in_o your_o field-book_n the_o length_n of_o any_o line_n you_o may_v set_v it_o thus_o if_o you_o please_v with_o a_o stop_n between_o the_o chain_n and_o link_n as_o 15_o chain_n 15_o link_n 15.15_o or_o without_o as_o thus_o 1515_o it_o will_v be_v all_o one_o in_o the_o cast_n up_o of_o instrument_n for_o the_o take_n of_o a_o angle_n in_o the_o field_n there_o be_v but_o two_o material_a thing_n towards_o the_o measure_n of_o a_o piece_n of_o land_n to_o be_v do_v in_o the_o field_n the_o one_o be_v to_o measure_v the_o line_n which_o i_o have_v show_v you_o how_o to_o do_v by_o the_o chain_n and_o the_o other_o to_o take_v the_o quantity_n of_o a_o angle_n include_v by_o these_o line_n for_o which_o there_o be_v almost_o as_o many_o instrument_n as_o there_o be_v surveyor_n such_o among_o the_o rest_n as_o have_v get_v the_o great_a esteem_n in_o the_o world_n be_v the_o plain_a table_n for_o small_a enclosure_n the_o semicircle_n for_o champaign_n ground_n the_o circumferentor_n the_o theodolite_a etc._n etc._n to_o describe_v these_o to_o you_o their_o part_n how_o to_o put_v they_o together_o take_v they_o asunder_o etc._n etc._n be_v like_o teach_v the_o art_n of_o fence_v by_o book_n one_o hour_n use_v of_o they_o or_o but_o look_v on_o they_o in_o the_o instrument-maker_n shop_n will_v better_o describe_v they_o to_o you_o than_o the_o read_n one_o hundred_o sheet_n of_o paper_n concern_v they_o let_v it_o suffice_v that_o the_o only_a use_n of_o they_o all_o be_v no_o more_o or_o chief_o at_o most_o but_o this_o viz._n to_o take_v the_o quantity_n of_o a_o angle_n plain_a table_n place_v the_o table_n already_o fit_v for_o the_o work_n with_o a_o sheet_n of_o paper_n upon_o it_o as_o nigh_o to_o the_o angle_n a_o as_o you_o can_v the_o north_n end_v of_o the_o needle_n hang_v direct_o over_o the_o flower_n de_fw-fr luce_n then_o make_v a_o mark_n upon_o the_o sheet_n of_o paper_n at_o any_o convenient_a place_n for_o the_o angle_n a_o and_o lay_v the_o edge_n of_o the_o index_n to_o the_o mark_n turn_v it_o about_o till_o through_o the_o sight_n you_o espy_v b_o then_o draw_v the_o line_n ab_fw-la by_o the_o edge_n of_o the_o index_n do_v the_o same_o for_o the_o line_n ac_fw-la keep_v the_o index_n still_o upon_o the_o first_o mark_n then_o will_v you_o have_v upon_o your_o table_n a_o angle_n equal_a to_o the_o angle_n in_o the_o field_n to_o take_v the_o quantity_n of_o the_o same_o angle_n by_o the_o semicircle_n place_v your_o semicircle_n in_o the_o angle_n a_o as_o near_o the_o very_a angle_n as_o possible_o you_o can_v and_o cause_n mark_v to_o be_v set_v up_o near_o b_o and_o c_o so_o far_o off_o the_o hedge_n as_o your_o instrument_n at_o a_o stand_v then_o turn_v the_o instrument_n about_o till_o through_o the_o fix_a sight_n you_o see_v the_o mark_n at_o b_o there_o screw_v it_o fast_o next_o turn_v the_o movable_a index_n till_o through_o the_o sight_n thereof_o you_o see_v the_o mark_n at_o c_o then_o see_v what_o degree_n upon_o the_o limb_n be_v cut_v by_o the_o index_n which_o let_v be_v 45_o so_o much_o be_v the_o angle_n bac_n how_o to_o take_v the_o same_o angle_n by_o the_o circumferentor_n place_v your_o instrument_n as_o before_o at_o a_o with_o the_o flower_n de_fw-fr luce_n towards_o you_o direct_v your_o sight_n to_o the_o mark_n at_o b_o and_o see_v what_o degree_n be_v then_o cut_v by_o the_o south_n end_v of_o the_o needle_n which_o let_v be_v 55_o do_v the_o same_o to_o the_o mark_n at_o c_o and_o let_v the_o south_n end_v of_o the_o needle_n there_o cut_v 100_o subtract_v the_o lesser_a out_o of_o the_o great_a the_o remainder_n be_v 45_o the_o angle_n require_v if_o the_o remainder_n have_v be_v more_o than_o 180_o degree_n you_o must_v then_o have_v substract_v it_o out_o of_o 360_o the_o last_o remainder_n will_v have_v be_v the_o angle_n desire_v this_o last_o instrument_n depend_v whole_o upon_o the_o needle_n for_o take_v of_o angles_n which_o often_o prove_v erroneous_a the_o needle_n yearly_a of_o itself_o vary_v from_o the_o true_a north_n if_o there_o be_v no_o iron_n mine_n in_o the_o earth_n or_o other_o accident_n to_o draw_v it_o aside_o which_o in_o mountainous_a land_n be_v often_o find_v it_o be_v therefore_o the_o best_a way_n for_o the_o surveyor_n where_o he_o possible_o can_v to_o take_v his_o angle_n without_o the_o help_n of_o the_o needle_n as_o be_v before_o show_v by_o the_o semicircle_n but_o in_o all_o land_n it_o can_v be_v do_v but_o we_o must_v sometime_o make_v use_n of_o the_o needle_n without_o exceed_v great_a trouble_n as_o in_o the_o thick_a wood_n of_o jamaica_n carolina_n etc._n etc._n it_o be_v good_a therefore_o to_o have_v such_o a_o instrument_n with_o which_o a_o angle_n in_o the_o field_n may_v be_v take_v either_o with_o or_o without_o the_o needle_n as_o be_v the_o semicircle_n than_o which_o i_o know_v no_o better_a instrument_n for_o the_o surveyor_n use_v yet_o make_v public_a therefore_o as_o i_o have_v before_o show_v you_o how_o by_o the_o semicircle_n to_o take_v a_o angle_n without_o the_o help_n of_o the_o needle_n i_o shall_v here_o direct_v you_o how_o with_o the_o semicircle_n to_o take_v the_o quantity_n of_o a_o angle_n in_o the_o field_n by_o the_o needle_n screw_v fast_o the_o instrument_n the_o north_n end_v of_o the_o needle_n hang_v direct_o over_o the_o flower_n de_fw-fr luce_n in_o the_o chard_n turn_v the_o index_n about_o till_o through_o the_o sight_n you_o espy_v the_o mark_n at_o b_o and_o note_v what_o degree_n the_o index_n cut_v which_o let_v be_v 40_o move_v again_o the_o index_n to_o the_o mark_n at_o c_o and_o note_v the_o degree_n cut_v viz._n 85._o subtract_v the_o less_o from_o the_o great_a remain_v 45_o the_o quantity_n of_o the_o angle_n or_o thus_o turn_v the_o whole_a instrument_n till_o through_o the_o fix_a sight_n you_o espy_v the_o mark_n at_o b_o then_o see_v what_o degree_n upon_o the_o chard_n be_v cut_v by_o the_o needle_n which_o for_o example_n be_v 315_o turn_v also_o the_o instrument_n till_o through_o the_o same_o sight_n you_o espy_v c_o and_o note_v the_o degree_n upon_o the_o chard_n then_o cut_v by_o the_o needle_n which_o let_v be_v 270_o subtract_v the_o less_o from_o the_o great_a as_o before_o in_o work_v by_o the_o circumferentor_n remain_v 45_o for_o the_o angle_n mark_v if_o you_o turn_v the_o flower_n de_fw-fr luce_n towards_o the_o mark_n you_o must_v look_v at_o the_o norh_fw-mi end_n of_o the_o needle_n for_o your_o degree_n beside_o the_o division_n of_o the_o chard_n of_o the_o semicircle_n into_o 360_o equal_a part_n or_o degree_n it_o be_v also_o divide_v into_o four_o quadrant_n each_o contain_n 90_o degree_n begin_v at_o the_o north_n and_o south_n point_n and_o proceed_v both_o way_n till_o they_o end_v in_o 90_o degree_n at_o the_o east_n and_o west_n point_n which_o point_n be_v mark_v contrary_a viz._n east_n with_o a_o w._n and_o west_n with_o a_o e_o because_o when_o you_o turn_v your_o instrument_n to_o the_o eastward_o the_o end_n of_o the_o needle_n will_v hang_v upon_o the_o west_n side_n etc._n etc._n if_o by_o this_o way_n of_o division_n of_o the_o chard_n you_o will_v take_v the_o aforesaid_a angle_n direct_v the_o instrument_n so_o the_o flower_n de_fw-fr luce_n from_o you_o till_o through_o the_o fix_a sight_n you_o espy_v the_o mark_n at_o b_o then_o see_v what_o degree_n be_v cut_v by_o the_o north_n end_v of_o the_o needle_n which_o let_v be_v ne_fw-fr 44_o next_o direct_v the_o instrument_n to_o c_o and_o the_o north_n end_v of_o the_o needle_n will_v cut_v ne_fw-fr 89_o subtract_v the_o one_o from_o the_o other_o and_o there_o will_v remain_v 45_o for_o the_o angle_n but_o if_o at_o the_o first_o sight_n the_o needle_n have_v hang_v over_o ne_fw-fr 55_o and_o at_o the_o second_o see_fw-la 80_o then_o take_v 55_o from_o 90_o remain_v 35_o take_v 80_o from_o 90_o remain_v 10_o which_o add_v to_o 35_o make_v 45_o the_o quantity_n of_o the_o angle_n moreover_o if_o at_o the_o first_o sight_n the_o north_n end_v of_o the_o needle_n have_v point_v to_o nw_n 22_o and_o at_o the_o second_o ne_fw-fr 23_o these_o two_o must_v have_v be_v add_v together_o and_o they_o will_v have_v make_v 45_o the_o angle_n as_o before_o mark_v if_o you_o have_v turn_v the_o south_n part_n of_o your_o instrument_n to_o the_o mark_n than_o you_o must_v have_v have_v respect_n to_o the_o south_n end_v of_o your_o needle_n although_o i_o have_v be_v so_o long_o show_v you_o how_o to_o take_v a_o angle_n by_o the_o needle_n yet_o when_o we_o come_v to_o survey_v land_n by_o the_o needle_n as_o you_o shall_v see_v by_o and_o by_o we_o
be_v very_o necessary_a for_o he_o that_o intend_v to_o be_v a_o artist_n in_o the_o measure_v of_o land_n to_o begin_v with_o arithmetic_n as_o the_o groundwork_n and_o foundation_n of_o all_o art_n and_o science_n mathematical_a and_o at_o least_o not_o to_o be_v ignorant_a of_o the_o five_o first_o and_o principal_a rule_n thereof_o viz._n numeration_n addition_n substraction_n multiplication_n and_o division_n which_o suppose_v every_o person_n that_o apply_v himself_o to_o the_o study_n of_o this_o art_n to_o be_v skill_v in_o or_o if_o not_o refer_v he_o to_o book_n or_o master_n every_o where_o to_o be_v find_v to_o learn_v i_o shall_v name_v a_o six_o rule_n as_o necessary_a if_o not_o more_o to_o be_v understand_v by_o the_o learner_n which_o be_v the_o extraction_n of_o the_o square_a root_n without_o which_o though_o seldom_o mention_v by_o surveyor_n in_o their_o write_n a_o man_n can_v never_o attain_v to_o a_o competent_a knowledge_n in_o the_o art_n i_o shall_v not_o therefore_o think_v it_o unworthy_a my_o pain_n though_o perhaps_o other_o man_n have_v better_o do_v it_o before_o i_o to_o show_v you_o easy_o and_o brief_o how_o to_o do_v it_o how_o to_o extract_n the_o square_a root_n in_o the_o first_o place_n it_o be_v convenient_a to_o tell_v you_o what_o this_o square_a root_n be_v it_o be_v to_o find_v out_o of_o any_o number_n propound_v a_o lesser_a number_n which_o lesser_a number_n be_v multiply_v in_o itself_o may_v produce_v the_o number_n propound_v as_o for_o example_n suppose_v 81_o be_v a_o number_n give_v i_o i_o say_v 9_o be_v the_o root_n of_o it_o because_o 9_o multiply_v in_o itself_o viz._n 9_o time_n 9_o be_v 81._o now_o 8_o can_v not_o be_v the_o root_n for_o 8_o time_n 8_o be_v but_o 64_o nor_o can_v 10_o for_o 10_o time_n 10_o be_v 100_o therefore_o i_o say_v 9_o must_v needs_o be_v the_o root_n because_o multiply_v in_o itself_o it_o make_v neither_o more_o nor_o less_o but_o just_a the_o number_n propound_v viz._n 81._o again_o suppose_v 16_o be_v the_o number_n give_v i_o say_v the_o root_n of_o it_o be_v 4_o because_o 4_o multiply_v in_o itself_o make_v 16._o for_o your_o better_a understanding_n see_v this_o figure_n which_o be_v a_o great_a square_n contain_v 16_o little_a square_n any_o side_n of_o which_o great_a square_n contain_v 4_o little_a square_n which_o be_v call_v the_o square_a root_n root_n 1_o 2_o 3_o 4_o 5_o 6_o 7_o 8_o 9_o square_n 1_o 4_o 9_o 16_o 25_o 36_o 49_o 64_o 81_o here_o you_o see_v the_o root_n of_o 25_o be_v 5_o the_o root_n of_o 64_o be_v 8_o and_o so_o of_o the_o rest_n so_o far_o as_o 100_o in_o whole_a number_n your_o memory_n will_v serve_v you_o to_o find_v the_o root_n but_o if_o the_o number_n propound_v who_o root_n you_o be_v to_o search_v out_o exceed_v 100_o than_o put_v a_o point_n over_o the_o first_o figure_n on_o the_o right-hand_a which_o be_v the_o place_n of_o unite_v and_o so_o proceed_v to_o the_o lefthand_n miss_v the_o second_o figure_n and_o put_v a_o point_n over_o the_o three_o then_o miss_v the_o four_o point_v the_o five_o and_o so_o if_o there_o be_v never_o so_o many_o figure_n in_o the_o number_n proceed_v on_o to_o the_o end_n pointing_z every_o other_o figure_n as_o you_o may_v see_v here_o and_o so_o many_o point_n as_o there_o be_v of_o so_o many_o figure_n your_o root_n will_v consist_v which_o be_v very_o material_a to_o remember_v then_o begin_v at_o the_o first_o figure_n on_o the_o lefthand_n that_o have_v a_o point_n over_o it_o which_o will_v always_o be_v the_o first_o or_o second_o figure_n and_o search_v out_o the_o root_n of_o that_o one_o figure_n or_o both_o join_v together_o if_o there_o be_v two_o and_o when_o you_o have_v find_v it_o or_o the_o nigh_a less_o to_o it_o which_o you_o may_v easy_o do_v by_o the_o table_n above_o or_o your_o own_o memory_n draw_v a_o little_a crooked_a line_n as_o in_o division_n and_o there_o set_v it_o down_o for_o example_n let_v 144_o be_v the_o number_n who_o root_n i_o be_o to_o find_v i_o set_v it_o down_o and_o prick_v the_o figure_n thus_o then_o go_v to_o the_o first_o figure_n on_o the_o lefthand_n that_o have_v a_o price_n over_o it_o which_o be_v 1_o and_o see_v what_o the_o root_n of_o it_o be_v which_o be_v 1_o also_o i_o therefore_o draw_v a_o crooked_a line_n as_o in_o the_o margin_n and_o set_v down_o 1_o in_o the_o quotient_a then_o if_o 1_o admit_v of_o any_o multiplication_n i_o shall_v multiply_v it_o by_o itself_o but_o since_o once_o 1_o be_v but_o 1_o i_o subtract_v it_o out_o of_o the_o first_o prick_v figure_n on_o the_o lefthand_n and_o there_o remain_v 0_o so_o that_o i_o cancel_v that_o first_o figure_n as_o have_v whole_o do_v with_o it_o if_o any_o thing_n have_v remain_v after_o the_o substraction_n i_o shall_v have_v put_v the_o remainder_n over_o it_o the_o next_o thing_n to_o be_v do_v be_v to_o double_v what_o be_v already_o in_o the_o quotient_a which_o make_v 2_o which_z 2_o i_o write_v down_o under_o the_o next_o figure_n viz._n 4_o which_o have_v no_o point_n over_o it_o and_o then_o see_v how_o oft_o i_o can_v have_v 2_o in_o 4_o answer_v twice_o i_o therefore_o set_v down_o 2_o in_o the_o quotient_a and_o 2_o likewise_o under_o the_o next_o point_v figure_n which_o in_o this_o example_n be_v 4_o than_o that_o 22_o which_o stand_v under_o the_o 44_o must_v be_v multiply_v by_o theâ—_n in_o the_o quotient_a who_o product_n be_v 44_o which_o substract_v out_o of_o 44_o there_o remain_v 0_o but_o you_o may_v multiply_v and_o subtract_v together_o thus_o twice_o 2_o be_v 4_o which_o i_o take_v out_o of_o 4_o and_o there_o remain_v 0_o than_o i_o cancel_v the_o first_o 4_o and_o 2_o to_o the_o lefthand_n as_o have_v do_v with_o they_o then_o again_o twice_z 2_o be_v 4_o which_o take_v out_o of_o 4_o leaf_n 0_o and_o then_o i_o cancel_v the_o last_o 4_o and_o 2_o and_o the_o question_n be_v answer_v for_o there_o be_v 12_o in_o the_o quotient_a which_o be_v the_o root_n of_o 144_o which_o may_v easy_o be_v prove_v by_o multiply_v 12_o by_o 12._o take_v another_o example_n let_v the_o sum_n be_v first_o see_v what_o the_o root_n of_o 5_o be_v which_o be_v 2_o and_o place_n it_o in_o the_o quotient_a and_o under_o the_o first_o point_v figure_n both_o as_o you_o see_v here_o then_o say_v two_o time_n 2_o be_v 4_o which_o take_v out_o of_o 5_o there_o remain_v one_o and_o so_o have_v you_o do_v with_o the_o first_o point_n next_o double_v the_o quotient_a which_o make_v 4_o and_o place_n it_o as_o you_o see_v here_o under_o the_o figure_n void_a of_o a_o point_n then_o see_v how_o many_o time_n 4_o you_o can_v have_v in_o 14_o answer_z 3_o time_n which_o 3_o place_n both_o in_o the_o quotient_a and_o under_o the_o next_o point_v figure_n which_o be_v 7_o then_o multiply_v and_o subtract_v say_v three_o time_n 4_o be_v 12_o which_o take_v out_o of_o 14_o leaf_n 2_o which_z 2_o write_z over_z the_o 4_o and_o cancel_v both_o the_o 4_o and_o the_o 1_o as_o you_o do_v in_o division_n and_o three_o time_n 3_o be_v 9_o which_o take_v out_o of_o 27_o rest_v 18_o which_o write_v over_o head_n and_o cancel_v what_o figure_n you_o have_v do_v with_o no_o otherwise_o than_o in_o division_n and_o so_o have_v you_o do_v with_o the_o first_o two_o point_n now_o for_o the_o three_o point_v figure_n or_o if_o there_o be_v never_o so_o many_o more_o of_o they_o they_o be_v do_v altogether_o as_o the_o second_o viz._n double_v again_o your_o quotient_n it_o make_v 46_o which_o put_v down_o as_o you_o see_v here_o always_o observe_v this_o rule_n that_o the_o last_o figure_n of_o the_o double_a quotient_n i_o mean_v that_o in_o the_o place_n of_o unite_v stand_v under_o the_o next_o void_a of_o point_n and_o those_o of_o your_o left_a hand_n of_o he_o viz_o in_o the_o place_n of_o ten_o or_o hundred_o in_o order_n before_o he_o as_o you_o do_v in_o division_n as_o you_o may_v see_v here_o then_o proceed_v and_o say_v how_o many_o time_n 46_o can_v i_o have_v in_o 185_o or_o rather_o how_o many_o time_n 4_o in_o 18_o here_o essay_n as_o you_o do_v in_o division_n and_o see_v if_o you_o can_v have_v it_o four_o time_n remember_v the_o 4_o that_o must_v be_v put_v down_o under_o the_o point_a figure_n and_o when_o you_o find_v you_o can_v have_v it_o four_o time_n write_v it_o down_o in_o the_o quotient_a and_o also_o under_o your_o last_o point_a figure_n then_o say_v four_o time_n 4_o be_v 16_o out_o of_o 18_o there_o rest_v 2_o which_o write_v down_o and_o cancel_v the_o 18_o and_o 4._o again_o four_o
time_n 6_o be_v 24_o out_o of_o 25_o rest_v 1_o which_o put_v down_o and_o cancel_v the_o 2_o 5_o and_o 6._o again_o four_o time_n 4_o be_v 16_o out_o of_o 16_o rest_v 0_o and_o so_o have_v you_o do_v and_o find_v the_o root_n to_o be_v 234._o i_o will_v add_v but_o one_o example_n more_o for_o your_o practice_n let_v the_o number_n who_o root_n be_v require_v be_v see_v the_o work_n of_o it_o but_o in_o this_o you_o see_v there_o be_v a_o fraction_n remain_v and_o so_o there_o will_v be_v in_o most_o number_n for_o we_o seldom_o happen_v upon_o a_o number_n exact_o square_a the_o fractional_a part_n must_v therefore_o thus_o be_v take_v before_o you_o begin_v to_o extract_v add_v to_o your_o number_n give_v two_o cipher_n if_o you_o desire_v to_o know_v but_o to_o the_o ten_o part_n of_o a_o unite_n but_o if_o to_o a_o hundred_o part_n add_v four_o cipher_n if_o to_o a_o thousand_o part_n of_o a_o unite_v add_v six_o cipher_n and_o then_o work_v as_o before_o as_o if_o it_o be_v all_o one_o entire_a number_n and_o look_v how_o many_o point_n be_v place_v over_o the_o number_n first_o give_v so_o many_o place_n of_o integer_n will_v be_v in_o the_o root_n the_o rest_n of_o the_o root_n towards_o the_o right-hand_a will_v be_v the_o numerator_n of_o a_o decimal_n fraction_n for_o example_n let_v 143_o be_v the_o number_n give_v to_o be_v extract_v and_o to_o know_v the_o decimal_n fraction_n as_o near_o as_o to_o the_o hundred_o part_n of_o a_o unite_n i_o write_v it_o down_o as_o before_o annex_v four_o cipher_n to_o the_o end_n of_o it_o as_o you_o see_v hereunder_o and_o after_o have_v wrought_v it_o there_o come_v out_o in_o the_o quotient_a 1195_o but_o because_o i_o have_v but_o two_o point_n over_o the_o first_o number_n give_v viz._n i_o therefore_o at_o the_o end_n of_o two_o figure_n in_o the_o quotient_n put_v a_o point_n which_o part_v the_o whole_a number_n from_o the_o fraction_n that_o 11_o on_o the_o lefthand_n be_v integer_n and_o the_o 95_o on_o the_o right_a centesm_n of_o a_o unite_v which_o you_o may_v either_o write_v as_o above_o or_o thus_o 11_o 95_o 95_o 100_o if_o you_o please_v there_o be_v other_o way_n teach_v by_o arithmetician_n for_o find_v out_o the_o square_a root_n of_o any_o number_n but_o i_o know_v no_o way_n so_o concise_a as_o this_o and_o after_o a_o little_a practice_n so_o easy_a and_o ready_a or_o to_o be_v wrought_v with_o as_o few_o figure_n to_o do_v it_o indeed_o by_o the_o logarithm_n or_o artificial_a number_n be_v very_o easy_a and_o pleasant_a but_o surveyor_n have_v not_o always_o book_n of_o logarithm_n about_o they_o when_o they_o have_v occasion_n to_o extract_v the_o square_a root_n however_o i_o will_v brief_o show_v you_o how_o to_o do_v it_o and_o give_v you_o one_o example_n thereof_o when_o you_o have_v any_o number_n give_v who_o square_a root_n you_o desire_v seek_v for_o the_o give_v number_n in_o the_o table_n of_o logarithm_n under_o the_o title_n number_n and_o right_a against_o it_o under_o the_o title_n logarithm_n you_o will_v find_v the_o logarithm_n of_o the_o say_a number_n the_o half_a of_o which_o be_v the_o logarithm_n of_o the_o root_n desire_v which_o half_o seek_v for_o under_o the_o title_n logarithm_n and_o right_a against_o it_o under_o the_o title_n number_n you_o will_v find_v the_o root_n example_n let_v 625_o be_v the_o number_n who_o root_n be_v desire_v first_o i_o seek_v for_o it_o under_o the_o title_n number_n and_o right_a against_o it_o i_o find_v this_o which_o i_o divide_v by_o 2_o or_o take_v the_o half_a of_o it_o as_o you_o see_v log._n 2,795880_o half._n 1,397940_o and_o find_v that_o half_a under_o the_o title_n log._n right_a against_o it_o be_v 25_o the_o root_n desire_v see_v the_o same_o do_v by_o the_o former_a way_n with_o less_o trouble_n chap._n ii_o geometrical_a definition_n appoint_v be_v that_o which_o have_v neither_o length_n nor_o breadth_n the_o least_o thing_n which_o can_v be_v imagine_v and_o which_o can_v be_v divide_v common_o mark_v as_o a_o full_a stop_n in_o write_n thus_o a_o line_n have_v length_n but_o no_o breadth_n nor_o thickness_n and_o be_v make_v by_o many_o point_n join_v together_o in_o length_n of_o which_o there_o be_v two_o sort_n viz._n streight_n and_o crooked_a as_o ab_fw-la be_v a_o straight_a line_n bc_n two_o crooked_a line_n a_o angle_n be_v the_o meeting_n of_o two_o line_n in_o a_o point_n provide_v the_o two_o line_n so_o meet_v do_v not_o make_v one_o straight_a line_n as_o the_o line_n ab_fw-la and_o the_o line_n ac_fw-la meet_v together_o in_o the_o point_n a_o make_v the_o angle_n bac_n of_o which_o right-lined_n angle_n there_o be_v three_o sort_n viz._n right_o angle_v acute_a obtuse_a when_o a_o line_n fall_v perpendicular_o upon_o another_o line_n it_o make_v two_o right_a angle_n example_n let_v cab_n be_v a_o right_a line_n da_n a_o line_n perpendicular_a to_o it_o that_o be_v to_o say_v neither_o lean_v towards_o b_o or_o c_o but_o exact_o upright_a then_o be_v both_o the_o angle_n at_o a_o viz._n dab_n and_o dac_n right_a angle_n and_o contain_v each_o just_a 90_o degree_n or_o the_o four_o part_n of_o a_o circle_n but_o if_o the_o line_n dam_fw-ge have_v not_o be_v perpendicular_a but_o have_v lean_v towards_o b_o then_o have_v dac_n be_v a_o obtuse_a angle_n or_o great_a than_o a_o right_a angle_n and_o dab_n a_o acute_a angle_n or_o lesser_a than_o a_o right_a angle_n as_o you_o see_v hereunder_o all_o figure_n contain_v under_o three_o side_n be_v call_v triangle_n as_o a_o b_o c._n where_o note_n the_o triangle_n a_o have_v three_o equal_a side_n and_o be_v call_v a_o equilateral_a triangle_n the_o triangle_n b_o hath_z two_o side_n equal_a and_o the_o three_o unequal_a and_o be_v call_v a_o isosceles_a triangle_n the_o triangle_n c_o hath_z three_z unequal_a side_n and_o be_v call_v a_o scalenum_n of_o four_o side_v figure_n there_o be_v these_o sort_n first_o a_o square_a who_o side_n be_v all_o equal_a and_o angle_n right_o as_o a._n second_o a_o long_a square_n or_o parallelogram_n who_o opposite_a side_n be_v equal_a and_o angle_n right_o as_o b._n three_o a_o rhombus_fw-la who_o side_n be_v all_o equal_a but_o no_o angle_n right_o as_o c._n four_o a_o rhomboide_n who_o opposite_a side_n only_o be_v equal_a and_o no_o right_a angle_n as_o d._n all_o other_o four_o side_v figure_n be_v call_v trapezia_n as_o e._n other_o figure_n that_o be_v contain_v under_o 5_o 6_o 7_o or_o more_o side_n i_o call_v irregular_a as_o fg_v etc._n etc._n except_o such_o as_o be_v make_v by_o divide_v the_o circumference_n of_o a_o circle_n into_o any_o number_n of_o part_n for_o than_o they_o be_v regular_a figure_n have_v all_o their_o side_n and_o angle_n equal_a and_o be_v call_v according_a to_o the_o number_n of_o right_a line_n the_o circle_n be_v divide_v into_o or_o more_o proper_o according_a to_o the_o number_n of_o angle_n they_o contain_v as_o a_o pentagon_n hexagon_n heptagon_n octogon_n etc._n etc._n which_o in_o plain_a english_a be_v no_o more_o than_o a_o figure_n of_o five_o six_o seven_o or_o eight_o angle_n which_o angle_n be_v all_o equal_a one_o to_o another_o and_o their_o side_n consequent_o all_o of_o the_o same_o length_n and_o thus_o though_o i_o mention_v no_o more_o than_o 8_o the_o circumference_n of_o the_o circle_n may_v be_v divide_v into_o as_o many_o part_n as_o you_o please_v and_o the_o regular_a figure_n arise_v out_o of_o such_o division_n be_v call_v according_a to_o the_o number_n of_o part_n the_o circle_n be_v divide_v into_o see_v for_o your_o better_a understanding_n these_o two_o or_o three_o follow_v pentagon_n hexagon_n heptagon_n the_o diameter_n of_o a_o circle_n be_v a_o line_n which_o pass_v through_o the_o centre_n cut_v the_o circle_n into_o two_o equal_a part_n or_o the_o long_a straight_a line_n that_o can_v be_v make_v in_o any_o circle_n as_o bc._n the_o semi-diameter_n be_v the_o half_a of_o the_o abovementioned_a line_n as_o ab_fw-la ac_fw-la or_o ad_fw-la either_o of_o which_o be_v call_v a_o semi-diameter_n a_o chord_n be_v any_o line_n short_a than_o the_o diameter_n which_o pass_v from_o one_o part_n of_o the_o circumference_n to_o another_o as_o ef._n a_o semicircle_n be_v the_o half_a of_o a_o circle_n as_o bdc_n or_o bec_n a_o section_n segment_n or_o part_n of_o a_o circle_n be_v a_o piece_n of_o the_o circle_n cut_v off_o by_o a_o chord_n line_n and_o be_v great_a or_o less_o than_o a_o semicircle_n as_o ecfg_v be_v a_o segment_n of_o the_o circle_n ebdcg_n likewise_o ebdcf_n be_v the_o great_a segment_n of_o the_o same_o circle_n a_o superficies_n be_v that_o which_o have_v both_o length_n and_o breadth_n
but_o no_o thickness_n who_o bound_n be_v line_n as_o a_o be_v a_o superficies_n or_o plain_n contain_v in_o these_o line_n bc_n de_fw-fr bd_o ce_fw-fr which_o have_v length_n from_o b_o to_z c_z and_o breadth_n from_o b_o to_z d_o but_o no_o thickness_n when_o these_o bound_a line_n be_v measure_v and_o the_o content_a of_o the_o superficies_n cast_v up_o the_o result_n be_v call_v the_o area_n or_o superficial_a content_n of_o that_o figure_n example_n suppose_v the_o line_n bc_n to_o be_v twelve_o foot_n in_o length_n and_o the_o line_n bd_o to_o be_v four_o foot_n long_o they_o multiply_v together_o make_v 48_o therefore_o i_o say_v 48_o square_a foot_n be_v the_o area_n or_o superficial_a content_n of_o that_o figure_n a_o diagonal_a line_n be_v a_o line_n run_v through_o a_o square_a figure_n divide_v it_o into_o two_o triangle_n begin_v at_o one_o angle_n of_o the_o square_n and_o proceed_v to_o the_o opposite_a angle_n in_o the_o square_n abcd_v ad_fw-la be_v the_o diagonal_a line_n chap._n iii_o geometrical_a problem_n prob._n i._n how_o to_o make_v a_o line_n perpendicular_a to_o a_o line_n give_v the_o line_n give_v be_v ab_fw-la and_o at_o the_o point_n c_o it_o be_v require_v to_o erect_v a_o line_n which_o shall_v be_v perpendicular_a to_o ab_fw-la open_v your_o compass_n to_o any_o convenient_a wideness_n and_o set_v one_o foot_n of_o they_o in_o the_o point_n c_o with_o the_o other_o make_v a_o mark_n upon_o the_o line_n at_o e_o and_o also_o at_o d_o then_o take_v off_o your_o compass_n open_v they_o a_o little_a wide_o than_o before_o and_o set_v one_o foot_n in_o the_o point_n d_o with_o the_o other_o describe_v the_o arch_a ff_n then_o without_o alter_v your_o compass_n set_v one_o foot_n in_o the_o point_n e_o and_o with_o the_o other_o describe_v the_o arch_n gg_n last_o lay_v your_o ruler_n to_o the_o point_n c_o and_o the_o intersection_n of_o the_o two_o arch_n gg_n and_o ff_n which_o be_v at_o h_n and_o draw_v the_o line_n hc_n you_o have_v your_o desire_n hc_fw-la be_v perpendicular_a to_o ab_fw-la see_v it_o here_o do_v again_o after_o the_o very_a same_o manner_n but_o may_v perhaps_o be_v plain_a for_o your_o understanding_n prob._n two_o how_o to_o raise_v a_o perpendicular_a upon_o the_o end_n of_o a_o line_n ab_fw-la be_v the_o line_n give_v and_o at_o b_o it_o be_v require_v to_o erect_v the_o perpendicular_a bc._n if_o you_o have_v room_n you_o may_v extend_v the_o line_n ab_fw-la to_o what_o length_n you_o please_v and_o work_v as_o above_o but_o if_o not_o then_o thus_o you_o may_v do_v it_o open_v your_o compass_n to_o a_o ordinary_a extent_n and_o set_v one_o foot_n in_o the_o point_n b_o let_v the_o other_o fall_n at_o adventure_n no_o matter_n where_o in_o reason_n as_o at_o the_o point_n ☉_o then_o without_o alter_v the_o extent_n of_o the_o compass_n set_v one_o foot_n in_o the_o point_n ☉_o and_o with_o the_o other_o across_o the_o line_n ab_fw-la as_o at_z d_o also_o on_o the_o other_o side_n describe_v the_o arch_n e_o then_o lay_v your_o ruler_n to_o d_o and_o ☉_o draw_v the_o prick_a line_n d_o ☉_o f._n last_o from_o the_o point_n b_o you_o begin_v at_o through_o the_o interjection_n at_o g_o draw_v the_o line_n b_o g_o c_o which_o be_v perpendicular_a to_o ab_fw-la another_o way_n to_o do_v the_o same_o i_o think_v more_o easy_a though_o indeed_o almost_o the_o same_o let_v ab_fw-la be_v the_o give_v line_n by_o the_o perpendicular_a require_v set_a one_o foot_n of_o your_o compass_n in_o b_o and_o with_o the_o other_o at_o any_o ordinary_a extent_n describe_v the_o arch_n cefd_n then_o keep_v your_o compass_n at_o the_o same_o extent_n set_v one_o foot_n in_o c_o and_o make_v a_o mark_n upon_o the_o arch_n at_o e_o also_o set_v one_o foot_n in_o e_o make_v another_o mark_n at_o f_o then_o open_v your_o compass_n or_o else_o with_o the_o same_o extent_n which_o you_o please_v set_v one_o foot_n in_o e_o and_o with_o the_o other_o describe_v the_o arch_n gg_n also_o set_v one_o point_n in_o f_o make_v the_o arch_a hh_n then_o draw_v a_o line_n through_o the_o intersection_n of_o the_o arch_n g_o and_o h_o to_o the_o point_n first_o propose_v b_o you_o have_v the_o perpendicular_a line_n ib_n prob._n iii._o how_o from_o a_o point_n assign_v to_o let_v fall_v a_o perpendicular_a upon_o a_o line_n give_v the_o line_n give_v be_v ab_fw-la the_o point_n be_v at_o c_o from_o which_o it_o be_v desire_v to_o draw_v a_o line_n down_o to_o ab_fw-la that_o may_v be_v perpendicular_a to_o it_o first_o set_v one_o foot_n of_o your_o compass_n in_o the_o point_n c_o with_o the_o other_o make_v a_o mark_n upon_o the_o line_n ab_fw-la as_o at_o d_o and_o also_o at_o e_z then_o open_v your_o compass_n wide_a or_o shut_v they_o close_o either_o will_v do_v set_v one_o foot_n in_o the_o point_n of_o intersection_n at_o d_o and_o with_o the_o other_o describe_v the_o arch_a gg_n the_o like_a do_v at_o e_o for_o the_o arch_a hh_n last_o from_o the_o point_n assign_v through_o the_o point_n of_o intersection_n of_o the_o two_o arch_n gg_n and_o hh_n draw_v the_o perpendicular_a line_n cf._n this_o be_v no_o more_o but_o the_o first_o problem_n reverse_v the_o same_o you_o may_v do_v by_o the_o second_o problem_n viz._n let_v fall_v a_o perpendicular_a nigh_o the_o end_n of_o a_o give_v line_n prob._n four_o how_o to_o divide_v a_o line_n into_o any_o number_n of_o equal_a part_n ab_fw-la be_v a_o line_n give_v and_o it_o be_v require_v to_o divide_v it_o into_o 6_o equal_a part_n make_v at_o the_o point_n b_o a_o line_n perpendicular_a to_o ab_fw-la as_o bc_n do_v the_o same_o at_o a_o the_o contrary_a way_n as_o you_o see_v here_o open_v your_o compass_n to_o any_o convenient_a wideness_n and_o upon_o the_o line_n bc_n and_o ad_fw-la mark_v out_o five_o equal_a part_n for_o it_o must_v be_v always_o one_o less_o than_o the_o number_n you_o intend_v to_o divide_v the_o line_n into_o which_o part_v you_o may_v number_v as_o you_o see_v here_o those_o upon_o one_o line_n one_o way_n and_o the_o other_o the_o contrary_a way_n the_o lay_v your_o ruler_n from_o no._n 1._o on_o the_o line_n bc_n to_o no._n 1._o on_o the_o line_n ad_fw-la it_o will_v intersect_v the_o line_n ab_fw-la at_o e_z which_o you_o may_v mark_v with_o your_o pen_n and_o the_o distance_n between_o b_o and_z e_z be_v one_o six_o part_n of_o the_o line_n so_o proceed_v on_o till_o you_o come_v to_o no._n 5._o and_o then_o you_o will_v find_v that_o you_o have_v divide_v the_o give_v line_n into_o six_o equal_a part_n as_o require_v prob._n v._n how_o to_o make_v a_o angle_n equal_a to_o any_o other_o angle_n give_v the_o angle_n give_v be_v a_o and_o you_o be_v desire_v to_o make_v one_o equal_a to_o it_o draw_v the_o right_a line_n bc_n then_o go_v to_o the_o angle_n a_o set_v one_o foot_n of_o your_o compass_n in_o the_o point_n h_o and_o with_o the_o other_o at_o what_o distance_n you_o please_v describe_v the_o arch_n ik_fw-mi then_o without_o alter_v the_o extent_n of_o the_o compass_n set_v one_o foot_n in_o b_o and_o draw_v the_o like_a arch_n as_o fg_v after_o that_o measure_n with_o your_o compass_n how_o far_o it_o be_v from_o k_o to_o i_o and_o the_o same_o distance_n set_v down_o upon_o the_o arch_n from_o g_o towards_o f_z which_o will_v fall_v at_o e_o after_o draw_v the_o line_n bed_n and_o you_o have_v do_v prob._n vi_fw-la how_o to_o make_v line_n parallel_v to_o each_o other_o ab_fw-la be_v a_o line_n give_v and_o it_o be_v require_v to_o make_v a_o line_n parallel_n unto_o it_o set_a one_o foot_n of_o your_o compass_n at_o or_o near_o the_o end_n of_o the_o give_v line_n as_o at_o c_o and_o with_o the_o other_o describe_v the_o arch_n ab_fw-la do_v the_o same_o near_o the_o other_o end_n of_o the_o same_o line_n and_o through_o the_o utmost_a convex_a of_o those_o two_o arch_n draw_v the_o parallel_n line_n c._n d._n prob._n seven_o how_o to_o make_v a_o line_n parallel_n to_o another_o line_n which_o must_v also_o 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c_z 21_o which_o be_v no_o more_o but_o perform_v the_o rule_n of_o three_o in_o line_n as_o if_o we_o shall_v say_v if_o a_o 14_o give_v b_o 18_o what_o shall_v c_z 21_o give_v answer_v 27._o but_o to_o perform_v the_o same_o geometrical_o work_v thus_o and_o here_o for_o a_o while_o i_o shall_v leave_v these_o problem_n till_o i_o come_v to_o show_v you_o how_o to_o divide_v any_o piece_n of_o land_n and_o to_o lay_v out_o any_o piece_n of_o a_o give_v quantity_n of_o acre_n into_o any_o form_n or_o figure_n require_v and_o in_o the_o mean_a time_n i_o shall_v show_v you_o what_o be_v necessary_a to_o be_v know_v chap._n iu._n of_o measure_n and_o first_o of_o long_a measure_n which_o be_v either_o inch_n foot_n yard_n perch_n chain_n etc._n etc._n note_v that_o twelve_o inch_n make_v one_o foot_n three_o foot_n one_o yard_n five_o yard_n and_o a_o half_a one_o pole_n or_o perch_n four_o perch_n one_o chain_n of_o gunter_n eighty_o chain_n one_o mile_n but_o if_o you_o will_v bring_v one_o sort_n of_o measure_n into_o another_o you_o must_v work_v by_o multiplication_n or_o division_n as_o for_o example_n suppose_v you_o will_v know_v how_o many_o inch_n be_v contain_v in_o twenty_o yard_n first_o reduce_v the_o yard_n into_o foot_n by_o multiply_v they_o by_o 3_o because_o 3_o foot_n make_v one_o yard_n the_o product_n be_v 60_o which_o multiply_v by_o 12_o the_o number_n of_o inch_n in_o one_o foot_n give_v 720_o and_o so_o many_o inch_n be_v contain_v in_o 20_o yard_n length_n on_o the_o contrary_a if_o you_o will_v have_v know_v how_o many_o yard_n there_o be_v in_o 720_o inch_n you_o must_v first_o divide_v 720_o by_o 12_o the_o quotient_n be_v 60_o foot_n that_o again_o divide_v by_o 3_o the_o quotient_n be_v 20_o yard_n the_o like_v you_o must_v do_v with_o any_o other_o measure_n as_o perch_n chain_n etc._n etc._n of_o which_o more_o by_o and_o by_o long_o link_n foot_n yard_n perch_n chain_n mile_n inches_n 7.92_o 12_o 36_o 198_o 792_o 63360_o  _fw-fr link_n 1.515_o 4.56_o 25_o 100_o 8000_o  _fw-fr  _fw-fr foot_n 3_o 16.5_o 66_o 5280_o  _fw-fr  _fw-fr  _fw-fr yard_n 5.5_o 22_o 1760_o  _fw-fr  _fw-fr  _fw-fr  _fw-fr perch_n 4_o 320_o  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr chain_n 80_o see_v this_o table_n of_o long_a measure_n annex_v the_o use_n whereof_o be_v very_o easy_a if_o you_o will_v know_v how_o many_o foot_n in_o length_n go_v to_o make_v one_o chain_n look_v for_o chain_n at_o top_n and_o at_o the_o lefthand_n for_o foot_n against_o which_o in_o the_o common_a angle_n of_o
have_v find_v the_o place_n for_o b_o there_o make_v a_o angle_n of_o 51_o degree_n draw_v the_o line_n till_o it_o intersect_v ac_fw-la etc._n etc._n you_o may_v also_o survey_v a_o field_n after_o this_o manner_n by_o set_v up_o a_o mark_n in_o the_o middle_n thereof_o and_o measure_v from_o that_o to_o any_o one_o angle_n also_o in_o the_o observation_n round_o the_o field_n have_v respect_n to_o that_o mark_n as_o you_o have_v here_o to_o the_o angle_n a._n it_o be_v too_o tedious_a to_o give_v example_n of_o all_o the_o variety_n beside_o it_o will_v rather_o puzzle_v than_o instruct_v a_o neophyte_n how_o to_o take_v the_o plot_n of_o a_o large_a field_n or_o wood_n by_o measure_v round_o the_o same_o and_o take_v observation_n at_o every_o angle_n thereof_o by_o the_o semicircle_n suppose_v abcdefg_n to_o be_v a_o wood_n through_o which_o you_o can_v see_v to_o take_v the_o angle_n as_o before_o direct_v but_o must_v be_v force_v to_o go_v round_o the_o same_o first_o plant_v the_o semicircle_n at_o a_o and_o turn_v the_o north_n end_v of_o the_o diameter_n about_o till_o through_o the_o fix_a sight_n you_o see_v the_o mark_n at_o b_o then_z move_z round_o the_o index_n till_o through_o the_o sight_n thereof_o you_o espy_v g_z the_o index_n there_o cut_v upon_o the_o limb_n 146_o degree_n 2._o remove_v to_o b_o and_o as_o you_o go_v measure_v the_o distance_n ab_fw-la viz._n 23_o chain_n 40_o link_n and_o plant_v the_o instrument_n at_o b_o direct_v the_o north_n end_v of_o the_o diameter_n to_o c_o and_o turn_v the_o index_n round_o to_o a_o it_o then_o point_v to_o 76_o degree_n 3._o remove_v to_o c_o measure_v the_o line_n as_o you_o go_v and_o set_v your_o instrument_n at_o c_o direct_v the_o north_n end_v of_o the_o fix_a diameter_n to_o d_o and_o turn_v the_o index_n till_o you_o espy_v b_o and_o the_o index_n then_o cut_v 205_o degree_n which_o because_o it_o be_v a_o outward_a angle_n you_o may_v mark_v thus_o thus_o in_o your_o field-book_n 4._o 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00_o fg_n 13_o 60_o g_z 110_o 00_o give_v 19_o 28_o to_o protract_v this_o draw_v a_o dark_a line_n at_o adventure_n as_o ab_fw-la upon_o which_o set_v off_o the_o distance_n as_o you_o see_v it_o in_o your_o field-book_n 23_o chain_n 40_o link_n from_o a_o to_o b_o then_o lay_v the_o centre_n of_o your_o protractor_n upon_o a_o and_o the_o diameter_n upon_o the_o line_n ab_fw-la the_o north_n end_v or_o that_o of_o 00_o degree_n towards_o b_o on_o the_o outside_n of_o the_o limb_n make_v a_o mark_n against_o 146_o degree_n through_o which_o mark_v from_o a_o draw_v the_o line_n agnostus_n so_o have_v you_o the_o first_o angle_n and_o first_o distance_n 2._o place_v the_o centre_n of_o the_o protractor_n upon_o b_o and_o turn_v it_o about_o until_o 76_o degree_n lie_v upon_o the_o line_n ab_fw-la there_o hold_v it_o fast_o and_o against_o the_o north_n end_v of_o the_o diameter_n make_v a_o mark_n through_o which_o draw_v a_o line_n and_o set_v off_o the_o distance_n bc_n 15_o chain_n 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