scale_n by_o which_o the_o triangle_n be_v protract_v will_v show_v at_o how_o many_o chain_n and_o links-end_n you_o be_v to_o make_v your_o divide_v line_n on_o the_o field_n itself_o 2._o the_o proportion_n by_o which_o you_o be_v to_o divide_v be_v not_o always_o so_o formal_o give_v as_o in_o the_o former_a example_n but_o be_v sometime_o to_o be_v find_v out_o by_o arithmetical_a work_n as_o in_o this_o case_n suppose_v a_o triangular_a field_n of_o 6_o acre_n 2_o rood_n and_o 31_o perch_n must_v be_v divide_v so_o as_o the_o one_o of_o the_o two_o part_n shall_v be_v 4_o acre_n 3_o rood_n and_o 5_o perch_n and_o the_o other_o consequent_o 1_v acre_n 3_o rood_n and_o 26_o perch_n reduce_v both_o measure_n into_o perch_n and_o the_o one_o will_v be_v 765_o and_o the_o other_o 306._o their_o sum_n be_v 1071_o which_o by_o their_o common_a measure_n be_v reduce_v into_o their_o low_a term_n of_o proportion_n in_o whole_a number_n will_v be_v 5_o 2_o and_o 7_o which_o show_v that_o the_o triangle_n be_v divide_v into_o 7_o equal_a part_n the_o one_o must_v have_v 5_o of_o those_o 7_o part_n and_o the_o other_o 2._o and_o observe_v that_o it_o will_v be_v sufficient_a to_o find_v the_o common_a measure_n between_o the_o sum_n of_o the_o term_n and_o either_o of_o the_o term_n the_o method_n whereof_o be_v show_v in_o every_o arithmetic_n book_n for_o reduce_v fraction_n into_o their_o low_a term_n but_o if_o my_o unlearned_a reader_n can_v skill_v of_o that_o work_n he_o may_v multiply_v either_o of_o the_o part_n as_o suppose_v 765_o by_o the_o length_n of_o the_o base_a which_o we_o will_v suppose_v to_o be_v 8_o chain_n and_o 75_o link_n or_o 875_o link_n and_o that_o product_v divide_v by_o 1071_o the_o content_a of_o the_o whole_a close_a in_o perch_n give_v by_o the_o rule_n of_o three_o direct_v 625_o link_n or_o 6_o chain_n and_o 1_o pole_n the_o true_a distance_n from_o either_o end_n of_o the_o base_a that_o his_o mind_n or_o occasion_n may_v direct_v he_o to_o begin_v with_o to_o the_o point_n of_o division_n for_o the_o division_n must_v be_v not_o only_o for_o proportion_n or_o quantity_n but_o also_o as_o to_o position_n or_o situation_n of_o part_n upon_o the_o paper_n as_o it_o be_v require_v to_o be_v on_o the_o ground_n 3._o in_o these_o and_o all_o other_o division_n
of_o measure_v only_o the_o stationary_a distance_n be_v very_o proper_a for_o set_v out_o the_o figure_n of_o each_o particular_a close_a provide_v the_o distance_n of_o the_o station_n be_v large_a and_o take_v if_o possible_a upon_o pretty_a even_a ground_n which_o sometime_o may_v be_v do_v though_o most_o of_o the_o close_a be_v uneven_a and_o the_o work_n so_o order_v as_o not_o to_o make_v too_o acute_a angle_n but_o because_o this_o require_v skill_n and_o care_n i_o rather_o advise_v my_o young_a artist_n to_o use_v the_o circle_a way_n as_o ordinary_o most_o commodious_a in_o my_o poor_a judgement_n but_o not_o prejudice_v other_o man_n that_n may_v differ_v from_o i_o in_o opinion_n and_o where_o need_n require_v let_v he_o observe_v the_o direction_n in_o the_o 17_o chapter_n but_o which_o way_n soever_o you_o go_v to_o work_v ☞_o there_o be_v one_o very_o necessary_a rule_n to_o be_v observe_v if_o the_o ground_n be_v uneven_a considerable_o you_o must_v not_o give_v up_o the_o content_a by_o measure_v the_o base_n and_o perpendicular_o of_o the_o triangle_n on_o the_o paper_n by_o your_o scale_n but_o you_o must_v measure_v the_o line_n correspondent_a to_o they_o on_o the_o ground_n and_o cast_v up_o the_o content_a according_a to_o that_o measure_n and_o if_o it_o be_v desire_v that_o you_o shall_v adjoyn_v to_o your_o plot_n as_o be_v usual_a a_o scale_n of_o chain_n to_o measure_v distance_n by_o you_o must_v either_o by_o make_v the_o form_n of_o hill_n erect_v and_o reverse_v or_o some_o other_o note_n in_o writing_n mark_v out_o your_o uneven_a ground_n lest_o those_o that_o try_v it_o by_o the_o scale_n judge_v your_o work_n erroneous_a for_o though_o you_o make_v that_o scale_n exact_o correspondent_a to_o that_o you_o protract_v by_o as_o you_o ought_v to_o do_v the_o hill_n and_o dale_n in_o the_o ground_n true_o measure_v may_v make_v a_o considerable_a alteration_n it_o be_v convenient_a when_o you_o plant_v your_o table_n that_o the_o needle_n hang_v just_a over_o the_o north-point_n of_o the_o compass_n under_o it_o in_o the_o box_n then_o may_v you_o by_o the_o line_n overthwart_o the_o frame_n of_o the_o table_n easy_o draw_v two_o line_n quite_o through_o the_o plot_n cut_v one_o another_o at_o right_a angle_n the_o one_o point_v at_o north_n and_o south_n and_o the_o other_o at_o east_n and_o west_n and_o if_o your_o skill_n serve_v you_o to_o make_v the_o two_o and_o thirty_o point_n of_o the_o compass_n upon_o the_o place_n where_o they_o intersect_v and_o to_o draw_v the_o form_n of_o the_o house_n wood_n and_o other_o remarkable_a thing_n upon_o the_o demesn_a and_o the_o course_n of_o brook_n and_o river_n run_v through_o it_o it_o will_v add_v to_o your_o commendation_n and_o so_o it_o will_v also_o if_o you_o take_v in_o such_o parcel_n of_o land_n bound_v it_o whether_o common_a or_o peculiar_a to_o other_o man_n as_o will_v make_v your_o plot_n to_o look_v handsome_o like_o a_o perfect_a square_n or_o oblong_o but_o however_o that_o be_v you_o must_v be_v sure_a to_o protract_v true_o all_o lane_n go_v into_o it_o or_o through_o it_o and_o all_o close_v of_o other_o man_n mix_v with_o it_o and_o also_o all_o considerable_a pond_n way_n and_o outlet_n with_o the_o name_n of_o the_o close_n and_o quality_n of_o the_o ground_n whether_o meadow_n pasture_n arable_a etc._n etc._n chap._n xvi_o concern_v shift_n of_o paper_n in_o such_o work_n as_o that_o of_o the_o last_o chapter_n it_o may_v sometime_o fall_v out_o through_o the_o multitude_n and_o largeness_n of_o field_n that_o one_o sheet_n will_v not_o hold_v your_o whole_a plot_n in_o which_o case_n you_o may_v help_v yourself_o by_o shift_a paper_n as_o we_o call_v it_o thus_o fig._n 33_o let_v abcd_n represent_v our_o sheet_n of_o paper_n that_o cover_v the_o table_n upon_o which_o the_o plot_n of_o the_o large_a piece_n of_o land_n efghik_n shall_v be_v draw_v have_v make_v my_o first_o station_n at_o e_o and_o the_o second_o at_o f_o i_o find_v my_o paper_n will_v not_o receive_v the_o line_n fg_v but_o however_o i_o draw_v so_o far_o as_o it_o will_v go_v to_o the_o edge_n of_o the_o paper_n and_o plant_v my_o table_n again_o at_o e_z proceed_v in_o my_o circuition_n the_o contrary_a way_n to_o k_o and_o i_o where_o i_o find_v myself_o again_o at_o a_o loss_n for_o my_o line_n ih_v but_o draw_v it_o also_o to_o the_o edge_n of_o the_o paper_n then_o with_o the_o point_n of_o my_o compass_n strike_v the_o line_n po_n parallel_n to_o the_o edge_n of_o the_o paper_n bc_n and_o the_o line_n qo_n parallel_n to_o dc_o and_o cut_v po_n in_o o_o i_o throw_v aside_o that_o paper_n for_o a_o while_n cover_v the_o instrument_n with_o a_o new_a one_o which_o i_o mark_v with_o the_o figure_n 2_o for_o my_o second_o sheet_n fig._n 34_o upon_o which_o second_o sheet_n the_o lead_a part_n whereof_o be_v represent_v by_o the_o three_o line_n meet_v in_o the_o angular_a point_n a_o and_o b_o i_o draw_v po_n parallel_v to_o ab_fw-la the_o lead_a edge_n of_o the_o paper_n and_o cross_v it_o at_o right_a angle_n in_o the_o point_n o_o by_o a_o parallel_n to_o bc_n viz._n the_o line_n or_o be_v of_o the_o same_o distance_n from_o bc_n that_o qo_o in_o the_o former_a sheet_n be_v from_o dc_o then_o with_o a_o rule_n and_o a_o sharp_a penknife_n i_o cut_v off_o the_o end_n of_o the_o first_o sheet_n at_o the_o line_n po_n and_o apply_v the_o edge_n of_o it_o to_o the_o line_n po_n of_o the_o second_o sheet_n so_o as_o it_o may_v touch_v that_o line_n all_o along_o and_o the_o line_n qo_o of_o the_o former_a touch_v the_o line_n or_o in_o the_o latter_a so_o as_o to_o make_v one_o line_n with_o it_o i_o draw_v the_o line_n pg_n be_v the_o remainder_n of_o the_o line_n fg_v and_o the_o line_n oh_o being_n the_o remainder_n of_o the_o line_n ih_v and_o from_o their_o extremity_n the_o line_n gh_n and_o if_o the_o plot_n require_v it_o you_o may_v proceed_v on_o in_o the_o second_o sheet_n and_o annex_v a_o three_o and_o a_o four_o etc._n etc._n as_o there_o be_v occasion_n these_o sheet_n may_v be_v piece_v together_o with_o mouth-glew_a or_o fine_a paste_n apply_v the_o edge_n of_o the_o former_a as_o you_o do_v upon_o the_o table_n to_o the_o line_n po_n of_o the_o latter_a and_o note_v here_o once_o for_o all_o that_o when_o i_o speak_v of_o apply_v the_o edge_n of_o the_o paper_n to_o a_o line_n i_o mean_v the_o precise_a edge_n cut_v by_o the_o line_n po_n but_o when_o i_o speak_v of_o draw_v line_n to_o the_o edge_n of_o the_o paper_n upon_o the_o table_n i_o hope_v none_o will_v think_v i_o so_o absurd_a as_o to_o mean_v the_o edge_n that_o be_v couch_v under_o the_o frame_n but_o that_o my_o meaning_n be_v that_o the_o line_n must_v be_v continue_v on_o the_o paper_n till_o they_o touch_v the_o frame_n chap._n xvii_o concern_v the_o plot_v of_o a_o town-field_n where_o the_o several_a land_n butt_n or_o doles_n be_v very_o crooked_a with_o a_o note_n concern_v hypothenusal_a or_o sloap_a boundary_n common_a to_o this_o and_o the_o fiftâ—enth_o chapter_n fig._n 35_o suppose_v abcde_v divide_v in_o the_o manner_n of_o a_o common_a field_n into_o seven_o part_n or_o doles_n belong_v to_o seven_o several_a man_n first_o plot_v the_o whole_a as_o before_o have_v be_v teach_v then_o measure_v from_o a_o to_o b_o upon_o the_o land_n set_v one_o note_v down_o as_o you_o go_v along_o at_o how_o many_o chain_n or_o link_n or_o both_o the_o division_n be_v between_o dole_n and_o dole_n and_o according_o mark_v they_o out_o by_o the_o help_n of_o scale_n and_o compass_n in_o the_o line_n ab_fw-la on_o the_o paper_n plot_n in_o the_o very_a same_o manner_n you_o must_v measure_v and_o mark_v out_o the_o line_n oc_fw-fr and_o ed_z which_o be_v do_v take_v the_o paper_n off_o the_o instrument_n and_o lay_v it_o before_o you_o on_o a_o table_n with_o the_o side_n ae_n towards_o you_o the_o compass_n must_v be_v so_o open_v and_o place_v as_o by_o a_o few_o trial_n they_o may_v that_o one_o foot_n rest_v upon_o the_o table_n the_o other_o may_v pass_v through_o the_o point_n of_o division_n upon_o all_o the_o three_o line_n viz._n ab_fw-la oc_fw-la and_o ed_z as_o in_o this_o figure_n they_o do_v if_o the_o content_a of_o any_o one_o or_o more_o of_o these_o part_n butt_n or_o doles_n be_v desire_v without_o plot_v it_o may_v easy_o be_v do_v without_o your_o plain-table_n thus_o take_v the_o breadth_n by_o your_o chain_n at_o the_o head_n middle_a and_o low_a end_n and_o add_v these_o number_n together_o the_o three_o part_n of_o their_o sum_n be_v the_o equated_a breadth_n by_o which_o multiply_v the_o
length_n measure_v down_o the_o ridge_n or_o middle_a the_o product_n give_v the_o content_a but_o both_o in_o this_o case_n and_o that_o mention_v in_o the_o 15_o chapter_n the_o figure_n of_o a_o plot_n may_v be_v somewhat_o disorder_v not_o only_o by_o the_o unevenness_n of_o the_o ground_n within_o for_o which_o i_o have_v give_v due_a caution_n already_o that_o be_v both_o the_o more_o common_a and_o more_o considerable_a case_n but_o also_o by_o the_o great_a diclivity_n of_o the_o ground_n where_o the_o boundary-line_n go_v either_o of_o the_o whole_a plot_n or_o particular_a parcel_n for_o whereas_o in_o plot_v every_o line_n be_v presume_v to_o be_v horizontal_n or_o level_a that_o it_o may_v pass_v from_o angle_n to_o angle_v the_o short_a way_n and_o that_o every_o part_n may_v be_v due_o situate_v and_o none_o thrust_v another_o out_o of_o its_o right_a place_n if_o it_o be_v not_o level_a but_o fall_v down_o towards_o a_o valley_n or_o rise_v up_o hill_n or_o compound_v of_o both_o a_o line_n over_o such_o ground_n though_o true_a for_o the_o measure_n and_o for_o give_v up_o the_o content_a will_v be_v false_a as_o to_o the_o plot_n and_o therefore_o must_v be_v reduce_v to_o a_o level_n and_o so_o take_v off_o the_o scale_n and_o protract_v for_o the_o do_n of_o this_o there_o be_v several_a instrument_n very_o proper_a especial_o mr._n rathbourne'_v quadrant_n upon_o the_o head_n of_o his_o peractor_n though_o it_o be_v better_a to_o have_v a_o semicircle_n than_o a_o quadrant_n so_o place_v and_o divers_a other_o but_o suppose_v my_o country_n friend_n to_o have_v no_o other_o but_o such_o as_o i_o have_v already_o describe_v i_o shall_v show_v he_o a_o plain_a easy_a way_n much_o use_v by_o practical_a surveyor_n especial_o in_o ireland_n as_o some_o of_o themselves_o have_v tell_v i_o be_v the_o very_a same_o that_o he_o may_v meet_v with_o in_o mr._n leybourn_n book_n entitle_v the_o complete_a surveyor_n i_o mean_v the_o second_o way_n by_o he_o discover_v fig._n 36_o suppose_v abc_n to_o be_v part_n of_o a_o hill_n fall_v within_o my_o plot_n my_o boundary-line_n go_v crooked_o from_o a_o to_o b_o follow_v the_o surface_n of_o the_o ground_n to_o find_v the_o horizontal_n line_n equal_a to_o ac_fw-la i_o cause_v one_o to_o stand_v at_o the_o point_n a_o the_o foot_n of_o the_o hill_n and_o to_o hold_v up_o the_o end_n of_o the_o chain_n to_o a_o convenient_a height_n and_o gentle_o ascend_v the_o hill_n i_o draw_v it_o level_n and_o make_v a_o mark_n where_o it_o touch_v the_o hill_n observe_v the_o number_n of_o link_n betwixt_o my_o assistant's_a hand_n and_o that_o place_n where_o he_o must_v take_v his_o second_o stand_v and_o hold_v it_o up_o as_o before_o and_o so_o i_o draw_v it_o out_o level_a again_o till_o it_o touch_v the_o place_n where_o he_o must_v take_v his_o three_o stand_v note_v the_o link_n as_o before_o and_o so_o proceed_v till_o at_o last_o from_o his_o five_o stand_v i_o draw_v the_o chain_n level_v to_o the_o high_a point_n within_o my_o plot_n viz._n the_o point_n b._n and_o now_o as_o the_o prick_a line_n of_o this_o figure_n put_v together_o and_o evident_o equal_a to_o the_o line_n ac_fw-la so_o be_v the_o link_n note_v down_o at_o every_o station_n when_o sum_v up_o equal_a to_o the_o horizontal_n line_n of_o that_o part_n of_o the_o hill_n in_o the_o very_a same_o manner_n only_o invert_v the_o order_n you_o may_v find_v the_o horizontal_n line_n go_v downhill_o where_o that_o be_v most_o convenient_a and_o if_o there_o be_v both_o ascent_n and_o descent_n in_o one_o line_n betwixt_o two_o angle_n the_o horizontal_n line_n of_o both_o must_v be_v find_v and_o join_v together_o in_o protraction_n all_o this_o concern_v declivity_n of_o rise_v or_o fall_v ground_n be_v to_o be_v understand_v when_o they_o be_v considerable_a and_o a_o very_a exact_a plot_n require_v for_o small_a one_o especial_o when_o much_o exactness_n be_v not_o expect_v be_v not_o regardable_a chap._n xviii_o concern_v plot_v a_o piece_n of_o ground_n by_o the_o degree_n upon_o the_o frame_n of_o the_o plain-table_n several_a way_n and_o protract_v the_o same_o hitherto_o i_o have_v show_v the_o use_n of_o the_o plain-table_n as_o such_o and_o i_o think_v my_o direction_n have_v be_v near_o as_o plain_a as_o the_o instrument_n itself_o at_o which_o some_o quarrel_n for_o its_o over-plainness_n expose_v the_o art_n to_o proud_a ignorant_a people_n who_o judge_v the_o rest_n of_o the_o surveyor_n work_v to_o be_v as_o easy_a as_o look_v through_o sight_n at_o a_o mark_n and_o draw_v line_n by_o a_o rule_n be_v apt_a to_o undertake_v to_o use_v it_o or_o slight_v the_o skill_n of_o such_o as_o do_v other_o say_v and_o that_o true_o that_o for_o vast_a thing_n such_o as_o forest_n chase_n etc._n etc._n the_o circumferentor_n be_v more_o proper_a and_o every_o one_o must_v grant_v that_o in_o wet_a wether_n either_o that_o a_o peractor_n a_o theodolite_a or_o semicircle_n must_v needs_o be_v better_a than_o the_o plain-table_n cover_v with_o the_o paper_n which_o can_v endure_v wet_a hence_o it_o be_v that_o some_o artist_n have_v to_o good_a purpose_n show_v how_o the_o box_n screw_v to_o the_o index_n and_o that_o make_v to_o turn_v on_o the_o head_n of_o the_o three-legged_a staff_n become_v a_o circumferentor_n and_o if_o these_o thus_o fix_v be_v turn_v about_o upon_o the_o centre_n of_o the_o table_n they_o will_v say_v some_o with_o good_a reason_n mr._n leybourn_n for_o one_o perform_v the_o work_n of_o the_o peractor_n much_o better_a than_o the_o peractor_n itself_o other_o show_v as_o i_o shall_v brief_o that_o take_v the_o instrument_n as_o it_o be_v without_o the_o charge_n of_o further_a fit_v it_o or_o trouble_v of_o remove_v the_o box_n the_o index_n turn_v upon_o the_o centre_n will_v by_o help_n of_o the_o degree_n on_o the_o frame_n perform_v the_o work_n of_o the_o theodolite_a to_o which_o the_o semicircle_n be_v near_o of_o kin_n and_o though_o i_o may_v easy_o answer_v all_o these_o objection_n by_o say_v the_o first_o be_v frivolous_a such_o foolish_a arrogance_n be_v easy_o contemn_v or_o check_v if_o worth_a the_o while_n by_o put_v such_o conceit_a fool_n upon_o the_o hard_a part_n of_o the_o work_n the_o second_o impertinent_a to_o our_o purpose_n who_o design_v not_o to_o plot_v such_o vast_a parcel_n of_o land_n and_o the_o three_o concern_v only_o a_o extraordinary_a case_n and_o that_o well_o provide_v for_o otherways_o for_o sure_o no_o man_n that_o have_v not_o a_o body_n of_o the_o same_o metal_n with_o his_o instrument_n will_v ordinary_o measure_v land_n in_o continual_a rain_n a_o sudden_a shower_n may_v be_v fence_v against_o by_o a_o cover_n and_o if_o any_o be_v so_o eager_a upon_o his_o work_n i_o have_v show_v â—how_v it_o may_v be_v do_v in_o the_o former_a chapter_n of_o this_o book_n without_o plant_v any_o instrument_n at_o all_o by_o chain_n scale_n and_o compass_n alone_o yet_o i_o shall_v show_v how_o the_o plot_n of_o a_o field_n may_v be_v taâ—en_v by_o the_o degree_n on_o the_o frame_v not_o every_o way_n that_o i_o can_v imagine_v nor_o that_o i_o can_v transcribe_v for_o that_o will_v be_v tedious_a but_o two_o way_n only_o whereof_o the_o one_o be_v proper_a for_o a_o ordinary_a close_n where_o all_o the_o angle_n may_v be_v see_v from_o 〈◊〉_d station_n within_o it_o the_o other_o fit_v any_o parâ—â—l_n of_o land_n though_o much_o large_a whatever_o be_v the_o figure_n of_o it_o for_o the_o former_a take_v this_o example_n fig._n 37_o let_v abcde_v represent_v the_o figure_n of_o field_n to_o be_v plot_v by_o the_o plain-table_n in_o rain_n weather_n i_o put_v on_o the_o frame_n without_o a_o papâ—â—_n the_o graduated_a side_n upward_o and_o plant_v it_o iâ—_n some_o convenient_a place_n whence_o i_o can_v see_v aâ—â—_n the_o angles_n as_o at_o o_o then_o place_v the_o index_n upon_o thâ—_n table_n so_o as_o the_o fiducial_a edge_n do_v 〈◊〉_d the_o same_o time_n go_v through_o the_o centre_n upon_o the_o table_n and_o the_o line_n upon_o the_o frame_n of_o thâ—_n table_n cut_v it_o perpendicular_o at_o 360_o wheâ—â—_n the_o degree_n begin_v and_o end_v and_o 180_o the_o 〈◊〉_d act_v half_a i_o turn_v about_o the_o table_n upon_o the_o staâ—â—â—head_n till_o through_o the_o sight_n the_o side_n markeâ—_n with_o 180_o being_n next_o my_o eye_n i_o see_v thâ—â—_n angle_v a_o and_o then_o screw_v it_o fast_o observe_v where_o my_o needle_n cut_v and_o by_o back-sighâ—_a cause_v a_o mark_n to_o be_v set_v up_o in_o the_o line_n cd_o 〈◊〉_d the_o point_n f_o that_o the_o instrument_n may_v be_v keâ—â—_n firm_a from_o move_v or_o be_v rectify_v if_o it_o be_v move_v during_o the_o work_n and_o now_o the_o liâ—â—_n aof_o
00_o my_o reader_n may_v now_o perhaps_o expect_v that_o i_o teach_v he_o how_o to_o take_v a_o plot_n at_o two_o or_o more_o station_n when_o all_o the_o angle_n can_v be_v see_v from_o one_o but_o because_o this_o be_v so_o easy_a from_o the_o ground_n already_o lay_v to_o any_o that_o be_v ingenious_a and_o in_o part_n render_v unnecessary_a by_o the_o method_n present_o follow_v i_o shall_v content_v myself_o to_o give_v this_o general_a hint_n when_o you_o have_v from_o one_o station_n take_v in_o all_o the_o angle_n you_o can_v see_v from_o thence_o and_o then_o be_v to_o remove_v to_o your_o second_o station_n do_v just_a as_o you_o will_v do_v if_o the_o table_n be_v cover_v with_o a_o paper_n only_o it_o be_v at_o your_o choice_n whether_o you_o will_v guide_v yourself_o for_o back-sight_n by_o a_o line_n that_o may_v be_v rub_v off_o draw_v upon_o the_o table_n itself_o from_o the_o centre_n to_o the_o degree_n on_o the_o frame_n along_o the_o fiducial_a edge_n or_o by_o note_v only_o what_o degree_n it_o cut_v on_o either_o side_n of_o the_o centre_n the_o edge_n pass_v through_o it_o that_o by_o the_o help_n thereof_o and_o the_o needle_n the_o instrument_n may_v be_v place_v in_o the_o same_o line_n and_o situation_n as_o before_o for_o take_v in_o the_o rest_n of_o the_o angle_n if_o it_o can_v be_v if_o not_o another_o station_n must_v be_v take_v after_o the_o same_o manner_n but_o now_o to_o my_o second_o method_n fig._n 38_o let_v abcde_v be_v the_o figure_n of_o a_o field_n to_o be_v plot_v the_o wether_n be_v bad_a i_o send_v my_o assistant_n to_o find_v the_o length_n of_o every_o side_n measure_v it_o about_o cum_fw-la sole_a begin_v at_o a_o who_o return_v i_o such_o a_o account_n of_o every_o side_n in_o chain_n and_o link_n as_o i_o have_v note_v they_o upon_o the_o figure_n and_o in_o the_o table_n follow_v viz._n ab_fw-la 3_o chain_n 73_o link_n bc_n 4_o chain_n 91_o link_n etc._n etc._n in_o the_o mean_a season_n i_o make_v haste_n to_o find_v the_o angle_n and_o without_o curiosity_n plant_v the_o instrument_n at_o b_o and_o lay_v the_o index_n on_o the_o centre_n i_o look_v at_o c_o and_o find_v the_o index_n cut_v 10_o deg._n 15_o min._n and_o look_v at_o a_o it_o cut_v 126_o deg._n 45_o min._n out_o of_o which_o if_o i_o subtract_v 10_o deg._n 15._o min._n there_o rest_v 116_o deg_n 30_o min._n for_o the_o angle_n a_o but_o because_o i_o like_v not_o my_o quarter_n so_o well_o as_o to_o subtract_v there_o i_o set_v they_o down_o thus_o b_o a_o 126._o 45_o c_o 10._o 15._o the_o meaning_n whereof_o be_v that_z b_o note_n the_o angle_n and_o ca_n the_o line_n meet_v there_o cut_v such_o degree_n on_o the_o frame_n and_o the_o reason_n why_o i_o set_v a_o above_o be_v for_o more_o ready_a subtract_v afterward_o then_o remove_v to_o the_o angle_n c_o and_o thence_o look_v at_o b_o and_o d_o i_o find_v the_o index_n to_o cut_v as_o here_o express_v c_o b_o 153._o 10_o c_o 15._o 40._o in_o like_a manner_n i_o find_v at_o d_o thus_o d_o c_o 96._o 05_o e_z 28._o 50_o at_o e_z thus_o e_z d_o 141._o 20_o a_o 11._o 45._o and_o last_o at_o a_o i_o find_v they_o thus_o a_o e_o 98._o 30_o b._n 9_o 20_o an._n d._n m_o sides_n ch._n l._n a_o 89_o 10_o a_o b_o 3_o 73_o b_o 116_o 30_o b_o c_o 4_o 91_o c_z 137_o 30_o c_o d_o 1_o 88_o d_o 67_o 15_o d_o e_o 6_o 64_o e_z 129_o 35_o e_o a_o 2_o 29_o this_o be_v do_v i_o have_v under_o covert_n and_o by_o subtraction_n find_v 116_o deg._n 30_o m._n for_o the_o angle_n b._n 137_o deg._n 30_o m._n for_o c._n 67_o deg._n 15_o min._n for_o d._n 129_o deg._n 35_o min._n for_o e._n and_o 89._o deg._n 10_o min._n for_o a_o as_o you_o find_v they_o on_o the_o figure_n and_o in_o this_o table_n together_o with_o the_o length_n of_o the_o line_n note_v that_o there_o be_v a_o way_n to_o find_v the_o angle_n without_o subtraction_n if_o at_o every_o station_n you_o lay_v the_o fiducial_a edge_n over_o the_o centre_n and_o the_o division_n 180_o and_o 360_o turn_v about_o the_o head_n of_o the_o instrument_n upon_o the_o staff_n till_o through_o the_o sight_n you_o see_v one_o of_o the_o neighbour_a angle_n for_o the_o index_n turn_v upon_o the_o centre_n to_o the_o other_o angle_n will_v give_v you_o the_o quantity_n of_o the_o angle_n you_o be_v at_o but_o this_o exact_a plant_n at_o every_o angle_n be_v more_o tedious_a than_o the_o other_o and_o therefore_o not_o so_o fit_a for_o wet_a weather_n but_o now_o to_o protract_v this_o plot_n first_o by_o my_o scale_n rule_n and_o compass_n i_o draw_v the_o line_n ab_fw-la in_o length_n 3_o chain_n 73_o link_n end_v at_o the_o pont_n b_o then_o lay_v the_o centre_n of_o my_o protractor_n upon_o the_o line_n ab_fw-la so_o as_o the_o centre_n of_o it_o be_v upon_o the_o point_n a_o and_o that_o end_n of_o the_o diameter_n from_o which_o the_o number_n be_v reckon_v on_o the_o arch_n or_o limb_n towards_o b_o i_o make_v a_o point_n for_o the_o angle_n a_o at_o 89_o deg._n 10_o min._n by_o the_o guidance_n whereof_o and_o the_o point_n a_o i_o draw_v the_o line_n ae_n which_o according_a to_o my_o scale_n must_v be_v 2_o chain_n 29_o link_n in_o like_a manner_n place_v the_o diameter_n upon_o ae_n just_a as_o it_o be_v upon_o ab_fw-la and_o the_o centre_n upon_o the_o point_n e_o i_o mark_v out_o by_o the_o limb_n for_o the_o angle_n e_z 129_o deg._n 20_o min._n by_o which_o i_o draw_v the_o line_n ed_z 6_o chain_n 64_o link_n in_o the_o next_o place_n i_o bring_v the_o centre_n of_o the_o protractor_n to_o the_o point_n d_o its_o diameter_n lie_v on_o the_o line_n ed_z and_o its_o limb_n towards_o a_o by_o which_o i_o prick_v out_o 67_o deg._n 15_o min._n for_o the_o angle_n at_o d_o and_o draw_v the_o line_n 1_o chain_n 88_o link_n last_o the_o centre_n be_v at_o c_o and_o the_o diameter_n upon_o the_o line_n dc_o in_o such_o manner_n as_o before_o at_o other_o angles_n i_o prick_v out_o by_o the_o limb_n or_o arch_n 137_o deg._n 30_o min._n and_o draw_v the_o line_n cb_n for_o at_o b_o my_o plot_n shall_v close_v and_o if_o right_o do_v the_o angle_n at_o b_o will_v be_v 116_o deg._n 30_o min._n and_o the_o side_n bc_n 4_o chain_n 91_o link_n which_o by_o measure_n i_o find_v so_o to_o be_v but_o if_o i_o plot_v by_o a_o line_n of_o chord_n i_o be_o not_o bind_v to_o this_o order_n but_o may_v go_v from_o a_o to_o b_o and_o so_o round_a that_o way_n if_o i_o please_v which_o i_o can_v not_o so_o well_o do_v with_o a_o protractor_n without_o reckon_v my_o number_n backward_o yet_o it_o must_v be_v grant_v that_o a_o line_n of_o chord_n neither_o do_v the_o work_n so_o quick_o nor_o convenient_o for_o this_o be_v the_o way_n when_o i_o have_v draw_v the_o line_n ab_fw-la of_o a_o right_a length_n i_o set_v the_o compass_n to_o the_o radius_fw-la and_o place_v one_o foot_n of_o the_o compass_n in_o the_o point_n b_o and_o with_o the_o other_o describe_v a_o arch_n of_o a_o competent_a length_n begin_v at_o that_o side_n of_o the_o line_n ab_fw-la that_o be_v design_v to_o be_v the_o inward-side_n and_o upon_o this_o arch_n 116_o deg._n 30_o min._n must_v be_v set_v but_o because_o my_o line_n of_o chord_n give_v i_o only_o 90_o i_o set_v they_o first_o on_o from_o the_o line_n ab_fw-la and_o then_o take_v off_o the_o remainder_n 26_o deg._n 30_o min._n i_o join_v they_o to_o the_o 90_o upon_o the_o arch_n make_v a_o point_n through_o which_o the_o line_n b_o must_v be_v draw_v of_o a_o due_a length_n in_o the_o like_a manner_n must_v i_o do_v at_o ce_fw-fr but_o the_o angle_n at_o a_o and_o d_o need_v no_o such_o piece_n be_v capable_a of_o be_v measure_v out_o by_o a_o line_n of_o chord_n at_o once_o nor_o do_v your_o angle_n only_o give_v you_o trouble_v in_o this_o kind_n of_o work_n but_o ofttimes_o your_o line_n will_v be_v find_v too_o short_a to_o receive_v the_o touch_n of_o a_o arch_n upon_o the_o radius_fw-la especial_o if_o the_o line_n of_o chord_n be_v large_a and_o your_o scale_n little_a and_o so_o it_o may_v often_o fall_v out_o when_o you_o use_v the_o protractor_n upon_o such_o short_a line_n as_o ae_n and_o cd_o of_o this_o last_o figure_n in_o which_o case_n a_o rule_n must_v be_v apply_v to_o they_o and_o they_o must_v be_v extend_v to_o a_o due_a length_n that_o the_o arch_n may_v meet_v they_o without_o the_o figure_n and_o if_o those_o extension_n of_o line_n and_o describe_v of_o arch_n spoil_v the_o beauty_n of_o your_o plot_n the_o
that_o purpose_n the_o foot_n of_o your_o compass_n first_o in_o one_o of_o the_o intersection_n of_o the_o give_v line_n and_o then_o in_o the_o other_o you_o may_v by_o lay_v a_o rule_n upon_o the_o assign_a point_n and_o the_o intersection_n of_o the_o two_o arch_n draw_v a_o perpendicular_a from_o the_o say_v assign_v point_n cut_v the_o give_v line_n at_o right_a angle_n note_v ☞_o that_o all_o these_o problem_n touch_v perpendicular_n aim_v at_o no_o great_a matter_n than_o what_o may_v be_v perform_v in_o a_o mechanical_a way_n with_o exactness_n enough_o and_o much_o more_o neat_o by_o avoid_v unhandsome_a prick_n and_o arch_n by_o the_o help_n of_o a_o small_a square_n exact_o make_v or_o for_o want_v thereof_o a_o plate_n quadrant_n or_o broad_a rule_n have_v a_o right_a angle_n and_o true_a side_n for_o if_o you_o apply_v one_o leg_n of_o such_o a_o square_a to_o any_o line_n so_o as_o the_o angle_n of_o the_o square_n may_v touch_v the_o end_n of_o the_o say_a line_n or_o any_o other_o point_v where_o the_o perpendicular_a be_v to_o be_v raise_v you_o may_v by_o the_o other_o leg_n draw_v the_o perpendicular_a in_o like_a sort_n to_o let_v fall_v a_o perpendicular_a from_o a_o point_n assign_v you_o need_v only_o to_o apply_v one_o leg_n of_o the_o square_n to_o the_o line_n so_o as_o the_o other_o may_v touch_v at_o the_o same_o time_n the_o assign_a point_n whence_o you_o may_v draw_v the_o perpendicular_a by_o that_o leg_n that_o touch_v the_o point_n if_o the_o angle_n of_o your_o square_n be_v a_o little_a blunt_a either_o through_o ill_a make_n or_o long_o use_v you_o must_v allow_v for_o it_o when_o you_o apply_v it_o to_o the_o point_n in_o a_o line_n and_o when_o you_o be_v draw_v a_o perpendicular_a you_o must_v stop_v before_o you_o reach_v the_o give_v line_n and_o then_o by_o apply_v the_o leg_n of_o your_o square_n to_o that_o part_n of_o the_o perpendicular_a already_o draw_v so_o as_o part_v of_o that_o leg_n may_v pass_v clear_o over_o the_o give_v line_n you_o may_v draw_v the_o rest_n of_o your_o perpendicular_a as_o exact_o as_o if_o the_o angle_n have_v be_v true_a the_o like_a course_n be_v to_o be_v take_v when_o a_o line_n be_v to_o be_v cross_v by_o another_o draw_v quite_o through_o it_o at_o right_a angle_n v._o a_o angle_n be_v give_v to_o make_v another_o equal_a to_o it_o fig._n 4_o the_o angle_n xad_v be_v give_v and_o a_o line_n draw_v at_o pleasure_n as_o be_v the_o low_a from_o the_o point_n e_o open_v your_o compass_n to_o any_o convenient_a distance_n and_o set_v one_o foot_n in_o a_o describe_v the_o arch_n bc._n then_o with_o the_o same_o extent_n set_v one_o foot_n in_o e_o with_o the_o other_o describe_v the_o arch_n gh_o long_o enough_o to_o equal_v or_o exceed_v the_o other_o then_o take_v the_o distance_n bc_n between_o the_o point_n of_o your_o compass_n set_v one_o in_o g_o and_o with_o the_o other_o mark_v the_o point_n h_n in_o the_o arch_n gh_o through_o which_o point_n h_n a_o line_n be_v draw_v from_o the_o point_n e_o will_v make_v a_o angle_n with_o the_o line_n eglantine_n equal_a to_o the_o angle_n give_v note_v ☜_o when_o we_o speak_v of_o the_o quantity_n of_o angles_n their_o equality_n or_o unequality_n we_o never_o regard_v the_o length_n of_o the_o line_n for_o if_o you_o extend_v or_o contract_v they_o at_o pleasure_n the_o angle_n be_v still_o the_o same_o but_o that_o be_v the_o great_a angle_n who_o line_n be_v far_a distant_a from_o one_o another_o at_o the_o same_o distance_n from_o the_o angular_a point_n or_o the_o place_n where_o its_o line_n meet_v vi_o any_o three_o line_n be_v give_v equal_a or_o unequal_a so_o as_o no_o one_o of_o they_o be_v long_o than_o the_o other_o two_o join_v together_o to_o make_v a_o triangle_n of_o they_o fig._n 5_o the_o line_n a_o b_o c_o be_v give_v set_v the_o line_n a_o from_o d_o to_z e_z then_o with_o your_o compass_n take_v the_o length_n of_o the_o line_n b_o and_o set_v one_o foot_n in_o d_o describe_v 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i_o set_v one_o foot_n in_o the_o intersection_n of_o the_o circle_n by_o the_o line_n a_o and_o with_o the_o other_o foot_n make_v a_o mark_n in_o the_o circumference_n of_o the_o circle_n upward_o towards_o the_o right-hand_a and_o through_o it_o draw_v the_o dry_a line_n boy_n in_o the_o next_o place_n i_o subtract_v the_o angle_n 76._o 15_o from_o 157._o 35_o where_o the_o index_n cut_v for_o the_o angle_n c_o and_o there_o rest_v 81_o deg._n 20_o min._n which_o i_o take_v off_o the_o line_n as_o before_o and_o set_v it_o upon_o the_o circumference_n from_o the_o intersection_n by_o boy_n towards_o the_o end_n of_o the_o diameter_n mark_v with_o f_o and_o through_o the_o point_n be_v it_o fall_v draw_v the_o dry_a line_n co._n in_o like_a manner_n i_o subtract_v 157_o deg._n 35_o min._n from_o 225_o deg._n 20_o min._n and_o the_o difference_n be_v 67_o deg._n 45_o min._n which_o i_o set_v from_o the_o intersection_n by_o the_o line_n co_z downward_o past_o the_o prime_a diameter_n 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to_o be_v for_o it_o shall_v be_v the_o compliment_n of_o 276_o deg._n 50_o min._n to_o 360_o and_o so_o it_o be_v and_o for_o further_a satisfaction_n i_o sum_v up_o the_o degree_n and_o minute_n of_o all_o the_o five_o angle_n which_o for_o plainness_n sake_n i_o have_v note_v in_o every_o one_o of_o they_o on_o the_o outside_n of_o the_o circle_n in_o the_o figure_n so_o often_o refer_v to_o and_o their_o sum_n be_v 360_o as_o it_o ought_v to_o be_v and_o as_o here_o be_v evident_a 76._o 1â—_n 81._o 20_o 67._o 4â—_n 53._o 3â—_n 81._o 1â—_n 360._o
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